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| Logo of site by name loop insight. The insight to take away is that you have to carefully look for those infinities |
The Unruh effect is the predicted, but so-far not observed, particle production seen by an accelerated observer in flat space. It is a result obtained using quantum field theory and does not include gravity, and the particles are thermally distributed with a temperature that is proportional to the acceleration. The origin of the particle production is that the notion of particles, like the passage of time, is observer-dependent, and so what is Bob’s vacuum might be Alice’s thermal bath.
The Unruh effect can be related to the Hawking effect, that is the particle production in the gravitational field of a black hole, by use of the equivalence principle. Neither of the two effects has anything to do with quantum gravity. In these calculations, space-time is treated as a fixed background field that has no quantum properties.Loop Quantum Gravity (LQG) is an approach to quantum gravity that relies on a new identification of space-time degrees of freedom, which can then be quantized without running into the same problems as one does when quantizing perturbations of the metric. Or at least that’s the idea. The quantization prescription depends on two parameters, one is a length scale normally assumed to be of the order of the Planck length, and the other one is a parameter that everybody wishes wasn’t there and which will not be relevant in the following. The point is that LQG is basically a modification of the quantization procedure that depends on the Planck length.
In a recent paper now Hossain and Sadar from India claim that using the loop quantization method does not reproduce the Unruh effect
- Absence of Unruh effect in polymer quantization
Golam Mortuza Hossain, Gopal Sardar
arXiv:1411.1935 [gr-qc]
The Unruh effect has not been measured yet, but experiments have been done for some while to measure the non-gravitational analog of the Hawking effect. Since the Hawking effect is a consequence of certain transformations in quantum field theory that also apply to other systems, it can be studied in the laboratory. There is some ongoing controversy whether or not it has been measured already, but in my opinion it’s really just a matter of time until they’ve pinned down the experimental uncertainties and will confirm this. It would be theoretically difficult to claim that the Unruh effect does not exist when the Hawking effect does. So, if it’s true what they claim in the paper, then Loop Quantum Gravity, or its quantization method respectively, would be pretty much ruled out, or at least in deep trouble.
What they do in the paper is that they apply the two quantization methods to quantum fields in a fixed background. As is usual in this calculation, the background remains classical. Then they calculate the particle flux that an accelerated observer would see. For this they have to define some operators as limiting cases because they don’t exist the same way for the loop quantization method. They find in the end that while the normal quantization leads the expected thermal spectrum, the result for the loop quantization method is just zero.
I kinda want to believe it, because then at least something would be happening in quantum gravity! But I see a big problem with this computation. To understand it, you first have to know that the result with the normal quantization method isn’t actually a nice thermal distribution, it is infinity. This infinity can be identified by a suitable mathematical procedure, in which case one finds that it is the zero of a delta function in momentum space. Once identified, it can be factored out, and the prefactor of the delta function is the thermal spectrum that you’ve been looking for. One can trace back the physical origin of this infinity to find it is, roughly speaking, that you’ve looked at the flux for an infinite volume.
These types of infinites appear in quantum field theory all over the place and they can be dealt with by a procedure called regularization that is the introduction of a parameter, the “regulator”, whose purpose is to capture the divergences so that they can be cleanly discarded of. The important thing about regularization is that you have to identify the divergences first before you can get rid of them. If you try to divide out an infinite factor from a result that wasn’t divergent, all you get is zero.
What the authors do in the paper is that they use a standard regularization method for the Unruh effect that is commonly used for the normal quantization, and apply this regularization also to the other quantization. Now the loop quantization in some sense already has a regulator, that’s the finite length scale that, when the quantization is applied to space-time, results in a smallest unit of area and volume. If this length scale is first set to zero, and then the regulator is removed, one gets the normal Unruh effect. If one first removes the regulator, the result is apparently zero. (Or so they claim in the paper. I didn’t really check all their approximations of special functions and so on.)
My suspicion therefore is that the result would have been finite to begin with and that the additional regularization is an overkill. The result is zero, basically, because they’ve divided out an infinity too much.
The paper however is very confusingly written and at least I don’t see at first sight what’s wrong with their calculation. I’ve now consulted three people who work on related things and neither of them saw an obvious mistake. I myself don’t care enough about Loop Quantum Gravity to spend more time on this than I already have. The reason I am telling you about this is because there has been absolutely no reaction to this paper. You’d think if colleagues go about and allegedly prove wrong the theory you’re working on, they’d be shouted down in no time! But everybody loop quantum just seems to have ignored this.
So if you’re working on loop quantum gravity, I would appreciate a pointer to a calculation of the Unruh effect that either confirms this result or proves it wrong. And the rest of you I suggest spread word that loop quantum gravity has been proved wrong, because then I’m sure we will get a clarification of this very very quickly ;)
That's a very interesting subject!
ReplyDeleteThere's also this paper that seems to put out of play LQG e for which I don't heard anything from LQG theorists: http://journals.aps.org/prd/abstract/10.1103/PhysRevD.83.121301
I do not want go out of topic but just to show that it is not the first time that a paper put into discussion the whole theory.
And what about string theory?
"The origin of the particle production is that the notion of particles, like the passage of time, is observer-dependent, and so what is Bob’s vacuum might be Alice’s thermal bath."
ReplyDeleteI wonder whether the reason of the failure has to be look for in Lorentz invariance, the real Achilles heel of LQG, more then in the quantization.
I made some comments about this in your fb page but I don't quite remember it now and I can't find the relevant post; I think it has some relevance with what you say in the post.
ReplyDeleteNemo,
ReplyDeleteThat paper that you refer to is a very old story just with new numbers. Vacuum birefringence was never a prediction of LQG and still is not, so you can't rule out LQG with it. Yes, certain people who shall remain unnamed have gone around and proclaimed that LQG is testable because of its Lorentz-deformation, and some people still do that, but it has never been true. And yes this means basically LQG is as unfalsifiable as string theory. Best,
B.
Giotis: The fb thread is here.
ReplyDeleteI would think the much bigger problem is LQG's apparent lack of any limits describable by either semi-classical GR, or effective quantum field theory.
ReplyDeleteAnother serious or fatal issue is that LQG apparently yields the incorrect logarithmic BH entropy correction: http://arxiv.org/abs/1205.0971
Euclidean triangles' three internal angles sum to exactly 180°. Earth's surface triangles' three internal angles never sum to 180°. Given Euclid, cartography suffers perturbations. 45 years' intense pursuitw by armies of our finest minds disgorged elegant hectares of gravitations absent empirical connection. A shared founding postulate is empirically defective.
ReplyDeleteNo measurable observable violates the Equivalence Principle (EP) ̶ classical, quantum mechanical, relativistic, gravitational (strong EP). Geometric chirality cannot be measured. Enantiomorphic alpha-quartz single crystal test masses violate the EP in a geometric Eötvös experiment. A good idea need only be testable. Theory has proposed no good ideas. Give theory a testably empirical origin.
Yes, basically what I’m saying is that it is not consistent to take the Lmin-->0 limit of the box (and thus δ-->0) with polymer quantization since polymer presupposes a discrete space.
ReplyDeleteThe fact that δ-->0 is the root cause of their null result.
I think more or less my claim is similar to your argument if I understood it correctly.
Thanks for this post. I'm curious about your opinion on the suggestion that the Unruh effect can be (or actually has been) observed in electron storage rings. If I understand correctly, this suggestion was first made in:
ReplyDeleteElectrons as accelerated thermometers
J.S. Bell, J.M. Leinaas
Nuclear Physics B
Volume 212, Issue 1, 7 February 1983, Pages 131–150
http://www.sciencedirect.com/science/article/pii/0550321383906016
There are now several follow-up papers on this topic, but I have never read them in detail.
My impression is that it remains ambiguous as to whether it should be claimed that the Unruh effect has been seen experimentally. (After all, any number of noise sources could cause a spin-polarized electron beam to lose polarization.) Nevertheless, when I recently learned about this, I was pleasantly surprised to hear that the temperatures involved are at an order of magnitude that it is even plausible to achieve experimental detection with a terrestrial experiment.
How the speculative theory could be falsified with speculative phenonema?
ReplyDeleteI have conceptual objections which meet in this paper.
ReplyDelete1) The use of exponentiation as in hyperbolic sines is at best a description rather than a proof even if consistent.
2) A transformation of a scalar is not necessarily invariant even if some ultimate geometry as curved, materially empty on not in a spacious chiarally neutral Flatland.
3) The ad hoc description of 26 + 1 as a proposed spacious Planck lenght is but one point of relations as a pivot for a totality of actual matter or gravitational effects measurable or not at some fundamental scale of variance in the idea of degrees of freedom.
4) An arbitrary sequence of events in a closed dimensional system would naturally balance at simplicity two loops corresponding high and low values paired yet as complexity the variance of implied or hidden dimensions is at least factorial as to remote, parallel, or near distances.
5) Dirac and Eddington geometric methods compliment each other over the still essential question of dimensionless constants.
I don't work in LQG myself, but LQG deals with diffeomorphism invariant states, both spatial and timelike. So, an LQG state would be in a superposition over all possible coordinate systems, including Cartesian and Rindler plus a whole lot of other coordinate systems. You just can't fix the coordinate system in LQG.
ReplyDeleteI haven't read the paper carefully, so maybe I will take another look and come back.
ReplyDeleteOne quick comment I may offer is that it is not entirely clear what the right way to polymer quantize a scalar field is. What Hosain and Sardar do in this paper is to fourier expand the field and conjugate momenta and polymer quantize the fourier modes as one would polymer quantize individual degrees of freedom, a method initiated by Hosain, Hussain and Seahra in a paper from 2009 . There's a choice involved in this - you may either take the momenta or the fields to be well defined operators. In this work I think fields are well defined. It is also possible to obtain a polymer/ background independent quantization of scalar fields directly - this was done by Ashtekar and Lewandowski. However unlike in lqg the demand of background independence doesn't fix a unique kinematic Hilbert Space. Also, for polymer quantization, mode expanding and quantizing don't in general commute. So this result may not be robust in this sense, which is probably why there is not much noise about this.
However one feature of all these quantizations is that if you started with a Lorentz invariant theory, the polymer quantized theory would break Lorentz invariance. This is simply because as either momentum (or field )is ill-defined one defines an approximate momentum(or field) using an additional parameter mu and this ends up making theory not L.I. So it's also that in the polymer quantum theory there is no notion of accelerated/ inertial frames. Generally speaking, putting the parameter mu to zero one usually recovers the standard results. So in that sense this is a little surprising.
Also,I suspect it would be straightforward to repeat the Unruh's detector calculation for this case using the polymer scalar propagator derived in Hosain, Hussain and Seahra and check for consistency between the two approaches.
ReplyDeleteFizz and others,
ReplyDeleteOver all coordinate systems the relations to duality and compliments within foundational extreme dimensions do have invariants. It depends on if we can physically observe separation or condensation of pairs that do not cancel at zero. As in superconductivity and temperature scalings. So Lorentz is not broken ultimately.
Does it not seem that mass and gravity transcend all scales. Gravity is deeper than curves and Flatland. It is more the interplay between 3D and 4D mappings. These have indirect alternative transformations. How do we tell if the rim of a half light cone is different from an impact crater if it conceptually the same description?
ReplyDeleteGiotis:
ReplyDeleteI thought the same thing at first - I wrote an email to one of the authors of the paper and asked him about it. He pointed out, correctly, that they do *not* quantize space-time. The space-time background remains entirely classical, as usually in the semi-classical approximation. Thus it should be possible to take this limit. The L_min of the volume does not a priori has something to do with the l* in the quantization of the fields on the background.
Now one can go and debate whether that limit exists in LQG at all. But if it doesn't exist then LQG is in even deeper trouble. So I just assumed that the semi-classical limit exists in some way, then what they are doing looks ok to me.
Best,
B.
Nirmalya:
ReplyDeleteSee the thing is that if you swap the limits you do get the standard results. You can see this in their calculation. Thus my confusion. If you say that it's not even clear how to do the calculation at all, that sounds to me even worse, but maybe that's just me. In any case, the way that they define the operators in the paper looks fine to me, though I admittedly don't know much about this quantization procedure. Best,
B.
Fizz: The same comment to you as to Giotis - they do *not* quantize space-time. They apply the loop quantization procedure to fields on space-time, ie, they have a coordinate system etc. They basically assume that the semi-classical limit exist. Which it better should. Best,
ReplyDeleteB.
Buchholz had a paper a couple of days ago on grqc arguing, rather convincingly, that nobody is ever going to see unruh radiation anyway....
ReplyDeleteI guess what I was trying to say is that the reason people are not more excited about it is probably that there are different ways of quantizing the scalar field and defining the operators within lqg and these give inequivalent dynamics.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteRastus,
ReplyDeleteSo, beyond a certain limit of the very large and very small it is difficult to see if not reason.
But all that is in between seems to have the same problem. As an observers frame of that in principle is not necessarily observable intimately can be considered as much an anthropic view as general objectivity. But at least one observation of the universe allows for such implied effects. Here, even if hidden and not observable, all around us by thought or experiment is not necessarily without measure.
Sabine, what was the other "pesky problem or method" you mentioned other than this polymer approach, briefly if it is outside the scope of LQG in the discussion?
The paper on the Unruh effect in LQG is wrong. The Unruh effect is a low-energy effect, not a high-energy effect. There are many derivations. Some are convoluted and go through high-energy calculation and renormalisation. But some are straightforward and completely avoid the high-energy sector of the theory. For instance, it suffices to take the two-point function of the qft with the legs on an accelerated trajectory, and notice that its expression as a function of the proper time along the trajectory satisfies the KMS condition. Standard arguments then imply that a detector moving along this trajectory thermalises. Since the authors say explicitly that the LQG corrections are only at high energy, their result is obviously contradictory.
ReplyDeleteIn fact, rereading carefully Sabine's initial post, I think that she has her finger right on the mistake: in a theory which essentially has a cut off if you subtract away an infinite quantity you make a mistake...
ReplyDeleteI see Lubos must read this blog as he quoted from two posters here.
ReplyDeleteHow can one maintain three space is a hologram of flat space if the information is not there? Or that two space is not possible? He declares his views of string theory as "morally" right and LQG is a moot debate as that approach has been dead for 20 years.
The new result of the relation of superconductivity and temperature I regard as evidence of effects discussed here, experimental evidence of a new state of matter. At the remote extremes 4 or 8 abstract quasifinite points (I imagine like David Hogan's tetrahedral 6j arithmetic) I get the same numbers two in 0D and two in 5D. Lubos has an alien view of the universe I find hard to imagine.
Not a string theory choice as gravity is superior approached by LQG ultimately although past unification attempts with prizes now said the spirit of it morally right. And that is my memo Lubos Motl.
Dear Edgar, Sabine's blog is indeed in my bookmarks that I open at least every day.
ReplyDeleteThe empty flat space - if we know it's empty - carries zero entropy, and therefore zero information. When it comes to space without matter, only event horizons (black hole horizons or cosmic horizons) may be assigned a large amount of information, S = A / 4G.
"It would be theoretically difficult to claim that the Unruh effect does not exist when the Hawking effect does."
ReplyDeleteI guess you mean that it would be difficult to claim that the Unruh effect exists and at the same time claim that the Hawking effect does. However, what you wrote could be read as "difficult to claim that the Unruh effect does not exist even though the Hawking effect has been demonstrated", which I guess is not what you mean.
Phillip,
ReplyDelete"However, what you wrote could be read as "difficult to claim that the Unruh effect does not exist even though the Hawking effect has been demonstrated", which I guess is not what you mean."
That is exactly what I mean. See, I have argued above that a non-gravitational analog of the Hawking effect has been pretty much observed, modulo some controversy around the experimental details that don't matter all that much for me, they'll settle this sooner or later. Thus, if you have a theory that doesn't have the Unruh effect (which has not been observed and probably won't be observed for a long while) you have to argue that you can have the Hawking effect but not the Unruh effect, which is theoretically difficult. That's what I meant and that's what I wrote. At least I thought so.
Besides this, I am pretty sure that you could repeat their calculation in a black hole background and find the same thing for the Hawking effect. Problem is of course that the logic is a little thin there because it's even less clear then which background to use. Best,
B.
1)How did they respond to your loophole argument?
ReplyDelete2)What is the difference between your loophole argument and my comment? I can't pinpoint the differences very well.
"That is exactly what I mean. See, I have argued above that a non-gravitational analog of the Hawking effect has been pretty much observed"
ReplyDeleteOK; I would have been surprised if the Hawking effect had been observed, but you mean the non-gravitational analog of the Hawking effect has been observed. OK, makes sense. Do you have a reference for this?
Phillip:
ReplyDeleteYou can start here and follow references therein. As I said, I don't think it's really settled yet, but I don't know enough about the subtleties to be able to tell you what the status is. Best,
B.
Giotis:
ReplyDelete1) I didn't follow up on this. Honestly, I just kinda forgot about the whole thing after my email exchange. Not sure the authors have yet seen this post or Lubos post.
2) It is incorrect what you say that taking the limit L_min (so delta) to zero is inconsistent with the quantization prescription used in the paper because the former regulator (minimal length/volume) refers to an integration over space-time, whereas the latter is a regulator for the fields propagating on space-time. In the paper, space-time is unquantized, so there is no reason why you shouldn't be able to take the limit L_min to zero at the end of the calculation.
What I am saying instead is that it was probably unnecessary to do the L_min regulation to begin with for the fields that have been quantized by the loop-procedure. Before you apply a regularization procedure to discard infinities you have to check that you are actually discarding only the unphysical divergence. In the paper they are applying the same regulation procedure to both quantization prescriptions without doing this check. Best,
B.
"You can start here and follow references therein. As I said, I don't think it's really settled yet, but I don't know enough about the subtleties to be able to tell you what the status is."
ReplyDeleteThanks. I particularly enjoyed this bit: "The sound waves emitted by a yelling fish as it goes over a waterfall which goes supersonic at the red line." :-)
I see now the root cause of the misunderstanding and it is completely my fault; my wording was very bad.
ReplyDeleteWhat I meant to say is that the polymer has already (or presupposes) an intrinsic regulator/cut-off (which when polymer is applied to the quantization of space in the case of LQG presupposes a discrete space) and that’s why it is inconsistent to take the Lmin-->0. I know that they don’t quantize space.
So this is the reason why I thought my comment was similar to your argument if I understood it correctly.
Another point that confuses me is whether (in case the paper is correct) this would have direct implications for LQG itself or for the application of the polymer quantization in the specific situation. You seem to imply it is the same thing.
Anyway the whole thing is confusing and a waste of time in my opinion since LQG does not have a well defined semiclassical limit to begin with.
I have two objections on Carlo Rovelli's rebuttal of the conclusions of the paper at hand.
ReplyDeleteThe first one concerns the KMS character of the propagator with the legs on the accelerated trajectory: this is true only if the propagator is the standard Lorentz-covariant one, which polymer quantisation fails to reproduce.
The second one concerns subtraction of infinities: the subtraction is indeed needed (and it is totally under control) in the Fock case, but NOT, as far as I can see, in the Polymer case, where the delta -> 0 is finite already.
Or am I missing something?
Someone,
ReplyDeleteIt seems to me in evaluating and debating our impressive ediface of speculative physics we have forgotten the simple first formulation of thermodynamics as it relates to the species of magnetism (such as in electron or background spin, paramagnetic) . New physics will be found on the next deeper structural level if any as fine tuning falls thru our gods of the gaps. There can be more to uncertainty and indeterminate differences of infinity than our still vague idea of the super-random.
I think it’s worth looking again at what Unruh said:
ReplyDelete”However, if one examines Hawking’s original calculation, there are some severe problems with his derivation. While mathematically unimpeachable, they are nonsense physically…
The question thus arises– if the derivation relies on such absurd physical assumptions, can the result be trusted? If the physics of the emission process really does depend on the physics of the field at those frequencies, then surely one can regard the effect as at best highly speculative, and and at worst almost certainly wrong…”
He then goes on to talk about the waterfall and the yelling fish, but note this: a gravitational field alters the motion of light through space, but it doesn’t suck space in. We do not live in some Chicken-Little world where the sky is falling in because space is falling down. The waterfall analogy is wrong.
Could black holes be connected to one another and to the beginning and end of time?
ReplyDeleteInstead of opening into another universe(s), why not this one?