Saturday, November 23, 2019

What is Dark Energy?

What’s the difference between dark energy and dark matter? What does dark energy have to do with the cosmological constant and is the cosmological constant really the worst prediction ever? At the end of this video, you will know.


First things first, what is dark energy? Dark energy is what causes the expansion of the universe to accelerate. It’s not only that astrophysicists think the universe expands, but that the expansion is actually getting faster. And, here’s the important thing, matter alone cannot do that. If there was only matter in the universe, the expansion would slow down. To make the expansion of the universe accelerate, it takes negative pressure, and neither normal matter nor dark matter has negative pressure – but dark energy has it.

We do not actually know that dark energy is really made of anything, so interpreting this pressure in the normal way as by particles bumping into each other may be misleading. This negative pressure is really just something that we write down mathematically and that fits to the observations. It is similarly misleading to call dark energy “dark”, because “dark” suggests that it swallows light like, say, black holes do. But neither dark matter nor dark energy is actually dark in this sense. Instead, light just passes through them, so they are really transparent and not dark.

What’s the difference between dark energy and dark matter? Dark energy is what makes the universe expand, dark matter is what makes galaxies rotate faster. Dark matter does not have the funny negative pressure that is characteristic of dark energy. Really the two things are different and have different effects. There are of course some physicists speculating that dark energy and dark matter might have a common origin, but we don’t know whether that really is the case.

What does dark energy have to do with the cosmological constant? The cosmological constant is the simplest type of dark energy. As the name says, it’s really just a constant, it doesn’t change in time. Most importantly this means that it doesn’t change when the universe expands. This sounds innocent, but it is a really weird property. Think about this for a moment. If you have any kind of matter or radiation in some volume of space and that volume expands, then the density of the energy and pressure will decrease just because the stuff dilutes. But dark energy doesn’t dilute! It just remains constant.

Doesn’t this violate energy conservation? I get this question a lot. The answer is yes, and no. Yes, it does violate energy conservation in the way that we normally use the term. That’s because if the volume of space increases but the density of dark energy remains constant, then it seems that there is more energy in that volume. But energy just is not a conserved quantity in general relativity, if the volume of space can change with time. So, no, it does not violate energy conservation because in general relativity we have to use a different conservation law, that is the local conservation of all kinds of energy densities. And this conservation law is fulfilled even by dark energy. So the mathematics is all fine, don’t worry.

The cosmological constant was famously already introduced by Einstein and then discarded again. But astrophysicists think today that is necessary to explain observations, and it has a small, positive value. But I often hear physicists claiming that if you try to calculate the value of the cosmological constant, then the result is 120 orders of magnitude larger than what we observe. This, so the story has it, is the supposedly worst prediction ever.

Trouble is, that’s not true! It just isn’t a prediction. If it was a prediction, I ask you, what theory was ruled out by it being so terribly wrong? None, of course. The reason is that this constant which you can calculate – the one that is 120 orders of magnitude too large – is not observable. It doesn’t correspond to anything we can measure. The actually measureable cosmological constant is a free parameter of Einstein’s theory of general relativity that cannot be calculated by the theories we currently have.

Dark energy now is a generalization of the cosmological constant. This generalization allows that the energy density and pressure of dark energy can change with time and maybe also with space. In this case, dark energy is really some kind of field that fills the whole universe.

What observations speak for dark energy? Dark energy in the form of a cosmological constant is one of the parameters in the concordance model of cosmology. This model is also sometimes called ΛCDM. The Λ (Lambda) in this name is the cosmological constant and CDM stands for cold dark matter.

The cosmological constant in this model is not extracted from one observation in particular, but from a combination of observations. Notably that is the distribution of matter in the universe, the properties of the cosmic microwave background, and supernovae redshifts. Dark energy is necessary to make the concordance model fit to the data.

At least that’s what most physicists say. But some of them are claiming that really the data has been wrongly analyzed and the expansion of the universe doesn’t speed up after all. Isn’t science fun? If I come around to do it, I’ll tell you something about this new paper next week, so stay tuned.

265 comments:

  1. Replies
    1. the charge that is conserved under time-translation invariance

      Delete
    2. Or perhaps we could just say that energy is the (0,0) component of the quantity on the right-hand side of the field equations that is proportional to the Einstein tensor.

      The point being that you can choose to lump the cosmological constant term in with the stress-energy-momentum tensor if you choose.

      This is one of those cases where it really is hard to explain what is going on without appealing to the math: if you grasp the math, of course you can just add a term proportional to the metric tensor, which will have negative pressure (if the "energy" is positive), and of course it will be invariant between frames.

      For people who do not grasp the math... hard to make it seem obvious.

      Delete
    3. So basically as I understand it, the Universe is not time-translation invariant since it expands. So the energy conservation would only work locally, when the effects of expansion are negligible.

      Can it allow (even in principle at the galactic scale) to produce free energy?

      Delete
    4. The 00 component of the stress energy tensor is an energy-density, not an energy.

      Delete
    5. Cyberax,

      As I said, the accelerated expansion of the universe actually does "produce" energy. It isn't only that the effects of the expansion are negligible locally, the universe does not expand in gravitationally bound systems (like our galaxy). I explained this here.

      Delete
    6. Sabine wrote:
      >The 00 component of the stress energy tensor is an energy-density, not an energy.

      Well, yes, but of course when we talk about "dark energy" we are also actually talking about an energy density. I.e., no one ever tries to actually talk about the total dark energy in the universe! That would be infinite, of course, if the universe is infinite. And, in any case, in curved spacetime, if you tried to integrate all the dark energy in the universe, you would have an issue of parallel transport.

      Anyway, since the covariant derivative of the metric is zero, the ordinary energy is conserved without including the dark energy. Indeed, you can add any constant multiple of the metric tensor to the usual stress-energy-momentum tensor (the constant does not have to be lambda) and still get a conserved quantity.

      The reason we choose the particular quantity that adds lambda times the metric to the usual stress-energy-momentum tensor is that this is what appears on the RHS of the gravitational field equation.

      (For non-physicists, we should explain that in talking about energy being "conserved," we are talking about the differential covariant form of energy-momentum conservation. Which is complicated -- see Sean Carroll's explanation of the complexities here: https://www.preposterousuniverse.com/blog/2010/02/22/energy-is-not-conserved/ . Some people may find Ethan Siegel's explanation clearer, based actually on some of Carroll's work: https://www.forbes.com/sites/startswithabang/2018/07/28/ask-ethan-where-does-the-energy-for-dark-energy-come-from/#e4bb5231268d . )

      Delete
    7. PhysicistDave,

      You can very well integrate rho over a finite volume and get a finite result and you'll see that for the cosmological constant it actually increases if the volume increases because (drums please) the constant is constant. But, yeah, as I said/wrote in GR we deal with densities and local conservation laws and not with integrated quantities.

      Fwiw, I think the world would be a better place if we could generally stop talking about energies and momenta and stick with local quantities, but then maybe that's just me.

      Delete
    8. "the charge that is conserved under time-translation invariance"
      This is the first time I've come across such a satisfying statement about what energy is, I'm used to reading that energy's definition is "hard to pin down." What do you mean when you say "charge"? Are you referring to energy as the charge for the gravitational force?

      Delete
    9. Sabine wrote to me:
      >Fwiw, I think the world would be a better place if we could generally stop talking about energies and momenta and stick with local quantities, but then maybe that's just me.

      At least in GR, I agree. But, of course, you and I have each just demonstrated that we all find it irresistible to talk about energy and momentum themselves, rather than just the densities!

      And, now, after our little discussion here, I need to go back and think much more carefully about exactly what the local conservation law really means in GR vis a vis Sean Carroll's work.

      Ah, a physicist's work is never done!

      All the best (and thanks for forcing me to think),

      Dave

      Delete
    10. "This is the first time I've come across such a satisfying statement about what energy is, I'm used to reading that energy's definition is "hard to pin down." What do you mean when you say "charge"? Are you referring to energy as the charge for the gravitational force?"

      Look up Noether's theorem (the one physicists like to cite; she has several theorems). Emmy Noether, of course; her father Max also has several theorems named after him.

      Delete
    11. the charge that is conserved under time-translation invariance"
      This is the first time I've come across such a satisfying statement about what energy is, I'm used to reading that energy's definition is "hard to pin down." What do you mean when you say "charge"? Are you referring to energy as the charge for the gravitational force?

      Perhaps we can consider rest mass to be a global charge and 'relatistic mass' to be the local charge.

      Gauge invariance in a Nutshell!

      Delete
    12. As Phillip says, this is Noether's theorem. Every (continuous) symmetry has a conserved quantity, usually called a charge or current. Somewhat misleading maybe, because in general it has nothing to do with what we colloquially call charge or current (that suggests it has something to do with electricity). Energy is the conserved charge that belongs to time-translation invariance.

      Delete
    13. Energy is as Sabine says what is constant under time translations. With general relativity this definition is not universal. The reason is that in a general spacetime if you define a Gaussian surface to enclose this "charge" of mass-energy something funny happens. The first is that the surface can be diffemomorphic with respect to the dynamics of space. This means one can't define an invariant meaning of mass-energy it encloses. The other is that mass-energy more or less uniformly distributed in a spatial surface does not permit such a surface to define mass-energy in the spacetime.

      In the ADM "space plus time" approach to general relativity this finds itself in the Hamiltonian constraint NH = 0. Here N is a lapse function, H = G_{ijkl}π^{ij}π^{kl} + R(3) for π^{ij} the momentum metric conjugate to the spatial metric g_{ij}, G_{ijkl} a superspace metric and R(3) the Ricci curvature of the 3-manifold of space chosen by the analyst. This means the only generally effective definition of energy is zero.

      The only spacetimes that admit conservation of energy are those with a timelike Killing vector. This Killing vector projects onto the 4-momentum as a constant and if this is in a time direction it defines a Noetherian symmetry for the conservation of energy. Metrics that have no explicit time dependence and with mass-energy located in a region permit this Killing vector. A black hole is such a spacetime, where the mass or ADM mass of the black hole can be defined.

      Delete
    14. Dave,

      I also had to do it some month ago - I found the links in here helpful. (Enlarge “+” to see more pages in A. Zee.)

      Delete
    15. Sabine,

      the charge that is conserved under time-translation invariance

      This seems to me only a mathematical description. What is the physical definition of energy; what constitutes energy in empirical reality?

      Delete
    16. From the new paper’s abstract and conclusion: “Thus the cosmic acceleration deduced from supernovae may be an artefact [sic] of our being non-Copernican observers, rather than evidence for a dominant component of ‘dark energy’ in the Universe... Given the observational evidence that [the universe is flat], this possibility must be taken seriously.”

      So, Sarkar et al. argue that our place in the cosmos violates the Copernican principle. It’s of course not true, but FWIW, wouldn’t that be special.

      Delete
    17. @bud rap "Mathematical description.." well, that what physics deals with :) Sabine is right, it's the Noether charge associated with time translation invariance. This is true in both classical and quantum theory. Symmetries of the Lagrangian lead to conserved quantities.

      The real question is - does energy exist as a conserved quantity in GR? That is a much more delicate problem, and the simple answer is, in general, no, because there is no generally valid (covariant) local conservation law for it. There are complex arguments to define energy integrals in particular cases and globally, but the thing to which Sabine refers is exactly what is missing in GR.

      Schroedinger has a very interesting discussion of the role of invariant integrals in GR and the role of the energy tensor, in his little book from the early 1950s "Space-Time Structure". You can find a PDF online.

      -drl

      Delete
    18. "artefact [sic]"

      Both "artefact" and "artifact" are accepted spellings. (FWIW, the former is more correct etymologically and is the preferred spelling outside of the USA.)

      Delete
    19. The idea that potential energy is a real physical thing somehow stored in fields or bound systems is THE problem with modern physics.

      Delete
    20. Bracketed "sic." a priori affirms as correctly quoted that which many might consider misquoted, so FWIW: Americans (credit Webster). Bracketed “replacement text” is useful to simplify portions for clarity, e.g. later on in the quote (wouldn’t’ve that been the more interesting feature to’ave challenged, as does Rameez?).

      Delete
    21. Greg Feild,
      "The idea that potential energy is a real physical thing somehow stored in fields or bound systems is THE problem with modern physics."

      I'm really curious what you mean by this, please elaborate if you have the chance? Is potential energy not a meaningful (real/physical) quantity you can associate with fields or bound systems? Are you saying that potential energy isn't directly measured, rather it's just a mathematical construct explaining our observations? If so, how is this a problem?

      Also, thanks everyone for the fascinating/informative discussion on energy and Noether's theorem!

      Delete
    22. Hello Thomas Payne,

      Potential energy is defined as the work done (by 'someone') in moving a charge to a certain position (from 'infinity', ideally) against an external 'force field'.

      It is a mathematical place holder for the kinetic energy that would result if that someone let the charge go.

      If you raise a rock above your head, the rock gains potential energy.
      When you let the rock go, it falls to the ground 'releasing' the potential energy you gave to it.

      Greg

      P.S. The definition of a field is even more problematic. It is defined as the force per unit 'test charge' as the value of the test charge goes to zero.

      No (test) charge, no field!

      Delete
    23. Greg Field,
      Thanks for the response! I'm clear on the concepts, I'm just not sure I agree with the statement that PE (function of position in a field) is any less real that KE (function of velocity). You could also say that KE is a mathematical placeholder for the potential energy that could be realized. I think your point is that velocity is a real physical thing, while a field is a mathematical construct (and thus not real). I don't agree with this, but I think it's more of an ontological question.

      Delete
    24. No one has ever been killed by potential energy.

      (I apologize for the graphic language.)

      Delete
    25. @Greg Field: Sure they have, just drop a large rock from a great height. It's all very well saying it's the kinetic energy at the point of contact; but the point remains without the potential energy stored by the gravitational field the rock would never had fallen...

      Delete
    26. The point I am trying to make is that there is no energy stored in the gravitational field.

      The rock falls because the earth exerts a 'force' on it.

      Perhaps these are the same level of abstraction...

      Delete
  2. Adam Riess dropped a bomb on dark energy with his latest research:

    https://arxiv.org/abs/1903.07603

    I am not sure the Hubble constant is linear, which could say a lot about our underlying assumptions around Dark Energy

    ReplyDelete
    Replies
    1. The Hubble constant is a number. What do you mean by a non-linear Hubble constant?

      Delete
    2. Even if the claims in the above paper hold up, how has it "dropped a bomb on dark energy"?

      Delete
    3. Perhaps you can call it Hubble parameter which can vary in space and time.

      Delete
    4. "Perhaps you can call it Hubble parameter which can vary in space and time."

      The Hubble constant does vary in time, except in some very special cases, even in very simple models with no cosmological constant. In contrast to the cosmological constant, it is called the Hubble constant not because it is constant in time, but because it is a constant like a and b in the equation y=ax+b. Yes, some people call it the Hubble parameter in order to avoid the impression that it is constant in time, but this creates more confusion than it resolves, because it gives the impression that Hubble thought of it as constant in time but now we are looking at models where that is not the case. No, that's not how it works.

      Could it vary in space? Maybe, but if so we could measure that only indirectly. Could it vary depending on the direction of observations which measure it? Some people are claiming that. However, if this is supposed to somehow resolve the tension between "local" and other measurements of the Hubble constant, it would have to do so without messing up anything else.

      Delete
    5. My bad on the use of "constant", I agree it's a parameter. It is my understanding that Riess showed that the measurements from the Large Megallanic Cloud breaks the linear relationship v = HR at least as close as LMC is to us. There could be other factors, but the candle determination from Cepheid variables seems pretty reliable so a variation in redshift is hard to write off as an error in distance measurement. We are having trouble accepting that Hubble's law is non-linear, but it would explain dark energy pretty well if we accept this.
      https://www.google.com/url?sa=t&source=web&rct=j&url=http://www.ptep-online.com/2008/PP-15-03.PDF&ved=2ahUKEwimqMvj8IrmAhWHrJ4KHVoHDHQQFjAAegQIAxAB&usg=AOvVaw0Mr8acOlAyLcnD16-34fFY&cshid=1574874563570

      Delete
    6. From Occam's razor, what's more likely..that a dark energy source (that has still not shown up in any experiments on Earth) is accelerating the universe against gravitational pull... or we made some incorrect assumptions about the linearity of the Hubble law?

      Delete
    7. mh, you write "It is my understanding that Riess showed that the measurements from the Large Megallanic Cloud breaks the linear relationship v = HR at least as close as LMC is to us." Do you have a paper by Reiss that you can cite, in which he makes such a case?

      Also, I have no idea why you cited something from ptep-online; what makes you think that this is not just a journal where crackpot ideas get published with essentially no checking?

      Delete
    8. Jean, PTEP online is "Progress in Physics" a peer-reviewed journal by faculty from University of New Mexico. Frankly, what makes us think that dark energy isn't a "crackpot" scheme to begin with? When "professionals" can't hit the mark reliably by proposing concepts such as multiverse, SUSY and other fictional items that have no verifiable basis in reality, I think I would prefer any other speculation, especially if it didn't have tax dollars funding it and especially if "professionals" aren't claiming it's real and asking for more money after not being able to verify it with the most expensive collider ever built. "Crackpot* takes on new meaning when we spend $10 billion in tax dollars get no results.

      Delete
    9. Riess paper is here:

      https://arxiv.org/abs/1903.07603

      Delete
    10. "Riess showed that the measurements from the Large Megallanic Cloud breaks the linear relationship v = HR at least as close as LMC is to us."

      But the LMC is gravitationally bound to our galaxy (and to Andromeda). Why would the LMC would follow the Hubble relationship?

      Delete
    11. @mh: if you think ptep is a reliable physics journal, I have a bridge you will want to buy!

      Seriously, one of the people who have "papers" published there has an idea that will guarantee free energy, in a way that makes perpetual energy machines look soooo yesterday (I'll tell you how you can make such a machine, based on his ideas; I won't even ask for a commission after you've become a trillionaire!).

      Thanks for the Riess cite.

      Delete
    12. mh, you wrote: "It is my understanding that Riess showed that the measurements from the Large Megallanic Cloud breaks the linear relationship v = HR at least as close as LMC is to us."

      I have no idea how you came to that conclusion, based on the Riess paper you cited! :O

      Can you explain please?

      Delete
    13. Hi Rob van Son,

      Yes, the LMC and Andromeda are gravitationally bound to the Milky Way, I believe they compensate for this redshift as part of the anchor distance in the paper. Because we are closer the LMC the standard candle accuracy should be better across the color range so the compensation for acceleration towards us should be better as well. The error budget that they show appears to be within a range that still provides a significant margin for the measurement of H0.

      Delete
    14. My bad on the use of "constant", I agree it's a parameter. It is my understanding that Riess showed that the measurements from the Large Megallanic Cloud breaks the linear relationship v = HR at least as close as LMC is to us. There could be other factors, but the candle determination from Cepheid variables seems pretty reliable so a variation in redshift is hard to write off as an error in distance measurement. We are having trouble accepting that Hubble's law is non-linear, but it would explain dark energy pretty well if we accept this.

      This pretty well demonstrates the confusion I mentioned. In the meantime, there is some new stuff in this area.

      Delete
    15. Jean,

      I would be interested in seeing the paper you quoted about free energy, the editors I know at PTEP (Rabunski in particular would never consider such a thing). On the topic of free energy though, the multiverse have a pretty high energy budget without explanation but still finds itself in prominent publications. The current trends in physics have set the standard pretty low so there appears to be lots of energy to go around and perhaps be used by other theories.

      Delete
    16. mh, I got sucked into a crackpot swamp by replying to a comment in the YouTube version of Sabine's Have we really measured gravitational waves. A certain Steve Crothers wrote a comment that is essentially marketing for crackpot YouTube videos (you can check this for yourself, the comment was posted ~6 November). The particular vid is by PM Robitaille; among other things, he has a strange take on Kirchoff's laws, and hence thermodynamics. It is a consequence of this crackpot idea that leads to free energy.

      PTEP has quite a few papers by Robitaille, and Crothers also. There's also one which tries to smuggle in Velikovskian nonsense without once mentioning Velikovsky or the Grand Canyon being created by a giant lightning bolt from Venus (which happened to be just a few tens of thousand km away at the time), just a few kya. I'll leave it to you to find the relevant Robitaille paper(s); I'll describe how a free energy device would work, using Robitaille's take on Kirchoff's laws, if you're interested ...

      Some PTEP papers would make good teaching material for physics 101 or 201 ... how not to do physics! I regard PTEP as a viXra competitor.

      Delete
  3. What are the differences between dark energy and quintessence?

    ReplyDelete
  4. Martinus Veltman on dark matter: "I think it doesn't exist."
    George Smoot: "Everytime there's a deviation, people introduce dark matter--and then later,dark energy--in order to continue with Newtonian and Einstein gravity and be able to do calculations in a straightforward way..." Quotes originate from a Youtube video where Martinus Veltman and George Smoot are being asked... Is dark matter real ? It is interesting that the latest Review of Particle Physics Data Book says this: "But it may be that the phenomenon of dark energy is entirely illusory." (Olive and Peacock, page 362).

    ReplyDelete
    Replies
    1. "Everytime there's a deviation, people introduce dark matter--and then later,dark energy--in order to continue with Newtonian and Einstein gravity and be able to do calculations in a straightforward way..."

      This is in essence the problem, except that it is not Newtonian or Einstein gravity that is the issue. Rather it is the proclivity to retain assumptions of mathematical convenience (e.g. point masses) in systems where they are completely inappropriate. When the resulting calculations don't agree with observations, suddenly - dark (invisible or transparent) matter and energy are invoked to bring the model into agreement with physical reality.

      Remarkably, this results in a claim that the model (ΛCDM) is a great success, not withstanding the complete absence of any empirical evidence for the actual existence of the entirely ad hoc invocations.

      Delete
    2. I'm curious, bud rap, just what do you mean by "empirical evidence"?

      I assume "independently verified" is part of this, as is "objective" (but maybe I shouldn't assume?). Also, something about causal chains, for instruments/equipment where the output data ("readings") are the result of a long chain, from a photon liberating an electron to the A/D converter (say).

      Delete
    3. Jean Tate,

      In the context of my previous comment, empirical evidence is a direct observation of whatever it is that is being claimed to exist. And let me assure you that I am not going to engage in any sophomoric philosophical digressions into the nature of reality. If you don't know the difference between what is real and what is not, you're not much of a scientist, and I can't really help you.

      Delete
    4. Thanks bud rap.

      Taking your definition ("empirical evidence is a direct observation of whatever it is that is being claimed to exist"), black holes do not exist, right? I mean, there is no "direct observation" of any, right? And one can certainly observe an emission line at 500.7nm, in a wide variety of astronomical sources, but how is that a direct observation of a "forbidden" transition of an ionized oxygen atom?

      Delete
  5. "There are of course some physicists speculating that dark energy and dark matter might have a common origin"

    Where might I read more about this?

    ReplyDelete
    Replies
    1. On “common origin”: there’s a show recorded somewhere of Sir Roger discussing creation myths with Dame Laura & High Priest Sean, moderated by an indeterminate Naïve, wherein said Dame lets it slip that some time ago said Knight was responsible for the Dark Energy evocation that called forth that mystical 120 magnitude orders disparity (only it was actually 123), the consequence of which finds him & said Priest therein arguing (besides speculating about what would-be-Sir Stephen might’ve thought) about whether we should be living within an infinity of eons, or spatially parallel with respect to other infinitely many worlds, as the Dame – lamenting ostensive zero probability of ever starting a world either way – prophesized that eventually we’ll have to merge the two points of view into one, even as the naive Naïve wonders why the infinite parallel ones shouldn’t have their own infinite eons too, to which the Knight patiently explains that those ones don’t have parallel ones in the first place, but unsatisfied the impudent Naïve then wants an explanation of why sequential eons (without beginning) should be preferred over parallel worlds (with beginnings, though as Dame points out there’d be infinitely many of them), whence the Knight blames the Dame for bringing up the troublesome 124 to begin with, whereupon the persistent Naïve reminded him it was 123, which got him informed -- as the Dame laughed but the Priest just shrugged -- that that was before Dark Matter became convincingly present; so, based on that last part, it would seem they’re not unrelated.

      Delete
    2. Emmette Davidson 11:40 PM, November 24, 2019

      Empirically, there is zero evidence of "parallel" universes; it's unknown whether the universe had a beginning or not; the estimate out by an order of 120, if it is, is a bad estimate not a mystery; according to Dr. H in another post, there is a possibly unjustified assumption in the calculation of gravity in galaxies that could mean there is no Dark Matter. Dark Energy also sounds like it could be something in a model, rather than in reality. So "the jury's out" appears to be the answer on all of this.

      Delete
    3. Indeed. But here is no brief of knowns, as the petulant Naïve persists. Rather it's what the Dame warrants, that these things are not unknowable.

      Delete
  6. Great video, Sabine. Is there any chance that dark energy and dark matter can both be explained by modified gravity? I was thinking in particular of a quadratic form of the Einstein-Hilbert action.

    ReplyDelete
    Replies
    1. @ Bill: The idea of a quadratic Lagrangian in quantum gravitation is interesting. I think of this as a Lagrangian density as

      L = √{g}[R + (1/128π)R_{abcd}R_{efgh}ε^{abef}ε_{cdgh}+ (1/96π)R_{abcd}R^{abef}ε_{cdef}].

      The first of these is the classical Hilbert-Palatini action with the Ricci curvature. The second when integrated

      χ = (1/128π)∫dtd^3xR_{abcd}R_{efgh}ε^{abef}ε_{cdgh}

      is the Euler characteristic and the third

      η = (1/96π)∫dtd^3xR_{abcd}R^{abef}ε_{cdef}

      is the Hirzebruch characteristic. We may think of R_{abcd}R^{abef}ε_{cdef} as R·*R that is analogous to the tensor product of gauge fields in F·*F. This terms is E·B in edge states. These are symmetry protected topological states, which in solid state physics have fascinating implications for superconductivity and Mott insulators.

      This term may then emerge from a boundary. The Gauss-Bonnett curvature in two dimensions

      χ = (1/2π)[∫_mKda + ∫_{∂m}kds]

      for a 2-dim manifold m with boundary ∂m defines the Euler characteristic with K the Gaussian curvature and k the geodesic deviation or curvature on the boundary. A 2-sphere S^2 can be obtained as a quotient space of a 2-disk with its boundary S^2 = D^2/S^1 or D^2/U(1). If we think of the degrees of freedom with the boundary we are modding out as conserved these may then becomes Hopf fibration terms or a gauge bundle on the manifold. We may then have this “edge term” as a sort of gravi-gauge field in the manifold.

      I have played around a bit with this to give some idea of the foundation of Verlinde's term. If this is a gauge-like field with spacetime physics then it may mean there is a gravity field in space that behaves as 2-space plus time GR, or BTZ-like physics. This might then be connected to inflation if the boundary of the inflationary bubble is “pinched off” so the spatial manifold that results at the lower vacuum energy is a topologically closed space. In this way the observable universe does not have this rather unfortunate boundary to it, but where signatures of this boundary remain in degrees of freedom that we might interpret as Verlinde's odd deviation from GR. A 2-space plus time gravity in 3-space plus time would have a gravitational potential that is logarithmic ~ log(r/a).

      Of course this could be wrong, most likely is, but current ideas of dark matter seems to be lacking. It might be then new approaches are needed.

      Delete
  7. "We do not actually know that dark matter is really made of anything ..." Did you mean energy here?
    "what makes the universe expands" Should be "expand"?
    "thatreally".
    "Dark energy in form" Should be "in the form"

    ReplyDelete
    Replies
    1. "Dark energy is what makes the universe expand"

      No. Consider the fact that a Friedmann universe with no dark energy also expands. Or contracts. It depends on the initial conditions.

      At best, you can say that dark energy makes the universe accelerate, but only if its value is high enough. If it is negative, there is never acceleration, and neither is there if it is positive but small, but in our universe it is large enough so there is acceleration.

      Delete
  8. I think you got the galaxy in your video rotating the wrong way...

    ReplyDelete
    Replies
    1. Yes... I noticed this too late. Sorry about that :/

      Delete
  9. Well instead of boring you with a lot of irrelevant information, I'll just point out the very first place the CC shows up - and it had not yet become cosmic, it was just a constant. This reference..

    Annalen der Physik 49 (1916), 769-822

    PDF
    http://www.physik.uni-augsburg.de/annalen/history/einstein-papers/1916_49_769-822.pdf

    See footnote on page 804.

    This was the culmination of a series of 4 papers in which general relativity was born. Apparently Einstein realized at a late stage, when the paper was almost ready for printing - an arduous task involving international snail mail - that a claim he made about 2nd rank tensors in the development was in fact only true up to an additive multiple of the metric tensor. This multiple later evolved into the cosmological constant. The late appearance of this arbitrary constant must have really bugged him, because he immediately set about finding a use for it, once he realized it could not be avoided. That was the paper on the Einstein static world that appeared a year later. As soon as Lemaitre and de Sitter showed that an empty, expanding world was a solution, he completely gave up on the CC, although he never really stopped thinking about it.

    (PS, essentially what Einstein had realized at the last minute was that the covariant derivative of the metric was = 0, not just its divergence.)

    -drl

    ReplyDelete
    Replies
    1. That's not true. Scientific American had a blog article in Feb 2017 discussing a preprint paper that made the same claim you are making, but in the published version of that paper the claim was removed. The footnote in question refers to the "trace" term, not the cosmological term.

      Delete
    2. @Amos - the linked PDF above *is* the published version. The footnote on page 804 does indeed refer to the very same constant that later showed up as the CC in the Einstein static world. No idea what you are referring to. There is only one such constant available.

      -drl

      Delete
    3. Your link is just to Einstein's 1916 paper, in which the footnote in Section 14 contains his first mention of the trace term, which you've misinterpreted as the cosmological term. Einstein's paper uses different symbols, such as Buv for the Ricci tensor (and the first Engligh translation used still different symbols), but the full field equations in terms of modern conventional symbols are Ruv - (1/2)g_uv R - lambda guv = -8pi Tuv. Einstein's 1916 paper never mentions the third term on the left side, which is the cosmological term. The footnote in Section 14 just refers to the second term on the right side, the so-called "trace" term. (Remember, g^ab R_ab = R.) At that point in the paper he is just discussing the vacuum field equations, Ruv = 0, in which the trace term is irrelevant and can be omitted, as he notes. He happens to use the symbol lambda for the coefficient of that term here. Later in the paper, when discussing the field equations with non-zero Tuv, he realizes that he needs the covariant derivative of the left side to vanish, so he needs "lambda" = -1/2, as in equation 53 (where he uses the trace "T" instead of "R"). That "lambda" is obviously not the cosmological constant, it is just the coefficient of the trace term. You can read about this in any good book on the history of relativity.

      The "published paper" I mentioned is a recent 2017 paper on the centennial of Einstein's 1917 cosmological paper, discussed in advance of publication on the Scientific American site, where a lot of people saw the mistaken claim about the cosmological constant allegedly first appearing in Einstein's 1916 paper. The published version of that centennial 2017 paper deleted the claim, because the authors learned during refereeing that the footnote actually just refers to the trace term, not the cosmological term.

      Delete
    4. @Amos thanks, OK I think I misunderstood you. No, the footnote is not about the CC as it appears in the static world, but the operative word is "L is a constant" and not "L is a scalar". He's talking about identifying a class of tensors that are no higher than 2nd derivative in gmn and linear in those, and the arbitrariness he discovers in the footnote has the same origin as the CC proper, the arbitrary length scale in Riemannian geometry. So if you know one, you know the other - there is only one arbitrary constant to play with. thanks.

      -drl

      Delete
    5. To clarify, your original statement was that a term having the form of the cosmological term first appeared in a footnote in Einstein’s 1916 paper, but I think we’re agreed now that the footnote in question does not refer to a term of that form. To the contrary, the footnote very explicitly describes the trace term (see the Hilbert controversy). The value of “lambda” in that footnote is later shown to be -1/2 in order for the covariant derivative of the local energy-momentum to vanish. Note that the trace R is a scalar but it is not a constant, so this term does not have the trivial form of the “cosmological” term, nor does it have any arbitrariness (without breaking local conservation and general covariance).

      Now you seem to be making a new claim: You’re saying that “the arbitrariness [Einstein] discovers in the footnote has the same origin as the CC proper…”. Again, to the contrary, Einstein shows that this trace term doesn’t introduce any arbitrariness at all, first because it doesn’t affect the vacuum equations, regardless of the value of the coefficient, and second because with non-zero Tuv the coefficient must have the unambiguous value of -1/2. This term is essentially just an expression of the Bianchi identities, but Einstein didn’t know that, and it was not trivial.

      In contrast, it is quite trivial and obvious that one could add a term that is just an arbitrary constant multiple of the metric tensor and still satisfy all the formal conditions, but there was no motivation to do that (at the time), it would have affected the vacuum field equations, and it definitely is not what that footnote is about. So, in summary, there is no mention, implicit or explicit, of a term having the form of the cosmological term in the 1916 paper.

      Delete
    6. @Amos OK now I see what you are saying and yes, you are right. That seems to have gone through my 5-hole as they say in hockey :) This is all very fascinating.

      -drl

      Delete
  10. Great summary, Dr H.
    So when you say the Cosm. Const. is measurable, does that mean that the accelerating expansion of the universe is measured and then the theoretical assumption is made that this is due to the constant as in Einstein's equations as originally expressed, and then you derive the figure?
    Is it expected that the question marks against the observations in favour of acceleration will be easily answered by more observations (as you wrote about LIGO)?
    Isn't it funny how Brian Schmidt, who got a Nobel Prize for making the supernovae observations, wrote the preface to "A Fortunate Universe" which nonsensically claims the universe is fine-tuned because of the Cosm. Const. (logic??) and that baby Jesus' papa set the value? Every review of A Fortunate Universe" in international newspapers and physics publications fails to point out that it is speculative, meaningless, nonsensical, utter drivel written by cranks. Why don't you review it on here, Dr. H? It would follow on nicely from this post.

    Here is what Schmidt writes in the preface:
    "You will see that humanity appears to be part of a remarkable set of circumstances involving a special time around a special planet, which orbits a special star, all within a specially constructed Universe."

    Just to prove you can be as thick as mince and still win a Nobel Prize.

    ReplyDelete
    Replies
    1. Violence is the last refuge of the incompetent. Ad ad-hominem attacks in blog comments are the mark of a disturbed person.

      The biggest fool can say that the Sun rose this morning, but that doesn't make it dark out. Similarly, even if Barnes is a theist, that in no way weakens his arguments. Suppose that a terrorist blows up a school in the name of "free speech" or "the scientific method" or "equal opportunity". Does that somehow render those concepts invalid?

      Delete
    2. "So when you say the Cosm. Const. is measurable, does that mean that the accelerating expansion of the universe is measured and then the theoretical assumption is made that this is due to the constant as in Einstein's equations as originally expressed, and then you derive the figure?"

      It's the other way around. No cosmological test directly measures the acceleration, despite some claims to the contrary. What one does is work out how some observational quantity (e.g. magnitude--redshift relation, CMB power spectrum) depends on the cosmological parameters, fits for those parameters, then concludes what those parameters imply, such as acceleration, the age of the Universe, whether it is finite, etc.

      Delete
    3. Phillip Helbig4:24 AM, November 25, 2019

      "Violence is the last refuge of the incompetent. Ad ad-hominem attacks in blog comments are the mark of a disturbed person."

      I'm making 2 points, that the main claims in "A Fortunate Universe" are completely without evidence, and that anyone who thinks the book provides evidence is thick. If a Nobel Laureate puts his name and credibility to such drivel in the public realm then he can expect criticism. Although, every review of the book so far,including your whitewash, has failed to make the blindingly obvious point that the claims are completely without empirical evidence. It's absolutely staggering. One of the claims in the book is that the truth of some crazy primitive superstition follows from the undemonstrated fine-tuning, so Brian Schmidt should have advised Luke Barnes to get psychiatric help for his delusions, not recommended the nonsense in a preface.
      "A Fortunate Universe" has received a lot of publicity because of the backing of a Nobel Laureate, so it would be good if the purported evidence in the book were actually examined by a competent physicist, and Dr. H sometimes reviews pop physics books...

      "even if Barnes is a theist, that in no way weakens his arguments"
      But he doesn't have a single argument. And the fact that he includes his preferred primitive superstition in the book as following from the undemonstrated fine-tuning tells us his delusions are a motivation. He's clearly desperate to show that natural science doesn't rule out his silly primitive superstitions. But superstitions are nonsense to begin with. Luke Barnes has recently claimed that he has evidence not only of fine-tuning, but that his evidence rules out a multiverse as an explanation. So far he has received around $550,000 from the Templeton Foundation to come up with this nonsense. So he's corrupt as well as insane.

      "the incompetent"
      And so I ask you, for the umpteenth time, to provide a single reason to show that the observable universe can be any other way than it is. And don't run away this time like you always do. Finish the discussion, then admit there is zero evidence for universal fine-tuning.

      Delete
    4. Phillip Helbig8:49 AM, November 25, 2019

      "It's the other way around. No cosmological test directly measures the acceleration, "
      I see. Thanks. It doesn't sound wholly convincing on the face of it. I'll have a read about it. Can you recommend any popular books on Cosmology....?

      Delete
    5. 'm making 2 points, that the main claims in "A Fortunate Universe" are completely without evidence, and that anyone who thinks the book provides evidence is thick. If a Nobel Laureate puts his name and credibility to such drivel in the public realm then he can expect criticism. Although, every review of the book so far,including your whitewash, has failed to make the blindingly obvious point that the claims are completely without empirical evidence. It's absolutely staggering. One of the claims in the book is that the truth of some crazy primitive superstition follows from the undemonstrated fine-tuning, so Brian Schmidt should have advised Luke Barnes to get psychiatric help for his delusions, not recommended the nonsense in a preface.
      "A Fortunate Universe" has received a lot of publicity because of the backing of a Nobel Laureate, so it would be good if the purported evidence in the book were actually examined by a competent physicist, and Dr. H sometimes reviews pop physics books...


      Note that you have provided no evidence at all for your claims. Maybe you should think about why none of the reviewers agrees with you. If it is really so obvious, then we must all be stupid. I don't think so.


      But he doesn't have a single argument. And the fact that he includes his preferred primitive superstition in the book as following from the undemonstrated fine-tuning tells us his delusions are a motivation. He's clearly desperate to show that natural science doesn't rule out his silly primitive superstitions. But superstitions are nonsense to begin with. Luke Barnes has recently claimed that he has evidence not only of fine-tuning, but that his evidence rules out a multiverse as an explanation. So far he has received around $550,000 from the Templeton Foundation to come up with this nonsense. So he's corrupt as well as insane.

      Again, you are making a fundamental error in logic: the competence of a person is independent of the claims made. I gave some examples to illustrate this. What is it about this that you don't get? Yes, Barnes himself might have superstitious and/or financial motivations, but that doesn't invalidate his claims. Barnes also believes that the Hubble constant is between 50 and 100. Should we now rule that out because he has accepted Templeton money? Note also that the other author is not a theist and favours the multiverse explanation, yet they agree on the question of fine-tuning. (Barnes probably doesn't favour the multiverse explanation.)

      Unless you accept standard rules for debate, you will never convince anyone.

      And so I ask you, for the umpteenth time, to provide a single reason to show that the observable universe can be any other way than it is. And don't run away this time like you always do. Finish the discussion, then admit there is zero evidence for universal fine-tuning.

      You're asking the wrong question. The question whether the universe is fine-tuned is independent of the question whether it could be any other way. There is some confusion in terminology. I'm working on a paper to clear this up and will post a link when it has been published.

      Delete
    6. "It's the other way around. No cosmological test directly measures the acceleration, "
      I see. Thanks. It doesn't sound wholly convincing on the face of it.


      Why not?

      I'll have a read about it. Can you recommend any popular books on Cosmology....?

      My standard recommendation is to start with Edward Harrison's Cosmology: The Science of the Universe.

      Other introductory books I recommend (with caveats mentioned in the corresponding reviews) for stuff like this (other books might be better for other questions) are the following numbers on the list:
      2, 15, 23, 24, 36, 39, 42.

      Delete
    7. Phillip Helbig 4:24 AM, November 25, 2019

      I hear that Luke Barnes is bringing out a book of his theory applied to biology. Its title is "If my fortunate aunt had balls she'd be my finely tuned uncle". In the book he describes how if his aunt had had just two more testes, incredibly, she would have been his ball-scratching uncle. The probability that his aunt turned out to be exactly his aunt with no propensity to fart and yawn during dinner? A barely comprehensible 1 in 2 (that's a 2 followed by no zeroes, said "two"). The Tons of Temples Fraudation is paying Lucre Barnes enough money to save 5,000 starving non-Christian children to photoshop two elliptical orbiting testes onto an image of his aunt to simulate a gravitationally stable uncle. In the book's deface, Nobbled Laureate, Brainov Schidt, describes Lucre's aunt as a specially female special relative without any testes especially.

      Delete
    8. Phillip Helbig 5:31 AM, November 26, 2019

      Your "arguments" for universal fine-tuning depend on an *unjustified assumption* that fundamental constants follow a statistical distribution, and *a schoolboy error with modus ponens* - just because you can change values in a model it doesn't mean they are physically possible.

      "The question whether the universe is fine-tuned is independent of the question whether it could be any other way. "
      This is the most stupid comment I have ever read. If the universe can't be fundamentally different then it isn't "tuned". Tuning implies that it could be different. As soon as you start saying if this constant or that constant were "slightly" different then you are *outside known physics*, so the speculated consequences of such a change are also *outside known physics*. Do you not understand this simple, simple, simple, simple, simple, simple point?

      "Unless you accept standard rules for debate, you will never convince anyone."
      I have provided counter-arguments before to your claims. Please don't lie, it's tiresome.

      "There is some confusion in terminology."
      Nope. There is only known to be one universe, and nobody has any idea whether it could have been fundamentally different. Simple. Simple. Simple. Simple. Do you genuinely not understand this fact?

      " Maybe you should think about why none of the reviewers agrees with you."
      They don't understand that the conclusion below relies on both conditions 1) AND 2) being fulfilled. Condition 2) alone doesn't lead to the conclusion i.e. they are very, very thick.

      1) The physical constants can be many different values
      2) For almost all of these many different values the universe would not have been complex.
      Conclusion: A complex universe is unusual and special.

      Delete
    9. Phillip Helbig 5:45 AM, November 26, 2019

      "Why not?"
      Because there's no direct measurement and it's all relatively new work. It was just a first impression though.

      "My standard recommendation is to start with Edward Harrison's Cosmology: The Science of the Universe.
      Other introductory books I recommend (with caveats mentioned in the corresponding reviews) for stuff like this (other books might be better for other questions) are the following numbers on the list:
      2, 15, 23, 24, 36, 39, 42."
      Thanks, I've bookmarked it. I see No. 31 is not on the list. You've certainly been beavering away at the old Cosmology over the years.

      Delete
    10. PH wrote this, but it's context independent: "No cosmological test directly measures the acceleration, despite some claims to the contrary."

      There will be a more-or-less direct observation of the expansion of the universe, acceleration included, starting ~2040 but with good data only from ~2060 or so. The EELT (42m optical telescope!) will very likely undertake thousands of hours of observations of quasars, and using laser frequency combs, will measure the relative line-of-sight velocity accurately and precisely enough that after 20-40 years the expansion will show up unambiguously in the data.

      Delete
    11. JeanTate 8:54 AM, November 27, 2019

      Sounds good. Do you mean any acceleration would show up in the data? The expansion already shows up in data, I believe.

      Delete
    12. Steven Evans: at a very simple level (details matter, am happy to expand if you're interested), we observe that galaxies and quasars (and ...) have a redshift that is linear with their distance from us (the Hubble relationship). Converting observed redshift to apparent line-of-sight velocity is easy, but has assumptions (for some regulars here, unacceptable assumptions). The empirical relationship implies expansion.

      If the universe is expanding, then the redshift of a galaxy measured today will be greater than that measured yesterday. Plot the observed redshift every day for a decade, and accelerating expansion (or not) will be clear.

      Hope that answers your question.

      Delete
    13. Phillip Helbig 5:31 AM, November 26, 2019

      And sure enough, you run away faster than a universe of accelerating expansion.

      There is no point you writing a paper on fine-tuning as either you will be making wild assumptions about constants having statistical distributions based on 1 data point, and so will be writing a theology paper. Or you will be defining something as fine-tuning but unable to show that it isn't just natural in the one observed universe. In which case it is an abuse of language.

      If you can't even answer these 2 obvious points from a layperson, then you will just be wasting your time writing a paper. I'm sure PASA would publish it, though ;) Just look where Luke Barnes has published and you will know it to be a crank journal with no standards.

      Delete
    14. JeanTate 12:50 PM, November 27, 2019

      Many thanks.

      Delete
    15. Phillip Helbig 5:31 AM, November 26, 2019

      " Maybe you should think about why none of the reviewers agrees with you."

      Reviewer 1 Brian Schmidt, Nobel Laureate Apparently, in the preface:
      ""You will see that humanity appears to be part of a remarkable set of circumstances involving a special time around a special planet, which orbits a special star, all within a specially constructed Universe.""
      This is all patently untrue. Humanity is the result of adaptation to the environment. There are exoplanets found almost daily, some similar to Earth. There are billions of stars like the Sun. The universe is not known to have been "constructed"; it is off-the-charts insane to suggest there is evidence for this.

      Reviewer 2 "Physics Today" Marcelo Gleiser is the Appleton Professor of Natural Philosophy and a professor of physics and astronomy at Dartmouth College

      "funny new book"
      It's not real humour, it's false humour to cover up anger.

      " After all, in the vast parameter space of hypothetical universes, life is a tight fit."
      Only one universe is known to be physically possible. There isn't known to be any parameter space. It is not known how common life is in this universe, nor what forms of life might exist if other universes were physically possible, which we don't know is the case.

      "Change the fundamental constants, or the basic laws of physics, or the low-entropy, free-energy-rich initial state of the universe, and the story on Earth would have been radically different. Life has very little wiggle room."

      DOH! But we don't know they can be changed. Dartmouth Physics professor doesn't even understand modus ponens. Is it Dartmouth in Devon?

      "Multiple universes may exist in addition to ours"
      No evidence for this.

      " in them the values of the fundamental constants might differ."
      FFS. Or they might not. Nobody knows. You can change values in a model but that doesn't mean it's physically possible.

      " We could be a rare statistical fluke in a vast landscape of potential universes."
      You can't create statistical distributions based on 1 data point.

      "why the fundamental constants appear to be fine-tuned"
      It is an abuse of language to call something fine-tuned that cannot be changed or "tuned".

      "if scientists were one day to be in possession of such a metatheory, one could ask why nature operates by that metatheory "

      And then you could ask about the metametatheory, ad infinitum, and you would not come up with 1 single fact about physics because it's all mental masturbation by low-IQ halfwits.

      "It’s wiser to accept our ignorance with humility and embrace uncertainty than to claim certainty with blind arrogance"

      It is Barnes and Lewis who are making the crazy claims based on no evidence.

      So you see, Phillip Helbig, that's a Nobel Laureate and a Dartmouth Physics professor shown to be talking utter gibberish and making schoolboy error after schoolboy error.

      As I said earlier, the reviewers are thick.

      Delete
    16. And would not you know it! I thought I recognized the lunatic tone in Gleiser's review:

      MARCELO GLEISER AWARDED 2019 TEMPLETON PRIZE

      "his doctrine of “humancentrism” — by revealing the improbable uniqueness of our planet"

      "The Templeton Prize, valued at 1.1 million British pounds,"

      Humancentrism??? Gleiser is as bent and as insane as Barnes.

      Now will you review "A Fortunate Universe", Dr. H? These are deliberate, corrupt attempts to try to remove the requirement for observation from natural science.

      Delete
    17. Steven Evans, a bit upthread you wrote:
      "1) The physical constants can be many different values
      2) For almost all of these many different values the universe would not have been complex.
      Conclusion: A complex universe is unusual and special.
      "

      In logic, a conclusion is only as good as its premises. Other than a fun thought experiment, why would you accept 1)?

      2) is problematic for a different reason: the (mathematical) space of varying constants is infinite and vast. Proving the "almost all" and "not complex" parts is surely an incredibly difficult challenge, is it not?

      Delete
    18. " I see No. 31 is not on the list."

      It's not an introductory cosmology book.

      Delete
    19. "There will be a more-or-less direct observation of the expansion of the universe, acceleration included, starting ~2040 but with good data only from ~2060 or so. The EELT (42m optical telescope!) will very likely undertake thousands of hours of observations of quasars, and using laser frequency combs, will measure the relative line-of-sight velocity accurately and precisely enough that after 20-40 years the expansion will show up unambiguously in the data."

      Right, but this is in the future. What it will measure is the change of redshift with time. Whether this counts as a "direct" measurement of acceleration is another question. In any case, FRW cosmology makes definite predictions for this (sometimes called the Sandage-Loeb effect).

      Delete
    20. "Steven Evans: at a very simple level (details matter, am happy to expand if you're interested)"

      The universe is also happy to expand. :-)

      Delete
    21. JeanTate8:59 AM, November 28, 2019

      I'm saying that people who claim there is evidence for universal fine-tuning are making a schoolboy error with modus ponens.
      1) A is True 2) A => B is True. Fine-tuners forget that you need 1) AND 2) to demonstrate B is true. It's a blog comment so it's roughly expressed, but I think the simple point is made.

      Delete
    22. Phillip Helbig11:33 AM, November 28, 2019

      " It's not an introductory cosmology book."

      Ha! It's a fantasy book. When are you going to answer the points about fine-tuning?

      Delete
    23. Phillip Helbig 11:56 AM, November 28, 2019

      "Whether this counts as a "direct" measurement of acceleration is another question. "

      It's a more direct measurement than fitting a complex model to observations. If one believes that red shift observations now show the universe is expanding, then presumably one would believe more precise red shift measurements which showed the expansion is accelerating. The principle is the same, just the precision will be greater.

      Delete
    24. JeanTate 8:59 AM, November 28, 2019

      "Other than a fun thought experiment, why would you accept 1)?"

      You wouldn't. That's my point. And it wouldn't be fun, it should be clear in a few nanoseconds that it is a waste of time.

      Delete
    25. Phillip Helbig11:57 AM, November 28, 2019

      "The universe is also happy to expand. :-)"

      But you're not happy to expand on the obvious criticisms of fine-tuning, are you?
      You've published in journals, you've written all those reviews for the Observatory, you've translated a Galaxies Atlas from German to English, you've written dozens of comments to this post.
      And yet you refuse to respond to the obvious criticisms of fine-tuning: given the unlikelihood of the universe is pure speculation, and the uniqueness of the universe is a possibility as far as anybody knows, claiming anything is universal fine-tuning is just an abuse of language.

      Now why is it that your writings are so incontinent on this area, but you refuse to answer these points?

      Delete
    26. JeanTate8:59 AM, November 28, 2019

      " Proving the "almost all" and "not complex" parts is surely an incredibly difficult challenge, is it not?"

      Not for a genius of the calibre of Luke Barnes. Why don't you get him on your Universe Today podcast and ask him, given we have absolutely no idea whether any other universe than the observed one is physically possible how can one claim the universe is "fine-tuned" and simultaneously claim to be a member of the species Homo Sapiens?

      Delete
    27. @Stephen Evans, re 1) and 2): thanks for the clarification. Yes, it's easy to misunderstand blog comments.

      I think there's a lot more to physical constants can vary than the 1) you write. For example, there have been (and still are) various experiments testing hypotheses that one or more do in fact vary (there's some interesting astronomy literature on one such search, for example). Also, value of the fine structure constant turns out to be dependent on energy, consistent with the relevant theory. And looking for an underlying theory out of which at least some constants "fall" is serious physics, wouldn't you agree?

      And of course schoolgirls never make errors with modus ponens ;-)

      Re measuring the expansion of the universe via redshifts: I did note that details matter. And already some have raised their heads. For example, PH correctly points out that what I described is in the future (long after I'll be gone, sadly), so who knows what surprises, if any, await?

      BTW, Universe Today is owned and run by Fraser Cain. I was a "staff writer" for a time, but it's now quite a while since I stopped contributing.

      Delete
  11. Steven Weinberg:"physics thrives on crisis." (The Cosmological Constant Problem, 1989 Rev Mod Phys). This is a great article worth re-reading ! It is interesting to see the concept of 'wormholes' find its way into the exposition (via Sidney Coleman's 1988 paper). How far have we progressed since publication of Weinberg's paper ?

    ReplyDelete
  12. One of the many synonyms for Quintessence is Aether, coincidence ?

    ReplyDelete
    Replies
    1. Dark energy is a field that permeates the universe, so is quintessence, so is the aether, so is the Higgs, and so on.

      Delete
  13. My question is inspired by the fact thst quintessence literally means fifth element (after earth, water, air and fire). This word chosen by Caldwell seems to suggest a pendant for aether.

    ReplyDelete
    Replies
    1. Your point being what? I am totally not interested in debating the etymology of names people have given to scalar fields.

      Delete
    2. Quintessence only existed in the celestial sphere.

      Everything old is new again!

      Delete
    3. Sabine,

      I just assume that the choice of giving a hypothetical field the name of Fifth Element (originally aether) has some special meaning. If so, I like to know what that special meaning is. Maybe it is just Caldwell having a special sense of humor.

      Delete
    4. The cosmological constant may really be a parameter that depends on scalar fields. We may then have Λ = Λ(φ, dφ/ds) and the derivative of the scalar field may be extended to variation in space. This idea of Steinhardt et al. is then that there may be variations in Λ with spatial direction or angular perspective. The CMB has ruled this out on a scale comparable to this surface of last scatter out some 46 billion light years.

      Delete
    5. I am not aware of any special meaning.

      Delete
    6. There is no special meaning, it just sounded cool as the name the ancients gave to the stuff which makes up the heavens. Ironically, in contrast to the other four elements, its defining characteristic was the fact that it is unchanging, whereas quintessence, as opposed to the cosmological constant, has as its defining characteristic that it is not constant, so in that sense it is a bad name.

      But it doesn't matter. You could it "Arthur" and it wouldn't matter. A rose, by any other name, would smell as sweet.

      Delete
    7. I thought of something both physical and clear like Mambo number five, sorry.

      Delete
  14. "In order to realize the cosmic acceleration today,the mass of Quintessence needs to be extremely small. In general there is a difficulty to reconcile such an ultra light mass with the energy scales appearing in particle physics." (2013, Tsujikawa, arXiv 1304.1961.v2, Quintessence: A Review). An intriguing aspect of this review is the section pertaining to supersymmetry (pages 15-17).

    ReplyDelete
  15. The exponential expansion of the universe can be derived just using Newtonian mechanics. For any one interested this is something I demonstrated here:

    https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542

    This is much the same as what you get with general relativity in the Friedmann-Lemaitre-Robertson-Walker metric, but without the term -k/a^2, for a the scale factor of the universe. This additional term has this factor k = {1, 0, -1} for a spherical space, flat space and hyperbolic space. Generally most think space is flat, though it could be spherical, but just very large. One of Jorge Borge's strange short stories has this featured. What this assumes is there is just a constant energy density in space, and the result is this expansion that can be understood with Newtonian mechanics.

    Where does this energy density come from? In quantum mechanics and quantum field theory the quantum operators for fields are described by a harmonic oscillator. This is seen in the motion of a mass on a spring or the small swinging oscillation of a pendulum. With the Hamiltonian, or energy function, H = ½p^2 - ½q^2 for p and q the momentum and positions of the moving particle. We have these operators that lower and raise quantum states a|n⟩ = √n|n-1⟩ and a^†|n⟩ = √(n+1)|n+1⟩ and this above Hamiltonian is H = ½ħω(a^†a + aa^†), for these operators written according to p and q, and the operator corresponding to an angular frequency ω and ħ the quantum unit of action or angular momentum. Quite often this is written in the form H = ħω(a^†a + ½[a, a^†]) for [a, a^†] = 1 a commutator. Well in general we sum these over all possible modes and we then have this embarrassing summation sum_n ħω_n/2, that in principle sums to the Planck energy. That is awkward! It implies there is this huge density of mass-energy everywhere.

    Well it turns out for quantum field theory that since these virtual modes are not connected to anything we can just drop them. This is sometimes referred to as normal ordering. A tiny measure of these do couple to real particle-fields and these are the internal lines and loops in Feynman diagrams. These have a real contribution to QFT. However, this runs into trouble with gravitation, where even if these are removed from QFT, their mass-energy content will still have spacetime curvature associated with them. This is in my simple Newtonian derivation a huge vacuum energy ρ that is 123 orders of magnitude larger than the energy density predicted from the observed cosmological constant Λ = 8πGρ/c^2 ≈ 10^{-52}m^{-2}. Using the Planck energy density we expect more on the order of Λ ≈ 10^{66}m^{-2}.

    This is one of the bases for inflationary cosmology, where the inflationary manifold with an extreme accelerated expansion and huge vacuum tunnels into a configuration with a small vacuum energy. The difference in vacuum energy is what during so called reheating generated the particles and radiation of the observable universe. How this resulted in the asymmetry of matter vs antimatter is a big problem of course. So there is then by Vilenkin et al this eternal inflationary manifold that has local vacuum instabilities that generate lower vacuum energy spacetimes or regions.

    Returning to my Newtonian derivation it is interesting this can be derived from classical physics. However, in general relativity anything near an event horizon is observed to be time dilated and Lorentz contracted to one dimension less, squashing out the dimension radial to the horizon. This then suggests in some strange way the observable universe, which may include the inflationary spacetime, is some holographic projection. This would be on some spacetime of 5 dimensions, which could be a holographic screen in AdS_5. These holographic screens are either on the boundary of AdS_5 or vacuum junctions bounding causal wedges.

    ReplyDelete
  16. It seems a good argument that the accelerated expansion is a measurement problem. But the proposal linked above is a very complicated explanation. There are simpler and more plausible ones.

    Why do we think that the recession speed is increasing? How is this speed measured? It is measured by evaluating the red shift using the Doppler Effect. But we should notice that the speed of light c is used in the Doppler formula. And why do we believe that c is / was constant during all times?

    Hendrik Lorentz has shown already in 1889 that the constancy of c is only a measurement result and not real physics. Einstein’s assumption that c is truly constant in all frames on the other hand is a postulation, Lorentz’s position was never disproved. And what does the constancy of c mean in an expanding space? To what is a speed c related then? Does a statement like this make any sense?

    If we are open for the assumption that c was a bit higher in former times, then Doppler yields a higher speed for those times and the whole problem of Dark Energy is gone.

    ReplyDelete
    Replies
    1. Einstein’s assumption that c is truly constant in all frames on the other hand is a postulation,

      Einstein postulated (Special Relativity) that the speed of light, c, is constant in inertial reference frames. Inertial reference frames are a limiting case that only approximately exist in physical reality.

      In General Relativity, c is not constant, but varies with position in a gravitational field. That is an empirically established fact.

      Delete
    2. @antooneo

      Don't know where you got that information about Lorentz, Einsten, and C, but it's not so (and it goes much against my understanding of history). The speed of light is either 1, or infinity, and has nothing to do with light as such - light goes at this speed because the EM field is mediated by a massless boson. The speed of light is a structural element of spacetime geometry (Minkowski geometry), determined from experience. There are many examples of the derivation from homogeneity, isotropy, and reciprocity that lead to the Lorentz transformation and the role of the parameter C. (I'll point one out below). You can always choose units such that C=1, and if it is 1 here, it is 1 everywhere. The situation is even simpler from the point of view of projective geometry. Euclidean geometry is also characterized by a fixed parameter, only it is i, the imaginary unit, instead of 1. Again, this is not even physics, it is elementary math. The speed of light is a parameter determined from experience, it is not a scalar field that changes from place to place. Anyone who practices such an idea has not learned his/her special relativity correctly.

      Reference - there are many others along the same lines, this one is recent.

      https://www.mdpi.com/2073-8994/8/9/94

      -drl

      Delete
    3. Regarding the constancy of the speed of light c, that is a very interesting and important point.

      Every measurement of c yields the same result. But that does not reflect the physical reality by a very simple reason. It is the consequence of Einstein’s rule to synchronize clocks.

      Einstein said in his original paper of 1905 about clocks:
      If clocks are at different positions, they have to be synchronized. To be done in the following way: A light signal shall be sent from clock A to clock B and a signal from B to A. Then the assumption is made that light takes the same time from A to B as from B to A, and the clocks are set accordingly. This in any inertial frame. That is it! This synchronization has to be done prior to a measurement in the actual inertial frame.

      If these clocks A and B are now used to measure the speed of light, then the result will always be that the speed is the same in both directions. Very simply because the measurement of c is a repetition of the synchronization process. Einstein has admitted that his precondition is only an assumption; but he finds that it is good as it does not cause logical conflicts. (But it leads to conflicts as it was often shown.)

      This rule of Einstein is a typical case of circular reasoning.

      The point for Dark Energy is, however, a bit different: How do we know that c did have the same value since all times? The true Einsteinians say that c is an eternal constant. But the example above shows that Einstein’s position to c is in no way justified.

      Delete
    4. antooneo,

      What you say is incorrect because there is nothing preventing you from moving the clocks. This is basically how the Michaelson-Morley experiment works.

      Delete
    5. No Sabine, it is correct because,

      if you make a one-way-measurement of the speed of light c, then you need two clocks, one at the beginning and one at the end of the measurement distance. These clocks have to be at rest in relation to the frame of the observer or in the same motion state in which c is measured later on. This is the case addressed by Einstein in 1905. And the result of the measurement is necessarily c is as I have explained it.

      There is another case of measuring c, that is the two-way measurement. In this case a light signal is sent to a mirror and then reflected back to its starting point. In this case only one clock is used and clock synchronization is not applicable. Also in this case the result is always the nominal value of c and not the real physical speed. The reason is that in the case of motion the measurement distance shrinks and the (one) clock runs more slowly. This can be shown by a very simple calculation.

      The Michelson-Morley experiment using an interferometer is a special case of a two-way experiment, but for an interferometer no clock is needed. The result of this process is also the nominal c, because the apparatus shrinks in the direction of motion. Also this can be shown by a quite simple calculation. This was the argument of Lorentz 1889 to explain the null-result of MM after Oliver Heaviside has shown that fields contract in motion as a result of Maxwell’s electrodynamics.

      Delete
  17. As a form of energy, is dark energy quantized? What force carrier would a gradient in dark energy be mediated by, a graviton?

    ReplyDelete
  18. @LC "However, in general relativity anything near an event horizon is observed to be time dilated and Lorentz contracted to one dimension less, squashing out the dimension radial to the horizon. This then suggests in some strange way the observable universe, which may include the inflationary spacetime, is some holographic projection."

    I really don't know what to say about a statement like this. I would regard this as an elementary blunder on a special relativity test, and not give a single point of credit. The Lorentz contraction is an effect on spatial coordinates and has no invariant spacetime significance. None, zero, nothing. Example - assume a perfectly spherical Moon and a perfectly spherical Sun. Let said Moon and said Sun be exactly the same apparent diameter, and consider a perfect eclipse, the Moon exactly covering the Sun. Does the Lorentz contraction of the moving Moon ruin the eclipse? No - of course it doesn't. A moving sphere always appears spherical. There is no visible (actual, involving pencils of light rays) contraction along the direction of motion. This is an elementary fact from special relativity, involves no dynamics, no laws of motion, no anything but the geometry of spacetime and its kinematical relationships. The simplest proof is with 2-spinors in the complex plane, but there are also direct proofs with ordinary vectors.

    This sort of vague tossing around of unrelated and misunderstood ideas that have no actual connection with each other is the real source of pathology in modern physics. It's the people who should know better that do the most damage.

    -drl

    ReplyDelete
    Replies
    1. You might want to bring this up with Susskind, for he uses exactly this language of Lorentz contraction.

      Special relativity has some additional optical features. In Newtonian mechanics an object moving in space would appear elongated. The Lorentz contraction cancels that out, so a sphere moving near the speed of light appears to be a sphere. However, the sphere may appear rotated. This is the Terrell rotation. This can be demonstrated without spinors, but it is tricky with lots of optical ray tracing.

      https://www.youtube.com/watch?v=JQnHTKZBTI4

      We are though not talking about special relativity, but general relativity. In this setting with black holes an object approaching the black hole will contract along the radial direction as seen by an asymptotic observer. Susskind refers to this as Lorentz contraction. There is a sort of general Lorentz gamma factor Γ = 1/√(1 - 2GM/rc^2 - v^2/c^2) that does appear to compress objects falling in a gravitational field.

      Delete
    2. This comment has been removed by the author.

      Delete
    3. This comment has been removed by the author.

      Delete
    4. @LC

      "We are though not talking about special relativity, but general relativity."

      This phrase is often trotted out to cover up misunderstandings. Of course it is not correct - the curved manifold is built up from charts in which SR holds, and so it inherits locally the same properties that obtain in SR, which are those of Minkowski geometry. The Lorentz contraction means nothing in GR or in SR because it is a relation only between spatial coordinates and has no invariant significance. And I'm not really interested in Susskind's opinion, this isn't a matter of opinion.

      "Special relativity has some additional optical features. In Newtonian mechanics an object moving in space would appear elongated. The Lorentz contraction cancels that out, so a sphere moving near the speed of light appears to be a sphere. "

      This is simply false. See Penrose's original paper, also that of Terrell. It is not exactly a rotation of the sphere, the surface features crawl around, but the bottom line is that the truly invariant thing is the pencil of light rays that define the object. A moving sphere appears to be a sphere because that is how the actual invariant configurations of spacetime work out - not because one non-invariant configuration cancels out or modifies another non-invariant configuration. That would be like saying a meter stick is 25cm in its one half, and 75cm in its other, and they add up to 100cm so it's all good in the end.

      I worked all this out for myself as a student. I later discovered that Penrose beat me to it. So arguments to authority are not going to change my mind.

      -drl

      Delete
    5. I am well aware of the spinor approach to SR. However, You are wrong with respect to an object approaching a black hole.

      Suppose an object with a diameter d approached a black hole. We the distant observers witness the object and document the clock rates at different point on that object. These clock rates slow down, according to the tortoise coordinate transformation t' = t - 2m ln|r - 2m|, and as they approach the horizon the clocks approach a stop. However, we have a conundrum if the body does not contract. The clock at the leading edge of this object indeed slows down and stops, but if the object does not contract then we witness the clock at the trailing edge and it marks time at a faster rate if it maintains an apparent distance d from the horizon so r - 2m = d permanently. If the body appears to stop before crossing the horizon either this clock keeps marking time, according to its distance from the horizon by the tortoise coordinate, or it appears to stop with the other clocks contrary to what is expected. We then have a contradiction.

      I am not likely to respond again to this, but you are I think wrong on this with respect to general relativity.

      Delete
    6. I'm gonna wait to see what Sean Carroll thinks!

      Delete
  19. Question: Could dark energy simply be a consequence of temporal geometry?

    I ask this only because geometry seems to provide some oddly simple ways to explain accelerating expansion. Please pardon me first for some scenario buildup. Also, I try scrupulously to avoid topology terminology, since the main ideas easily fall within the capability spectrum of unaided primate visual comprehension.

    To start with a whimsical image, imagine that yours truly is an American-style donut, that is, a donut with a hole through the center, not one with jelly inside (Ich bin kein Berliner). The baker added a bit too much dough to this particular donut, causing its hole to close to a point at its exact center. (My doctor recommends that I cut down on carbs.)

    Next, imagine a pair of loop-like universes forming at the center of the hole, each with an energy content that is the negation of the other. One loop moves upwards over the donut surface, and the other moves downward. (Incidentally, since like virtual particles these loops recombine to give zero net energy, it's not quite correct to think of them as matter and antimatter; the symmetry is more exact than that.)

    The loops represent a virtual pair of closed one-dimensional universes, or, more interestingly, slices of similarly closed three-dimensional universes. Time is defined for the top loop by its constant and mostly upward movement across the surface of the donut, and time for the lower loop is similarly defined by its downward movement.

    Notice that the perimeter-length 'volumes' of these loop universes increase as they move farther away from the center, since their diameters grow as the hole curves outwards. Also, as the loops move farther from the center — as they evolve over time — their rates of expansion increase. This is because as their local time vectors shift towards a faster-expanding outbound radial configuration: They begin moving more outward than up or down. Finally, since the donut surface defines time and is independent of the number of spatial dimensions, the same configuration works for closed 3-space universes. In that scenario, this loop example simply becomes a lower-dimensional slice in which only one spatial dimension is shown.

    So, after all this buildup, here is my attempt at a dark energy analogy:

    Creating pairs of closed virtual universes on a donut-like time topology causes such universes to expand faster as they age. But can such a topology-first models of accelerating expansion be made mathematically equivalent to dark energy?

    I have no idea. Thoughts, anyone?

    ReplyDelete
    Replies
    1. I have many thoughts on that theme but not here, work is in progress. I can only shortly say that considering those antipodal universes not virtual but continuously pairing observables by holographic principle, it seems to be possible to achieve the model of two 2-manifolds (or expanding opposite sides of the same double-phase-manifold) as the spacetime - maybe like a flat closed Klein bottle topology.

      Delete
    2. Eusa, thanks, it's encouraging to know that folks like you are working on such topics! I hope you will keep all of us informed. I'm guessing Sabine's topics will provide occasional appropriate contexts for you to give us updates.

      My own interest in hypertorus topologies emerged from consciously trying out various configurations of axiom sets. One of my more interesting and productive axiom sets places the following axiom at or very close to the top: Everything is a virtual pair. That is, everything emerges from nothing and, in time, returns to nothing, usually very quickly. However, in a few very special cases, the 'return' part gets delayed a bit… say by a few billion years. This happens only when sufficient chaos and 'rigidity' (e.g. consensus spatial coordinates for conserving spin) makes an easy return problematic.

      This is why I feel that pairs of universes make a lot more sense than isolated big bangs. I'm certainly not the only who has played with that idea, e.g. both Turok at PI and Sean Carroll talk about matter-antimatter universe pairs. However, folks seem to keep getting one critical detail a bit wrong: Yes, the other universe must look just like 'antimatter' in terms issues such as particle charges and the view that they are ordinary particles moving 'backwards' in time. However, when speaking of virtual universes, one must pay excruciatingly close attention to the particular version of time being used.

      There is the non-information-generating 'small scale' or quantum time, and then there is information-generating 'big scale' or causal time. The difference is critical because the sign of the shared information (yes, information has a sign, like momentum) also determines the sign of mass-energy. Antimatter can exist in our universe, but only by breaking this sign rule, which is what also causes the slight chirality violations that get everyone so upset.

      Our true doppelganger universe has a separate information field with its own shared time vector, exactly opposed to ours. To an external observer the contents of this universe would look like what we call antimatter, but on closer examination it would lack CP violations. It would instead show true CPT symmetry, with a catch: To get large-scale, information-rich CPT, you have to create a separate universe, one with its own independent time vector, information, and energy signs.

      I should note that true CPT also occurs within our universe, but only at the non-information-generating quantum level. As long as no information is generated, the time-energy uncertainty model of virtual pairs accommodates the formation of short-lived positive-negative energy particle pairs, which incidentally also makes the vacuum density 'problem' a non-issue. This idea parallels the formation of momentum pairs, except along the time axis instead of along the spatial axes.

      So that was a lot of talk, but my reason for it is to get back to Clifford tori and Klein bottles: Why should time fold back on itself in a torus? That is, while it's easy to assert on paper that time follows a hypertorus path, the deeper question is always why reality should behave in such an odd way.

      The (proposed!) answer for this axiom set is that there can never be such a thing as fully separated virtual pair, not at any scale, not even at the scale of universes. While the chaotic emergence of information may have locked these positive and negative clumps of mass-energy into paths that are currently hurtling away from each other in time, in the end the piper must still be paid. The extreme phase rigidity of both space and its associated coherent causal time vector can only delay this process, not stop it. The simplest topology for paying the piper while still satisfying conservation-centered rigidity constraints is for the time paths of the two universes to curve slowly and inexorably back on themselves.

      At which point both will return to the void, at the literal end of time.

      Delete
    3. Terry,

      To (mis)quote Laplace, "We have no need of that hypothesis."

      You want physicists to take your ideas seriously, you need to put them in (precise) mathematical terms as Einstein did.

      And, then, you have to show that the math actually gives results that agree with current observational and experimental results.

      Also, it would be very nice if you could make some new quantitative predictions that could be confirmed (or, more likely, disconfirmed) by future observations.

      What gives science its strength is that it ties together, in very precise ways, many observations that are surprising or unanticipated (the fossil record, the expansion of the universe, the Rutherford experiment, and so much more).

      If you cannot do that, or don't even try, your verbal musings are, at best, bad philosophy.

      Delete
    4. Dave, Dave, Dave… really?

      First, I should point out that I am open source to the core, meaning that I don't always think first in terms of how to achieve maximum benefit for myself. Please don't be fooled by how casually I put out some of my ideas. I even won't bother posting ideas here if they don't have a good potential for testability. Can you say the same? Does it really bother you that much that I might consciously try to inspire ideas about how to think about equations, instead of giving equations first? Also, and this may seem weird to you, I actually think it's both fun and productive to brainstorm sometimes, instead of reflexively going for the dismissive shut-down insult first.

      Speaking of that, and with no intent to belittle individual participants — the devils and angels are always in the details — I'd say that the general domain of theoretical physics has about the least room to criticize any other science, or even any other philosophy, of a lack of mathematically quantifiable predictive precision. Here's a simple ratio to back that up: zero experimentally meaningful predictions created, divided by tens if not hundreds of millions of research dollars spent. Capiche? Or do you want that in equation form?

      It's not even hard to understand how sorry state of affairs came about. Let's take 50 years of string theory, for example. That entire body of work is absolutely and inextricably based on one of the most cockamamie, cult-like Great Revelations ever put down in a supposedly scientific paper. Some folks took the quite real string-like vibration modes found in hadron Regge trajectories, and then magically and quite arbitrarily pushed the associated math down 20 magnitudes of scale, simultaneously freeing them from all meaningful constraints. Why? Because, hey dude, you know, Regge string vibrations sort of look like some of the mathematically self-contradictory 1970s musings about how spin 2 quantized gravity might look — so you know, it's all so cool man, right? And hey, why not also make an infinite sum equal -1/12 by breaking all those darned Convergence Rules of the Math Man, you know? Power to the Strings, dude!

      And with that kind of conceptual foundations to back you up, you are objecting because I hypothesized that perhaps virtual universes, just like virtual particles, may also have a total mass energy that adds up to zero, in contrast to the (independent) Carroll and Turok models that instead create pairs by playing complicated and unavoidably slightly asymmetric games with matter, antimatter, and space energy? Wow. Which part of my assertion you find 'imprecise'?

      I truly don't expect you to understand game theory and problem space exploration heuristics, Dave, but it seems to me that if folks in theoretical physics were a bit more like open source folks in their willingness to exchange ideas and analyses at every level of discourse, equations and ideas equally, there would be a much better chance of breaking out of half a century of accomplishing almost nothing. And the first rule of exchanging ideas is simple: Explain your idea well, and in terms that are comprehensible to as broad and audience as possible. The second rule is just as important, though: Try listening sometimes. If physicists can't get a lot better at both of those rules, it may be another 50 years before anything truly interesting happens again.

      Delete
    5. Terry wrote to me:
      > Here's a simple ratio to back that up: zero experimentally meaningful predictions created, divided by tens if not hundreds of millions of research dollars spent. Capiche? Or do you want that in equation form?

      We're talking about General Relativity, which has some very, very meaningful predictions (Pound-Rebka experiment, deflection of light by the sun, precession of the perihelion of Mercury), which have worked out very nicely indeed.

      Terry also wrote:
      >It's not even hard to understand how sorry state of affairs came about. Let's take 50 years of string theory, for example. That entire body of work is absolutely and inextricably based on one of the most cockamamie, cult-like Great Revelations ever put down in a supposedly scientific paper.

      No, it's not "cockamamie." It is mathematically suggestive and interesting: so far, unfortunately, no one can get actual observational predictions out of string thoery. I do agree with Peter Woit (and, I think, Sabine) that it has been over-hyped by some people.

      Terry also wrote:
      >And hey, why not also make an infinite sum equal -1/12 by breaking all those darned Convergence Rules of the Math Man, you know? Power to the Strings, dude!

      There are restrictions on how you can renormalize the string energy for physical reasons. When you follow those restrictions, yes, you get the -1/12 (this can be shown in general via Euler-Maclaurin). I do agree that the standard textbooks do not explain this clearly: I suppose that someday I should write it up in simple, elementary form.

      Terry also wrote:
      >And with that kind of conceptual foundations to back you up, you are objecting because I hypothesized that perhaps virtual universes, just like virtual particles, may also have a total mass energy that adds up to zero...

      No, I object because I think you have a slew of words in search of an actual concrete idea: "word salad" as people say.

      But prove me wrong: present an actual, precise, quantitative physical theory.

      Delete
    6. Terry

      Not sure how much of your 'time geometry/paired universes' post I agree with or understand, but it has provoked some thoughts.

      Penrose's CCC model has a single universe undergoing phoenix-like cycles with AFAIK no mention of dark energy. I view it by analogy as like a blown soap bubble at first expanding and then popping. The end part of the cycle is discontinuous and that may be convenient as in the first part of the cycle entropy is increasing but, in the end part, entropy is or one would think should generally be decreasing. By further analogy with particle interactions the end of cycle could be comparable with wave function collapse. I presume there are no such discontinuities in your twin universe model.

      One thing I like about the CCC model is that each cycle is created out of the previous one. That suits my preon model where no preons are lost or gained at an interaction. In the Standard Model matter can be created out of energy. So if the universe is viewed as a quantum particle it should have been created out of pre-existing energy. This view may require two time dimensions.

      In my view of the CCC model, expansion is driven by bosons (initially the universe is all bosons in a condensate in one state) converting to fermions, and fermions need extra space because of the exclusion principle (which in itself seems to be a repulsive force between fermions?).

      The idea of Unitary seems to imply that dark energy if it exists is part of a self-contained universe. So the popping of the soap bubble, in that analogy, is not good as 'blowing' is required as continuous input. If the universe were to be inside a BH, then there could be continual accretion of material, equivalent to continuous 'blowing' of a bubble? Would infalling material reinforce a BH horizon layer or stretch and weaken it? If the horizon somehow 'popped', would that destroy the supposed hologram universe too?


      Austin Fearnley

      Delete
    7. Austin: Thanks for your thoughtful response. You are referencing works with which I am not familiar, at least recently (the bubble idea has been around for quite a while, yes?) The paired universes hypothesis is so different I don't immediately know how to comment meaningfully. But your description was interesting, and I deeply appreciate the simple "here's what I think" approach you're taking there.

      Delete
    8. Hi Dave,

      Your last line was:
      "But prove me wrong: present an actual, precise, quantitative physical theory."

      There! Dispensing with unnecessary ad hominem attacks on my intelligence via phrases like "word salad" wasn't all that hard, at least for one sentence, was it?

      No, I have not published precise, quantitative physical theories on any of the following: zero-net-energy virtual universe pairs, non-holographic particle- (vs Planck-) granularity space-as-entanglement, or photons as gluons in an anisotropic color charge 3-space (and yes, the model includes weak). If and when I get to the point of making mathematically precise predictions on those topics, I'll publish them (or try!). Conversely, if the ideas don't work out I'll abandon them (terminate the search branch), though papers on why some failed could have value.

      On the flip side, please note that I have posted mathematically precise explanations of why there are (n-2) distinct ways to drill holes through a compact n-object in n-space, with the hole types for 4-space being hollow spheres and rings. (Didn't someone win a Fields Medal related to that?) However, be warned that even there I mostly used plain English and simple visual techniques. Tsk!

      My game-theory inspired methods have landed me more than once on ideas I found to be a bit loopy, like paired universes and space as entanglement. But I later found out that very similar ideas had been independently proposed by Real Physicists. For that reason I'm inclined to keep following up on similarly scored paths that have not been confirmed or proposed by others. My information-first axiom very much falls in that category, since it scores remarkably well on consolidation.

      Other notes: Dave, come on, are you seriously trying to claim Einstein's GR work from nearly 100 years ago is a "success" that justifies the incredible waste of bucks that has been going in the last 50 years? Or did you honestly misread the half-century part? In any case, it's the post-Standard-Model lack of physics theory results I was complaining about, not all of that truly amazing work (including SR, GR, QM, and the Standard Model) that came before.

      You said: "There are restrictions on how you can renormalize the string energy for physical reasons. When you follow those restrictions, yes, you get the -1/12 (this can be shown in general via Euler-Maclaurin). I do agree that the standard textbooks do not explain this clearly: I suppose that someday I should write it up in simple, elementary form."

      There's a great phrase I've heard recently for this kind of long explanation of a simple point. I think it was "word salad"? :)

      Be frank. All they did was declare the average of a non-converging, oscillating function to be a limit, which flatly violates centuries of math. Here's another old math idea, one from logic: If you start with a paradox, all implications are true. My logic teacher phrased it this way: "If the stone dogs in front of the house hear thunder, they run under the porch." Well, why not? If stone dogs can hear, why can't they also run? Thus if infinity can become -1/12, an entire infinity of mischief becomes possible!

      With expansion (please correct me wrong):
      "[the spin-2 string-like excitations of some hadrons] is mathematically suggestive and interesting [if transformed down 20 orders of magnitude to gravitons]: so far, unfortunately, no one can get actual observational predictions out of string theory"

      "Mathematically suggestive" is weak tea indeed for that pairing.

      More bluntly, it feels more like numerology. Sure, it merited a short exploration of perhaps one to ten papers. But someone should then have declared "this idea did not fix the gravitons," and let it die.

      Instead, decades have passed, and many are thinking "Uh, folks… when are you going to admit this tenuous and gigantic jump from real to untestable physics just didn't work?"

      Delete
    9. Terry wrote to me:
      >Be frank. All they did was declare the average of a non-converging, oscillating function to be a limit [when getting the -1/12 in string theory], which flatly violates centuries of math.

      No: I am trying to tell you that that is not what they did and that you are ignorant of what they did. Specifically, the function in question is not oscillating, and they did not take an average.

      You have to renormalize the string "energy" by some subtraction and only certain subtractions are allowed by the physics of the situation (reparametrization invariance and such).

      It turns out mathematically that if you take a cutoff function f such that f(0)=1, f '(0)=1, f vanishes nicely at infinity, and f is sufficiently smooth, then, by Euler-Maclaurin, the sum from zero to infinity of n f(ϵ n), which is the sum you need, is one over ϵ squared times the integral of x f( x) minus 1/12 (other terms vanish as ϵ goes to zero).

      f is the cutoff function to regularize the "energy." The one over ϵ squared term can be subtracted out by an allowed counter-term to give an "energy" that does not depend on ϵ. But the physics does not allow any counter-term to get rid of the -1/12. You're stuck with it.

      As you can see, it is hard to format the math to present it here in the comments section. But I have given enough detail that any competent physicist can work out the further details.

      It is not true, as you claim, that this "flatly violates centuries of math." In fact, it uses well-established classic math going back three centuries, to Euler and Maclaurin.

      You just do not understand it.

      As I have said many times, there are a lot of problems with string theory, which Peter Woit has lovingly documented. Most notably, we cannot solve the math of string theory to get predictions that can be compared to observations.

      But the one specific thing you pointed to is not a problem.

      You do not know what you are talking about.

      Delete
    10. Terry asked me:
      >Other notes: Dave, come on, are you seriously trying to claim Einstein's GR work from nearly 100 years ago is a "success" that justifies the incredible waste of bucks that has been going in the last 50 years?

      In terms of its ability to explain and predict very surprising observations (gravitational time dilation, the correct factor for light bending by the sun, the precession of the perihelion of Mercury, etc.), yes, General Relativity is indeed a stunning success.

      If you disagree, by all means show us how you know these observations are wrong.

      On the face of it, Einstein's general theory is one of the great achievements of the human mind.

      As to the cost, "the incredible waste of bucks" as you put it, that is a social and political decision, not a scientific one. I'll just point out that the money spent on work on General Relativity is rather small compared to the total amount spent on scientific research during the last fifty years.

      Delete
  20. As Sean Carroll pointed out, everything has energy and many things are dark, so "dark energy" is a really bad name. To concentrate on the defining aspects of the cosmological constant, he suggested "smooth tension", but that hasn't caught on.

    ReplyDelete
  21. " But some of them are claiming that really the data has been wrongly analyzed and the expansion of the universe doesn’t speed up after all. Isn’t science fun?"

    Yes, it is often fun. To be fair, you should point out that there is also much valid criticism of this paper.

    Even if the analysis stands up, it in no way disproves accelerated expansion, for two reasons. First, even the authors of this paper claim that the data are still consistent with accelerated expansion. Second, the concordance model is called the concordance model for a reason. The burden is on the authors to explain why combinations of other tests, or, these days, just the CMB alone, give values of the cosmological parameters which imply accelerated expansion.

    That's the beauty of, and the point of, the concordance model. One can always find something which could screw up any one test, but it is much harder to find a credible explanation for why many independent tests give the same, but wrong, answer.

    The situation is similar to the realization that molecules and atoms are real, based on many independent lines of evidence (Einstein also wrote an important paper on this topic). Sure, any one test could have been wrong, but the convergence of independent lines of evidence on the same value was convincing, and turned out to be right.

    ReplyDelete
    Replies
    1. The burden is on the authors to explain why combinations of other tests, or, these days, just the CMB alone, give values of the cosmological parameters which imply accelerated expansion.

      No, not really. The burden of proof lies with those whose model makes extraordinary, empirically baseless, claims about the nature of physical reality - that model being ΛCDM.

      With its unobservable and inexplicable original condition and a current state of the "universe" 95% composed of invisible stuff, the only salient characteristics of which are, it makes the otherwise failed model "work", the scientific burden of proof rests squarely on the shoulders of ΛCDM's true believers.

      The inference of a cosmological expansion, let alone an accelerating one, lies entirely within the framework of the early 20th century assumptions that form the theoretical basis of modern cosmology. As long as those assumptions are considered sacrosanct and not subject to reconsideration, the standard cosmological model will remain an unscientific mess, bearing no resemblance to the cosmos we actually observe.

      ...it is much harder to find a credible explanation for why many independent tests give the same, but wrong, answer..

      Not hard at all. If the same independent tests are evaluated in the context of the same wrong model, you'll get the same wrong answers. That should be obvious.

      Delete
    2. "The burden of proof lies with those whose model makes extraordinary, empirically baseless, claims about the nature of physical reality - that model being ΛCDM."

      I was at a conference discussing (serious) alternatives to ΛCDM. Some people were happy with their theories. George Efstathiou, defending the orthodoxy (he was once a radical challenger to orthodoxy: he does the right thing, support the theory for which their is evidence, rather than being a conformist or non-conformist as a matter of principle) set the bar really law by saying that if anyone who had a theory which did nothing more than explain all currently known data as well as ΛCDM explains it, then he would give them a job. I don't think that he has hired anyone on the basis of this challenge.

      In other words, come back when you can present the CMB power spectrum as calculated in your theory.

      Delete
    3. It is hard to reconcile the statements

      1. The universe is 95% invisible stuff

      2. GR is a well-tested, well-confirmed
      theory.

      Delete
    4. In other words, come back when you can present the CMB power spectrum as calculated in your theory.

      That's a bogus argument, just a disingenuous attempt to change the subject. I don't have to present or produce a separate model in order to criticize the standard model.

      The argument, that ΛCDM describes a cosmos that does not resemble in any of its particulars, the cosmos we observe, stands on its merits. You have no response for that argument - so you want to change the subject and talk about some other model.

      People like you are doing physics backwards proceeding from an inherited and unquestioned mathematical model (the FLRW "universe"), which you continuously patch at each predictive failure, adding new parameters by invoking entities and events that are not part of observed reality. That approach has been an unmitigated scientific disaster.

      Until the FLRW "universe" is discarded and its foundational assumptions reconsidered the modern cosmological model will remain a scientifically embarrassing absurdity. No matter how many brilliant mathematicists testify to the contrary, empirical facts are more important than a tired, century-old, mathematical theory.

      Delete
    5. @bud rap: would you care to say, in specific terms, what "People like you" (i.e. Phillip Helbig, Sabine Hossenfelder, Lawrence Crowell, PhysicistDave, et al.) should actually do?

      Yeah, discard the FLRW, reconsider foundational assumptions ... but how, specifically?

      And what specific "empirical facts" are you referring to?

      Delete
    6. Jean,

      First of all, Sabine doesn't belong in your list - it is quite evident that she knows how to think about physics, not just mathematical models.

      Yeah, discard the FLRW, reconsider foundational assumptions ... but how, specifically?

      Think, Jean, think - about physics, not mathematics. The problem you and others seem to have is that you don't understand the difference. You apparently perceive math to be foundational to physics rather than being simply a very useful modeling tool.

      That attitude has resulted in ridiculous modeling errors, like using Keplerian/Newtonian simplifications appropriate to the solar system, to model galactic rotation curves.

      The empirical fact is that there is no empirical evidence for the existence of dark matter and dark energy. They are only model dependent inferences, and since they cannot be empirically demonstrated to exist, the model that requires them should be considered a scientific failure. It is only your mathematicist beliefs, about the primacy of math, that permits you to think otherwise.

      Until mathematical models of the cosmos are constructed on a sound qualitative model, that is itself constructed on the basis of current observational evidence, not simplistic, century-old assumptions, modern cosmology will continue to wallow in unscientific absurdity.

      Delete
    7. It is useful to look at this graph of data see how well ΛCDM works.

      https://ncatlab.org/nlab/show/standard+model+of+cosmology

      The FLRW is a pretty decent approximate metric for this. It is not exact because it has an exponential tail off as t → -∞, and with inflation it is likely this metric cuts-off into a deSitter-like configuration with a large Λ. Another reason it is not exact is the gravitational perturbation of matter within it.

      Within the framework of this Newtonian-like perspective the constraint equation is

      (a'/a)^2 = 8πG(ρ_m + ρ_dm + ρ_r + ρ_de)/3c^2,

      for ρ_m + ρ_dm = k/a^3 the matter plus dark matter density, ρ_r = k'/a^4 the radiation density and ρ_de = const the dark energy density that I will just call ρ. I just ran this through Hamilton's equation numerically and it gives a decreasing curve that transitions into an exponential growth.

      It does no good to just be a naysayer or contrarian. One can look at this and understand its limits. These are in particular what is the ρ for dark energy and how does this emerge from quantum field theory. However as a phenomenological model FLRW does pretty well.

      Delete
    8. So, bud rap, I asked you what, in specific terms, should {certain people} actually do.

      Here's what you said: "Think [...] think - about physics, not mathematics."

      Not exactly helpful, wouldn't you say?

      Thanks for clarifying what you mean by "empirical facts".

      Just to be clear, by your standard, there is no empirical evidence for the existence of black holes, neutron stars, gravitational wave radiation (you have made that clear!), even [OIII] 5007. After all, "[t]hey are only model dependent inferences, and since they cannot be empirically demonstrated to exist, the model that requires them should be considered a scientific failure."

      As you can probably tell, I am having a lot of difficulty understanding what you write.

      Delete
    9. bud rap wrote:
      >That's a bogus argument, just a disingenuous attempt to change the subject. I don't have to present or produce a separate model in order to criticize the standard model.

      Well... as a matter of fact you do, if you want to be taken seriously.

      We have a model that works tolerably well: i.e., no clear, well-established observations decisively prove it to be wrong.

      You want us to dump that model, then, yes, you do have to come up with something better.

      Delete
    10. PhysicistDave,

      We have a model that works tolerably well: i.e., no clear, well-established observations decisively prove it to be wrong.

      As I keep pointing out to you, that model describes a "universe" that does not, in any way, resemble the cosmos we observe. The fact that the model can be massaged into agreement with actual observations is a math trick as old as Ptolemy.

      If you want me to take your arguments seriously, you're going to have to show me that you know how to think about cosmology beyond merely regurgitating what you memorized in graduate school. It really doesn't mater if you can calculate the correct answers on the test, if you don't understand the underlying subject matter.

      Delete
  22. "The cosmological constant in this model is not extracted from one observation in particular, but from a combination of observations. Notably that is the distribution of matter in the universe, the properties of the cosmic microwave background, and supernovae redshifts. Dark energy is necessary to make the concordance model fit to the data."

    Certainly true historically. Despite the paper linked to above, the supernova data alone, and (these days) the CMB data alone, also demonstrate the existence of a cosmological constant. (That the values are in agreement, and compatible with those from other tests, is the "concordance" part.)

    ReplyDelete
  23. The 120 order of magnitude "prediction" is truly a prediction that is derived from quantum mechanic. Now, it doesn't rule out QM because the theory is very solid elsewhere. A good reasoning will be that, yes it is a prediction, calculated and derived from QM, and that what we can measure in the cosmos is very far from this, so we have discovered, not that QM is wrong, but a possible limit to its domain of applicability, opening the door to new theories, like the "UV catastrophe" that lead to QM.

    ReplyDelete
  24. What I don't understand in all this is the concept of negative pressure. Sure, I don't completely understand general relativity either, so it could just be a "non-intuitive constant" feature (essentially like the negative particle mass-squared constant in the in the standard Higgs mechanism).

    So could someone explain what it means ... if anything, of course, other than that.

    But still ... intuitively, one expects positive pressure to (tend to) expand the region containing it. Of course in gravity theory, any form of (ordinary) matter or energy acts as a source of gravity (and thus tends to attract .. which, intuitively, would be like a negative, not positive, pressure.)

    Or ... do the astronomers simply use a reverse sign convention compared to us chemists?

    ReplyDelete
    Replies
    1. It doesn't "mean" anything if you mean by "mean" is there a description in terms of microscopic constituents. As I already said.

      Normal (positive) pressure is a type of energy and gravitates as any type of energy.

      Delete
    2. This here helped me to accept that P=-Λ is “reasonable”.

      Delete
    3. dtvmcdonald asked:
      >So could someone explain what [negative pressure] means ... if anything, of course, other than that....

      >Or ... do the astronomers simply use a reverse sign convention compared to us chemists?

      No, physicists and astronomers are not using a strange sign convention.

      Take your writing pen. Hold it between your two hands and squeeze it. You're exerting positive pressure on it, right?

      Now, take the same pen and hold one end in each hand and pull. We would, in normal English, say you are exerting a stress or tension on the pen. I hope you can see why that is considered a negative pressure. If you know anything about the physics of materials, that should be obvious.

      So, what does this have to do with General Relativity?

      Well, in one of the ways of writing the field equations for GR, you have a quantity called the Ricci tensor on the left-hand side of the equation, which describes how tidal forces distort the volume of a small ball of dust. Einstein initially postulated that the right-hand side was the stress-energy-momentum tensor.

      That turns out not to work: mathematically, it violates something called the "Bianchii identities." There is also a fairly simple way to show it will not work physically.

      One way to fix the problem is to add to the RHS a term that, in effect, means that not only mass-energy but also pressure acts as a source of the gravitational field. (There is a mathematically equivalent way to fix things by replacing the Ricci tensor on the LHS by the so-called "Einstein tensor," but when you do it that way it is not as clear that pressure will now serve as an additional source for the gravitational field.)

      So, pressure serves as an additional source for the gravitational field, besides just local mass-energy.

      Why does the cosmological constant involve a negative pressure? Because the cosmological constant means adding to the stress-energy-momentum tensor a multiple of the metric, which, in locally Minkowskian coordinates, is a matrix with (+1,-1,-1,-1) down the diagonal. It is the relative sign of those -1's on the diagonal, compared to the leading +1, that makes the pressure for dark energy negative and hence repulsive. (I'm following the "West Coast" sign convention: in any case, it's only the difference in sign between the leading term on the diagonal and the other terms that matters.)

      I realize this all sounds rather opaque, and, frankly, I do not much like the way this is all written up in the standard textbooks.

      But, if you grasp the underlying physics and how it is expressed in math, you will see that you really have no choice in everything I have just described, unless, of course, you somehow go beyond Einstein's field equations (best of luck!).

      Dave

      Delete
    4. Another word for negative pressure is tension.

      Somewhat counter to the naive impression, positive pressure is energy and hence gravitates in GR, which is why negative pressure (tension), which normally pulls things together (think of the tension in a spring or rubber band), pushes things apart in GR.

      Delete
    5. Negative pressure is analogous to the outward tension on a spring that is compressed.

      Delete
    6. Phillip Helbig wrote:
      >positive pressure is energy...

      Phil, that's not really correct.

      For an ideal gas at a fixed temperature, it is true that the pressure is proportional to the energy density (ignoring the rest mass, of course) but for a trivial reason: the energy per atom only depends on the temperature and, since density of atoms is proportional to pressure for an ideal gas at fixed temperature, we find energy density proportional to pressure.

      On the other hand, for almost any other state of matter, it's not that simple. Take a hunk of steel or a gallon of water and you can increase the pressure quite dramatically without a proportional increase in energy density, the reason being of course that those states of matter are not very compressible (the change in energy is of course -PdV, and dV, the change in volume is small).

      In any case, adding some pressure contribution to the internal energy to somehow get the real energy would be double counting. The energy is already accounted for by all of the normal terms for energy.

      If anyone wants to bring up the PV term in "enthalpy," the PV term in enthalpy is there to account for the work required to push the atmosphere up when the volume expands due to the reaction. I.e., the PV term in enthalpy is there to account for the increased gravitational potential energy of the atmosphere, not the energy of the reactants (which is why you use enthalpy for experiments open to the atmosphere, but not experiments carried out in fixed volume).

      Anyway, this is obvious from the terminology: if "enthalpy" meant "energy," we would not need a separate word for it!

      I realize that you may just have been being concise and really meant "In terms of its role in the GR field equations, positive pressure acts in the same way as positive energy." But, I think it may be worth making this clear for non-physicists.

      By the way, the explanation I gave in my earlier comment as to why there is an additional term for pressure in the field equations is not something I myself worked out but merely a recapitulation of the actual sequence of Einstein's own work.

      Misner, Thorne, and Wheeler have excerpts form translations of Einstein's own papers that lay this out clearly; Einstein only figured this all out at the last minute in November 1915: see p.433 of MTW, which can be read online at https://books.google.com/books?id=w4Gigq3tY1kC&printsec=frontcover&dq=page+433+of+misner+thorne+wheeler&hl=en&newbks=1&newbks_redir=0&sa=X&ved=2ahUKEwiDlMm9uYnmAhXJpJ4KHV5aCogQ6AEwAHoECAEQAg#v=onepage&q=433&f=false .

      This remains the standard explanation in modern texts because, after all, that is really how it works: The fact that pressure is an additional term that also acts as a source for the gravitational field is not an obvious fact but is in fact needed for the field equations to be mathematically and physically consistent, a bit like Maxwell's discovery of the "displacement current."

      It was a surprise to Einstein and should still be a surprise today.

      I'm also happy to note that Einstein added the extra terms on the RHS where the stress-energy-momentum tensor is, rather than adding a different term to the Ricci tensor on the LHS to produce the "Einstein tensor" as some people, including Misner, Thorne, and Wheeler, prefer today.

      On this, I'm with Einstein, rather than my old teacher, Kip Thorne (the two methods are mathematically equivalent, of course, even though you add different terms to the two sides).

      All the best,

      Dave

      Delete
    7. @dtvmcdonald Good question, I don't really understand it either. Seems to come out of GR just formally. (A de Sitter space which is devoid of matter has a negative pressure, so it cannot be the kind of pressure we are familiar with, e.g. of a box of gas). If DE is not the CC but a field, what does it mean for a field to have a negative pressure? Are there any such known fields or is there an analogue system which can help us to better understand the concept?
      There is a nice article which shows that there is also confusion among experts:
      https://www.discovermagazine.com/the-sciences/the-physics-of-negative-pressure

      Delete
    8. The answer to my question about pressure appears to be that

      1) ordinary thermodynamic (PV=nRT for a gas) pressure in the universe (due to dust) is essentially negligible.

      2) the pressure being discussed actually appears as an energy (source) term in the usual dynamical equations of general relativity.

      3) the pressure being discussed, if from PV=nRT, would be positive energy since it comes from the kinetic evergy. Since that's negligible we need only use that for sign intuition.

      Thanks, its now clear to me. Very enlightening.

      3)

      Delete
    9. ...the-physics-of-negative-pressure: “The universe doesn't just blow - sometimes it sucks.” - LOL - great.
      But now let´s get serious:
      ... how water gets to the tops of trees ...”?

      I would like to pass this question to all of you who believe that this can be described via a single, exclusively unitary evolution in QM - i.e. without myriads of measurements in between.

      Delete
    10. “... how water gets to the tops of trees ...”?

      That's rather simple thermodynamics. However, describing the thermodynamics of water molecules in narrow tubes using basic QM is unproductive and unilluminating.

      Delete
    11. "I'm also happy to note that Einstein added the extra terms on the RHS where the stress-energy-momentum tensor is, rather than adding a different term to the Ricci tensor on the LHS to produce the "Einstein tensor" as some people, including Misner, Thorne, and Wheeler, prefer today.

      On this, I'm with Einstein, rather than my old teacher, Kip Thorne (the two methods are mathematically equivalent, of course, even though you add different terms to the two sides)."


      I agree. Interestingly, the first person to suggest putting Lambda on the matter side, i.e. some fluid with the corresponding equation of state as some sort of vacuum energy, already in 1917, was none other than Erwin Schrödinger.

      (By the way, I try to tune the answers to the question without making them completely wrong.)

      Delete
  25. I like how James Hartle describes 'negative pressure': "a negative pressure is something like tension in a rubber band. It takes work to expand the volume rather than work to compress it." (see pages 376 and 482; Gravity, chapter 18, cosmological models).

    ReplyDelete
  26. How about that:

    1. At the moment, we assume that space without matter could exist and is flat. Let's have a look at the hypothesis that the flat space doesn't exist, even not far away from all matter. That the space far away from the Center of gravity keeps on becoming not more flat - but more and more thinner.

    2. Then, between the galaxies (in empty space) exists space which is thinner than that within the galaxies.

    3. If light crosses such space, it will experience first a redshift while moving INTO that "thin space"(like the light moving away from the sun), than experience a blueshift while moving out.

    4. If the universe expands during this process, the blueshift will be a little bit more than the redshift.

    5. If the star emitting the light is very far away the light will cross more of those thin space-regions. That will lead to a relative blueshift in comparison to the light from stars which are not so far away. Therefore, if there would be such thin-space regions but we would expect the space to be flat, we had to assume that the expanding velocity is increasing.
    Right?

    ReplyDelete
    Replies
    1. I think you are describing something like the Sachs-Wolfe effect; are you?

      WP: https://en.wikipedia.org/wiki/Sachs%E2%80%93Wolfe_effect

      Delete
  27. I'm looking forward to Sabine's analysis of the paper, which challenges the accelerated expansion of the Universe, that she mentioned towards the end of her post.

    ReplyDelete
  28. The concept of the universe as a quantum object is very hypothetical. I am sure that cosmology can be built in the framework of classical science, as well as the cosmological constant:
    https://arxiv.org/abs/1804.02988
    https://pos.sissa.it/335/039/pdf

    ReplyDelete
  29. Why do we think that the "speed" of the time flow is all the times constant?

    If light cames out of the past (as all light do) and the "speed of time" had been slower in former times, we would observe redshift, or not?

    The space expansion is a pure hypothesis. Don't forget.

    Without expansion no dark energy ...

    Hypotheses on hypotheses on hypotheses on ...

    ReplyDelete
    Replies
    1. weristdas asked:
      >Why do we think that the "speed" of the time flow is all the times constant?

      But, we don't. We think, for example, that time runs much more slowly in a deep gravitational well.

      However, we have a very detailed, quantitative theory that has been tested in a number of ways: so far, it works.

      You want to replace it, you need a precise, quantitative theory that works even better.

      Best of luck!

      Delete
    2. One shouldn't say time runs more slowly in certain reference frames (relative to "our time"), because it is *not* the same time.

      Delete
  30. ... or we are in a black hole and the red shift which we observe is gravitational forced ... and the horizon is bend around, so we see the black hole in all directions ...


    hypotheses beyond hypotheses beyond hypotheses beyond hypothesis ...

    ... but physicist seem to have only little phantasm, so they stick to only one "narrative".

    ReplyDelete
    Replies
    1. Do you have an alternative "narrative"?

      Delete
    2. If the universe were a black hole the Weyl curvature would result in tidal distortions that would red shift along the radial direction and blue shift along the local plane perpendicular to the radius. That sort of extreme anisotropy is not observed. Distant galaxies are red shifted with a high degree of isotropy.

      Delete
    3. Lawrence Crowell7:30 AM, November 28, 2019

      "Weyl curvature"? A Hypothesis?

      If the black hole is seen all around us since the gravitation bends the light - how could there be any differences by directions?

      Delete
    4. The Riemann curvature tensor components to look at are

      R^r_{trt} = -2m/r^3, R^θ_{tθt} = (r - 2m)m/r^2.

      A variation of the geodesic equation leads to the geodesic deviation equation

      dU^a/ds + R^a_{bcd}X^bU^cX^d = 0.

      Let us apply this with the spacetime vectors X^a = U^t ≈ 1 for nearly motion galaxies that is not highly relativistic, along with the approximation d/ds ≈ d/dt. We end up with the differential equations

      dU^r/dt - (2m/r^3)U^r = 0

      dU^θ/dt + [(r - 2m)m/r^2]U^ θ = 0.

      It is not hard to see the first of these has a solution of the form U^r ~ exp(2mt/r^3) that is going to grow as r → 0. The second of these has a solution U^θ = exp[-t(r – 2m)m/r^2] that is decreasing and similarly the distance between two particles with an angular separation will shrink.

      Physically this means if you have a spherical shell of particles that approach a gravitating body that the leading and trailing particles will have different gravitational attraction and will separate. Correspondingly two particles at equal radial distance will move towards each other. This is what happens with tidal forces, even with the weak gravity of the moon.

      Delete
  31. @Emmette 'It’s of course not true'. Why not? Current concordance cosmology takes the Cosmological and Copernican principles rather religiously as prior assumptions in data analysis, that directions in the sky can be ignored when combining data, and that average properties of the local Universe represent average properties of the Universe as a whole. We are merely challenging this rather constrained definition of the Copernican principle. Within our text we point out that how the bulk flow of the local Universe has been dealt with in the data are rather arbitrary and unscientific.

    I am one of the authors of this paper (preferably addressed by my second first name, Rameez).

    If you want a longer discussion, and if Sabine doesnt mind me linking this here, have a look at:

    https://4gravitons.com/2019/11/15/guest-post-on-the-real-inhomogeneous-universe-and-the-weirdness-of-dark-energy/

    ReplyDelete
    Replies
    1. Because, ultimately, space is not flat, which “prior assumption” too might be put to Bayesian test.

      Delete
  32. Dark energy is what dark energy does(free after Jon kenneth Galbraith).

    ReplyDelete
  33. Pure mathematicians - even to some degree applied mathematicians and computational scientists - have it easy: Since mathematical entities (models) are fictions, they have the freedom to do anything that's "logical". But physicists have to (one would think) stand on the credibility of the match between mathematical fictions and physical reality. When the match fails, perhaps the mathematical language used was wrong to begin with, and a new one has to be invented.

    ReplyDelete
  34. Suppose I claimed that the CC was the result of the decoupling of electrodynamics and gravitation? That is, suppose that a gravitational field always produced an electromagnetic field, in a manner reciprocal to the production of a gravitational field itself by an electromagnetic field (via the stress-energy tensor of the e.m. field)? And then you want these to decouple in a certain limit, and the artifact of the decoupling was the CC?

    Such an situation actually exists! :) I know it's hard to believe, I could hardly believe it myself at first. But it is so. That's why I am convinced that the CC is the ghost of the missing part of GR that leads it into so many intractable problems, not the least of which is absolute resistance to quantization.

    -drl

    ReplyDelete
    Replies
    1. "Such an situation actually exists!" as in "a gravitational field always produce[s] an electromagnetic field, in a manner reciprocal to the production of a gravitational field itself by an electromagnetic field"

      Where? When? How? Empirical evidence?

      Delete
  35. Hi SABINE !!;

    I hope your day is going well,

    Your intelligence
    Is so attractive.

    Love Your Work.

    ReplyDelete
  36. It is worth mentioning that the CC already exists in Newton's gravitation. That is, one has the modified Poisson's equation for the gravitational potential F

    del^2 F - L F = 4 pi G rho

    which has a solution

    F = -(4 pi G / L) rho0

    for a constant rho0, that is a uniform constant matter density rho0 filling all space. If we demand that the matter density be zero at sufficient distance, then only L=0 is possible. Thus the CC is intimately bound up with the idea of boundary conditions at infinity, and again is seen to arise in global considerations. Likely Einstein realized that in a spatially closed universe, the boundary conditions at infinity lost their heuristic value.

    -drl

    ReplyDelete
  37. Hi SABINE !!;

    I hope your day is going well,

    Your intelligence
    is sooooo attractive.
    (not to mention Everything else about you.)
    Love Your Work.

    - Oh, and, yeah;
    please don't publish.

    - Thanks


    ReplyDelete
  38. «...not only mass-energy but also pressure acts as a source of the gravitational field.»

    « ...pressure serves as an additional source for the gravitational field, besides just local mass-energy. »

    « The fact that pressure is an additional term that also acts as a source for the gravitational field is not an obvious fact but is in fact needed for the field equations to be mathematically and physically consistent... »

    Dave,

    Sorry but I don’t get it.
    I thought that (positive) pressure was a property of the gravitional field. I don’t understand that something more than the distribution of matter/energy is needed to describe it. If you don’t add this pressure term, what kind of description do you get?
    Does this addition acts as a qualitative term vs the quantitative aspect of mass/energy?

    ReplyDelete
    Replies
    1. The stress-energy tensor for a distribution of matter is

      T^{ab} = (ρ + p/c^2)U^aU^b + pg^{ab}

      for ρ density and p pressure. The trace of this is then T^{ab}g_{ab} = T = 3p/c^2 - ρ. For a constant energy density there is T^{ab} = (ρ + p/c^2)g^{ab}. The condition for dark energy is that p = -ρc^2. This is the infamous w = -1 in ρc^2 + wp = ε condition with dark energy.

      Delete
  39. Felker asked me:
    >I thought that (positive) pressure was a property of the gravitional field.

    Well, perhaps someone has some way of describing General Relativity in which he somehow assigns "pressure" to the gravitational field.

    But, if you simply look directly at the field equations, on the LHS you have a quantity (what is known mathematically as a tensor) that is formed out of the Riemann curvature tensor by the operation of contraction, which is analogous to taking the trace of a matrix. This LHS tensor can be either the Ricci tensor or the Einstein tensor, depending on which of the (mathematically equivalent) forms you choose for the field equations.

    This LHS side of the field equations describes the behavior of gravitational tidal forces: i.e., the changes in gravitational acceleration over small displacements in spacetime.

    The RHS has either the stress-energy-momentum tensor (often just called the stress-energy tensor), if you have the Einstein tensor on the LHS, or the stress-energy-momentum tensor combined with its contraction, if you choose to have the Ricci tensor on the LHS.

    The stress-energy-momentum tensor contains all the information about the mass-energy and the stress/pressure due to matter and radiation: this is the source for the gravitational fields.

    Because of the mathematical transformation properties of tensors, it is actually sufficient to look at the purely time-like components (the (0,0) components) of these tensors in all frames of reference: this turns out to determine all components of the tensors in any specific frame of reference.

    Felker also asked:
    > If you don’t add this pressure term, what kind of description do you get?
    >Does this addition acts as a qualitative term vs the quantitative aspect of mass/energy?

    That's the point of the link I provided above (p.433 in MTW) to excerpts from Einstein's original papers. The most obvious analog to Newton's equations is to put the Ricci tensor on the LHS and the stress-energy-momentum tensor alone on the RHS.

    That is as close as you can get to having mass-energy alone as the source of the gravitational field and is the first equation that Einstein tried on the page I referenced.

    That approach is mathematically and physically inconsistent: it does not work.

    You can fix it by adding a role for pressure as part of the source of the gravitational field: one form of expressing this, the one I prefer, is the second equation on the page I referenced. That works, mathematically and physically.

    To answer your question, this is an actual, quantitative change in the field equations, and you have to do it.

    So, no, it is not just a "qualitative term vs the quantitative aspect of mass/energy." It is a real, quantitative, physically observable effect.

    If you find all this marvelously confusing, I am actually at work on a monograph that shows how to get the same results without all the tensors! But what I have described here is what Einstein actually did and what is still presented in textbooks today.

    Dave

    ReplyDelete
  40. @PD said

    "The stress-energy-momentum tensor contains all the information about the mass-energy and the stress/pressure due to matter and radiation: this is the source for the gravitational fields."

    Schroedinger had a different conception which I find compelling. That is - the EFE defines the energy tensor - the latter is not the source of the gravitational field. When the Einstein tensor is zero, that means there is no energy-momentum present. This is very much like EM - when div E is not zero, that means there is charge density present. There is a reciprocal relationship between the electromagnetic field and the charge current. You need another set of equations, the Lorentz force derived from the energy tensor, to show how the field acts on the source - this half is missing in GR. So Wheeler's famous statement "Matter shows spacetime how to curve, and curvature shows matter how to move" is actually an exaggeration. It is true in electrodynamics, but not in GR, because one half of the reciprocity is missing.

    PD, look up the little book "Space-Time Structure" by Schroedinger. You will love it. PDF is available online.

    Let's keep this thread going. It is very good stuff.

    -drl

    ReplyDelete
    Replies
    1. drl,

      “... how the field acts on the source - this half is missing in GR.” - what do you mean with this?
      What about the geodesic equation?
      And combining it with classical EM also poses no problem - see eq.2 in here.
      What are you missing?

      Delete
    2. @Reimond - Forget about the form of the energy tensor. What Schroedinger is saying, is that the EFE is itself a definition of the energy tensor of matter in terms of the Einstein tensor. If the Einstein tensor vanishes, then there is no matter present. Einstein of course hoped to "cook" matter out of geometry itself, in terms of invariant geometro-topological configurations, completing the reciprocity as with electromagetism. That never came about. It was soon discovered that one could have dynamically changing spacetimes without any matter at all, which was the final nail in the coffin of Einstein's original hopes for GR, which was to have a completely geometric representation of matter and spacetime in interaction.

      It is an historical accident that this extremely interesting problem is no longer appreciated. People have been too busy since the quantum revolution of the 1930s to pay much attention to GR and its ontology.

      -drl

      Delete
    3. Are 'space time' and 'gravitational field' equivalent terms ?

      Delete
    4. No, fields are defined over space-time. The gravitational field is best identified with deviations of the metric tensor from flat space, though making this well-defined requires further assumptions that are in general gauge-dependent.

      Delete
  41. Steven Weinberg presents a nice account of the stress-energy-momentum tensor, emphasizing that "gravitational fields do carry energy and momentum and must therefore contribute to their own source." (page 151, Gravitation and Cosmology). Weinberg goes further and presents "another derivation" of Einstein's field equations via group-theoretical arguments (page 171, also see his 1965 article Photons and Gravitons in Perturbation Theory, Phys. Rev. 138, B988).

    ReplyDelete
  42. I think that this discussion here (about Dark Energy) has shown very clearly how complicated this matter is. On the other hand, it would be extremely simple if we would follow the assumption that the speed of light c was a little bit greater in former times; because c is a factor in the Doppler formula which is used to determine the speed - also of the older stars – from the red shift.

    Could it be that we spend this great effort to understand a phantom? A phantom which we have once gotten from Einstein, when he has declared certain physical rules, which are in fact only postulates?

    ReplyDelete
  43. Replies
    1. It's a cut in a fibre bundle over a manifold. Could you please avoid submitting identical comments multiple times.

      Delete

PLEASE READ THE COMMENT RULES BEFORE COMMENTING.

Comment moderation on this blog is turned on.
Submitted comments will only appear after manual approval, which can take up to 24 hours.
Comments posted as "Unknown" go straight to junk. You may have to click on the orange-white blogger icon next to your name to change to a different account.