Friday, September 06, 2019

The five most promising ways to quantize gravity

Today, I want to tell you what ideas physicists have come up with to quantize gravity. But before I get to that, I want to tell you why it matters.



That we do not have a theory of quantum gravity is currently one of the biggest unsolved problems in the foundations of physics. A lot of people, including many of my colleagues, seem to think that a theory of quantum gravity will remain an academic curiosity without practical relevance.

I think they are wrong. That’s because whatever solves this problem will tell us something about quantum theory, and that’s the theory on which all modern electronic devices run, like the ones on which you are watching this video. Maybe it will take 100 years for quantum gravity to find a practical application, or maybe it will even take a 1000 years. But I am sure that understanding nature better will not forever remain a merely academic speculation.

Before I go on, I want to be clear that quantizing gravity by itself is not the problem. We can, and have, quantized gravity the same way that we quantize the other interactions. The problem is that the theory which one gets this way breaks down at high energies, and therefore it cannot be how nature works, fundamentally.

This naïve quantization is called “perturbatively quantized gravity” and it was worked out in the 1960s by Feynman and DeWitt and some others. Perturbatively quantized gravity is today widely believed to be an approximation to whatever is the correct theory.

So really the problem is not just to quantize gravity per se, you want to quantize it and get a theory that does not break down at high energies. Because energies are proportional to frequencies, physicists like to refer to high energies as “the ultraviolet” or just “the UV”. Therefore, the theory of quantum gravity that we look for is said to be “UV complete”.

Now, let me go through the five most popular approaches to quantum gravity.

1. String Theory

The most widely known and still the most popular attempt to get a UV-complete theory of quantum gravity is string theory. The idea of string theory is that instead of talking about particles and quantizing them, you take strings and quantize those. Amazingly enough, this automatically has the consequence that the strings exchange a force which has the same properties as the gravitational force.

This was discovered in the 1970s and at the time, it got physicists very excited. However, in the past decades several problems have appeared in string theory that were patched, which has made the theory increasingly contrived. You can hear all about this in my earlier video. It has never been proved that string theory is indeed UV-complete.

2. Loop Quantum Gravity

Loop Quantum Gravity is often named as the biggest competitor of string theory, but this comparison is somewhat misleading. String theory is not just a theory for quantum gravity, it is also supposed to unify the other interactions. Loop Quantum Gravity on the other hand, is only about quantizing gravity.

It works by discretizing space in terms of a network, and then using integrals around small loops to describe the space, hence the name. In this network, the nodes represent volumes and the links between nodes the areas of the surfaces where the volumes meet.

Loop Quantum Gravity is about as old as string theory. It solves the problem of combining general relativity and quantum mechanics to one consistent theory but it has remained unclear just exactly how one recovers general relativity in this approach.

3. Asymptotically Safe Gravity

Asymptotic Safety is an idea that goes back to a 1976 paper by Steven Weinberg. It says that a theory which seems to have problems at high energies when quantized naively, may not have a problem after all, it’s just that it’s more complicated to find out what happens at high energies than it seems. Asymptotically Safe Gravity applies the idea of asymptotic safety to gravity in particular.

This approach also solves the problem of quantum gravity. Its major problem is currently that it has not been proved that the theory which one gets this way at high energies still makes sense as a quantum theory.

4. Causal Dynamical Triangulation

The problem with quantizing gravity comes from infinities that appear when particles interact at very short distances. This is why most approaches to quantum gravity rely on removing the short distances by using objects of finite extensions. Loop Quantum Gravity works this way, and so does String Theory.

Causal Dynamical Triangulation also relies on removing short distances. It does so by approximating a curved space with triangles, or their higher-dimensional counterparts respectively. In contrast to the other approaches though, where the finite extension is a postulated, new property of the underlying true nature of space, in Causal Dynamical Triangulation, the finite size of the triangles is a mathematical aid, and one eventually takes the limit where this size goes to zero.

The major reason why many people have remained unconvinced of Causal Dynamical Triangulation is that it treats space and time differently, which Einstein taught us not to do.

5. Emergent Gravity

Emergent gravity is not one specific theory, but a class of approaches. These approaches have in common that gravity derives from the collective behavior of a large number of constituents, much like the laws of thermodynamics do. And much like for thermodynamics, in emergent gravity, one does not actually need to know all that much about the exact properties of these constituents to get the dynamical law.

If you think that gravity is really emergent, then quantizing gravity does not make sense. Because, if you think of the analogy to thermodynamics, you also do not obtain a theory for the structure of atom by quantizing the equations for gases. Therefore, in emergent gravity one does not quantize gravity. One instead removes the inconsistency between gravity and quantum mechanics by saying that quantizing gravity is not the right thing to do.

Which one of these theories is the right one? No one knows. The problem is that it’s really, really hard to find experimental evidence for quantum gravity. But that it’s hard doesn’t mean impossible. I will tell you some other time how we might be able to experimentally test quantum gravity after all. So, stay tuned.

150 comments:

  1. What does it mean to say that Loop Quantum Gravity "solves the problem of combining general relativity and quantum mechanics" but "it has remained unclear just exactly how one recovers general relativity." It sounds like it starts with GR, so what exactly needs to be "recovered."?

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    1. That's the point, if you start with GR and quantize it, you still need to show that you get back GR in a suitable limit, called the "semi-classical limit". It isn't a priori clear that this works.

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  2. "That’s because whatever solves this problem will tell us something about quantum theory, and that’s the theory on which all modern electronic devices run, like the ones on which you are watching this video. Maybe it will take 100 years for quantum gravity to find a practical application, or maybe it will even take a 1000 years. But I am sure that understanding nature better will not forever remain a merely academic speculation."

    Perhaps true, but irrelevant. Basic research is its own reward.


    “Science is like sex: sometimes something useful comes out, but that is not the reason we are doing it. ”

    ― Richard P. Feynman

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    1. I really like this citation from Dick Feynman. Unfortunately, most scientists nowadays have to produce plenty of meaningless publications, in order to be in the science business.

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    2. Is dodgy science, like thinking the universe is fine-tuned without a single reason, equivalent to masturbation then? It feels good but nothing useful comes of it?

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    3. Dear Steven, to answer with Feynman I would say "What Do You Care What Other People Think?" Do *you* have a problem with masturbation? I can tell you it is quite natural. If you dont like it, you dont have to... Freedom of science means, that scientists are allowed to follow their own personal research interests, who will know in advance, if the research is successful? Gerd Binnig is a quite good example. He got the Nobel Price in 1986 for the development of the scanning tunneling microscope. When he started, nobody believed, that one could ever see individual atoms. He was considered to be a crank. He succeded because IBM gave him a job, with a *wildcard* topic. He was allowed to do, whatever he wanted. Unfortunately this kind of jobs are very rare nowadays.

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    4. The comment was aimed at Phillip Helbig who claims so nobly that research is its own reward, but you don't need to bother doing research if you just make up the answers and lie about their being evidence. e.g. fine-tuning.
      If you are so interested in searching for the truth, Phillip, why didn't you call out Luke Barnes' book as the religiously motivated, evidence-free drivel that it is in your review of it? The guy is a complete fraud but you just sucked it up.

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    5. Hi Steven, I completely agree with Phillip that research has its own reward. If you dont see this, you might better go to industry, it's easier to get a reward in terms of financial security there.
      Lying about evidence is not so rarely as you migth think. It's quite natural to lie about evidence, but in the end, you are cheating yourself. It's a good scientific tradition, to derive predictions from your theoretical considerations, which can experimentally be tested. If a theory makes no predictions, it is not worth looking at it. Personally, I am not able to judge the ideas of Luke Barnes' book, I have not even heard about it. But if Phillip likes some part of the content and he finds it useful for his own research, what is the problem with it? If you dont believe in fine tuning its also completely o.k. Good Science require people having different expiriences and opinions. In my view it is a very bad idea, always to follow mainstream. Sabines Blog has many followers all over the world. Thats great. In my personal view, the blog reveals, that mainstream HEP physics might have a serious problem of running into the wrong direction.

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    6. ps. I remember, that many experimentalists at LEP were disappointed, not finding any supersymetric particle. That was about twenty years ago... At the LHC, the situation has not changed too much. Theorists are very fexibel, when their predictions have failed...

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  3. Are there even any toy theories where gravity is emergent?

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    1. Also Erik Verlinde 's paper "On the Origin of Gravity and the Laws of Newton" is interesting.
      https://arxiv.org/abs/1001.0785

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    2. Does Garret Lisi's E8 Theory make any promising attempt to quantize gravity? I was under the impression that it tries to unify GR and the standard model in a single geometric framework.

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    3. Sabine, thanks for the link. The 2012 Sindoni overview of emergent models for gravity provides a nice summary of the field, and aptly brings out some of the greatest difficulties with such models.

      To me the most disconcerting sentence was this one (typo fixes in brackets are mine):

      "Touching [as] foundational [of a] notion of physics as time does not come without a huge price to be [paid]. First of all, in models in which Lorentz invariance is emerging from a Euclidean theory as [in] the last models described, Lorentz symmetry breaking is unavoidable."

      While attempts to find Lorentz symmetry breaking are excellent and appropriate experimental work, the unforgiving bottom line is that no such violations have ever been found. Poincaré and Einstein (really more Poincaré I think) seem to have nailed it very squarely on the head when they first postulated the relevance of this symmetry to the physical universe.

      My point is this: If someone seriously wants to propose an emergent theory of gravity, they need to show in mathematical detail why the associated emergent spacetime infrastructure requires the emergence of a resolutely inviolate Poincaré symmetry for that universe, rather than continuing to hope forlornly that someday someone will find an extreme ultraviolet violation.

      The universe may someday prove to be delightfully simple, but that does not mean it will be stupidly simple. The history of physics has shown repeatedly that subtlety and non-obvious surprises are integral parts of advancement, particularly when dealing with dangling threads that refuse to go away.

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    4. Also in the examples here is mentioned Ted Jacobson’s paper where he derived the Einstein field equation from the assumption that entropy is proportional to a horizon area, i.e. dS~dA, the Unruh temperature T and δQ=TdS (*).
      “Viewed in this way, the Einstein equation is an equation of state. This perspective suggests that it may be no more appropriate to canonically quantize the Einstein equation than it would be to quantize the wave equation for sound in air.”

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      (*) The argument goes roughly like this: The infinitesimal amount of heat δQ crossing the horizon depends on T’’ integrated over the area, where ‘’=μν. The change in area dA in return depends on the curvature, the Ricci tensor R’’, where the Raychaudhuri equation plays a central role. This tells us how δQ is related to dA and thus how T’’ is related to R’’ which turns out to be just the Einstein field equation.

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    5. Nice call on this one. The Raychaudhuri equation gives for small parameter the relationship between area and entropy is equivalent to the Einstein field equation. It has been a long time since I read this paper.

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    6. Your argument is not conclusive because sound can be quantized. In some significant sense, phonons are quantized sound.

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    7. Arnold,

      It was Ted Jacobson’s argument 24 years ago. When I first read this sentence “... sound in air.”, I also asked myself the same question: “What about phonons?”

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    8. Lawrence,

      Here a nice account and since you emphasized it, in the paper in eq. 4 is a minor typo – it should be 1/3 θ², but this does not matter, he neglects this term anyway.

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    9. Arnold and Reimond,

      Indeed one could consider these as phonons in a solid that have a quantum mechanical basis. This derivation is strictly classical and Jacobson does not want to take it much further than that. In one part I can see his point, for a spacetime manifold is a classical object. Another problem with the phonon analogue is that with gravitation the modes are gravitons with two degrees of polarization. If optical phonon bunch or form HBT entanglements they might serve as analogues to gravitons. Optical phonons though must exist in a lattice; I doubt they can exist in a gas.

      The post on this blog about superposed spacetime connects with the double slit experiment and a mass having amplitudes for passing through both slits does carry with it some oddities, for this mass gravitates and this suggests there is a superposition of two spacetime manifolds. Yet a difficulty with quantum gravitation is that the field propagated is spacetime itself and it is difficult to know what is meant by propagating a quantum gravitational field.

      Jacobson write that the area increment is

      δA = ∫R_{ab}k^ak^bλdλdA

      from the Raychaudhuri equation

      dθ/dλ = -θ^2/3 - 2σ^2 - R_{ab}k^ak^b

      Here the assumption is that in the tiny neighborhood of a 2-sheet parallel to the horizon that θ ≈ σ ≈ 0. Within this approximation, which really means there are no fluctuation dynamics such as quantum mechanics to give an expansion factor, we have a classical background. This is a sort of adiabatic assumption and then with the Unruh equation we get the Einstein field equation.

      A chance to ponder, per chance to solve … . Laser coherent states are given by

      |p,q> = |z> = e^{za^† - z*a}|0> = e^{-½|z|^2}sum_n(z^n/√(n!))|n>,

      which is a strange thing for the basis is |p,q> which appears to be both momentum and position. This is a submanifold of Hilbert space that has a classical-like structure, but there is quantum dual |z-bar> so the quantum physics still lurks behind this. The ½|z|^2 = ½(p^2 + q^2) and is a classical Hamiltonian and the rest is a sum over a Fock basis of states. We might then think of the operators p → iδ/δg_{ij} = π^{ij} and the g → g^{ij}, where in a Huygen's principle setting the metric is modified by the Ricci curvature in the same way an optical path is changed with a medium of index of refraction. We then have an ADM Hamiltonian and for L = ∫π^{ij}dg_{ij} - NH the standard Lagrangian L = √g R occurs.

      The expansion factor θ can be thought of then as decoherent states that are not in this condensate or large entanglement of states that form the classical-like spacetime. In fact we could think of θ or θ^2 as a sum of a^† and a, similar to the coherent state case, but instead in a straight Fourier type series. These are the decoherent states that in this gravity setting would correspond to gravitons excited off the background state. Jacobson made reference to such deviations from the assumption θ ≈ 0. This might then correspond to some sum of raising and lowering operators corresponding to the absorption or emission of a quantum state.

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    10. more importantly, we can see that newton law and gravity emerge from quantum of information (or Entropy, Entropy is the opposite of Information)derived from the fact that infinite information cannot be extracted out of the position because of the Compton Wavelength, that appears clearly in the relation 3.5 p.7 of Verlinde 's article much less clearly in others articles.

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    11. I carry on my analysis of the BH Entropy relation used in Verlinde demonstration. I found very misleading and confusing the uses of number of bit expression as the total Surface divided by the square of Planck length, this is just the number of elementary planck cells on a surface at distance R. In this case working out the expression we find that the information given by the move of the test particle is equal to the information associated with Gravity radiated by a mass through each elementary cells. All of that deserve to pay more attention since we see a bridge between quantum phenomena and Gravity macroscopic effect. Regards to all of you.

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    12. Verlinde's entropic gravity describes the shifting of a holographic screen. I think there is a lot of confusion over that. The displacement of a holographic screen leads to a realization of gravity. This entropy is not associated with the motion of a test mass, for the force is conservative in an elementary manner.

      The holographic screen is a boundary of a holographic wedge, which has entropy determined by the RT or HRT formulas in an AdS setting. There is the AdS-black hole correspondence which makes this relevant for black hole physics.

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    13. To be frank, something is weird with the BH entropy.
      Usually an entropy is a "logarithm" of a number. This number
      has no unit and can be considered as the inverse of
      a probability as S=-log(p(x)) p(x). Then how comes a BH Entropy could be just only the ratio of 2 surfaces??? It doesn't look like an entropy but just the number of elementary cells on a sphere at distance R, unless it concerns a small variation of entropy dS, but it doesn't seem to be the case. From here start the confusion.

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    14. I tackle again this problem of BH Entropy. In order to have an entropy proportional to N number of elementary Planck cells on a sphere of radius R is to have a probability p=p0^(N) then
      S=-log(p)=-N*log(p0) where p0 is a kind of constant elementary proba. The interpretation is not obvious but it's not silly if we think that each cells are independent each other. Similarly if you have an image containing N pixels where N is equal to the total surface divided by the elementary pixel surface, if each pixel is coded by constant k bit, the total entropy (or information contained in the image) of a completely random image equals to N*k bits.

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    15. @ Harmond: As an exercise take p_n = 1/N for n summed from 0 to N. This corresponds to maximally mixed states which is similar to Hawking radiation. Now do the sum using properties of logarithms and you will find S = log(N).

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    16. @Lawrence It's what I meant above: usually S =-log(p(x)) since p(x)=1/N we find S=log(N) but it's not the Bekenstein Entropy which comes as S=k.N if you like (N is the number of planck cells on a surface) To understand the formula we have to use another p(x) which must come as p^N instead, then S=k.N where k is log(p) a constant.

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    17. Think of the case where you have binary strings of length n. How many possible binary string are there with that length? There are N = 2^n. The Boltzman log(N) is just the size of the macrostate, where there are 2^n possible microstates. This is where the entropy S = kn comes from, for the units of Planck area on the horizon count microstates. We have

      S = k ln(N) = k ln(2^n) = k n ln(2).

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    18. I agree completely. Obviously the number N of micro-states must be a power of n where n is the number of Planck cells on the Surface. 1st observation, that 's mean that all cells are independent each other, there is strictly no correlation between them, if there was a correlation between them the number of possible micro-state and then its entropy will be reduced . 2nd observation, the macro-sate is at its maximum level of Entropy and at its lowest level of information.3rd observation all of that is possible if we assume the existence of n quantized independent Planck surface cells but a question remains what is this micro-state we are talking about???

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    19. This depends upon what you mean by correlated. Entanglements conserve degrees of freedom of the constituent particles, or better said they transform them into other degrees of freedom. Two spins with (+,-) qubit states have 4 possible states and the bipartite entanglement has 4 Bell states.

      A black hole redshifts and time dilates any quanta emitted near the horizon so we never see anything cross the horizon. The only remaining physical observable are mass, charge and angular momentum. We can think of this as a massive entanglement of qubits on the stretched horizon. Duff et al pursue this line of reasoning.

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  4. We are getting closer and closer to the TOE, what shall we do then?

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    1. Hi attila, what mekes you so shure, that we are closer and closer to a TOE? What are youre requirements to a theory that really deserves the name "TOE".
      My personal believe is, that there will never be a "TOE" at all. M-Theory or the ideas of Max Tegmark of a "Mathematical Universe" are quite funny, but they don't face reality. All this attempts remind me on Hilberts Programm, and this program was definitely killed in the 30's by Kurt Gödels incompleteness theorem. I would only trust a TOE which is able to explain how to solve a Turing-Test with a binary computer ;-)

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    2. Any TOE will by definition always be 'Local' and bound to our observations either by scientific tools or not.

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    3. Joe, I completly agree with you, that a TOE should in principle be local. Classical theories like GR are local. With quantum theory however, it is not so simple. The standard model gives an extremely pricise description of our observations, as long as you just "shut up and calculate". If you look however at the different interpretations of quantum mechanics, you might however get in trouble with locality. So far, nobody understands quantum physics (Feynman!) In my personal view, we should nowadays try to understand better the transition from quantum description of the world to classical observable states. I cannot imagine that there will ever have a realistic Psi(SchrödingersCat) After all, classical physics is still required for understanding our universe.

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    4. I don't settle for a TOE. I am going for a FOOT, a Fundamental Ongoing Ontological Theory.

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    5. Quantum Field Theory may already be the TOE. Maybe it's perfectly precise and everything else is emergent from it. Down tools, everybody!

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    6. "Down tools, everybody!"
      Sounds to me like "Take no thought for tomorrow. Follow me!"
      Maybe not bad on a Sunday :-)

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    7. Steven, I would be very happy to see people working on a theory of emergence. Do you have any idea?

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    8. In the blog post - 5. Emergent Gravity

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    9. Steven, in my view, QFT is definitely not a TOE. Shurely, it describes in principle all known quantum phenomena, but it is not able to explain the emergence of the "classicaly" observable phenomena. There's still the measurement problem, again and again. Also most quantum phenomena in solid state physics have never been predicted, but were discovered by chance only.

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    10. “I cannot imagine...” indeed; ‘tis false premise, that humans are binary. Just because something is beyond the horizon doesn’t mean it’s not there. Just because you can’t feel something doesn’t mean it has no effect. Even “nothing” is something if it affects everything.

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    11. Steven again, almost all observable phenomena are emergent. The biosphere of our planet emegres from fundamental physical laws. Thus, a Theory of Emergence is much more than just emergent gravity.

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  5. Microscopic systems are quantized because particle interactions, decays, etc., are due to the absorption and emission of photons.

    The photon has an angular momentum L= h, and *is* one quantum of action.

    This is why the graviton cannot have spin 2, and why the phrase 'quantizing gravity' is leading people astray.

    All interaction is due to the exchange, absorption, and emission of single 'quantums of action', of wildly varying energies, of course.

    Greg

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    1. Greg wrote:
      >Microscopic systems are quantized because particle interactions, decays, etc., are due to the absorption and emission of photons.

      Greg, if I follow you correctly, you seem to think there are no quantum interactions except those involving photons.

      That's not true: there are most assuredly the weak and strong forces, both of which have to be described by quantum theory (QFT) and neither of which are mediated by photons.

      I'm afraid you are eighty years or so behind the progress of elementary-particle physics.

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    2. Dave
      Yes. I am saying QFT is wrong.
      Well spotted!
      Greg

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    3. Here is how to rectify aspects of QFT and spin with gravitons. Suppose you have an electron with spin ½ħ, where I set ħ = 1. A graviton has spin 2 because a gravitational wave has two helicities or directions of polarization. Now suppose an electron couples to a graviton with spins 2 - ½ = 3/2 So this three vertex interaction seems to produce a 3/2 particle. However, we have ΔJΔθ ≈ ħ/2, so we can have a spread of angular momentum within some uncertainty in angle measure. So this fluctuation of an electron with a spin 3/2 can turn into an electron and graviton in a second 3-vertex. The graviton has a longer wavelength indicating some momentum imparted to the electron.

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    4. Greg,

      QFT may or may not be wrong.

      But your apparent belief that all quantum processes are mediated by photons is simply bizarre and at odds with seventy years of research in high-energy elementary-particle physics.

      Again: the strong and weak nuclear forces cannot be explained via interactions involving only photons (prove me wrong: work out a way to do so -- in mathematical detail, please!).

      What you are saying is utter nonsense. You are completely ignorant of the relevant science.

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    5. I have worked it all out.
      I can only refer you to my books.

      Also a physicist,
      Greg

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    6. Greg wrote:
      >I have worked it all out.
      >I can only refer you to my books.

      I'd be pretty comfortable risking my life that you have not worked it out.

      One of the reasons is that we have to buy your books to see it.

      You can now publish on the Web for free. If you have really worked it all out, why not publish at least some key parts on the Web to prove to us that you have done it?

      And then we'd buy some of your books!

      Sort of like Sabine has done: she has revealed a huge amount of her thinking on this blog, so anyone can easily judge from her blog posts whether or not they might find her book worthwhile.

      I think I know why you are not pursuing this business model.

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    7. Sabine is a super hero.
      I am a mere mortal.
      We all have our own style, strengths, and limitations.

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  6. 4-derivative gravity is another possibility.

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  7. What affect does the measurement problem have on quantized gravity?

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  8. > it treats space and time differently, which Einstein taught us not to do

    Are there any somewhat credible attempts to walk Einstein back and re-separate space and time?

    I.e. and e.g., Minkowski's casting of special relativity in geometrical terms might have been perfectly fine and useful as a mathematical metaphor, but perhaps Einstein went an ontological step too far. Kinda like the ontological arguments about Schroedinger's Ψ.

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    1. Egad wrote:
      >Are there any somewhat credible attempts to walk Einstein back and re-separate space and time?

      It can be done. John Bell explains how in one of the chapters in his Speakable and Unspeakakble in Quantum Mechanics. Indeed, it seems unavoidable in the general Bohmian approaches to quantum mechanics (a number of physicists, including me, have tried to show that Bohmian mechanics can be combined with true Lorentz invariance -- thus far, we have all failed).

      The problem is, once you have broken with relativistic spacetime, it is extremely difficult to explain why Lorentz invariance seems to hold perfectly in the real world, even though it really does not.

      And, no one has (yet) gotten any results out of these various efforts that seem to really solve problems such as quantizing gravity. (Bohmian mechanics does, in the opinion of many of us, solve the "quantum measurement problem," but at a high and not credible cost.)

      Dave

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    2. here's a faster link to the Bedingham and Pearle paper https://arxiv.org/abs/1906.11510

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  9. Right now I see an emergent gravity promising - but wondering why modeling emergence as reduced information from gravitational volume to inertial point; I prefer logic for information loss from inertial knots to spherical volume like as non-inertial spacetime cell automata. This way it's more understandable, still being not different in itself.

    That means inertia is based discrete quanta side by side with matter quanta and emerging as continuous gravitational curved geometry associated with the concept of decoherence (quintessence ;]). Something like that, the process of scrutiny is rather unfinished...

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  10. sabine

    which of these 5 is your research interest in?

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  11. What is I think interesting is that all of these approaches may have some bearing on this problem. They may all tell us something.
    It was an objection that string theory was not background independent. It is the case one needs a Minkowski flat spacetime or an anti-de Sitter spacetime as a background. The string states defined excitations above this background. The LQG folks would object to this aspect of string theory. What is possible though is that classical spacetime defines a set of coherent states, or equivalently we might think of spacetime as a condensate or entanglement of a large number of states. Coherent states are a sub-manifold in a Hilbert space that has a symplectic structure. Within the context of a mutually unbiased basis (MUB) the symplectic transformation is the same as a Moebius transformation. This has a connection to the Riemann ζ-function. The zeros of the ζ-function have imaginary parts that are prime numbers and these may be quantum numbers or Godel numbering of quantum numbers for quantum states that make up this coherent set of states.
    The LQG is a spinor form of the canonical quantization of the conjugate variables g_{ij} and π^{ij} for a spatial surface in ADM relativity. The ADM Hamiltonian is NH = 0, for N a lapse function and H the Hamiltonian formed from the trace of the extrinsic curvature. The quantum form of this equation is then HΨ[g] = 0, which is a constraint equation. In effect this annuls states on the contact manifold. What is interesting is this might connect to the zeros of the ζ-function for these coherent states.
    String states of gravitons are then excited states not in the condensate. We might then compare this to the Einstein coefficients for photons, where the excited states and coherent states of photons correspond to gravitons and the large N entanglement or coherent states of classical spacetime.
    We may of this situation as different people looking through different keyholes into a room and getting a different view of the same thing.

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    1. "The zeros of the ζ-function have imaginary parts that are prime numbers"
      That's not right, is it? The imaginary parts of the non-trivial zeroes aren't even integers, are they?

      " getting a different view of the same thing. "
      But unfortunately that same thing isn't reality...Dun, Dun, Duuuuuun!!

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    2. The Riemann zeta function gives the distribution of prime numbers. The big open question of course is a proof of this.

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    3. The imaginary parts of the zeroes aren't primes, though. Maybe you can say the zeroes are dual to primes. Also, it's already known that the distribution of the primes can be written in terms ofζ asymptotically. RH true would show the error terms to be best-case bounded.

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  12. Hi Sabine-I thing your use of "respectively" in "It does so by approximating a curved space with triangles, or their higher-dimensional counterparts respectively" is missing something - you need to say what the higher dimensional triangles are approximating - presumably space-time?

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  13. 'Physicists analyze rotational dynamics of galaxies and influence of the photon mass'
    https://www.techexplorist.com/physicists-analyze-rotational-dynamics-galaxies-influence-photon-mass/21340/

    > "the mass of photons, which are particles of light is responsible for the rotational dynamics of galaxies"

    Dark matter is a sea of massive photons which are displaced by ordinary matter. The state of displacement of the sea of massive photons is the quanitization of gravity.

    The sea of massive photons displaced by the quarks the Earth consists of, pushing back and exerting pressure toward the Earth, is the quantization of gravity.

    The sea of massive photons displaced by the quarks the Earth consists of, pushing back and exerting pressure toward the Earth, is gravity.

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  14. The fact that more effort in theoretical physics went into the above approaches to quantum gravity than all theoretical physics that took place on the planet before 1960 tells us something. Quantizing gravity probably will not succeed. #6 on the list should be - 6) Gravity is not quantized.

    See https://link.springer.com/article/10.1007/s10701-013-9770-0 for example. Another view is https://arxiv.org/pdf/1212.0454.pdf :)

    It's nice that experiments that look doable that can tell if at low energies gravity is quantized. https://arxiv.org/abs/1808.05842

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  15. A respond to this blog post would be way too long to fit here.

    Therefore I published a respond in my own blog

    I hope you do not mind me promoting my new blog here.

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  17. I see it as a problem that we take QM and relativity too seriously. Both are having big unresolved problems.

    1) In the case of relativity some fundamental principles of Einstein are falsified. (Has been discussed here earlier.) And the open cases of Dark Matter and Dark Energy are indications of our poor understanding of gravity.
    2) In the case of QM we have the Higgs theory for mass which is not even able to tell us the real mass of well-known particles. And we have this discrepancy of virtual energy of 120 orders of magnitude (“Vacuum catastrophe”). - Whereas there exist for instance classical explanations for the mass which provide the actual mass of particles from the scratch with high precision. – I am not allowed to give references here but you may look into the internet with the string “The origin of mass”.

    It may be the superior way to develop first a better understanding of both theories before we try to unify them. I personally guess than after this there will be quite simple solutions for Quantum Gravity at hand.

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    1. antoneo wrote:
      >In the case of relativity some fundamental principles of Einstein are falsified.

      I'm a physicist, and I know of no principles of relativity that have been falsified. What are you talking about? Maybe just the fact that it is hard to see how to unify GR and QM? (No, dark energy does not falsify GR: the cosmological constant has been known to be part of GR from the early days.)

      antoneo also wrote:
      > Whereas there exist for instance classical explanations for the mass which provide the actual mass of particles from the scratch with high precision. – I am not allowed to give references here but you may look into the internet with the string “The origin of mass”.

      I did search as you suggested: I found some articles by Wilczek and others (including Sabine) explaining the mass of hadrons and its connection to the running QCD coupling constant, etc: this is not a "classical" explanation.

      Aside from that, all I can find is a bit of crack-pottery that does not even pretend to give "the actual mass of particles from the scratch with high precision."

      You're going to have to do better than that.

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    2. 1) The equivalence principle, which states the identity of gravity and acceleration, is the essential basis for Einstein's GR (by his own words). It is falsified by two aspects (which have been discussed here last week):
      a) A charged object radiates when accelerated, but does not radiate when at rest in a gravitational field
      b) In a gravitational field there is dilation, but not with respect to acceleration (proven e.g. at CERN)
      So both, gravity and acceleration, can be distinguished, which falsifies Einstein’s GR by common understanding.
      2) There is another article with this title "The origin of mass" with the funny addition "Relativity without Einstein". And that one shows - as an example - how the mass of the electron can be determined classically with a precision of better than 10^-5; and further particle properties. That method also applies for quarks.

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    3. antooneo wrote:

      >The equivalence principle, which states the identity of gravity and acceleration, is the essential basis for Einstein's GR (by his own words). It is falsified by two aspects (which have been discussed here last week).

      You are wrong: you have not looked into the relevant science (yes, I know you may have discussed this with others who do not know the relevant science either -- the blind leading the blind!).

      anto wrote:
      >A charged object radiates when accelerated, but does not radiate when at rest in a gravitational field

      It is well-understood that whether or not a particle is radiating depends on the frame of reference if one insists on using non-inertial frames of reference. Just one more of those "relative" things about "relativity."

      The E and B fields are local: to transform from one frame of reference to another, you just need the E and B fields at the point in question in the first frame.

      But, whether or not radiation has occurred cannot be determined by just looking at the fields at a single spacetime point. In fact, there is no simple, generally-agreed upon approach as to the exact definition of "radiation" (look into the literature: there are all sorts of things about "near-field" vs. "far-field," for example).

      If you want to learn more about this, check out the topics "Rindler coordinates" and "Unruh radiation."

      Bottom line: interesting (and complicated) but no violation of the equivalence principle.

      anto also wrote:
      >In a gravitational field there is dilation, but not with respect to acceleration (proven e.g. at CERN)

      Wrong again: the time dilation is not due to the gravitational acceleration per se but to being at different depths in the gravitational potential. And, again, this is well-understood and consistent with the equivalence principle: check out "Rindler coordinates." Indeed, I know how to use this equivalence to derive the Schwarzschild solution without going through all the messy differential geometry.

      The details of these two topics are, I know, quite advanced and would take you a good deal of work to understand. But, the fact that you know too little to understand the literature says nothing about the equivalence principle, just your level of understanding.





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    4. Antooneo, what you tell us, seems to be quite intersting. However, I'm wondering why there is no public awareness about this topic. Not too many people know the author of the book, you recommend. In my view, that is not a very scientific attitude. The ideas may be relevant, but as a scientist you have to discuss your ideas e.g. on conferences or by publishing your ideas in the commonly known scientific journals.

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    5. @ PhysicistDave

      > It is well-understood that whether or not a particle is radiating depends on the frame of reference if one insists on using non-inertial frames of reference. Just one more of those "relative" things about "relativity."

      > The E and B fields are local: to transform from one frame of reference to another, you just need the E and B fields at the point in question in the first frame.

      >But, whether or not radiation has occurred cannot be determined by just looking at the fields at a single spacetime point. In fact, there is no simple, generally-agreed upon approach as to the exact definition of "radiation" (look into the literature: there are all sorts of things about "near-field" vs. "far-field," for example).

      I have formerly worked at an electron accelerator and radiation by acceleration was an everyday business. If there is radiation then there are photons emitted which can be detected. The existence of those photons does not depend on the frame.

      > Wrong again: the time dilation is not due to the gravitational acceleration per se but to being at different depths in the gravitational potential. And, again, this is well-understood and consistent with the equivalence principle: check out "Rindler coordinates." Indeed, I know how to use this equivalence to derive the Schwarzschild solution without going through all the messy differential geometry.

      > The details of these two topics are, I know, quite advanced and would take you a good deal of work to understand. But, the fact that you know too little to understand the literature says nothing about the equivalence principle, just your level of understanding.

      I did not say anything about “gravitational acceleration”. Dilation depends on the gravitational potential, that is true. On the other hand acceleration does not create dilation. You can find this in every textbook about relativity. And at CERN it was shown by a muon accelerator. The life time of the muons was extended according to their actual speed. But the huge acceleration in the ring did not have any influence. If it would have had, the muon lifetime would have been extended by another factor of 100 to 1000. That was not observed.

      And in addition: The Schwarzschild solution can quite easily be deduced without any reference to the equivalence principle. Do you want see this?

      And perhaps this was lost now: The equivalence principle means the non-distinguishability of gravitation and acceleration. That is disproved by the given examples.

      @ A former LEP expermentalist

      The mentioned particle model was presented about 25 times at physical conferences and formal meetings. The interest was great enough to fill even bigger lecture halls; with still increasing interest. So there was an auditory of about 1500 participants over the time. There have not been major objections from the auditory. In addition the model was discussed with the research director of a big electron accelerator. This man did not like the model very much because the assumption of an extended elementary particle was not familiar for him. However he did not find arguments against it.

      And the mentioned web sites are being accessed about 100 times per DAY. I wonder if any physical institute has such rates on its web site.
      The general problem – also for the publication on physical papers - is that main stream physics do not like deviating approaches. That seems to be a human problem.

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    6. antooneo wrote to me:
      >I have formerly worked at an electron accelerator and radiation by acceleration was an everyday business. If there is radiation then there are photons emitted which can be detected. The existence of those photons does not depend on the frame.

      Well, I worked on calculating the fields inside the drift chamber used at the PEP experiment at SLAC back in 1976 -- I created the algorithm de novo used for this purpose.

      So, my experience trumps yours!

      Now, that we have gotten that silliness out of the way (what I just said is true, of course), let's deal with the physics.

      First of all, in one of Schwinger's original papers on synchrotron radiation, he pointed out that, in fact, if you have a completely uniform ring of circulating charges, there will be no radiation, even if the centripetal acceleration is very, very high indeed and the charges are moving at nearly light speed.

      I have the paper around someplace: I'll get you the cite if you want.

      This is indeed obvious from Maxwell's equations: the fields produced only depend on the current distribution and the charge distribution. A uniform constant current must produce the same fields as a DC current: i.e., no radiation at all.

      Synchrotron radiation is due solely to the "lumpiness" of the current, as Schwinger points out. Of course, it has to be a little but lumpy, due to the discreteness of the electrons, but if you could smooth it out completely, there would be no radiation.

      Because: Maxwell's equations.

      I know you can find textbooks that say the opposite, but they disagree with Maxwell's equations (and with Schwinger). By all means, don't trust me, but do think about whether Maxwell and Schwinger are right or you are right. Just sayin'.

      And, you are also obviously wrong about radiation being independent of the frame of reference if you allow non-inertial (i.e., accelerated) frames of reference.

      Move at a constant acceleration and hold a charge in your hand. Now, use Rindler coordinates. The whole system is invariant under the time-like Rindler coordinate. The fields will therefore not change in the Rindler reference system. No oscillating fields, no fields changing at infinity. Nothing like radiation.

      But, of course, you and I agree that there will be radiation from the viewpoint of an inertial frame of reference.

      Again, this fact that whether or not there is radiation depends on your (non-inertial) frame of reference is familiar to anyone who studies Unruh radiation, but I have just proven it is true also in the classical case.

      I know these facts go against the "folk wisdom" known to older physicists, but Maxwell's equations do not lie. And, if you insist on an argument from authority, I have Schwinger on my side for case one and all the work on Unruh radiation for case 2.

      I prefer Maxwell's equations to arguments from authority, but either way you are wrong.

      I am, by the way,, working on a monograph on the subject, which is why I have been researching Schwinger's papers, etc. I started this when I and some young people did some calculations that showed the "folk wisdom" was wrong, although, as I just explained this is obvious from first principles.

      You have proven that the monograph really is needed. Time to spread the word about Maxwell and Schwinger!

      Dave

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    8. Please do not forget our original question. Einstein says that an observer, who feels a force acting on him, cannot distinguish between the causes "gravitation" and "acceleration". This is the basis of his General Relativity. And, as the logic of a theory is, there is just one counterexample sufficient to disprove his assumption and so his theory.

      An observer does not have to be in a relativistic context. So no Rindler coordinates. It may be an everyday situation. And if this observer notices a radiation at his charged object in the case of a force, then he knows that he is accelerated and the cause is not (solely) a gravitational field. This has only to happen once in a situation to falsify Einstein.
      Regarding the synchrotron radiation: Our electron ring radiated all the time and that was noticeable for everyone.

      And quite independent of all this: also the described cases of dilation is in conflict with Einstein's assumption.

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    9. Antooneo,

      Since I'm not a theorist, I'm not able to judge the realibility of your arguments, but for me it is absolutely plausible, that "the research director of a big electron accelerator" does not like models, he is not familiar with. Just keep on trying... “Science is the belief in the ignorance of experts”

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    10. Antooneo, the answer of PhysicistDave might be quite relevant for you. He created an algorithm making it easy to compare the prediction with experimental data.

      During my time at CERN, publications from phenomenologists have been discussed quite extensive, but when it comes to the question to test their ideas, only a very few people were interested in writing the required code for the implementation into MC generator models. In most cases, only those models have been tested, where the phenomenologists supported the experimentalists by writing an easy to be integrated code by thenselves.

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    11. Radiation is the emission of photons.
      You can't make a particle disappear by charging reference frames!

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    12. Greg Field wrote:
      >Radiation is the emission of photons.
      >You can't make a particle disappear by charging reference frames!

      Well, strangely enough, you can -- if one of the reference frames is non-inertial.

      Google "Unruh radiation": this is very well-established physics. There are, by the way, various ways to show that this happens, which is why I am so bemused that people who claim to be physicists are ignorant of it.

      It is also well-known that this happens classically: the Wikipedia article on the paradox of radiation of charged particles in a gravitational field is actually pretty good on this (although the last two sentences make no sense): in any case, Wikipedia gives the standard references.

      As the article says: "Likewise, a charged particle at rest in a gravitational field does not radiate in its rest frame, but it does so in the frame of a free falling observer. The equivalence principle is preserved for charged particles."

      By the way, the coordinate system used in Wikipedia is Rindler coordinates, as I mentioned above. Using Rindler coordinates, it is straightforward to actually calculate the E field observed by an observer co-moving with an accelerated charge and observe that, in the accelerated frame, there is no radiation.

      (No, I did not learn about all this from Wikipedia: I worked it out myself before seeing the Wikipedia article -- all this should be obvious to any competent physicist. But, in this case, Wikipedia happens to be a decent reference that is easily available.)

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    13. A former LEP expermentalist11 wrote:
      >Antooneo, the answer of PhysicistDave might be quite relevant for you. He created an algorithm making it easy to compare the prediction with experimental data.

      Well, thanks for attributing the algorithm to me! But, in fact, the algorithm was worked out in the mid-forties by Julian Schwinger and has, I suppose, been validated in pretty much every high-energy storage ring built since.

      Schwinger's work is most clearly explained in his 1945 paper, "On Radiation by Electrons in a Betatron."

      In his first paragraph, Schwinger declares in passing, "[A] steady current... of course, does not radiate." Of course, indeed: all competent physicists know this.

      More interestingly, Schwinger goes into detail on how a constant current can be approached as a limiting case (p.18):
      >"It is evident that this expression does imply the possibility of a substantial reduction of the radiation by destructive interference, if the electrons are properly arranged on the path. As an extreme example, suppose [N] electrons to be uniformly spaced on the circular trajectory...all harmonics up to the N-th are completely suppressed. Therefore if N is appreciably greater than the critical harmonic,n0=(E/(mc^2))^3, the radiation is practically eliminated."

      Indeed: practically eliminated.

      But, even more than this, most of the paper is taken up with detailed analyses of the radiation that will occur because of the "lumpiness" of the electrons: both the fact that electrons are discrete charges, and, more importantly, that the electrons will not be distributed exactly evenly around the circle (p.19: "In the actual situation, however, we must certainly regard the electrons as uncorrelated in position and randomly distributed around the circular path."). That is what produces synchrotron radiation.

      Now, I realize that none of this will convince our friends. But, please, realize that if you deny these results, you are not arguing with lowly PhysicistDave but rather with Julian Schwinger and all of those who have relied on his work for three-quarters of a century.

      So, if you have proof that Schwinger is wrong, publish it.

      But, you might want first to read and work through the math in Schwinger's paper. And, maybe chat with some people who are really experts on synchrotron radiation.

      Best of luck!

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    14. One can't argue with Established Physics.
      History proves that again and again.

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    15. Greg Feild wrote "Radiation is the emission of photons.
      You can't make a particle disappear by charging reference frames!"

      What about the Unruh effect? The vacuum in an inertial frame appears to be vacuum plus particles or radiation in an accelerated frame.

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    16. Greg Field wrote:
      >One can't argue with Established Physics.
      >History proves that again and again.

      Well, of course, you can argue with Established Physics.

      But, if that Established Physics consists of well-validated experimental or mathematical facts, then history shows you will almost certainly make an utter fool of yourself.

      And, in my own lifetime I have seen such fools again and again and again.

      In any case, what we are arguing about here is that our friend antoo is claiming that there are certain results that are already well-established in physics that prove that the equivalence principle is wrong.

      On that, he is incorrect, as I hope I have shown rather conclusively -- the established results in physics, by very prominent (yes, "Establishment"!) physicists go against him.

      Couldn't antoo still be right and the well-established physics be wrong? Sure, but it is then antoo's obligation to show this and, in particular, antoo's obligation to publish his proof.

      antoo thinks he can prove very well-renowned and brilliant physicists such as Julian Schwinger (the synchrotron radiation issue) and Fritz Rohrlich (the electron in a gravitational field issue) to be wrong? And thereby prove that Einstein was wrong on the equivalence principle and therefore GR itself is wrong?

      Great. Let antoo publish his results in a form that other physicists can understand and in a manner that makes clear that antoo understands in great mathematical detail the analyses of Schwinger and Rohrlich.

      One sure sign of a crackpot is "I know I'm right and I'm so smart that I do not need to understand or address the contrary analyses of proven experts in the field because... well, did I mention I'm sure I'm right and I'm really smart?"

      antoo can play that game if he wishes, but he will, understandably, find that not many competent physicists will take him very seriously.

      Dave

      P.S. I just found out that the great Fritz Rohrlich died less than a year ago at the age of 97. He lived a fascinating and, in some ways horrifying, life: his parents died in the Holocaust, which he narrowly escaped. He was already considered a grand old man of the field back when I started college almost fifty years ago.

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    17. Dave,
      I think that we are losing sight of the original question, which is Einstein’s principle. Even if all your arguments are correct (regarding Unruh, Schwinger, etc), this does not help Einstein. It is sufficient that there is only once an observer who, when feeling a force, notices a radiation (i.e. a photon) to falsify Einstein. And this case has surely happened many times.

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    18. antooneo wrote to me:
      >And this case [a violation of the equivalence principle] has surely happened many times.

      No, not at all. Not a single time.

      You seem for some reason to take it for granted that everyone agrees that many violations of the equivalence principle are generally acknowledged by physicists to occur.

      I'm not sure how I can make this any clearer to you: I (and most physicists I know of) do not think that one single example of the violation of the equivalence principle has ever been observed.

      You have given some specific examples of cases in which you believe, without evidence, that the equivalence principle is violated.

      I have patiently explained to you that this belief on your part, in these cases, comes from your lack of understanding of certain aspects of relativity or classical electromagnetism, giving first my own proofs and then citing the well-known literature.

      And, yet, you still seem for some reason fixated on the idea that I and most physicists agree with you!

      We don't.

      If we did, this would be momentous news within the scientific community. It would prove Einstein wrong. There would be NY Times and WSJ stories about it. Textbooks on GR would have to proclaim that GR was proven wrong.

      Have you seen any of that?

      You wrote:
      > It is sufficient that there is only once an observer who, when feeling a force, notices a radiation (i.e. a photon) to falsify Einstein.

      What on earth are you talking about? I give you a shove, you feel a force, you notice some photons from the sun. So what?

      Perhaps you are trying to say that an observer in uniform accelerated motion in free space with a charge also in the same uniform accelerated motion near him, for a very long time (to take care of far field effects), must see the charge radiating. That would indeed violate the equivalence principle!

      That would be truly momentous! It would in fact violate Maxwellian electrodynamics, not just GR.

      It has also never been observed. (Indeed, it would be a difficult experiment to carry out, as a practical matter.)

      You say this has happened "many times." Fine: show me when and where the results have been published so many times. Remember: the observer has to be moving with the charge: the equivalence principle only applies when the whole lab (observer and observed charge) are accelerating together. And, it has to be uniform accelerated motion for a long enough time for transient effects to die out.

      Again, can you really not understand that, if you were right, the revolution would already have happened and almost all physicists would already have rejected GR???

      Don't you wonder even a bit why this has not happened???

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    19. Dave,
      I have worked for an electron accelerator, and the generation of photons by accelerating the electrons was daily business. And we used these photons for further reactions and investigations. So, no problems to generate them, and to detect them, and to use them in a quantitative way.

      But if you are having problems with this fact I refer you again to the fact of dilation. Dilation takes place in a gravitational field for an object at rest. But in case of acceleration there is no dilation. Both facts a clearly proven, the first case by atomic clocks, the second case by the muon ring at CERN. So, equivalence is violated also here.

      And what about the “missing revolution”? One can say that this has happened already 15 years before Einstein. Because at that time Hendrik Lorentz has started to develop relativity; and that was the better solution in comparison to Einstein. But why was Einstein favored? Lorentz needed for his relativity the existence of atoms, molecules, and elementary particles. That was not accepted physics at that time. Meanwhile we know that he was completely right with that. But why was there no change to Lorentz at a later time? I think that this is human nature.

      There was a small community in favor of Lorentz all the time, famous persons among them. And the benefits of Lorentz’ are great: No questionable principles needed, no 4-dimensional space-time, none of the well-known paradoxes. And no problems with e.g. cosmological inflation and dark energy. And much more.

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    20. antooneo wrote to me:
      >I have worked for an electron accelerator, and the generation of photons by accelerating the electrons was daily business. And we used these photons for further reactions and investigations. So, no problems to generate them, and to detect them, and to use them in a quantitative way.

      But that does not violate the equivalence principle!

      First of all, synchrotron radiation is not a matter of uniformly accelerated motion: obviously the direction of motion in uniform circular motion changes. Rapidly -- it keeps rotating so as to keep pointing to the center of the circle! Not the situation the equivalence principle addresses.

      Second, as I (and numerous other physicists) keep trying to explain, whether or not radiation occurs depends on your frame of reference, if you allow non-inertial frames. This is just a fact of special relativity and Maxwell's equations (you don't even need GR).

      Furthermore, to test the equivalence principle,the observer has to be in a co-moving accelerated frame with the source. Obviously not true when you observe synchrotron radiation: you are not zooming around with the electrons! (Of course, it would not matter anyway, since circular motion is not uniformly accelerated motion.)

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    21. antooneo also wrote to me:
      >But if you are having problems with this fact I refer you again to the fact of dilation. Dilation takes place in a gravitational field for an object at rest. But in case of acceleration there is no dilation. Both facts a clearly proven, the first case by atomic clocks, the second case by the muon ring at CERN. So, equivalence is violated also here.

      No, you are wrong again in claiming, "But in case of acceleration there is no dilation." You do not understand special relativity.

      Again, it is not acceleration per se that causes time dilation: it is being in different "vertical" positions relative to the acceleration that produces time dilation in the frame of an observer that is co-moving with the accelerated charge.

      Both facts are crucial: not just acceleration per se but being in different positions relative to the direction of the acceleration. And, as I keep reiterating, the observer has to be in a non-inertial frame co-accelerating with the charge: the whole point of the equivalence principle is that the observer has to be in a non-inertial frame -- that is the situation the equivalence principle is trying to explicate.

      And, yes, if you are in a rocket accelerating, say, at one gee, you will indeed see the same kind of "gravitational" dilation for "test clocks" in different physical positions relative to the direction of the acceleration, testable with, say, the Mossbauer effect, that we see in a true gravitational field.

      This is a practically trivial consequence of special relativity: see, for example, page 190 in Misner, Thorne, and Wheeler (MTW) for an explanation. (You disagree? Fine -- take it up with Professor Thorne, who is still alive: he might even reply if you are really polite instead of arrogant in your lack of knowledge. He's a nice guy -- I took GR from him.)

      This is in fact the simplest way to derive the gravitational time dilation: gravitational time dilation is not only consistent with the equivalence principle, it can most easily be derived from the equivalence principle.

      And, everyone with any serious knowledge of GR knows this.

      By the way, this actually could be tested experimentally, though I doubt it is worth the effort: as I said (and as MTW shows) it is an essentially trivial result of special relativity.

      Look: I keep patiently explaining to you classical results in physics that have been well-understood for longer than a half century and that are well-documented in the literature, literature you have not bothered to consult.

      But, again, I ask you: you keep claiming that well-known phenomena in physics clearly and obviously disprove the equivalence principle. If these so well-known phenomena so obviously disprove the equivalence principle, why on earth do you think that experts in the field -- Kip Thorne, Steve Hawking, Sean Carroll, and so many others -- have never mentioned this supposedly obvious fact?

      Do you think all of us are engaged in some massive conspiracy to deceive our students and the general public because of some bizarre desire to protect Einstein???

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    22. antooneo asked me:
      >And what about the “missing revolution”? One can say that this has happened already 15 years before Einstein. Because at that time Hendrik Lorentz has started to develop relativity; and that was the better solution in comparison to Einstein. But why was Einstein favored?

      Glad you asked, my friend. It's an interesting story, though explained less often than it should be.

      You know, physicists are not ignorant of Lorentz's work: there is a reason we refer to the "Lorentz transformation."

      What Lorentz did was show the if you assume the only force in nature is electromagnetism then all of the formulae of special relativity follow.

      Important work, we all agree.

      But, what if there are other forces in nature besides electromagnetism? Even at the turn of the twentieth century, that seemed likely -- there was certainly gravitation. And, we now know of the weak and strong nuclear forces and the Higgs interaction.

      Lorentz’s derivation did not really address that.

      Einstein leapfrogged over Lorentz. By showing that Lorentz's work could be derived from very general principles -- the invariance of the speed of light and the principle of relativity -- Einstein showed that Lorentz's equations were not specific to electromagnetism but necessarily applied to all physical processes.

      Einstein's insight was absolutely essential in developing theories of the weak and strong nuclear forces and, as Einstein himself showed, a successful theory of gravitation.

      Lorentz's work was indeed important, but Einstein's act of showing that Lorentz's equations were much more powerful and based on much simpler premises than Lorentz himself realized was truly crucial to the progress of fundamental physics for the rest of the twentieth century.

      Does that answer your question?

      (N.B. Yes, I realize the whole history is more detailed and complex – Henri Poincare, etc. I’ve given the Cliff Notes version here.)

      By the way, I sent you to MTW to learn about how gravitational time dilation is a consequence of the equivalence principle.

      If you happen not to have MTW, another standard source is page 137 of the second edition of Adler, Bazin, and Schiffer: the last paragraph on the page explains what I was talking about.

      Their preceding paragraph outlines Einstein's own derivation, using a rotating coordinate system: I consider that a bit dicey, because funny things can happen in a rotating coordinate system -- the Coriolis pseudo-force, the rotational velocity exceeding light speed if you are far enough from the center of rotation, etc. But, of course, Einstein still did get the right answer.

      You're welcome.

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    23. I guess antooneo is momentarily trapped in confirmation bias. Once the dust will have settled also this concise chapter here is worthwhile reading.

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    24. Reimond,

      Yeah, that might help. I'm pounding a bit on our friend antooneo because he is so sure about things that he really does not understand very well at all. People who do not know that much about a field should try to show a bit of restraint (I know: we should all try to be saints -- but we are all unlikely to succeed!).

      I'm bothering to respond to him because his confusions are indeed confusions that would strike lots of students. I remember long ago being confused about such things myself, and I am trying to hone my ability to explain these things to those who do not yet understand the basic principles of relativity.

      Of course, there are similar (though often simpler) "paradoxes" in special relativity without any acceleration being involved: I suppose we can divide people into those people who are willing to consider that we physicists actually are able to show that these paradoxes are not real and those people who stick with their initial impressions and will not listen to what physicists have discovered.

      It will be interesting to see which group antooneo ends up in!

      By the way, your linking to Tony Zee's book does raise a general point I myself have experienced: I often do not get a subject until I have read (parts of) multiple books by different authors on that subject. Sometimes, I just have to find the author whose style "clicks" for me, often different authors for different parts of the subject.

      Learning is hard work.

      Dave

      Delete
    25. To come to the original point again: Einstein has stated that gravity and acceleration are identical physical phenomena. Only our everyday experience gives us the impression that both are different phenomena. So, if we find one single example where we can distinguish between both, Einstein’s assumption is falsified. This is the starting point for the discussion about equivalence.

      An accelerated electron radiates (means: emits photons) irrespective of the kind of acceleration. In a storage ring acceleration is towards the center and with changing directions. In the case of bremsstrahlung it is (or can be) an acceleration into a constant direction. Both cases cause emission of photons. And the photons move at c, whereas the observer moves at a lower speed. So he will see the photon; or at least there is a chance that he sees the photon, and that is sufficient to falsify this principle.

      To dilation: Every textbook of SR says very clearly that acceleration does not cause dilation.

      Dave’s statement: “Again, it is not acceleration per se that causes time dilation: it is being in different "vertical" positions relative to the acceleration that produces time dilation in the frame of an observer that is co-moving with the accelerated charge.”

      This is NOT about a charge. Please observe! In the case of the muon ring the acceleration was vertical to the direction of motion. And the measuring observer, which were the muons themselves in this case, were in the same frame as the particles and even then did not notice any dilation, as their lifetimes were not extended by any acceleration.

      The main difference between the approaches of Einstein and Lorentz is that Einstein based his approach on principles whereas Lorentz based his approach on physical facts which are there independent of relativistic considerations. (And depart of this: any of Einstein’s principles can easily be falsified these days, as we now understand more about physics than Einstein could know.)

      Lorentz’s considerations about the contraction of fields were related to the electric force, true, because it was the only force known at that time. Meanwhile it was shown that field contraction is the case for all types of forces. - Time dilation is related to the internal oscillation of particles. That was in fact speculative at that time; but since the work of de Broglie and Dirac we know that this oscillation goes on in all elementary particles.

      Delete
    26. antooneo,

      Look: the essence of this discussion is that you are arguing that certain extremely well-known facts pf physics -- the existence of synchrotron radiation and the fact that acceleration does not produce time dilation from the viewpoint of an inertial observer -- obviously disprove the principle of equivalence and thereby obviously prove that General Relativity is nonsense.

      We have two possibilities here: either. for nearly a century, physicists -- from Einstein to Schwinger to Kip Thorne and his co-authors to Steve Hawking to Dick Feynman to Ron Adler and his co-authors to Sean Carroll and Tony Zee and down to Sabine and me and thousands of other physicists -- are intentionally ignoring these totally obvious facts and refusing to tell the truth to their students and the general public.

      Or the second possibility: just possibly you are wrong. Just possibly you are mistaken in denying that there can be radiation in one frame of reference but not in another accelerated frame of reference. Just possibly you misunderstand what special relativity asserts about time dilation for accelerated observers.

      I have explained the correct analyses to you in my own words, as have others. We have given you references to look at to find the results that are generally known to the physics community.

      But, you will not think about our analyses or try to understand the references we have provided. Because, after all, you know that all of us have been systematically lying to our own students and to the general public for just about a century.

      I congratulate you: you have laid bare the greatest conspiracy in human history -- thousands of physicists who know the obvious truth but who have nonetheless been systematically lying to their students and the public for nearly a century.

      You, antooneo, will go down in history as the greatest scientist who has ever lived, the courageous genius who exposed the greatest scientific lie and conspiracy in all of human history.

      You are without peer.

      Or maybe, just possibly, just conceivably, all of us know some things you do not know and you are mistaken.

      Do you think that is possible?

      Nah!

      I salute you!

      Delete
    27. Greg Field wrote, apparently in response to Lawrence Crowell:
      >The vacuum is not a thing.

      Well, in QFT it sorta is: have you heard, for example, of the fascination physicists have with "vacuum expectation values"?

      More importantly, as Lawrence points out, there is a well-understood phenomenon, Unruh Radiation, in which what counts as "the vacuum" depends on your state of motion (accelerated vs. inertial). This is not General Relativity, by the way: it is a consequence of QFT and special relativity alone.

      Oh, I forgot: You have proved QFT is false! Except you will not offer us any evidence at all that you have achieved this, unless we shell out a few books for your books.

      I am happy for you, just as I am happy for our friend antooneo.

      In future centuries, people will refer not to "Newton and Einstein" but to "Greg Field and antooneo"!

      Your mothers must be very proud.

      Delete
    28. antooneo wrote to me:
      >(And depart of this: any of Einstein’s principles can easily be falsified these days, as we now understand more about physics than Einstein could know.)

      No doubt I am a masochist for asking, but pray tell, which of Einstein's other principles "can easily be falsified these days" besides the principle of equivalence?

      I see that even I have underestimated your greatness: you are not only more brilliant than Einstein, but you will disprove any and all of his principles.

      How can one not admire a man so lacking in false modesty?

      Delete
    29. Dave,
      I understand that you do not have arguments as you do not answer to the details.

      State is that present physics are having great problems since many years, like:
      - Dark matter
      - Dark energy
      - Quantum gravity.

      Any attempts to solve these problems in the scope of peer-reviewed proposals failed completely. Not the faintest indication of a success. And they will fail in future.

      The approach which I have mentioned here has a presentation in the web. This presentation is accessed around 1500 times per DAY! And please note that it is not about sex but about theoretical physics. Do you know any peer-reviewed contribution which has such rate?

      Seeing this I am quite confident what one day the physical community will find solutions.

      Delete
    30. antooneo wrote to me:
      >I understand that you do not have arguments as you do not answer to the details.

      antooneo, I have given you details, both in my own words and by giving you references.

      But, you do not want to consider those details -- you have made that abundantly clear.

      You have not studied Schwinger's paper in detail, now have you?

      You have not worked through the analyses in MTW or ABS for which I gave you references, now have you?

      (By the way, if anyone has the first edition of Adler, Bazin, and Schiffer, the same analysis is on page 127 of the first edition.)

      You have not looked at Fritz Rohrlich's work in detail, now have you?

      When I give you standard references, after trying to explain it to you in my own words, I have zero obligation to keep trying to explain it to you in more detail when you yourself are simply too stubborn to try to understand the standard references.

      You are not paying me: I am graciously trying to help you stop making a fool of yourself to the entire physics community.

      But you don't care. You will not bother to try to understand the standard references I have provided to you.

      Most importantly, you have never answered my key question: what on earth do you think all of us physicists -- from Einstein to Schwinger to Kip Thorne and his co-authors to Steve Hawking to Dick Feynman to Ron Adler and his co-authors to Sean Carroll and Tony Zee and down to Sabine and me and thousands of other physicists -- are up to?

      You think it is totally obvious that the principle of equivalence has been definitively disproven. We keep telling our students and the general public that it has not been disproven.

      But you claim it is so obvious that all of us must know the truth.

      So, what do you think we are doing? Do you really think all of us are part of a grand conspiracy to lie about physics?

      I'm serious about this: why do you think all of us physicists are behaving this way?

      Will you please do us the courtesy of honestly answering that simple question?

      (NOTE: this reply was inadvertently posted outside of this subthread, so I have now posted it here where it belongs and deleted the version posted in the wrong place.)

      Delete
    31. It seems, alas, that our friend antooneo has left us.

      But, for the sake of anyone else who is confused as antooneo is, I did want to complete our discussion re the equivalence principle.

      antooneo wrote:
      >This is NOT about a charge. Please observe! In the case of the muon ring the acceleration was vertical to the direction of motion. And the measuring observer, which were the muons themselves in this case, were in the same frame as the particles and even then did not notice any dilation, as their lifetimes were not extended by any acceleration.

      No, it indeed does not matter whether or not they are charged. And, no, acceleration per se does not increase the lifetimes of the muons: no competent physicist expected that it would, least of all anyone who understands the principle of equivalence.

      Let's focus on antooneo’s claim that:
      >the measuring observer, which were the muons themselves in this case...

      The muons themselves are necessarily at the same distance with respect to the direction of the acceleration as themselves. But, as I and others have tried to explain, gravitational time dilation is about comparing time at two different vertical positions in the gravitational field.

      To use the equivalence principle in this case, you would similarly have to compare the lifetime of muons at two different positions in the pseudo-gravitational field of the rotating frame: i.e., the lifetime of muons in uniform circular motion at two different radii from the center of rotation.

      Of course, muons at different radii would obviously be moving at different speeds, and, simply from special relativity, they would therefore have different time dilation factors relative to each other.

      Easy to work out, and this will indeed give you the correct gravitational time dilation (despite my uneasiness at using a rotating frame of reference).

      Let me emphasize, as Reimond tried to make clear, that the way to use the principle of equivalence is to take a situation that can easily be analyzed by special relativity in an inertial frame and then see how that result looks in an accelerated frame and then finally transfer the result in the accelerated frame to the case of an actual gravitational field.

      Doing that, the case that antooneo appeals to, the muons in circular motion, is actually an example that confirms the principle of equivalence.

      Again, in more detail: You first analyze some scenario in an inertial frame, just using special relativity. Then you look at the exact same physical situation from the perspective of an accelerating frame, and strange things seem to be happening. And, you assume such strange things also happen in a gravitational field.

      This is the “equivalence principle” and it has always worked.

      Now, you have to play by the rules -- the equivalence principle is true "locally," meaning over distances small enough that tidal forces are negligible.

      And, you do have to be really careful when the acceleration is not uniform linear acceleration, as in the example of uniform circular motion and/or when your reference frame is rotating.

      Finally, for the case of uniform linear acceleration, here (sec. 2.1, p.3) is an example that works through the algebra and shows how to derive gravitational time dilation via the equivalence principle using uniform linear acceleration. Again, gravitational time dilation is not only consistent with the equivalence principle; it can be (and historically going back to Einstein has been) derived from the equivalence principle.

      Anyone who passed and actually understood a legitimate undergrad course on special relativity should find all of this easy to understand.

      Delete
    32. The equivalence principle says that gravity and acceleration is the same thing. But dilation is a clear disprove of this believe. There is dilation in a gravitational field but not related to acceleration. Both facts are the state of main stream physics; so main stream confirms this conflict with Einstein. – You did not give arguments in disfavor of this.
      I did not read all the references you gave me. Would be a lot of time consuming action. I could as well give you a lot of literature which shows you my position. For both this discussion is not the right frame. However, just one point: Unruh is saying that in case of acceleration there is always radiation appearing, even in vacuum and without a charge. It seems that already this is sufficient to confirm the conflict with gravity.

      I do not think that there is conspiracy. But present physics feels to me in some aspects like an epicycle theory. And that is not only my view.
      The philosopher Hans Reichenbach worked with Einstein and was promoted by him. And in his book “The Philosophy of Space and Time” he made the following comparison between the relativity of Einstein and Lorentz:
      - Einstein’s relativity is in some way analogue to the Ptolemaic system (and so with epicycles)
      - Lorentz’s relativity is analogue to the Copernican system.

      This is the way as I personally understand it. And not only regarding relativity but also some aspects of QM.
      And we should not overlook that also the epicycle theory did have precise results in some cases.

      No, I do not believe in conspiracy; but as Sabine has addressed in her book: There is a strong tendency in physical research groups to be in harmony with the colleagues; whereas the persons are normally not aware of it. My experience is even worse: there is a strong pressure.
      And regarding Copernicus: He was heavily attacked after publishing his view; but he was lucky that he did not have to fight with peer reviews. That could have changed the historical progress.

      Delete
    33. antooneo,

      "The equivalence principle says that gravity and acceleration is the same thing"

      No, it doesn't. This is wrong, as others have tried to tell you before. Please stop repeating wrong statements; I will no further approve them.

      Delete
  18. Thanks for a short and informative video, Sabine. Sure will stay tuned !

    ReplyDelete
  19. A couple of years ago there was a conference on

    The Path Integral for Gravity
    https://www.perimeterinstitute.ca/video-library/collection/path-integral-gravity



    ReplyDelete
  20. Space time is a basic notion of relativity theory, and the superposition principle is central in quantum mechanics. In qunatum gravity one can therefore expect to have "superpositions of spacetime". Could you tell us in which of the 5 approaches there is such a notion, and what "superposition of spacetime" means in the first place?

    ReplyDelete
  21. Under the heading "3. Asymptotically Safe Gravity", there is a typo in the first paragraph (third sentence): "that it seems" should be "than it seems". "that" should be "than".

    ReplyDelete
  22. bee,

    will you ever comment on conformal gravity and papers that show it reproduces MOND physics, arXiv:1812.03152, f(R) gravity, gauge gravity, Liouville quantum gravity, MacDowell–Mansouri gravity, group field theory? or complex GR and complex spacetime, as LQG is self-dual and fully covariant when the immirizi parameter is imaginary, leading to complex GR.

    i know that's a lot. there are wikipedia articles on all these, but that's just about it. how are they evaluated ? wikipedia also has articles on string theory and supergravity, but your commentaries are helpful.

    ReplyDelete
  23. Thanks for the summary. So the models, written in calculus, give unphysical results with a point because space-time isn't actually continuous and instead people are trying variously a line, a triangle, a cube and a circle?

    ReplyDelete
  24. Quantum Gravity is interaction between quantum particles
    of energy and quantum particles of mass
    (let say a large number of dark matter) at very short distance.
    #
    To understand their interaction we need to use the laws of thermodynamics (the Theory of Ideal Gas for dark matter)
    and Quantum theory (for energy particl).
    The scheme will be looked as:
    . . . E=h*f > E=kT(logW) / quantum gravity /
    #
    With time this quantum process is changed to star's gravity as . . . . . E=kT(logW) > E=h*f
    ========

    ReplyDelete
    Replies
    1. QM + GRT
      When quantum mechanics is combined with general relativity,
      it turns out, that the detailed nature of the physical laws
      that govern matter and energy actually depend on the
      physical scale at which you measure them.
      #
      Gravity effect is possible only in the presence of mass and energy
      The unity of QM + GRT is possible only if we take these two
      phenomena on the same equal physical quantum scale,
      where it can provide the correct description of nature.
      The unity of QM + GRT is very sensitive to the scale
      The scale cannot be ignored in Physics
      #
      We know what quantum energy is: E=h*f,
      but quantum of mass is known as ''dark matter''

      The problem QM + GRT is hidden in the puzzle
      what quantum of ''dark matter'' is.
      ======

      Delete
    2. How is possible to understand the quantum particle of ''dark matter''?
      The best way is to use ''The theory of Ideal Gas''
      Why?
      Because the ''dark matter'' and ''ideal gas''
      exist in the same very cold continuum: T=0K
      ''dark matter'' and ''ideal gas'' are an ideal ''marriage couple''
      =========

      Delete
    3. How is possible to know what particles of ''dark matter'' are?
      The best way is to use thermodynamics - ''The theory of Ideal Gas''
      because ''dark matter'' and ''ideal gas'' exist in the same
      very cold reference frame T=OK
      ''dark matter'' and ''ideal gas'' together are like an ideal ''married couple''
      #
      Gravity is evolutionally process:
      from quantum gravity to star's and planet's formations
      During this process all chemical elements were created
      (as above in the Sun so below on the Earth)
      ====

      Delete
  25. Entanglement seems to point in the direction that our day-to-day concept of space and time break down at small scales. Theories which try to explain space and time as emerging properties of something more fundamental than make intuitive more sense than theories which consider time and space to be a given framework.

    ReplyDelete
  26. "Emergent gravity is not one specific theory, but a class of approaches. These approaches have in common that gravity derives from the collective behavior of a large number of constituents, much like the laws of thermodynamics do."
    In my view, emergent gravity is very appealing, but the focus on gravity only might be to narrow. I would like to see a general theory of emergence. Emergence seems to be related to the collective behaviour of individual constituents and nature (eg. solid state physics) is full of examples, that new phenomena arise from the collective behaviour of individual (?) particles or costituents. In particular, phenomena arising from biological or cultural evolution (Richard Dawkins Meme Theory) stem from the collective behaviour of individual members of the whole population. Maybe phenomena like gravity is somehow related to evolutionary processes in the broadest sense. I've heard, that some people are working on formulating the quantum mechanical "natural laws" in terms of a process oriented description. I dont know any details however. Is there someone reading this forum who can provide me with more information about this?

    ReplyDelete
  27. I can't resist wild ideas, so-- we might be looking at spacetime through too much of a classical filter, imagining that we have a continuum with a definite metric, and imagining perhaps trajectories in that continuum (worldlines). But we could be more reductionist and suppose that spacetime only has definite characteristics when measurements are made. We have to have some way to make this less solipsistic, so we take the worldlines seriously enough to incorporate their intersections (events) and take these to be equivalent to measurements made in the lab. So we decompose spacetime into a matrix of event cells, in which we have information from which we infer all sorts of structure, like intervening spaces and metrical properties. But all we have, in fact, is a structure of discrete events that are correlated in various ways. QM, I think, hints at this. So we go from a continuum to a discrete event structure, and all we need then are the rules governing the information in these "event" cells, and how the rules of correlation connect the information in these discrete cells. From THAT abstract structure, everything else is emergent.

    ReplyDelete
  28. I would be interested in people’s thoughts about where Stephen Hawking’s 1974 prediction of a blackbody radiation spectrum emitted across the event horizons of black holes, would fit into efforts to quantize gravity. To me, it seems nothing short of remarkable that Hawking was able on the basis of the General Theory of Relativity alone, to derive for black holes, the same radiation spectrum with which Max Plank kicked off the quantum revolution in 1901.

    Yes, thermal radiation from macroscopic black holes in the cosmos presents some challenges regarding information loss. But the scale at which quantum gravity comes into play is the Planck mass M_P which is defined in terms of the Newton’s gravitational constant, the reduced Planck constant and the speed of light according the interaction strength G M_P^2 def h-bar c. And there, in what Wheeler dubbed the geometrodynamic vacuum, with positive energy fluctuations offset by negative gravitational energies, the Schwarzschild radius of an average fluctuation is twice as large as the average separation between the individual fluctuations, which means the entire space is one omnipresent blackbody black hole. And here, the information loss would seem no less troubling than that which occurs when we follow Boltzmann by understanding temperature in terms of the statistics of molecular fluctuations.

    Not believing that two entirely-different approaches -- Planck’s and Hawking’s -- both producing the blackbody spectrum is merely coincidence, it seems almost impossible to NOT think of the observed blackbody spectrum a manifestation of gravitation at the Planck scale, viewed from 20 or more orders of magnitude removed, and of the CMRB as this Hawking spectrum viewed from an observational energy (temperature) as removed as can be. So, when we apply heat to raise the temperature of a blackbody and thus blueshift its spectrum, we are in essence using temperature rather than energy or microscope precision to probe closer to the geometrodynamic vacuum.

    From a practical development standpoint, if, as Planck found, this spectrum cannot be represented without energy quantization, it seems that there ought to be a place in Hawking’s black hole solution where E=nhf fits in as well. Then, perhaps we can trace that back into its origin in the Einstein Equation to quantize the gravitational fields generally. By such an approach, we would actually root the unification of these two major pillars of physics into the very empirical data -- namely Planck’s blackbody spectrum -- which kicked off the quantum revolution and for which the empirical validity is unquestioned and unquestionable following what will soon be a century and a score.

    Then, if we mix in Dirac’s Quantum Theory of the Electron its.5 n h-bar angular momenta which also have deep observational support, and the tetrads which connect this to curved spacetime, we might really get somewhere.

    ReplyDelete
    Replies
    1. Jay,

      You asked:
      >"From a practical development standpoint, if, as Planck found, this spectrum cannot be represented without energy quantization, it seems that there ought to be a place in Hawking’s black hole solution where E=nhf fits in as well."

      Hawking used quantum field theory. The Planck relationship is built into quantum field theory. So, the connection is there from the beginning of Hawking's calculation.

      So, it is not quite true that, in your words:
      >"To me, it seems nothing short of remarkable that Hawking was able on the basis of the General Theory of Relativity alone, to derive for black holes, the same radiation spectrum with which Max Plank kicked off the quantum revolution in 1901."

      I.e., Hawking did not use GR alone; he started out, also, with quantum field theory.

      Now, why the Planck spectrum (almost -- there is the so-called "gray-body" factor) also for Hawking radiation?

      Good question: it comes out of the math in the end, but I recall no simple way to show why that is what you should expect. Of course, if you believe the whole story about black holes having entropy and temperature, it makes sense, but that would be reversing the historical sequence of discovery, I think.


      Delete
    2. >Dave, you said: “Hawking used quantum field theory. The Planck relationship is built into quantum field theory. So, the connection is there from the beginning of Hawking's calculation.” And I had said “it seems that there ought to be a place in Hawking’s black hole solution where E=nhf fits in as well.”

      If what you said is true – and it has been several years since I took a look at Wald’s book which handles this subject nicely – then I have a different question: Why then is what Hawking found not *already* regarded as a unification of quantum theory and gravitational theory? What is it still missing? And I still want to see exactly which lock the E=nhf key fits into. It must be there, IMHO.

      >Dave, you also mentioned “gray body” and said “if you believe the whole story about black holes having entropy and temperature, it makes sense, but that would be reversing the historical sequence of discovery, I think.”

      Gray body, so much the better. That puts in an extra parameter which, if I recall correctly, is just a number between 0 and 1. Makes things more general with wider coverage.

      It is always good to ask “what if A(=Hawking) had been discovered before B(=Planck) rather than the other way around as it really was?” Because while people can come up with lots of pretty symmetries that may or may not work in nature, I do think we are on safe ground to state that nature is invariant with respect to the order in which humans discover her secrets. Further, because it is easy even for physicists to become sociologically attached to one good explanation of some phenomenon, making unlearning in favor of an alternative harder than learning, the simple gedanken of reversing historical sequences helps to clear away mental barriers in thinking through a problem. SO: if GR and Hawking radiation had been discovered before Planck radiation, what would GR and QM together, look like?

      Best, Jay

      Delete
    3. I mentioned Wald's book on GR in a reply to Dave which should post soon, as presenting Hawking radiation well. Turns out the whole book is online, at: http://www.fulviofrisone.com/attachments/article/486/Wald%20-%20General%20Relativity.pdf.
      I suggest everyone who has an interest please review section 12 and Table 12.1: Black Holes and Thermodynamics, on page 337. I believe that Hawking found thermodynamics and black (or grey) body spectrum entirely from GR without QFT, but you all can review this and form your own conclusions.
      Then go to page 418 and the final paragraph of the whole book, which is worth reproducing here in full:
      “Thus, we appear to be in a situation with regard to black hole thermodynamics which is very similar to the situation with regard to ordinary thermodynamics prior to the discovery of the underlying basis of these laws arising from statistical physics. We have discovered the laws of black hole thermodynamics -- in this case by calculations and gedankenexperiments rather than by laboratory experiments -- but the underlying basis of these laws is not known and presumably will not be fully understood. until we have a quantum theory of gravitation. Nevertheless, the existence of the laws of black hole thermodynamics indicates the likelihood of a deep connection between gravitation, quantum theory, and statistical physics. It remains for future investigations to explore this connection further.”
      That is my point. And the next step in this direction is to take Hawking radiation from cosmological black holes to the Planck (geometrodynamic) vacuum which is a black hole space, with a black (or grey) body spectrum, and use this as the theoretical underpinning for experimental thermodynamics. If we reverse-ordered the discovery history as Dave raised, and knew GR and Hawking first, then discovered Planck’s law and thermodynamics, we would likely reach the conclusion that the Hawking spectrum and the Table 12.1 laws are what we are observing experimentally, at many of orders of magnitude removed from the Planck vacuum. And I will repeat for the third time: we need to find an E=nhf relation in Hawking’s physics and then backtrack to permeate that generally into the Einstein equation. Then, take the operator square root with tetrads for spatial curvature so you get to fermions and spin 1/2, and we may well have our quantum theory of gravity with ab initio empirical support built right in.

      Delete
    4. Jay,

      Section 12 in Wald's book describes black hole thermodynamics, which does not require any quantum mechanics.

      If you want to read about Hawking's radiation, you should check section 14.3 - Particle Creation near Black Holes. These calculations involve QFT in curved space-time.

      Delete
    5. If I might put the sharpest possible point on what I have said in my previous posts about Hawking radiation, it is this:

      IMHO, Stephen Hawking already discovered the basis for unifying General Relativity with Quantum Mechanics when he discovered the Planck blackbody spectrum and the laws of thermodynamics for black holes in 1974. However, this has not yet been widely recognized, and so has not yet been fully developed and detailed in the way it needs to be.

      Delete
    6. Jay asked:
      > Why then is what Hawking found not *already* regarded as a unification of quantum theory and gravitational theory? What is it still missing?

      It just does not allow one to calculate to arbitrary accuracy everything we would like to know about quantum gravity. Lots of things -- most notably what happens when the mass of the black hole gets down near the Planck scale.

      Jay also said:
      > I believe that Hawking found thermodynamics and black (or grey) body spectrum entirely from GR without QFT, but you all can review this and form your own conclusions.

      Well, find what you think is the actual derivation, go through it carefully, and see if you get Hawking radiation without using quantum mechanics (QFT). You just don't.

      One reason this is obvious is that Planck's constant h exists in QM but plays no role at all in GR. Since h shows up in Hawking radiation, somehow he must have used quantum theory (and he did).

      Sorry, but you keep insisting that you know how the derivation works when you have not actually gone through the derivation yourself -- physics is not a spectator sport.

      Delete
    7. I took a closer look at Wald which I had last studied about 6-7 years ago. Udi and Dave are correct that the black hole thermodynamics does not use QFT, but the blackbody derivation does. In Wald, the connection to what we will all recognize as the Planck spectrum is made at (14.3.7).

      The derivation which we now all agree uses QFT, is carried out in Hilbert space. But unless I missed something, (14.3.8) is the first place where Planck's constant appears, and this is done because (14.3.7) has the same mathematical skeleton as Planck's law which originally carries, and is then used to inject, the h.

      Delete
    8. Jay,

      you just pointed to a very important sentence. Thus, equation (14.3.7) is precisely ...” - the big question is why? (see also here)
      This also has to do with “back-reaction” the very name of this blog, but a semiclassical solution like in (14.3.20) is certainly wrong (since the word “natural” occurs ;-)

      Delete
    9. Reimond,

      I agree. And go down to the paragraph before (14.3.21) where Wald acknowledges this:

      "As discussed above, serious difficulties arise when one tries to use equation (14.3.20) to calculate the back-reaction effects..."

      Jay

      Delete
    10. Can anyone please point to a reference which makes crystal clear, mathematically, why Planck had to use E=nhf to combine the Rayleigh-Jeans and Wein laws into one? Even his original 1901 paper does not specifically contain n=1,2,3..., and this really only started to be understood after Einstein wrote about the photoelectric effect in 1905.

      To be clear, I do not need an explanation of the physics. I want to see the MATH details of why E=nhf was needed to get to the Planck spectrum from the prior infrared and ultraviolet spectra. Per Dave, I have no intention of being a mere "spectator" if there is a chance I can contribute to a solution.

      Delete
    11. Jay wrote:
      >The derivation which we now all agree uses QFT, is carried out in Hilbert space. But unless I missed something, (14.3.8) is the first place where Planck's constant appears, and this is done because (14.3.7) has the same mathematical skeleton as Planck's law which originally carries, and is then used to inject, the h.

      Jay, if you look right before eq. 14.3.7, Wald says:
      > "It follows directly from general properties derived in problems 2, 3, and 5 that the expected number of particles spontaneously created in the state represented by this packet is [Eq. 14.3.7]..."

      Here is a site where you can actually see problems 2, 3, and 5, (pp. 419-420).

      The problems are working out things having to do with various commutators, Hilbert space, etc. -- apparently QFT.

      Now, how do problems 2, 3, and 5 make eqs. 14.3.7 and 14.3.8 obvious from what has gone before? Beats me -- I have never found Wald easy to follow.

      No doubt if you carefully read through the chapter up to this point and understand it all (!), it does make sense.

      In any case, somehow QFT seems to already come in by eq. 14.3.7. (Wald seems to be setting Planck's constant equal to one in problems 2, 3, and 5, which may contribute to the confusion.)

      I think Wald is doing ray-tracing from early times to late times (I think similar to Hawking's original derivation). And then this should be used to implement a Bogoliubov transformation between "in" and "out" states.

      But I find Wald's explanation even more opaque than most other authors.

      Incidentally, I will confess that I am convinced that there has to be a clearer way to derive Hawking radiation than this standard approach, and, indeed, there are obvious problems with this approach (e.g., the so-called "trans-Planckian problem").

      After all, what is really happening is that the infalling matter that is forming the black hole changes the spacetime metric, and this ongoing change in the spacetime metric deforms the quantum vacuum so as to produce real physical particles.

      A complicated process indeed, but it's not clear why it should require thinking about modes at minus infinity or modes with trans-Planckian energies.

      If I find someone who has sorted this out (or sort it out myself), I will try to provide a link in the comments here on Bee's blog.

      For what it's worth, this is currently one of my major sources of intellectual irritation (hopefully, constructive irritation!).

      Dave

      Delete
    12. Planck didn't explain MATH details of (h),
      in books are written Planck fount (h) . . .
      "intuitively, instinctively, phenomenological" . . . .
      . . . . he took (h) '' from heaven '' . . .
      . . . but . . . this coefficient of action somehow works

      ===

      Delete
    13. Jay,

      for sure you mean something different than this here, p.65, but it is a nice overview anyway. And it mentions Munich (Max Planck), where soon ... counting beer glasses (Ludwig Boltzmann) becomes a major sports event again.

      Delete
    14. 1 - A black hole has a temperature within a few
      millionths of a degree above absolute zero: T=0K
      / Oxford. Dictionary./
      2. - A stellar black hole of one solar mass has a Hawking
      temperature of about 100 nanokelvins. This is far less
      than the 2.7 K temperature of the cosmic microwave background
      http://en.wikipedia.org/wiki/Black_hole
      3 - Previous Picture of the Day articles about black holes suggested
      that the terminology used to describe “gravitational point sources”
      is highly speculative: space/time, singularities, and infinite density
      are abstract concepts, precluding a realistic investigation into
      the nature of the Universe.
      / Black hole theory contradicts itself, by Stephen Smith. Oct 12, 2011 /
      4 - Book: ''' Stephan Hawking, A life in science,''
      / by Michael White and John Gribbin./
      #
      ''Together with Brandon Carter and Jim Bardeen, Hawking
      wrote a paper, published in Communications in Mathematical
      Physics , pointing out . . . . . the team commented,
      '' In fact the effective temperature of a black hole is
      absolute zero . . . . No radiation could be emitted from the hole.''
      / page 156./
      But later (!) , . . using concept of entropy and
      Heisenberg uncertainty principle and quantum fluctuations (!)
      Hawking changed his mind and wrote that black hole can emit
      ( Hawking radiation )
      #
      So, in the beginning (according to calculations) the ''black hole''
      had absolute zero temperature T=0K but . . . thanks to entropy,
      HUP and quantum fluctuations Hawking radiations was arisen.
      In others words:
      ''black holes'' are local micro- scheme of absolute zero vacuum: T=0K
      ''black hole'' is only another name of ''true vacuum'' : T=0K
      Homogeneous zero Vacuum is an absolute ''spacetime'' between Galaxies.
      Somehow different kinds of radiations, particles, heat can arise from T=0K.
      “Now we know that the vacuum can have all sorts of wonderful
      effects over an enormous range of scales, from the microscopic
      to the cosmic”,
      said Peter Milonni
      from the Los Alamos National Laboratory in New Mexico.
      Only vacuum can be the real basic structure of Nature and Physics.
      =======

      Delete
  29. Which prevents the collapse of the matter (when winning the degeneration pressure) from creating just a minor black holes for each of the elementary particle? If we assume the law that the inner side of event horizon cannot consist anything and event horizons cannot combine...

    I tried to solve geometrically that kinda spacetime and there seem to be possibility for freedom of "Tardis-space" where Shapiro effect will be huge and miniholes could orbit each others...

    Do anyone know some research of this theme?

    ReplyDelete
  30. Gravity effect is combination of Energy + Mass
    Quantum Gravity effect is combination of
    Quantum Energy + Quantum Mass
    #
    There is only one way to quantize gravity:
    to understand what quantum-mass-gravity particle is.
    We know what is quantum-energy particle is (E=h*f),
    we don't know what quantum-mass-gravity is.
    ============

    ReplyDelete
  31. This comment has been removed by the author.

    ReplyDelete
    Replies
    1. Why General Relativity stubbornly refuses to be "quantized" ?
      ===
      3D + time (interval contact) is known subject on our gravity-planet
      SRT's spacetime (non-gravity system) has another ''time'' . . .
      therefore events between these two (2) systems seem appeared as separation
      (quantum problem of measurement)
      Mainstream physics absolutely ignores this (non-gravity system) issue but . . .
      but . . . ''quantize gravity'' can be solved from this ''non-gravity system''
      =======
      P.S.
      Quotes about ''non-gravity system''
      #
      The problem of the exact description of vacuum, in my opinion,
      is the basic problem now before physics. Really, if you can’t correctly
      describe the vacuum, how it is possible to expect a correct description
      of something more complex?
      / Paul Dirac /
      #
      Book : ‘Dreams of a final theory’ by Steven Weinberg. Page 138.
      ‘ It is true . . . there is such a thing as absolute zero; we cannot
      reach temperatures below absolute zero not because we are not
      sufficiently clever but because temperatures below absolute zero
      simple have no meaning.’
      / Steven Weinberg. The Nobel Prize in Physics 1979 /
      #
      “‎In modern physics, there is no such thing as “nothing.”
      Even in a perfect vacuum, pairs of virtual particles are constantly
      being created and destroyed. The existence of these particles
      is no mathematical fiction. Though they cannot be directly observed,
      the effects they create are quite real. The assumption that they exist
      leads to predictions that have been confirmed by experiment to
      a high degree of accuracy.”
      ― Richard Morris
      ============
      " All kinds of electromagnetic waves ( including light"s)
      spread in vacuum . . . . thanks to the vacuum, to the specific
      ability of empty space these electromagnetic waves can exist."
      / Book : To what physics was came, page 32. by R. K. Utiyama. /
      ===========
      Although we are used to thinking of empty space as containing
      nothing at all, and therefore having zero energy, the quantum
      rules say that there is some uncertainty about this. Perhaps each
      tiny bit of the vacuum actually contains rather a lot of energy.
      If the vacuum contained enough energy, it could convert this
      into particles, in line with E-Mc^2.
      / Book: Stephen Hawking. Pages 147-148.
      By Michael White and John Gribbin. /
      ==========

      Delete
  32. Dear Mrs. Hossenfelder:

    I have been of mind that gravity is an emergent force for about thirty five years. And I was extatic when I read of verlinde's theory on that subject. Though it has some problems, Verlinde's theory explaines a lot of things, which the observations of our galaxy are showing us, that conflict with Instein's theory.

    That in itself was enough to keep me from thinking I was crazy for believing gravity was an emergent force. I am very gratful to Verlinde for his theory. As indeed, at times I thought I was crazy for wasting so much time thinking on this.

    On to my thoughts: It is a known fact that gravity effects time, which first made me consider the strong possibility that gravity is an expression of an emergent force generated by dimension, rather than a fundamental force.

    I just thought, gravity dances so well with the dimensions of space and time, because it is closely related to them, and it will not dance at all with the three fundamental forces because it's just not one of them. (a very simple thought)

    Unllike L. Randall's thoughts of gravity being a fundamental force flowing into ours from a higher dimension, I considered that it may be an emergent force generated by a lower dimension.

    With that mind set, I have a question, after I set the premiss for it.


    It is obvious the demensions of time and space have observable and measurable effects; the passing of time, the shadow on the ground, etc...


    But it seems the farther we get away from the third dimension, the less obvious the effects of particular dimensions are. Demonstrating the effect of dimension 1 becomes more difficult than explaining the effects of dimension 2.

    Furthermore, we can only show the effect of dimension 2, or one, or four, when its compaired to the third dimension. We could never observe, or explain any other dimension without comparison to the third. It is only in refrence to each other that we can demonstrate the effect of each seperate dimension has on each other.

    Now to the question: what about dimension 0? Why should it be that dimension 0 has no effect on the others. Why should it be that dimension 0 is nothing more than a mathmatical construct with no real place or purpous, other than in a quaint equation, on a some blackboard, in an obscure university's classroom?

    When I question others about this, like Prof. Tong, I am met with short comments about it being of no significance, other than being a construct of math.

    Frankly I think that is as silly as saying there is no effect a shadow has in expressing reduced tempature.

    It may be it was the third dimension which blockes the tempature causing light of the sun, but it's in the 2D shadow where the effect is measured. And so, I do believe dimension 0 has a real effect on all the other dimensions, in real life. I think it is possible this emergent effect is mistaken for something it is not.

    This effect may be a very weak effect compared to the effects of fundamental forces, but it would still effect higher dimensions, IE light, matter and time.

    Does that sound famillar? :)

    At any rate, I do realize I am most probably wrong about this, given what amounts to the formal fifth grade education I have obtained. But I am also most certain that those who still think gravity is a fundamental force are more wrong than I. They are trying to cram a square peg into a round hole, and that it does not fit should be very obvious to them.

    I say look for the hole into which the peg fits.

    Clearly, gravity and quantum theory are not a match.

    ReplyDelete
  33. I am happy to see comments focused on 0, or absolute vacuuum.
    It is one of the things I like about CCC theory. O has no size constraints, it is both small and large and at the same time.

    I firmly believe understanding the full effects of dimension 0 will give us the answers to the riddle of gravity.

    ReplyDelete
  34. I will assume that your comment was ment to be sarcastisc, not to me, butof the past history of set rules being overturned by new perspectives. After all, it was a fair assumprion that the earth was flat at one point in time.

    I hope folk never forget, science is not about knowing answers, but is about asking questions spawned by our current answers.

    ReplyDelete
  35. Book: ''To what physics was came''
    #
    '" All kinds of electromagnetic waves ( including light's)
    spread in vacuum . . . . thanks to the vacuum, to the specific
    ability of empty space these electromagnetic waves can exist.'"
    / page 32. by R. K. Utiyama. /
    #
    Even the cosmic microwave background radiation (CMBR) - 2,7K -
    - (as a vacuum fluctuations ) can be created from Zero Vacuum: T=0K

    Even all kinds of Gravity (quantum-gravity ---> star-gravity --->
    ---> planet-gravity formation) can be created from Zero Vacuum: T=0K
    ===========

    ReplyDelete
  36. I thought I would find some interesting ideas posted on this blog. But instead, all I have seen are comments that show the poster has 0 real knowledge of physics; to posts that show some small understanding, which is then bloated up with ego in an attempt to play scientist. I see so many silly posts, ranging from the mondane to the insane.

    Repeating old facts one has read in a book is not science. Telling one another how to think is not science. Asking good questions about the answers to previous questions is science.

    So many come here to pretend they are more knowledgeable than they are. Today, one person exclaimed "I have worked for a particle accelerator and their profile stated, "I hold multiple patents" WOW! What an irrevelent thing to say in a post and to place in a profile. Even if true (unlikely) those statements are meaningless.

    Here in the United States, we have a President who behaves that way. He doesn't seem to realize that people see through that ego bloating attitude and the same applies to people who post at this BLOG.

    Just so you all know, it painfully clear that the posts being left here expose the limited education, understanding and intellect of the posters.

    I for one have enough self esteem to admit I don't know everything. I admit I'm looking still for answers. I admit I make typos. I admit other people might know more than I do. I admit I did not come here to impress people with my IQ.

    I came here in the hope of possibly learning something new. It was a hope that, sadly, did not pan out.

    I am asking, please, for the sake of being real, stop all the bovine scatology. I does disservice to Sabine Hossenfelder.





    ReplyDelete
    Replies
    1. Rebelbee3xyz wrote:
      >Repeating old facts one has read in a book is not science.

      Well, actually, very often that is science.

      Science builds on the achievements of past scientists. And, those achievements are often documented in books.

      And, therefore, to communicate science to other human beings, often the best thing to do is to refer them to certain relevant books.

      He also wrote:
      >I came here in the hope of possibly learning something new. It was a hope that, sadly, did not pan out.

      No, and with your attitude it never will.

      Bye.

      Delete
    2. “...to communicate science to other human beings, often the best thing to do is to refer them to certain relevant books.” And precisely what else than humans might be of concern to the matter? Therefore to maintain such exclusivity, we’d suggest “... books not written by dragons.”

      Delete
    3. Emmette wrote to me:
      >Therefore to maintain such exclusivity, we’d suggest “... books not written by dragons.”

      Ah, but why rule out dragons as long as they understand the physics?

      Delete
    4. Rebelbee3xyz: BS indeed, but with deference to our esteemed host, and not to forget that certain Virginia gentleman who never rode in a plane, it seems fully half of the unconscious collective rather prefers SH (albeit transposed), as said equestrian among many other rebellious things once secretly warned a co-conspirator of finding diamonds in hills of it (ostensibly irrespective of flavor). And too there was that certain son of father of rebels of another sort* who on tape no less assured -- or asserted or pontificated or bloviated or whatever it is that (high priests and) bothersome physicists do to be believed -- that boosting the noise can clarify the signal. And twice too, everybody’s always known the rebel needle is to be found in a haystack. That’s three clear clearly relevant references; imagine that! So, as advocate for the advancement of your peculiar rebelgod’s asserted quantum totality, it would seem you should persevere in your relished quest of that elusive gem, even through and in awe of this our esteemed’s spot made to gather and hide it.

      Delete

  37. I want to ask a couple of very humble questions.

    My question is this. Does dimension 0 have any effect on other dimensions, in a real way?

    If your answer in NO, it does not, please expand on the logic behind that conclusion, again, moving past a repititon of what dimension 0 is.

    If your answer is yes, please explain that logic as well.

    I am not asking for solid answers to such a difficult question to answer, but rather some imaginitive points of view that might further inspire my own. I am very focused on the idea that 0 might have a real world effect on the other dimensions, which does not make it so, but does seem to be a question worth asking.

    Secondly, back in grade school I learned a fact that other than a sphear, the triangle is the only geometrical shape, when pinned together at the apex, is stable and will not collaps when pressure is applied at any point. The sphear, or circle, having no apex, is also stable. But I realized that a sphear can, like the triangle, be fully discribed with a triad: radius, diameter, circumference. Then I realized, so to, a wave can be described fully with a triad... frequency, length, and amplitude. Then I found out that white light is made up of three seperate colors, Red, Blue, and green. Then I remembered atoms were constructed of three smaller things called electrons, neutrons and protons. Then I read that protons and neutrons were each made of three smaller things called quarks, and that there were three kinds of quarks and three kinds of anti-quarks.

    As years went by, I compiled a list of hundreds of natural things nature had constructed which came in threes. Time, for instance, can be fully described as having three parts, past, present, future.

    But back in grade 5, I had asked myself, is there anything in the univers which is not matter, energy, or force? (3)

    On and on my list went with occurences of nature using three things by which to construct something.

    I am not compulsive about the #3, as Tesla was, but I am fascinated by the number of times the #3 occurs when nature constructs something; like a wave of light, or a proton, or time, and on and on. Even the process of logic involves three steps.

    Like the golden ratio, there is clearly something ubiquitous about the number thee in nature and it's rarely spoken of. That got me to thinking...


    Maybe that has something to do with why gravity does not play well with the fundamental forces that hold matter together.

    I thought perhaps gravity is not a fundamental force like the strong, weak and nuclear forces. And I thought, does matter need gravity at a fundamental level? Aren't the three other forces enough to hold an atom and it's constituent parts together?

    I thought perhaps gravity is not a fundamental force. Maybe gravity belongs in another group like the group of dimensions. Maybe thats why gravity and time dance so well together, because they belong to the same group. (SPACE, TIME, GRAVITY.)

    To be clear, this is only a thought, hardly a claim of fact. But Verlinde has given some evidence to showing that indeed, gravity is an emergent force, and not a fundamental one. I was extatic to hear about that, because since grade five, in 1968, I had thought that to be the case.

    It was about 1990 when I first considered the possibility that gravity was an emergent effect of dimension 0 which had not been examined. (noting my original question)

    So to sum all this up, I am simply curious if there is a relationship between gravity and dimension 0, creating a stable construct of space, time, and gravity.

    Notice I used no equations to express my thoughts. I do not seek equations. What I seek is some imagination on this subject. I seek good questions to ask.



    ReplyDelete
  38. Black hole that 'rings' like a bell shows Einstein was right
    16 September 2019
    By Leah Crane
    https://www.newscientist.com/article/2216409-black-hole-that-rings-like-a-bell-shows-einstein-was-right/
    #
    The black hole . . . ''is based on the no hair theorem''
    . . . but . . .
    But . . . '' measurements should allow physicists
    to nail down whether black holes have hair. ''

    https://www.newscientist.com/article/2216409-black-hole-that-rings-like-a-bell-shows-einstein-was-right/

    It seems ''black hole'' needs a good Barber with Occam's razor
    =======

    ReplyDelete
  39. This comment has been removed by the author.

    ReplyDelete
  40. So weary of this back and forth, please stop.

    ReplyDelete

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