Having said that, you can of course hypothesize Planck scale effects that do not respect Special Relativity and then go out to find constraints, because maybe quantum gravity does indeed violate Special Relativity? There is a whole paper industry behind this since violations of Special Relativity tend to result in large and measurable consequences, in contrast to other quantum gravity effects, which are tiny. A lot of experiments have been conducted already looking for deviations from Special Relativity. And one after the other they have come back confirming Special Relativity, and General Relativity in extension. Or, as the press has it: “Einstein was right.”

Since there are so many tests already, it has become increasingly hard to still believe in Planck scale effects that violate Special Relativity. But players gonna play and haters gonna hate, and so some clever physicists have come up with models that supposedly lead to Einstein-defeating Planck scale effects which could be potentially observable, be indicators for quantum gravity, and are still compatible with existing observations. A hallmark of these deviations from Special Relativity is that the propagation of light through space-time becomes dependent on the wavelength of the light, an effect which is called “vacuum dispersion”.There are two different ways this vacuum dispersion of light can work. One is that light of shorter wavelength travels faster than that of longer wavelength, or the other way round. This is a systematic dispersion. The other way is that the dispersion is stochastic, so that the light sometimes travels faster, sometimes slower, but on the average it moves still with the good, old, boring speed of light.

The first of these cases, the systematic one, has been constrained to high precision already, and no Planck scale effects have been seen. This has been discussed since a decade or so, and I think (hope!) that by now it’s pretty much off the table. You can always of course come up with some fancy reason for why you didn’t see anything, but this is arguably unsexy. The second case of stochastic dispersion is harder to come by because on the average you do get back Special Relativity.

I already mentioned in September last year that Jonathan Granot gave a talk at the 2014 conference on “Experimental Search for Quantum Gravity” where he told us he and collaborators had been working on constraining the stochastic case. I tentatively inquired if they saw any deviations from no effect and got a head shake, but was told to keep my mouth shut until the paper is out. To make a long story short, the paper has appeared now, and they don’t see any evidence for Planck scale effects whatsoever:

A Planck-scale limit on spacetime fuzziness and stochastic Lorentz invariance violationWhat they did for this analysis is to take a particularly pretty gamma ray burst, GRB090510. The photons from gamma ray bursts like this travel over a very long distances (some Gpc), during which the deviations from the expected travel time add up. The gamma ray spectrum can also extend to quite high energies (about 30 GeV for this one) which is helpful because the dispersion effect is supposed to become stronger with high energy.

Vlasios Vasileiou, Jonathan Granot, Tsvi Piran, Giovanni Amelino-Camelia

What the authors do then is basically to compare the lower energy part of the spectrum with the higher energy part and see if they have a noticeable difference in the dispersion, which would tend to wash out structures. The answer is, no, there’s no difference. This in turn can be used to constrain the scale at which effects can set in, and they get a constraint a little higher than the Planck scale (1.6 times) at high confidence (99%).

It’s a neat paper, well done, and I hope this will put the case to rest.

Am I surprised by the finding? No. Not only because I knew the result since September, but also because the underlying models that give rise to such effects are theoretically unsatisfactory, at least for what I am concerned. This is particularly apparent for the systematic case. In the systematic case the models are either long ruled out already because they break Lorentz-invariance, or they result in non-local effects which are also ruled out already. Or, if you want to avoid both they are simply theoretically inconsistent. I showed this in a paper some years ago. I also mentioned in that paper that the argument I presented does not apply for the stochastic case. However, I added this because I simply wasn’t in the mood to spend more time on this than I already had. I am pretty sure you could use the argument I made also to kill the stochastic case on similar reasoning. So that’s why I’m not surprised. It is of course always good to have experimental confirmation.

While I am at it, let me clear out a common confusion with these types of tests. The models that are being constrained here do not rely on space-time discreteness, or “graininess” as the media likes to put it. It might be that some discrete models give rise to the effects considered here, but I don’t know of any. There are discrete models of space-time of course (Causal Sets, Causal Dynamical Triangulation, LQG, and some other emergent things), but there is no indication that any of these leads to an effect like the stochastic energy-dependent dispersion. If you want to constrain space-time discreteness, you should look for defects in the discrete structure instead.

And because my writer friends always complain the fault isn’t theirs but the fault is that of the physicists who express themselves sloppily, I agree, at least in this case. If you look at the paper, it’s full with foam, and it totally makes the reader believe that the foam is a technically well-defined thing. It’s not. Every time you read the word “space-time foam” make that “Planck scale effect” and suddenly you’ll realize that all it means is a particular parameterization of deviations from Special Relativity that, depending on taste, is more or less well-motivated. Or, as my prof liked to say, a paramterization of ignorance.

In summary: No foam. I’m not surprised. I hope we can now forget deformations of Special Relativity.

## 58 comments:

"Having said that, it might come as a shocker, but I'm not actually opposed to the idea that a fundamental toe might have something to say about consciousness."I'm not sure, but maybe it could help us at least get a foot in the door. :-)

Hi Bee,

Just a short remark ---

"And please note that I didn’t say quantum gravitational effects “at short distances” because that is an observer-dependent statement and wouldn’t be compatible with Special Relativity."

When QG people talk about "short distances" they mean distances between *spacetime* events, i.e. a distance in 4D. Which is of course an invariant. And "short" usually means "somewhere around Planck length", where the Planck length is also an invariant.

It would be naive, at least in QG communities, to assume that people who use such phrases are ignorant of special relativity. :-)

vmarko,

The wavelength in question here is a component of a four-vector ("distance") and not a length of a four-vector (which would be a scalar). Now we can debate who is or isn't part of what you think is the "QG community", but I don't share your impression. Just look at foamy paper. Besides this, what you say doesn't make any sense to me. Are you sincerely trying to tell me that it is common among QG people to think that quantum gravitational effects become important at space-time invals of less than a Planck length? Which would be the case for anything on lightcones? The only case in which that is true to some extent I think are causal sets. I maintain that the standard thinking in the QG community is that effects become strong at Planckian curvature, which doesn't a priori have anything to do with distance. Best,

B.

Correction: It is actually the wave-vector which is a four-vector, but I think you know what I mean.

Euclid? Non-Euclidean cartography. Newton? Non-Newtonian cyclotrons, atomic spectroscopy, Mercury's orbit. Curve-fittings flag defective founding postulates. Massless boson photons detect no vacuum refraction, dispersion, dissipation, dichroism, or gyrotropy. Postulate

exactvacuum isotropy toward fermionic matter (quarks, hadrons). Parity violations, symmetry breakings, chiral anomalies, baryogenesis, Chern-Simons repair of Einstein-Hilbert action are vacuum trace chiral anisotropy acting only upon hadrons.Test for it, DOI: 10.5281/zenodo.15107. A two-page paper cannot be funded,

Phys. Rev.105(4) 1413 (1957) until after it is published.http://www.npl.washington.edu/eotwash/results

There is always another decade/decade of funding if you fail.

Is quantum foam the same as spin foam? Does this experiment rule out loop quantum gravity?

Marc,

Did you actually read what I wrote? First, I told you that the "foam" they talk about isn't well defined at all. It's neither quantum foam nor spin foam, and in fact the spin foam is the only foam I know which is well-defined but this is definitely NOT what the paper is about.

Second, as I wrote, these effects have not been derived from LQG, nor from any other approach to quantum gravity. Consequently, you can't rule out LQG with it. Best,

B.

I just read it again. I must had been sleepy the first time, sorry.

This is a real question about true physics :-)

This article leads me to this question : what about the possibility of the existence of a complete quantum field theory. The problem is, if I am not mistaken, the quantification of the Lorentz transformation which appears formally uncomputable. If the quantum Lorenz transformation is necessary because the universe uses it and that it is indeed formally uncomputable should we losing all hope of a complete quantum field theory ?

Is ok :) I didn't quite mean to be as unfriendly as it might have come across, sorry.

What about the QED fuzziness? It's quite odd to suppose plank fussiness before considering self interaction effects of the photon.

It's nothing, I always find this blog amazing and your patience remarkable. I understand that you can have the question of the reality sensitive. I hit the chord here (or the string).

Daniel,

Well the photon doesn't self-interact, at least not at tree-level. Yes, sure, people are looking for photon-selfinteractions (box diagrams), but it's a different story and not topic of this blogpost. Not sure what you're trying to say there. Best,

B.

Nicolas,

I don't know what you mean with 'quantum Lorentz transformation'. Lorentz transformations in quantum field theory are quite well understood. Do you mean the deformed Lorentz-algebras (that have been argued to be related to the "foam" in this paper)? These are sometimes referred to as "quantum deformations", but that doesn't make them uncomputable. And even if, I don't see how it matters. In some sense any prediction is strictly speaking "uncomputable" if you want to know it to infinite precision which in practice isn't possible. In practice you settle for finite precision, and that's computable enough.

(My previous comment that appeared at the same time as yours was actually meant for Marc.)

Best,

B.

Wheeler on his foam

Hi Bee,

"The wavelength in question here is a component of a four-vector"

I agree with that, my remark was only about your general statement regarding small distances. :-)

"Are you sincerely trying to tell me that it is common among QG people to think that quantum gravitational effects become important at space-time invals of less than a Planck length? Which would be the case for anything on lightcones?"

Well, ok, *spacelike* intervals of Planck size.

The prototype example of what I mean would be CDT --- a piecewise-linear Regge-like triangulation of spacetime with Planck-sized edges. When we look at large distances we see smooth spacetime, while at distances comparable to Planck length we see a PL structure. This has observable consequences: it imposes a cutoff on rest-energy (i.e. mass) for any matter field living in such a spacetime. Even in low curvature. Though technically on a PL manifold the curvature is actually zero inside the simplices and infinite on the faces, so you could argue that this is also a high-curvature effect...

A PL-manifold structure (or something similar to it) is common to CDT, quantum Regge models, spinfoam models, etc. And it is of course fully Lorentz-invariant. :-)

Try to think about this: if the speed of photons would depend on their wavelength, then the photons would be massive. If the photons would be massive, they would attract each other and they would travel inside of gamma ray burst as a single body. After then their arrival times wouldn't differ anyway - and this is IMO what we are observing by now.

Zephir,

The photons are not massive in the models under question here. Yes, massive photons also have a dispersion, but for that you don't need to modify Special Relativity. Photon masses are extremely tightly constrained, not because photons would gravitationally attract each other but because a photon mass term breaks gauge invariance. Best,

B.

vmarko:

So when you say "QG community" you mean "the three of us who work on CDT"? Well, for all I know the point of CDT is to let the lattice spacing got to zero. And if you're talking about space-like intervals of Planck-length, that too breaks Lorentz invariance. So does a cutoff on energy. Are you really saying that CDT results in this? That would surprise me because I haven't heard of it before. Of course they must have some intermediate course-graining structure, but I thought in the end it's supposed to go away. I have had several conversations with people about this and the answers were pretty ambiguous, in a nutshell: they didn't know whether the discretization will leave observable effects in terms of a 'minimal length' or modified dispersion relation. Best,

B.

Hi Bee,

"And if you're talking about space-like intervals of Planck-length, that too breaks Lorentz invariance."

I don't see where you get this from. Being either spacelike, timelike or lightlike, an interval is a Lorentz scalar, and therefore invariant.

The most elementary example is the flat Minkowski spacetime, triangulated using simplices with spacelike edges. I really don't see how that structure can break Lorentz symmetry of the Minkowski space, given that the length of every edge is an invariant. Also, curved PL manifolds are essentially the same thing, except that Lorentz invariance is only piecewise-local, rather than global (as one would expect in a curved space).

It appears we are talking past each other here. I really fail to understand why you think there is any breaking of Lorentz symmetry in these situations. Care to explain please?

vmarko,

I think I just misunderstand what you mean with space-like 'interval'. Do you mean a space-like vector (distance between points), or do you mean the length of that vector? I gather from your comment now that you actually mean the length of the vector, which I wouldn't call an interval, but anyway.

That the length of a space-like edge is invariant is of course true, but that doesn't mean the edges themselves are invariant! The structure you describe breaks Lorentz-invariance because the edges also have an orientation. If you boost the thing, the distribution of direction changes. It has to - the only way to avoid this is to only deal with points (which is what the CS people do). CDT has a slicing, that's another way to put it.

Best,

B.

" if the speed of photons would depend on their wavelength, then the photons would be massive. If the photons would be massive, they would attract each other and they would travel inside of gamma ray burst as a single body. After then their arrival times wouldn't differ anyway - and this is IMO what we are observing by now."No. Your argument doesn't hold up qualitatively. In a medium (i.e. not in vacuum), the speed does depend on wavelength, but this doesn't mean that the photons are massive. Certainly they don't attract each other so that all travel at the same speed. In other words, just because you have dispersion doesn't necessarily mean that photons are massive. Perhaps a better analogy: neutrinos are massive, and bursts of neutrinos from supernovae show dispersion. The neutrinos don't attract each other enough to cancel the dispersion.

Hi Bee,

By a "spacetime interval" I mean the quantity :-)

l(x,y) = sqrt(g_mn (x^m-y^m)(x^n-y^n))

where g is the Minkowski metric, while x^m and y^m are the coordinates of the two points, respectively. The quantity l is known by various names --- distance, interval, length of a vector from x to y (or y to x), norm of that vector, etc. But I'm not into discussing terminology.

However, I am actually surprised that you are discussing orientation of the edges in a triangulation. I've never seen that being introduced in any triangulation context (starting from Regge gravity, and onwards). Let alone for what purpose would edge orientations be useful. That said, sure, I don't see any obvious way to introduce orientations on spacelike edges in a Lorentz-invariant way. But I don't see them introduced anywhere to begin with, either.

A typical triangulation is constructed like this: sprinkle your manifold with some points, connect them suitably using (nonoriented) lines (perhaps only spacelike) so that they form simplices, and require the interior of every simplex to be flat. That's a PL manifold. No orientation of edges, unless you *want* to introduce them (and break Lorentz symmetry by doing that).

Do you have any reference to some example paper where edges have been oriented on a manifold triangulation? In what context would such orientations be useful? The closest example I can think of is the causal structure in causal set theory, but that is (a) not a triangulation, and (b) orientations have timelike character, which is not disturbed by boosts (and thus the structure is Lorentz invariant). Any other example?

vmarko,

You don't get a triangulation by sprinkling, the problem is the connection. You write

"connect them suitably using (nonoriented) lines (perhaps only spacelike) so that they form simplices"

There is no way to do this in a Lorentz-invariant way, not unless you want to end up with a space-filling "triangulation" which isn't really a discretization any more.

I'm not much into triangulations, but why should I give you a reference? You are the one claiming that something impossible is possible, so please show me ANY triangulation that is Lorentz-invariant. I don't know of any, and I am very sure it doesn't exist. (In fact, I've meant to write up a formal proof for this, but kind of haven't come around to do it. I don't think it's difficult.) Best,

B.

Hi Bee,

"show me ANY triangulation that is Lorentz-invariant"

Ok. Take a simple 1+1D flat Minkowski plane, with metric signature (-,+). Pick a coordinate system, and three points a=(0,0), b=(1,2), c=(0,4). Connect them with straight lines, to get a triangle. Calculate the lengths of the three lines:

l(a,b)=l(b,c)=sqrt(3),

l(a,c)=4.

Thus the three lines are spacelike (by construction). Then add another point d=(2,7), and connect it to b and c via straight lines. The lengths are l(b,d)=sqrt(24), l(c,d)=sqrt(5). They are also spacelike, and they form another triangle (b,c,d) adjacent to (a,b,c). Continue adding points like this until you fill the whole Minkowski plane with triangles. This defines a triangulation. Note that there is no orientation introduced for the lines connecting the points.

You can verify that a boosted observer sees different coordinates for points a,b,c,d..., using Lorentz transformations to calculate new coordinates from old. But he can still construct the same triangles between the points by connecting the same pairs of points with straight lines. Moreover, he calculates the very same lengths of those lines, so the whole set of triangles that he sees is completely identical to what the original observer sees. Both observers agree on values of edge lengths, triangle areas, angles between edges, etc., because all these properties are expressible as functions of edge lengths, which are invariant by definition. That's why the triangulation is said to be Lorentz invariant.

That's my example. Now please show me what in the above construction singles out any preferred reference frame, and thus breaks the Lorentz SO(1,1) symmetry.

vmarko:

Calculate average distance of points projected on x-axis. Boost. The average distance changes. Ergo, an observer can figure out the difference. It's not observer-independent. I think you're not really understanding the problem. Best,

B.

vmarko:

I think you're confusing Lorentz-invariance with Lorentz-covariance. Any triangulation can be trivially made Lorentz-covariance. But not Lorentz-invariant.

Hi Bee,

"Calculate average distance of points projected on x-axis. Boost. The average distance changes."

Sure, but that's not a property of the triangulation. Rather, it's a property of the projection of the triangulation on some specific hypersurface (the x-axis). It is clear that the boost will change the average, because the boost changes the choice of the x-axis. But not because the boost changes the triangulation itself --- it doesn't.

I don't find your argument convincing. You were talking about a proof that a Lorentz-invariant triangulation is impossible. You asked for a counterexample, and I provided one. Now you seem to be moving the goalposts from "invariant triangulation" to "invariant projection of a triangulation on a non-invariant hypersurface". That's not the same thing, sorry.

Also, I'd say that the triangulation itself is Lorentz-invariant, while its projection on a hypersurface is only Lorentz-covariant. I don't think that I'm the one confusing these two notions. :-)

vmarko:

"I don't find your argument convincing. You were talking about a proof that a Lorentz-invariant triangulation is impossible. You asked for a counterexample, and I provided one. Now you seem to be moving the goalposts from "invariant triangulation" to "invariant projection of a triangulation on a non-invariant hypersurface". That's not the same thing, sorry."

When I say "invariant", I mean "invariant", period. If you are claiming a triangulation is invariant, then ALL of its aspects must be invariant. You claimed that is possible.

Your construction does, as a matter of fact, single out preferred observers. I have told you expliclity how so. This breaks Lorentz-invariance. End of story.

"It is clear that the boost will change the average, because the boost changes the choice of the x-axis. But not because the boost changes the triangulation itself --- it doesn't."

Sure it's clear, that's what I've told you all along. It's obvious that it's not possible, you just didn't want to believe it.

Of course it doesn't change the triangulation (if it's a passive boost), but that's entirely irrelevant. If you boost any preferred slicing that doesn't change the slicing, but that's not the point. The point is that there is only one reference frame (one boost) that brings the slicing into a specific desired form. That's the very essence of observer-dependence. It expliclity breaks Lorentz-invariance. And once again, you're confusing Lorentz-invariance with Lorentz-covariance.

According to your logic, any square lattice is "Lorentz-invariant" which is obviously wrong. Before you produce more fog, please go and look it up.

Best,

B.

/* Photon masses are extremely tightly constrained..because a photon mass term breaks gauge invariance */

This looks like serious error... :-(

Which experiment would be violated with it, for example? And are we still talking about mass of real photon or about rather abstract rest mass of photon?

The combination of the contents of this post and the picture of Einstein made me laugh (that is, they went together well, not that the picture by itself made me laugh), and I don't laugh much these days (what with the Middle East problems, economic problems, environmental problems, and the political silliness and worse in dealing with them). Thank you!

Zephir,

The mass of the photon is the rest mass of the photon, if that's too "abstract" for you, then maybe physics isn't the right field for you. As to constraints, ask Wikipedia, it is quite well organized on that matter. Best,

B.

/* The mass of the photon is the rest mass of the photon, if that's too "abstract" for you, then maybe physics isn't the right field for you */

Does it imply, that the photon always remains at rest? Just asking, 'cause I'm a dull person, who is only tangentially interested about physics.

Great article,

The one thing that I've been wondering about is the distinction between the quantum foam mentioned in this article and the vacuum energy that you discussed in the previous article. I've always assumed that "quantum foam" conveyed a similar idea as vacuum energy, independent of whether or not it affects the speed of photons at different wavelengths.

You said at the end that there is no foam. Does this mean that there really is no roiling sea of energy at the foundation of space-time, or do you mean that "there is no foam that appreciably affects the propogation of light through space"?

Any help would be greatly appreciated!

Zephir,

The photon for all we presently know doesn't have a rest mass. If it had a rest mass it would be rest in the rest frame. It would of course not be at rest in all frames. Besides this, you could easily have answered this question with Google and I would appreciate if you tried this first the next time. Please make a little effort before clogging my comment section with unnecessary questions, will you? Best,

B.

Hi Bee,

"When I say "invariant", I mean "invariant", period. If you are claiming a triangulation is invariant, then ALL of its aspects must be invariant. You claimed that is possible."

Again, the projection of the triangulation on a hypersurface is not an aspect of the triangulation, but an aspect of the hypersurface. The fact that the hypersurface itself is not Lorentz-invariant has nothing to do with the invariance of the triangulation.

"Your construction does, as a matter of fact, single out preferred observers. [...] The point is that there is only one reference frame (one boost) that brings the slicing into a specific desired form."

A triangulation does not necessarily have any preferred slicing. I don't see where you get that from.

If a triangulation is special in the sense that it does have large-scale preferred directions, slicings, etc., that merely indicates the presence of global symmetries. And this has nothing to do with Lorentz invariance (I assumed throughout that we are talking about *local* Lorentz invariance here, because global is already known to be broken in ordinary GR). But a generic triangulation doesn't have any global symmetries, unless you purposefully build them in.

"According to your logic, any square lattice is "Lorentz-invariant" which is obviously wrong."

A square lattice is a very special structure, that has large-scale preferred directions. As I said above, that means it has global symmetries, which have nothing whatsoever to do with Lorentz invariance.

So yes, I claim that even a square lattice is in fact Lorentz invariant, and in addition it has one large periodic discrete global symmetry. I don't see that claim being "obviously wrong" in any sense.

I assume you understand that global and local symmetries are not the same thing.

Hi Bee,

"Before you produce more fog, please go and look it up."

Bee, this is uncalled for. I don't see the purpose for ad hominem in a serious discussion.

What is happening here? I have a feeling that I have defeated your opinion on Lorentz invariance of triangulations, and now you are becoming increasingly more brash, in order to shut me up or something. This is your blog and you can do whatever you want (including denigrating others), but this is unfair IMO.

I challenged your statement that spacetime triangulations break Lorentz invariance. You first invoked edge orientations as an argument. After I pointed out that orientations are unnecessary, you conjecture a hypothetical proof against invariance, and ask for a counterexample. After I provided it, you start talking about projecting the lattice on a subspace. After I point out that this has nothing to do with the triangulation itself, you come up with a square lattice and the issue of global symmetries, which are also a red herring and have nothing to do with Lorentz invariance.

And then you finish with a disparaging ad hominem comment.

I study spacetime triangulations for a living, it's my daily job and my main research area, in contrast to you (your own statement: "I'm not much into triangulations"). If I were to say something on the lines of "You know, I'm not so much into QG phenomenology, and I don't care to give any references to back up my claims, but Bee, your arguments are all wrong, go read up on some QG phenomenology and stop producing fog.", how would you feel about it?

You repeatedly accuse me of confusing Lorentz invariance with Lorentz covariance. But from where I stand, it is you who is confusing Lorentz invariance of a spacetime lattice with:

(a) lack of invariance of unnecessary structures like edge orientations,

(b) lack of invariance of hupersurfaces,

(c) potential existence of global symmetries.

Given that you're a serious scientist, knowledgeable in relativity, I would expect that you know better than to confuse these things.

I think I've made my point for any physics-educated reader who can think for themselves. You have produced nothing but a bunch of red herrings as your arguments, and I don't see your critique of triangulations holding any water whatsoever. As for the ad hominem stuff, I expected that your scientific expertise comes with some ethical and social integrity as well. If I was wrong to expect this, I don't want to continue discussing with you any more.

vmarko:

You should go and look up "ad hominem" because you don't seem to understand what it means.

What I have told you is simply that you are wasting my time and that I would appreciate you would first look up what I said.

"So yes, I claim that even a square lattice is in fact Lorentz invariant,"

This is just plainly wrong, and I have already told you why. It clearly has a preferred frame, ergo Lorentz-invariance is broken.

"Again, the projection of the triangulation on a hypersurface is not an aspect of the triangulation, but an aspect of the hypersurface."

It is an aspect of the relation between the triangulation and the hypersurface - that's exactly the reason why it breaks Lorentz-invariance. If it was Lorentz-invariant, then this aspect shouldn't depend on the hypersurface.

"I study spacetime triangulations for a living, it's my daily job and my main research area"

Worst thing I've heard all day. For the sake of quantum gravity, Marko, go and ask somebody about this, since you obviously don't want to believe me. There is no known triangulation of Minkowski space that is Lorentz-invariant. I have told you why, but you don't want to buy it.

"If I were to say something on the lines of "You know, I'm not so much into QG phenomenology, and I don't care to give any references to back up my claims, but Bee, your arguments are all wrong, go read up on some QG phenomenology and stop producing fog.", how would you feel about it?"

That, in fact, is an ad hominem attack. I'm done with this pointless discussion, further comments of yours will be deleted.

Thanks,

Sabine

I'm just making my own model, which features, among other exciting concepts, string orbit scalar intermodulation. Find me on facebook, to learn more about The Big Drag and the semiconductive quantum circuit of the fractal multiverse. peace Paul Adamson friend requests welcome

There's a point of QG discussions that I've never really understand so, i make the question:

As far as I understand the quantization belong by h. h has the dimension of the angular momentum. Why than it is so important to quantizy the space?

Is the space to be quantizied or the space-time?

I'm quite confused...

Of course if it is not too long...

Nemo:

h has the dimension of an action. It appears in the path integral. You have to quantize gravity because it couples to matter which we already know is quantized, and nobody knows how to consistently couple an unquantized to a quantized theory.

That's the short answer. This reminds me though I meant to write a blogpost about the question "why quantize gravity", so you'll get a longer answer then :) Best,

B.

Thank you very much Sabine. I'll read it!

I read it.

I understand why we should understand what happen to gravity at quantum level, but what I do not understand is why to reach the goal we should quantize the space.

Yes, I read that there's a big problem with the singularity and the information paradox, but I'm strangling with the idea of a bended space-time that is something really very different from what we experience every day about space and time.

Someone argued that time or space and time could be emergent property of our universe, but is it really the problem?

To say that gravity is an emergent property is not equivalent to argue about space and time.

General relativity give us a wonderful tool to study the Nature in a precise way, but to me space-time looks very abstract indeed to me.

To tell a story is not the same thing to make a story. No matter how precise you are.

All what we can measure is relevant to the quantum world. We can mesure the properties of the fundamental particles but what about space and the time?

The space and the time are something we use to make the measurements, but how to measure something that is used to measure?

P.S.

strangling = struggling :-D

Nemo:

A-ha-ha, you're right, I already wrote that. I was thinking it sounded kind of familiar...

You don't have to quantize space and/or time. I refer by 'quantum gravity' as anything that resolves the known inconsistencies in our theories. You also shouldn't confuse the quantization of the metric with the quantization of space itself.

Every measurement is a measurement of something by help of something else.

Hi Bee,

I agree with you that there is no sprinkling of points in a Lorentzian space-time that looks identical in all inertial frames. That is, there is always something which distinguishes one frame from the rest.

What I'm wondering is - is there are "fibration" of Lorentzian spacetime - a sprinkling of null geodesics that is Lorentz-invariant?

Thanks!

-Arun

^^^ no countable sprinkling of points. I suppose all bets are off on uncountable sets.

Dear Arun,

You're misunderstanding me. There is a (locally countable) Lorentz-invariant sprinkling, see

http://arxiv.org/abs/gr-qc/0605006

The point I was making is that you cannot make this into a network (ie connect points) without making this network locally space-filling. It works for points because points are trivially already Lorentz-invariant, whereas anything of dimension 1,2,3 is merely Lorentz-covariant. Best,

B.

Great article,

The one thing that I've been wondering about is the distinction between the quantum foam mentioned in this article and the vacuum energy that you discussed in the previous article. I've always assumed that "quantum foam" conveyed a similar idea as vacuum energy, independent of whether or not it affects the speed of photons at different wavelengths.

You said at the end that there is no foam. Does this mean that there really is no roiling sea of energy at the foundation of space-time, or do you mean that "there is no foam that appreciably affects the propogation of light through space"?

Any help would be greatly appreciated!

Hi Pete,

Yes, good point, sorry for being vague. What I meant was "there is no evidence for space-time foam that appreciably affects the propagation of light through space."

Regarding the vacuum energy - different foam, if you wish, it's basically the fluctuations in the other fields that contribute to the vacuum energy (or rather: should contribute). Best,

B.

Thanks, Bee, for setting me straight!

So, if I attempted to do a computation by first discretizing Minkowski space with a sprinkling, and then try, e.g., to approximate a derivative by a finite difference of values between "neighboring" points, I would find I have to deal with an infinity of "neighboring" points?

I find it very counterintuitive that in the continuum case, I have open sets that allow me to define derivatives, etc., but when I do a sprinkling, the open sets inherited by the sprinkling from the continuum are useless. But I have very little doubt that I'm not thinking about this in the right way. Maybe one day I'll get it (so speaks the eternal optimist) :)

-Arun

Thanks for the answer Bee. Much appreciated!

Arun,

The problem, in a nutshell, is that there is no Lorentz-invariant way to find a "neighbor" that does not lead to a space-filling network. I think I will actually write this up at some point and put it on the arxiv.

First, notice that the Causal Sets people have a procedure to find a "neighbor" (which leads to what they call "chains", that are paths of particles, essentially), but these take a momentum vector as input, ie they have by construction a preferred direction.

Now if you want to pick neighbors in a way that preserves Lorentz-invariance, then the problem is that the Lorentz-group isn't compact, which is another way of saying that the "neighbor" point that you picked has probability one to be arbitrarily close to the lightcone, and is thus at infinite spatial distance (in any coordinate system.

Now if you boost something of infinite length that's pretty much on the lightcone, it's indeed Lorentz-invariant, but now the problem is you've filled up space with infinitely many infinitely long lines. Now take any finite box and count the number of connections that pass through it, and you'll get infinitely many. Ie, the thing isn't locally finite any more.

This conclusion btw doesnt't depend on the exact form of the sprinkling at all.

Best,

B.

Hi Bee,

I understand what you wrote, I think. If you write up for arxiv, that would be really good, I always have a fighting chance of understanding what you write.

I know this is a bit of a leap, perhaps over a cliff, doesn't it suggest that analyticity of functions in Minkowski space puts stronger conditions on the function than in Euclidean space? I know, e.g., Yvonne Choquet-Bruhat, Cecile DeWitt-Morette, Analysis, Manifolds and Physics, Part 1: Basics, makes it kind of trivial (and defies my intuition so I gave up).

Thanks!

-Arun

Arun,

You mean in terms of convergence radius? Yes, could be. Interesting thought. Best,

B.

I think this article may be of some relevance to the above discussion. arXiv:1502.04320

Best,

D

I know this is dated - the discussion ended a while ago. But I'm still not sure which side of the coin I agree with regarding the triangulation of spacetime. I think the point that was argued boils down to the definition of "Lorentz invariance." Now, Lorentz covariance is well defined, but I think Lorentz invariance is not as well defined. I think the definition that should be used is "something that doesn't change under a Lorentz transformation." Easy enough. So to determine whether or not a triangulation is Lorentz invariant, we have to ask ourselves how we define the triangulation itself. If we define it relative to specific coordinates, clearly it is not Lorentz invariant. However, if we define it as the graph connecting a set of points (whose distribution

isLorentz invariant), then I would think that we can say it is Lorentz invariant - as was mentioned, all of the quantities that the graph itself cares about (not the points) should be Lorentz invariant.Thoughts? I'm new to this area, I just think that before any serious discussion takes place, definitions need to be agreed upon.

Sam,

Partly in response to the comments here, I wrote this paper, in which I have stated all definitions. It is especially meant for newcomers, so please have a look, I hope it will answer your questions.

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