Eric Hannah and Kenneth Eppley in 1977 presented a thought experiment that illuminated nicely why coupling a quantized to an unquantized field inevitably spells trouble, published in their article "The necessity of quantizing the gravitational field." The experiment is deceptively simple. You prepare a quantum particle in a state with a well-known momentum (in some direction). It doesn't necessarily have to be a momentum eigenstate, but something with a small momentum uncertainty. From Heisenberg's uncertainty principle, we know then that its position uncertainty will be large. Now you measure the position of the particle with a classical gravitational wave.
If gravity wasn't quantized, gravitational waves wouldn't have to fulfill the relation p = ℏk, which was famously shown to hold for photons by Einstein, using the photoelectric effect. It would then be possible to prepare a gravitational wave with a small wavelength (high frequency) but small momentum. If you use this gravitational wave to measure the position of the quantum particle, there are, so argue Hannah and Eppley, three different possible outcomes:
- You collapse the wavefunction of the quantum particle and measure its position to a precision determined by the short wavelength of the gravitational wave yet without transferring a large momentum. It is then possible to violate Heisenberg's uncertainty principle, thus the quantum part of the theory doesn't survive.
- You collapse the wavefunction of the quantum particle without violating Heisenberg's uncertainty principle, then you will violate energy conservation because your wave can't provide the necessary spread in momentum.
- You don't collapse the wavefunction, in which case you can use your measurement for superluminal communication. You then had two types of measurements, one that does and one that doesn't collapse the wavefunction. By spatially separating an entangled state and monitoring one part of it without collapsing it, you can find out, instantaneously, when a collapse was induced in the other part.
Since gravity is an extremely weak interaction, this experiment is far beyond experimental possibility; the detector's mass for example would have to exceed that of our galaxy. Hannah and Eppley claimed that their experiment would at least in principle be possible to construct with the matter content of our universe. It was however later shown by James Mattingly, in his paper Why Eppley and Hannah's Experiment Isn't (the title evidently did not make it through peer review), that Hannah and Eppley underestimated the experimental challenges. Mattingly crunched the numbers and showed that the cosmic background radiation spoils the sensitivity of the detectors and, worse, that the detector would have to be so massive it would sit inside a black hole.
Thus, Hannah and Eppley's experiment isn't even in principle possible. While their reasoning is physically plausible, this puts one into a philosophically difficult spot. There clearly is a theoretical problem with coupling a classical to a quantum field, but if we can show there are no practical consequences in our universe, is it a problem we should worry about?
I like Hannah and Eppley's thought experiment. It is not the best motivation one can have for quantizing gravity, but it is a lean way to illuminate the problem.
Dear Bee,
ReplyDelete"You collapse the wavefunction of the quantum particle" - this implies a particular interpretation of quantum mechanics, does it not? (To be frank, recent readings have me thoroughly confused.)
Is it possible to do the Eppley & Hannah thought experiment in a interpretation-independent way?
Thanks!
-Arun
This comment has been removed by the author.
ReplyDeleteInteresting. However, concepts related to the "Heisenberg Microscope" (finding position disturbs momentum and vice versa) are flawed, since we can measure position without interacting. (I don't just mean "interaction free measurements.") Imagine using for example a tiny object that flips chirality of C-pol light (so, a half-wave plate) - and its angle orientation doesn't matter for this, it will turn RH into LF and vice versa. So we illuminate the region it hides in with RH light, and use filters to look for the spot where light is turned into LH. Sure, it gets more angular momentum but that doesn't affect lateral momentum, yet we can see (to within resolution of wavelength used) just where the tiny HWP is, without pushing on it (so no linear impulse transfer.)
ReplyDeleteInstead, it seems that the HUP is more really about the intrinsic Fourier spread of the constituent momentum states, and so a pure momentum must be intrinsically spread out, and a wave packet confined to a small area must show a big momentum spread - all aside from any interaction issues (until "measurement" *changes* the relationships, if it does.)
- sorry about many deletions lately, I've made lots of typos, maybe need to slow down.
"Fine minds make fine distinctions."
Maybe I got it - perhaps the decoherence time for a quantum particle interacting with gravitons is probably greater than the age of the universe, and the quantum particle will decohere with the CMB before gravity gets a chance, etc.
ReplyDeleteArun - decoherence is irrelevant! The undeservedly popular argument that it matters, is circular and fallacious: you can't explain classicality itself, because you need a source of statistics first. They can't argue that decoherence turns quantum statistics into classical statistics, unless something collapsed the wave to start with - otherwise it would just be an evolution of coherent "waves" into incoherent "waves" per se.
ReplyDeleteWhen rigorous derivations converge to ridiculous conclusions, a founding postulate has selective error. Nothing constrains the vacuum to act identically toward massed fermions and massless bosons. The vacuum has fundamental selective asymmetries toward mass, not Chern-Simons corrections.
ReplyDeleteAnisotropic vacuum toward matter sources Milgrom acceleration in MOND, biases matter-antimatter abundance, allows divergent neutrino-antineutrino reaction channels, originates biological homochirality. Its Big Bang intense pseudoscalar field false vacuum decay powered cosmic inflation, leaving present-day trace value. It is testable in existing apparatus as geometric parity Eötvös experiments and geometric parity calorimetry experiments. The latter requires 24 hours on a bench top to be 16,000 times more sensitive than a 90-day composition Eötvös experiment running in its own isolation bunker.
40 years of physical theory have zero empirical validation. Einstein’s elevator has an obvious footnote – to a chemist. Observe that Unpolung. The worst it can do is succeed, explaining everything.
"You collapse the wavefunction of the quantum particle without violating Heisenberg's uncertainty principle, then you will violate energy conservation because your wave can't provide the necessary spread in momentum."
ReplyDeleteOk. Well, energy conservation is violated in any spacetime [like this one] that doesn't have a timelike Killing vector. So why worry?
Rastus: really, our space-time does *not* have the appropriate conserving KV? Yeah I heard how GR doesn't really achieve proper energy conservation, is that what you mean? The energy content of gravitational radiation can't be properly hashed out. (BTW anyone heard of the Feynman-Bondi "sticky bead paradox"? - see sticky bead.)
ReplyDeletePenrose's speculations about the effect of GR on QM particles lead him to hypothesize that the same kind of incompatibility described in your blog post is the cause of wave function collapse. He has suggested experiments (that are realistic with current technology) to prove or disprove his ideas. See, for example:
ReplyDeletehttp://en.wikipedia.org/wiki/Penrose_interpretation
http://arxiv.org/abs/quant-ph/0210001
Dear Arun,
ReplyDeleteYes, indeed, another criticism of Mattingly is that Eppley and Hannah work in the standard interpretation. I didn't mention this because while it is an objection to the argument, I don't see how it helps. It seems to me it doesn't really matter if the wavefunction "really" collapses (or not) as long as it appears that way. Best,
B.
Hi Neil,
ReplyDeleteYes, the uncertainty principle is actually a statement about Fourier transformation. I don't know how you want to measure a position to better than the wavelength of the light with that light. Best,
B.
Hi Rastus,
ReplyDeleteI believe we talked about this already in some other post, no? GR has a perfectly fine energy conservation, it's just not the total energy (which is an integrated quantity after all) that is conserved, but the energy momentum tensor, and it is covariantly and locally conserved. The stuff that goes into a space-time region still has to come out somewhere. Best,
B.
Hi Omh,
ReplyDeleteYes, I know about Penrose's suggestion. Can't say I'm very convinced of it. I can't say either I know many people who are convinced of it. It is a nice idea in principle, and a courageous one, but the details are not very appealing to me. Best,
B.
The last time I saw Penrose (and it's been a while) he was discussing plans for a concrete experiment with Zeilinger which could prove or disprove his interpretation. Does anyone know what came of that?
ReplyDeleteBee,
ReplyDeleteOn the contrary, choice of interpretation is vital to the argument. In which reference frame is wavefunction collapse instantaneous? E&H have chosen an assumption that is Lorentz-violating and used it to derive a conclusion that is Lorentz-violating. Nothing to see here.
Hi Andrew,
ReplyDeleteHuh? I didn't say anything about Lorentz-violation. The collapse is instantaneous in the frame of the medium that causes decoherence, in this case the detector. Best,
B.
Hi Philipp,
ReplyDeleteRight, I recall that too, but haven't heard anything either. Best,
B.
Hi Sabine,
ReplyDeleteI can see why QM and GR are in tension, it is rather clear with respect to their conflicting treatment of time. However I think the presence of singularities in GR is another, perhaps prefered, starting point for many studies of quantum gravity, and I fail to see why this ought to be a problem. Aren't black holes compelling evidence for singularities in our observable universe?
Your statement below appears to take a slightly different stance from the general "singularities are bad" rationale..you seem to imply that singularities such as black holes could still be fine if they could evaporate.
"More pressing is that general relativity, under very general circumstances, brings with it the formation of singularities, and without quantizing gravity black hole evaporation seems incompatible with quantum mechanics."
Could you please elaborate/correct me on that?
Bee,
ReplyDeleteInstantaneous collapse is Lorentz-violating as it is only instantaneous in a single frame. There is no physical justification for choosing any particular frame - if a detector consists of two parts moving wrt each other (say, an apparatus with a sensor on an armature, such as a hard disk), in what frame do we judge that the measurement was made?
In entanglement experiments it doesn't matter what frame we choose, or whether we take wavefunction collapse to be instantaneous or not, as it does not matter which measurement happened "first". This convenient luxury is not available to E&H.
Hi Bee,
ReplyDeleteRather than demonstrating as to why gravity needs to be quantalized I find it more indicative as to why quantum theory needs to be made a rational one. That is perhaps some of those options given are not all that untenable, just simply not found palatable by many as to being imagined as possible.
“To go back to the EPR dilemma between locality and completeness, it would appear from the Bell theorem that Einstein's strategy of maintaining locality, and thereby concluding that the quantum description is incomplete, may have fixed on the wrong horn. Even though the Bell theorem does not rule out locality conclusively, it should certainly make one wary of assuming it. On the other hand, since Einstein's exploding gunpowder argument (or Schrödinger's cat) supports incompleteness without assuming locality, one should be wary of adopting the other horn of the dilemma, affirming that the quantum state descriptions are complete and “therefore” that the theory is nonlocal. It may well turn out that both horns need to be rejected: that the state functions do not provide a complete description and that the theory is also nonlocal (although possibly still separable; see Winsberg and Fine 2003). There is at least one well-known approach to the quantum theory that makes a choice of this sort, the de Broglie-Bohm approach (Bohmian Mechanics). Of course it may also be possible to break the EPR argument for the dilemma plausibly by questioning some of its other assumptions (e.g., separability, the reduction postulate, or the eigenvalue-eigenstate link). That might free up the remaining option, to regard the theory as both local and complete. If it were made cogent, perhaps some version of the Everett Interpretation would come to occupy this branch of the interpretive tree.”
-Arthur Fine, "The Stanford Encyclopedia of Philosophy"
Best,
Phil
Bee,
ReplyDeleteSorry for the double post, but I thought of a better example.
Consider two identical conductors moving wrt each other, each with a comoving charge sensor and observer. As the observers pass each other, they simultaneously measure their charge sensor to see if an electron has tunneled between the conductors. In what frame does wavefunction collapse occur?
Maybe we can't perform the experiment in our universe but I'm sure other observers could perform it in principle in another patch of the Multiverse.
ReplyDeleteWe know from String theory that each patch must contain gravity and the principles of QM must apply in it. Thus the prerequisites are the same and the conclusions would have universal (sorry multiversal) applicability.
I think this should be the subject of your next paper Bee:-)
Hi Andrew,
ReplyDeletePreferred frames are not in conflict with Lorentz-invariance if they have a material origin, which is the case here. The world is full with preferred frames and they break Lorentz-invariance all the time. If you don't know what caused the wavefunction to decohere the best you can do is give a probability. Best,
B.
Hi Giotis,
ReplyDeleteYes, I was wondering the same thing, if not the existence of a multiverse changes the requirement of what is "possible in principle." Best,
B.
Hi T,
ReplyDeleteYes, that GR predicts singularities is one common motivation for searching for quantum gravity. I don't find it too convincing because it might after all be possible to find a classical way to solve the problem. However, it is plausible to expect that a quantized theory will also take care of this issue.
Observations that we have of black holes don't tell us anything about the singularity, since it is hidden by the horizon. We don't even know if the singularity is there. In fact, most of my colleagues including me believe it is not there.
As for the problem with black hole evaporation, I recommend you read this earlier post. Best,
B.
Bee,
ReplyDeleteWe can't even do that. How do you calculate a probability without a rigorous framework? It may be interesting to speculate, but it's not science. You certainly shouldn't use it as the basis for a thought experiment in nonlocality.
Hi Andrew,
ReplyDeleteThere is a rigorous framework. It's called quantum mechanics. The detector is a quantum mechanical thing too, you just don't know its details is what I'm saying, thus you trace out its degrees of freedom. In any case, maybe we should get back on topic. You were claiming the validity of Hannah and Eppley's argument depends on the interpretation of quantum mechanics. I don't see how, would you please explain? Best,
B.
Hi Bee, to clarify I didn't mean measure position to less than wavelength (realistically it's about 1/2 that). Rather, I explained a method to measure to wavelength, but without changing/making uncertain the object momentum by an amount comparable to photon momentum - which Heisenberg Microscope argument (now rather dated) implies we can't do. Note that quantum "interaction-free" measurements can do that already, albeit with some chance of failing per instance of checking.
ReplyDeleteBee,
ReplyDeleteThe propagation of the quantum state, as exemplified by QFT, is rigorous, Lorentz-invariant, and produces fantastic results. By contrast, the reduction to classicality has never been formalised at all. The standard interpretation says that the wavefunction collapses to a pure state randomly and instantaneously upon measurement, but does not define "measurement", and does not attempt to define "instantaneously" in a Lorentz-invariant manner.
But back on topic, all that E&H have shown is that GR is incompatible with instantaneous reduction. But since we know that instantaneous reduction violates SR, we haven't actually learned anything new.
Hi Andrew,
ReplyDeleteThanks for the clarification. I believe you have misunderstood what I wrote. The problem Hannah and Eppley talk about in case 3 is not instantenous collapse but superluminal information exchance. In normal qm, The instaneous collapse does not allow superluminal exchange of information and is thus actually perfectly compatible with special relativity. Not so any more if you try option 3, that's the point. Best,
B.
Hi Neil,
ReplyDeleteWhat does this have to do with Hannah and Eppley's thought experiment? Best,
B.
Bee,
ReplyDeleteNo, I do understand the distinction between instantaneous reduction and superluminal communication. I made that particular point in one of my earlier comments re: entanglement experiments. I think my argument is more philosophical - is it at all meaningful to talk about instantaneous reduction if one cannot define "instantaneous"? Just because one can get away with it under most circumstances (i.e. other than the E&H thought experiment) does not mean that it is universally valid.
Bee, here's the relation of HM thought experiment to Eppley and Hannah's TE:
ReplyDelete"You prepare a quantum particle in a state with a well-known momentum (in some direction). It doesn't necessarily have to be a momentum eigenstate, but something with a small momentum uncertainty. From Heisenberg's uncertainty principle, we know then that its position uncertainty will be large. Now you measure the position of the particle with a classical gravitational wave."
...
"You collapse the wavefunction of the quantum particle and measure its position to a precision determined by the short wavelength of the gravitational wave yet without transferring a large momentum. It is then possible to violate Heisenberg's uncertainty principle, thus the quantum part of the theory doesn't survive."
See, the latter part is what I'm saying, we can already do: "measure position to a precision ... yet without transferring a large momentum." I say they are wrong to continue, that we could then violate the HUP. No, because we can indeed find an apparently precise position without "transferring" a large momentum. IMHO the trick is, the Fourier composition means that with a precise position the momentum of the object is already spread out, it is not about "affecting" it by "transferring" momentum.
Instead, I suppose that we would find a specific position according to chances given by the spread of position states (ie, centering on the expectation value) but the superposition - however already broad - of momentum states is not *affected* by the interaction-free observation (as by my proposed method, or existing IFMs.) Cheers.
Hi Bee,
ReplyDeleteWhile the thought experiment you are discussing may not be a possible real experiment it is a good paradox generator. Paradox generators, as in the three possible interpretations you mention, show that something is amiss in our understanding. A paradox generator like this almost always means that there is a false assumption that is hidden within current theory.
I think the most interesting false assumption might be in number 3 - no wave function collapse and the ability to get
information superluminally on one end of an entangled pair. The uncertainty principle (to me) is mostly about the inability get information without exchanging energy. When particles get small enough the energy used to acquire information of state overwhelms the state of the particle itself. This would also apply to a quantum entangled particle pair. This in essence is why information normally can not be transmitted superluminally using quantum entanglement.
But if you could translate the same quantum entangled state to the gravitational regime it would look very much like a gravitational wormhole. The gravitational bodies on either side of the throat of the wormhole would act like mirror twins of each other. If these bodies acted in the GR regime and were big then you could probe one of them without substantially disturbing the entangled state. If for instance a person that was entangled to another started tying his shoe you would know the entangled opposite person was also. The photon exchange between you and the person you were observing would not be enough energy to collapse the wave function.
I think this has to be where the false assumption of superluninal communication lies. I wrote a paper dealing with a few of these issues many years ago.
The information is contained in "the light" Bee? It's a matter of elemental possibilities as a projection of the geometry?
ReplyDelete240 E₈ polytope vertices using 5D orthographic_projection to 2D using 5-cube (Penteract) Petrie_polygon basis_vectors overlaid on electron diffraction pattern of an Icosahedron Zn-Mg-Ho Quasicrystal.
Geometrical projections?:)
Best,
I believe we talked about this already in some other post, no?
ReplyDeleteDid we? Maybe I somehow missed your answer, sorry.
GR has a perfectly fine energy conservation, it's just not the total energy (which is an integrated quantity after all) that is conserved, but the energy momentum tensor, and it is covariantly and locally conserved.
I think I must be misunderstanding you. We know that you can put together something called the "gravitational pseudo-tensor" which sometimes helps you to do the book-keeping and do some calculations. But that thing doesn't really represent actual physical energy. On the other hand, you can convert divT = 0 [which is not a conservation law] into div(T(X)) = 0 [where X is a timelike Killing vector, and T(X) means the vector field that you get by treating T as a linear transformation], and this *is* a conservation law... but only if you have a timelike Killing vector. As you know, energy is certainly not conserved in cosmology for this very reason.
Sorry, I know you know all this, but my point is just this: we know that energy is not conserved in cosmology, in particular in an accelerating universe --- I think that this is the generally accepted way of thinking about it nowadays. The situation with gravitational waves is exactly the same; the only difference is that we have gotten used to the convenience of pretending otherwise because it helps us to compute how rapidly binary pulsars etc slow down. But as a matter of principle, energy conservation breaks down here too. So if one were to follow up on Eppley&Hannah, this is where one should focus: energy conservation breaks down quite routinely in GR, and we are doing GR here.
A few years ago I got a stern lecture about this from my thesis advisor, and it sort of stuck :-)
The stuff that goes into a space-time region still has to come out somewhere.
Well.... no, it doesn't. Not in GR when things aren't static.
Is another way of stating E&H's thought experiment - that if a gravity wave behaves like a classical measuring apparatus, then various contradictions ensue. Does this also mean that this is a proof that any classical apparatus must ultimately be composed of quantum particles?
ReplyDeleteHi Andrew,
ReplyDeleteOkay, sorry, then I misunderstood your point. Yes, the "instantanous collapse" is a deeply unsatisfactory concept. But that's entirely irrelevant for E&H's argument. Nonlocal Bell-type correlations are an experimental fact. If you could know what's on one side without affecting the state then you could use it for superluminal information exchange. Best,
B.
Hi Neil,
ReplyDeleteI still don't know what your point is here. I am reading one of two different statements that you might be trying to make: Are you saying A) H&E are wrong to conclude that they can violate the uncertainty principle? or B) We can already violate the uncertainty principle and should not worry about it? I disagree on both, so please clarify. Note that it is entirely irrelevant how well we can measure position of something by which method, what matters is if you can at the same time know the momentum (in the same direction). Best,
B.
Hi Rastus,
ReplyDeleteI definitely have a severe case of deja lu here. What I am saying is that in GR we have \nabla_a T^{ab} = 0. That's a perfectly fine local and covariant conservation law. What you want to do is to find a conservation law for an integrated quantity which in GR isn't generally possible. In any case, this distinction is entirely irrelevant for H&E's argument. If case 2 was for real, you'd have a particle with momentum x transferring a momentum y to another particle. Since x is basically zero, spacetime is essentially flat, so what are you trying to say? Best,
B.
Bee, I don't see how point 3 could work with the Many world interpretation where there is no notion of instantaneous wave collapse. The apparent wave collapse occurs only for the observer of the quantum measurement and not for the measurement in the space like separated region. The splitting of the wave function in this interpretation is not instantaneous.
ReplyDeleteCould you explain a bit?
Hi Giotis,
ReplyDeleteWell, I guess you'd have to interpret it differently. Let me see. You'd be able to monitor the wavefunction without branching on the one side, while the guy on the other side makes a measurement and finds himself either in the hop or flop universe. Now the only way you can still be in the same of the many worlds is if your measurement is compatible with his. It is maybe somewhat misleading to call it superluminal information exchange, it sounds more like a consistency requirement, but for all I can tell, it would still look the same. The observers in the two separated regions, when they live in the same branch, have to agree on one of three possibilities: a) the particle is in a superposition b) it is in region one c) it is in region two. Any mixture of these would be intrinsically inconsistent, so you would conclude they aren't anymore in the same universe. Best,
B.
Hi Bee,
ReplyDeleteIt depends on what one describes as being the ‘system’, as for instance there is something in Bohmian mechanics known as the "conditional wave function" related to what is called the “effective wave function”, which addresses wave function collapse locality and yet has Schrodinger’s to be maintained globally (universally) and thus option 3 could be satisfied from such a perspective. This approach also has option 1 not being an obstacle as the Heisenberg's uncertainty principle here is found resultant of the limits of what can be practically known (ignorance), rather than being an actual postulate of nature. Thus finding nature as intrinsically non-local and having the traditional collapse scenario as not a complete description can still be considered as an alternative for a need in to having ‘many realities’.
“The key element here is the notion of the conditional wave function of a subsystem of a larger system, described briefly in this section and discussed in some detail, together with the related notion of the effective wave function, in Dürr et al. 1992, Section 5.......................It is perhaps worth noting that orthodox quantum theory lacks the resources, namely, the actual configuration of the environment, that make possible the definition of the conditional wave function. Indeed, from an orthodox point of view what should be meant by the wave function of a subsystem is entirely obscure.”
-Sheldon Goldstein, "Bohmian Mechanics", Stanford Encyclopaedia of Philosophy
Best,
Phil
Hi Phil,
ReplyDeleteThe point isn't that 1,2 and 3 aren't compatible with any conceivably possible description of nature but just that they aren't compatible with quantum mechanics as we know it. Something has to give. Yes, maybe the uncertainty principle can be violated. And yes, if you believe it is a statement about our knowledge rather than one about the fundamental nature or reality this doesn't sound quite as blasphemous. But either way, we'd have to twiddle something in our current understanding. Best,
B.
Bee I lost you sorry; the other guy is space-like separated and there is no simultaneity. As I understand it the splitting of the wave function in the quantum measurement is a local event. There is no way for the other guy in the space-like separated region to know if splitting has occurred or not and if he is in the same or in another branch. Could you give an example of what you mean?
ReplyDeleteHi Giotis,
ReplyDeleteWhat I mean is if he'd ask the other guy he'd find out they were in the same branch all along. Best,
B.
Hi Bee,
ReplyDeleteI didn't mean to antagonize yet simply to bring to the table that what Eppley and Hannah point being is if the traditional treatment of Quantum Theory (CI perspective) is considered as complete (ontologically and metaphysically) then it would appear to necessitate that GR needing to be quantalized. That is on the other hand I just wanted it to be considered it still could mean that QM needs to be given serious consideration as to why physics finds itself in the current situation in relation to the extension and/or replacement of current theories. That is to use Arthur Fine’s words as in analogy there is still reason to look at all the horns before being satisfied if one or any of them are convincing enough to hang one’s hopes and therein convictions upon.
Best,
Phil
Hi Giotis,
ReplyDeleteCome to think about it, it would probably be more correct to say the version of the guy who asks is in the same branch, as opposed to when he asks he is in the same branch, because there's now a few versions of him in other worlds corresponding to other outcomes. Best,
B.
You mean they meet after the experiment and compare their results?
ReplyDeleteHow this would violate SR?
They'd conclude it couldn't have happened within SR. So this guy sits there and monitors his wavefunctions and on occasion they make jumps (say from 1/2 to 1) and he reads out just the message that the other guy intended to send. Of course he doesn't actually know that until he has some way to verify that this was actually what the other guy was sending. Now, as I said, you could just say that's a consistency requirement in the many worlds interpretation rather than superluminal information exchange, but either way, it's incompatible with observation and brings you into trouble with causality, unless you break Lorentz-invariance which brings other trouble.
ReplyDeleteHi Bee,
ReplyDeleteOne thought experiment deserves another?:)
How to be in Two Places At Once
Quantum Entanglement Benefits Exist after Links Are Broken By Charles Q. Choi
Best,
Bee, sorry such a clarity problem. I think it's better to say: no I don't think we can *violate* the HUP, but rather that H&E have misframed the nature of that issue. Remember there are basically two things we can say if to criticise someone:
ReplyDelete1. The framed the issue correctly but are wrong
2. They misframed the issue, and so some variant of "not even wrong" (as the extreme, with things in between.
They are saying, that being able to measure position to a precision without *disturbing* the momentum by the amount in the HUP relation, would violate the HUP. That low-disturbance measurement would happen if gravity waves do not carry the required momentum.
I say, that wouldn't violate the HUP; rather than to say we can already do so. That fits into what I've said above, the momentum would still be *intrinsically* spread due to Fourier issues, just not "affected" - so the classical gravity wave would measure the position very well, not "affect it" to the amount given by HUP, but the "intrinsic" uncertainty is just "there." Note also with IFMs we can already get position without disturbing!
Here's larger Pic
ReplyDeleteBest,
This comment has been removed by the author.
ReplyDeleteThis comment has been removed by the author.
ReplyDeleteBee,
ReplyDeleteBell violation tests only show that after the collapse of both wavefunctions, the states are correlated in a certain way. They do not require the entangled states to collapse in any particular order or timeframe. E&H's argument depends on when one considers the wavefunction to have collapsed. Depending on your choice of interpretation, wavefunction collapse may happen retrospectively, or not at all.
There may be other ways to deal with option 3 that do not require us to make any assumptions about the nature of collapse. Perhaps gravity can't distinguish between a collapsed and uncollapsed wavefunction - if it doesn't obey the uncertainty principle, then why should it pay any heed to collapse either? Once you open the non-QM-gravity can of worms, superluminality is only one of your problems.
Well, not to hem and haw (BTW how to say that in German?), then I am indeed saying, A) H&E are wrong to conclude that they can violate the uncertainty principle. Right, being able to closely measure position without "changing" momentum by some uncertainty, does not IMHO violate the HUP. IMHO the HUP is about intrinsic relations, not "changes" to something.
ReplyDeleteYet I think there's a reconciliation: we wouldn't "disturb" momentum with such classical waves, but maybe we still couldn't "measure" it to better than HUP says. Any attempt to measure would return something along a spread of values, it just wouldn't *change* that spread. Really, it's time we decouple "knowing" from "altering", now that we have IFMs, right?
And yes, there may be disagreements over whether measurement and uncertainty should be interpreted as I claim. My answer: well then, what about existing IFMs and my proposal about using change of CP light (no linear momentum transfer) to determine position - you need to deal with the implications (IOW, not just reiterate faith in traditional HUP, but deal specifically with the challenges posed.)
(again, sorry about many deletions/replacements)
My point is that violation of momentum conservation is the obvious way out. This has been discussed particularly well by these people:
ReplyDeletehttp://tigger.uic.edu/~huggett/Nick/My%20Work_files/why.pdf
[or search here:
http://tigger.uic.edu/~huggett/Nick
]
My additional point is that "gravitational energy" [and momentum] is an *extremely* dubious concept anyway, so it doesn't surprise me at all that a gravitational field can violate momentum conservation. The vacuum energy of our universe is increasing all the time, and *it* doesn't come from anywhere.... in other words, if you are going to violate conservation laws, a gravitational field is exactly how to do it.
Finally I don't buy your point about "basically zero" and "essentially flat". This could just be one of the many cases where "nearly zero" is basically different from "exactly zero". [Remember all those people who think that AdS with small curvature is "more or less the same as Minkowski space etc" ]. But I see what you are driving at, and it's a good point.
Rastus,
ReplyDeleteIf it was true what you'd say, then we'd find momentum violation all the time and everywhere! Look, put the interaction into a box and look at it from far away. The asymptotic mass of a region is conserved, temporarily curving the background doesn't help you anything with that. That's exactly why I find it very unfortunate that the statement GR can violate energy conservation (while technically true) has been spread so much, because it neglects to point out the more important fact, the energy and momentum densities are locally covariantly conserved. This has nothing whatsoever to do with "gravitational energy" which is just simply ill-defined. Best,
B.
Hi Neil,
ReplyDeleteWell, I'd say if they manage to measure \Delta x \Delta p < 1/2, they have violated the uncertainty principle. Best,
B.
Hi Andrew,
ReplyDeleteEPR type tests have also conclusively shown that the correlation exists already while the both events are spacelike separated. Basically, you have to make them far enough apart and measure quickly enough to exclude a causal information exchange can have happened. This has meanwhile been done many times. Interesting though you say this, at the time E&H wrote the paper they couldn't have know this. In any case, it is true of course that rather than quantizing gravity there might be some modification of quantum mechanics that allows to make sense of option 3, or you might not be concerned about superluminal exchange of information. But either way, the point is, something has to give. Best,
B.
Bee,
ReplyDeleteI agree absolutely that something has to give. As far as we know, all current QM interpretations lead to absurdities, even without introducing GR. But different interpretations lead to different absurdities, and E&H only treated a subset of these.
For example, in the EPR tests one could say that 'measurement' takes place only when the combined results are observed by an experimenter, and any correlation is due to the requirement that the observed history must be self-consistent. There is no need for superluminal wavefunction collapse in this case. The implications are absurd (as Schrödinger showed) but whether they are more or less absurd than superluminality is a matter of taste.
What E&H have done is analogous to what EPR did: find a loophole in QM that conceptually violates relativity, but which can never be exploited. But E&H's result is derivative of (an interpretation of) EPR's, so perhaps what it is really telling us is that QM can never be reconciled with GR until it is first reconciled with SR.
This comment has been removed by the author.
ReplyDeleteBee (if you're away, someone else please dig in, this is IMHO a big deal), in any case it presses: what if I prepare an object with a definite momentum in an imaging interferometer, set up to do IFMs (or whatever method you please)? This is something we can really do, right? What kind of position measurement could an IFM return? Now what, how to square that with HUP?
ReplyDelete(I do need to reformulate my point: E&H (why "H&E") say "... prepare a quantum particle in a state with a well-known momentum (in some direction)." - OK, so what if you try to measure its position with a classical wave? Maybe it would show *as* a smear, if that's what it "really is" (uh, yeah, ...). Either that, or it would just show apparent hits from all over the position spread. That way we wouldn't violate Δp Δx > ℏ/2, it would only "seem" to. - ? Earlier, I should have addressed initial prep.)
Hi Neil,
ReplyDeleteMaybe this helps. Best,
B.
A quantum particle interacting with a classical object does not always constitute a measurement.
ReplyDeletee.g., light passing through optical glass; atoms in a magnetic trap.
A measurement requires decoherence, something to carry away quantum phase information into the environment.
In the thought experiment of a classical gravity wave scattering off of a quantum particle there appears no mechanism for decoherence (unless there is some infrared catastrophe type emission of gravity waves as part of the scattering process). Therefore, the quantum particle's wave function will not collapse in such a scattering experiment.
There remains the question of why superluminal signalling is not possible.
James Mattingly presents the Eppley and Hannah argument as follows:
Suppose now that, rather than collapsing the particle’s wavefunction, the gravitational wave merely registers the
presence of the particle’s wavefunction. But a measurement of a particle’s wavefunction in this way would allow
super-luminal signalling. For before measurement, one can split the position-space wavefunction of the particle into
two spacelike separated parts. Then one can measure the shape of the wavefunction in one region. Depending upon
whether one finds no wavefunction, the full wavefunction, or half of the wavefunction, one can tell whether someone
else has either measured the other part of the wavefunction (by normal quantum mechanical means) and found
the particle, measured and not found the particle, or not made a measurement at all respectively. Thus there is a
prescription for super-luminal causation. One can (since we are assuming here that collapse is instantaneous) tell
instantly the state of the wavefunction in a spacelike separated region.
The picture seems to be that if (space-like) far away someone has made a measurement of the quantum particle and found it, then the gravity wave probe here will encounter nothing. If someone far away has either not made a measurement or made a measurement and not found the particle, then the gravity wave probe here will encounter something, and thus I get information about what happened far away superluminally.
But on further thought, this is just like the single electron wave that spreads between here and Alpha Centauri. If someone measures it at Alpha Centauri, I definitely do not find the electron here at the Sun; but if someone near Alpha Centauri doesn't make the measurement or makes the measurement and doesn't find the electron, I may find the electron here - the common paradox with quantum mechanical wave function collapse and having nothing to do with gravity waves and their quantization or non-quantization. Presumably the resolution can be found in "Consistent Quantum Theory" by Robert Griffiths.
Therefore, I don't think E&H's thought experiment works.
Arun,
ReplyDeleteAlternatively, I can take a fundamentalist Schrödinger view - that by measuring your part of the wavefunction, you have entangled yourself with the quantum state, and that it is only when I measure my part of the wavefunction that you collapse into a pure state consistent with my measurement. Or equivalently I can measure you and thereby collapse my half of the wavefunction. Of course, from your point of view it is I who gets entangled. And yet we both end up with the same result, because our subjective views are equivalent formulations of the same problem.
This (ultimately harmless) subjectivity is not dissimilar to the harmless subjectivity of time dilation. I came across this interesting post on quantum superpositions and reference frames, which might be worth a read. Perhaps what we call "measurement" is merely the quantum equivalent of transforming our personal reference frame.
Hi Arun and Andrew,
ReplyDeleteI know no one has commented on my earlier comment but I think one of my points has a bearing on this discussion. When physicists talk about the collapse of the wave function in quantum mechanics they refer implicitly to the realm of the small scale. Unfortunately, there is a vague and often changing definition in physics of the scale at which wave function collapse occurs. Often people take, (what I feel) is the lazy interpretation that, because this dividing line between quantum uncertainty and gravitational statistical classicism is vague, that it is also unimportant. I don't think that it is at all true.
In the thought experiment referenced here energies are being talked about that are immense, and probably impossible. I would guess that this immense energy would work against applying the wave function collapse paradigm that is usually applied to the small scale quantum world. You can't get around this. In the classical gravitational scale we don't observe wave function collapse. This is fact.
Most people always talk about quantizing gravity in their search for a theory of quantum gravity. But one could equally well talk about getting classical statistical analysis when moving a normal quantum event like quantum entanglement into the large scale regime. I think with the energies talked about in this thought experiment that is really what is happening. It doe not seem at all unreasonable to me that if you moved quantum entanglement from the world of small and low energy to the world of large and high energy that the first thing that would change would be no wave function collapse when measuring the the state of one of the quantum entangled bodies.
" It doe not seem at all unreasonable to me that if you moved quantum entanglement from the world of small and low energy to the world of large and high energy that the first thing that would change would be no wave function collapse when measuring the the state of one of the quantum entangled bodies."
ReplyDeleteI should add that it is unproven that this thought experiment is possible so you might be right that this isn't a valid TE. But given the premise that it's possible then option 3 seems to me to be the logical choice.
Is this post meant to:
ReplyDeletea)entertain the expert physicist
b)stimulate the budding physicist
c)inspire the layman to takeup physics(kinda like carr's book and ramanujam)
d)just a post
This is my first post on your blog. I'm welcome.
Hi Unknown,
ReplyDeletea),b),d) and c'): offer a motivation for the layman why quantizing gravity is an endeavor worth engaging in. I don't see it as my task to convince everybody they should take up physics. This would be a nightmare. Best,
B.
Dear Bee,
ReplyDeleteAny comments on this? It may be more rigorous than Eppley and Hannah?
http://arxiv.org/abs/quant-ph/0402092
Inconsistency of quantum--classical dynamics, and what it implies
Daniel R. Terno
(Submitted on 13 Feb 2004)
A new proof of the impossibility of a universal quantum-classical dynamics is given. It has at least two consequences. The standard paradigm ``quantum system is measured by a classical apparatus" is untenable, while a quantum matter can be consistently coupled only with a quantum gravity.
Hi Arun,
ReplyDeleteThanks for the reference, I'll look at that! Best,
B.
Hi Sabine, I am commenting on your old post because we just had a discussion with some people which directly relates to the discussion here.
ReplyDeleteI think Eppley and Hanna's argument have a different subtelty which has not been addressed and which touches the heart of the difference between gravity and electromagnetism.
The whole discussion of Eppley and Hannah, which you summarize here, treats the gravitational wave (and its interpretation as made by gravitons) as an equivalent of the electromagnetic wave: The amplitude of the wave squared gives the probability of the graviton to be somewhere, the frequency is the frequency of the graviton, Heisenbergs microscope imposes uncertainity relations and so on.
The problem is, electromagnetic waves can be measured both in their position and momentum Eigenstates. Even when the "wave" carries an order of one photon, one can easily design detectors for both.
I think a delocalized graviton, i.e., a graviton in close to a momentum Eigenstate, is unmeasureable, even in principle: The way gravitational waves are looked for is, essentially, to synchronize two clocks, take them apart, and see if there is a phase shift in one of them due to a passage of a gravitational wave. "apart" means "more apart than a wavelength".
The setups which Eppley and Hannah deal with, as well as similar setups like Feynman's sticky bread thought experiment, are basically generalizations of this, applied to many clocks and making the connection between time slowing down and energy decreasing.
In particular, this means if two clocks are located much closer than a wavelength (or if the bread's "structure" is finer than the wavelength), any effect of the wave is unmeasureable. But this is exactly the equivalent of a detector measuring momentum Eigenstates (the photon is measurable by a detector much smaller or much larger than a wavelength).
This doesent mean that gravitational waves dont exist in the classical limit of "many gravitons per wave" (Eppley and Hannah's ideas apply in this limit), but in this limit quantum effects should also average out.
What it means is that a gravitational wave "of one graviton" can at best measured in its position Eigenstate, but not in the momentum one, which essentially invalidates what Eppley and Hannah proposed at the root (as well as affecting such basic arguments as Heisenberg's microscope for gravitons).
Am I making a mistake here? I think there is no escaping the fact that measurement of gravitational waves will be by watching clocks and rods oscillate, and that is very different from the usual "quantum" gedankenexperiments used in non-gravitational contexts.
GIorgio (Torrieri)