I Quantum Measurements with Gravitational Waves

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Would using gravitational waves to measure position and momentum of an electron disprove HUP since grav. waves are not "made of" particles?
Would using gravitational waves to measure (it's obviously a gedankenexperiment!) position and momentum of, say, an electron in a specific state, disprove HUP since the quantum of energy of grav. waves does not exist? Would it be possibile to have an arbitrarily small uncertainty in position measurement, and in momentum measurement (e. g. with arbitrarily small wavelenght and arbitrarily small amplitude of the wave)?

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What makes you think a electron gives off gravitational waves? It creates an EM field that theoretically reveals its exact position and momentum. But, that's classical EM, which experimentally QM trumps.

QM (not GR) describes the dynamics of an electron. If anything the HUP disproves GR - if you want to put it like that.
 
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PeroK said:
What makes you think a electron gives off gravitational waves?

We can take a step back from even this. What makes you think QM forbids measuring both position and momentum?
 
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lightarrow said:
Would using gravitational waves to measure (it's obviously a gedankenexperiment!) position and momentum of, say, an electron in a specific state, disprove HUP since the quantum of energy of grav. waves does not exist?

Why do you think the quantum of energy of gravitational waves does not exist?
 
The relationship between QM and GR is maybe the biggest unknown in physics now. I certainly don't know the answer, and I have a strong suspicion that no one else does either; at least that's what everyone tells me.

If you want to make progress in this area, you'll want to clean up your question. For example, why do you presuppose that an electron even has "a position"? It's my understanding that the HUP doesn't say that an electron has a unique position and a unique momentum, but we can't measure it. I believe it says that the concept of a unique position and momentum are incompatible in a very fundamental way.

OTOH, physics has been revolutionized in the past with dramatic new theories that contradicted what everyone thought. So, I guess we'll see what develops.
 
PeroK said:
What makes you think a electron gives off gravitational waves? It creates an EM field that theoretically reveals its exact position and momentum. But, that's classical EM, which experimentally QM trumps.

QM (not GR) describes the dynamics of an electron. If anything the HUP disproves GR - if you want to put it like that.
No, I don't want to disprove GR, or HUP, or QM or anything else. I only would like to know if what I wrote could be seriously taken as strong clue of the existence of gravitons.
Concerning the fact an electron gives off g. waves, I am not sure; indeed, if I remember well, a dipole oscillation of mass can't generate g. w. Is this the case?

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Vanadium 50 said:
We can take a step back from even this. What makes you think QM forbids measuring both position and momentum?
If this question is referred to me: I haven't written that.

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lightarrow said:
I only would like to know if what I wrote could be seriously taken as strong clue of the existence of gravitons.

If we could actually make sensitive enough measurements involving gravitational waves for quantum aspects of such waves to be testable, then yes, we could test experimentally to see if such quantum aspects were present.

However, we are many, many orders of magnitude away from being able to make such measurements.

Theoretically, most physicists believe that gravity should have quantum aspects because everything else does. That is why one of the main theoretical efforts ongoing in fundamental physics is trying to find a theory of quantum gravity that works.

lightarrow said:
a dipole oscillation of mass can't generate g. w. Is this the case?

Yes. You need at least quadrupole oscillations. More precisely, you need a nonzero third time derivative of the quadrupole moment.
 
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lightarrow said:
If this question is referred to me: I haven't written that.

You might not have intended to, but you weren't very clear about what question you were asking until post #6. Prior to that, it certainly looked as though you were saying that measurements involving gravitational waves could violate the HUP.
 
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  • #10
PeterDonis said:
You might not have intended to, but you weren't very clear about what question you were asking until post #6. Prior to that, it certainly looked as though you were saying that measurements involving gravitational waves could violate the HUP.
Ok, it was a mistake I made in order to express my question.
Then, could, in theory a g. w. be scattered off an electron in such a way to theoretically measure the electron's position and momentum similarly to what we can do with an em wave?
Thanks.

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  • #11
lightarrow said:
Then, could, in theory a g. w. be scattered off an electron in such a way to theoretically measure the electron's position and momentum similarly to what we can do with an em wave?

I don't see why not, in principle. And in principle we would expect such a measurement to have the same quantum properties as an EM wave measurement does.

Of course in practice it is going to be a long, long time before we can do anything like this.
 
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  • #12
lightarrow said:
No, I don't want to disprove GR, or HUP, or QM or anything else.

Then why did you title this thread "Disproving Heisenberg principle with Gravitational Waves"?
 
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  • #13
As I wrote to PeterDonis, it was my mistake. I just wanted to focus the attention on grav. waves' presumed quantization using HUP: either g. w. are quantized or they cannot be used in measuring a particle's non-commuting observables. The concept should be: since HUP obviously holds (I never had doubts about it), does this imply that g. w. have to be quantized (without the need to make the experiment in reality)?

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  • #14
lightarrow said:
I just wanted to focus the attention on grav. waves' presumed quantization using HUP

Then the thread title needs to be changed. Done.

lightarrow said:
since HUP obviously holds (I never had doubts about it), does this imply that g. w. have to be quantized

This is one of the reasons why most physicists believe we will need a quantum theory of gravity, yes.
 
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  • #15
PeterDonis said:
Then the thread title needs to be changed. Done.

This is one of the reasons why most physicists believe we will need a quantum theory of gravity, yes.
Thanks.

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  • #16
Well, we should be forgiven that we thought you meant that this disproves HUP because a) it was in the title (now changed) and b) in the text (still there).

Now we have another issue - I can't for the life of me figure out what we are trying to show. That electrons do (or do not) interact with gravity waves? That gravity waves do (or do not) obey the HUP. Something else? Message #10 did not clarify it. Why don't you think about it and post exactly what you want to know.
 
  • #17
Vanadium 50 said:
Well, we should be forgiven that we thought you meant that this disproves HUP because a) it was in the title (now changed) and b) in the text (still there).

Now we have another issue - I can't for the life of me figure out what we are trying to show. That electrons do (or do not) interact with gravity waves? That gravity waves do (or do not) obey the HUP. Something else? Message #10 did not clarify it. Why don't you think about it and post exactly what you want to know.
In a discussion with a friend, he claimed that gravitons = quantum of g.w. have to exist, because if they didn't, it would be possibile to measure, e. g., an electron's position and momentum in some state with ∆x and ∆p (standard deviations) arbitrarily small, disproving HUP, which is impossible.
Actually I didn't believe this simple consideration could prove that g.w. have to be quantized, even if I know very little on the subject, so I asked here to have more... context and PeterDonis answered clearly that... I was wrong.

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  • #18
Nobody knows what gravitons are, because there's no satisfactory quantum (field) theory of gravitation yet. So it's useless to speculate about their properties. Whether or not there is a quantum theory including gravitation is not known either, i.e., it's not clear whether or not the fundamental formulation of QT has to be changed or not. So the question, whether or not the general Heisenberg-Robertson uncertainty relation (which is about state preparation not about the ability or disability to measure simultaneously any pair of observables) still holds in the present form or not in some future quantum theory including the gravitational interaction of not.
 
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  • #19
vanhees71 said:
Nobody knows what gravitons are, because there's no satisfactory quantum (field) theory of gravitation yet. So it's useless to speculate about their properties. Whether or not there is a quantum theory including gravitation is not known either, i.e., it's not clear whether or not the fundamental formulation of QT has to be changed or not. So the question, whether or not the general Heisenberg-Robertson uncertainty relation (which is about state preparation not about the ability or disability to measure simultaneously any pair of observables) still holds in the present form or not in some future quantum theory including the gravitational interaction of not.
So you're saying that the Gedankenexperiment I described cannot prove at all that g. w. are quantized?

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  • #20
lightarrow said:
So you're saying that the Gedankenexperiment I described cannot prove at all that g. w. are quantized?

No, he's saying that we currently have no theory that predicts what the result of your gedankenexperiment would be. A theory that could do that would have to be a theory that has General Relativity and our current quantum field theory as approximations in appropriate limits (roughly, the limit in which gravity is significant but quantum mechanics can be ignored, and the limit in which QM is significant but gravity can be ignored), and also explains what happens in cases, such as your gedankenexperiment, in which both gravity and quantum mechanics are significant and cannot be ignored.

However, if we were able to actually do your experiment, it wouldn't matter whether we had a theory; the experiment itself would tell us whether gravitational wave measurements obey the HUP or not.
 
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  • #21
lightarrow said:
So you're saying that the Gedankenexperiment I described

You haven't proposed a Gedankenexperiment. You have neither described the state preparation nor the measurement. When pressed, you say what you are proposing is the opposite of what you have written. Thus far, all we have is there's an electron, a gravitational wave, and then something something something.

I suspect that if you described a proper experiment - defined in enough detail that someone could in principle perform it - you would discover that you are insensitive to the effect that you are interested in, because the electron and whatever generates the gravitational radiation are still subject to quantum mechanics.
 
  • #22
I can only conclude that you don't have an experiment in mind - one defined in enough detail that someone could in principle perform it.
 
  • #23
PeterDonis said:
However, if we were able to actually do your experiment, it wouldn't matter whether we had a theory; the experiment itself would tell us whether gravitational wave measurements obey the HUP or not.

I don't think we do. I don't think we even have an experiment. But if the idea is to somehow look at the path of the recoil electron, that recoil electron obeys the HUP.
 
  • #24
vanhees71 said:
Nobody knows what gravitons are, because there's no satisfactory quantum (field) theory of gravitation yet. So it's useless to speculate about their properties. Whether or not there is a quantum theory including gravitation is not known either, i.e., it's not clear whether or not the fundamental formulation of QT has to be changed or not. So the question, whether or not the general Heisenberg-Robertson uncertainty relation (which is about state preparation not about the ability or disability to measure simultaneously any pair of observables) still holds in the present form or not in some future quantum theory including the gravitational interaction of not.
Thanks, vanhees.

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  • #25
PeterDonis said:
No, he's saying that we currently have no theory that predicts what the result of your gedankenexperiment would be. A theory that could do that would have to be a theory that has General Relativity and our current quantum field theory as approximations in appropriate limits (roughly, the limit in which gravity is significant but quantum mechanics can be ignored, and the limit in which QM is significant but gravity can be ignored), and also explains what happens in cases, such as your gedankenexperiment, in which both gravity and quantum mechanics are significant and cannot be ignored.

However, if we were able to actually do your experiment, it wouldn't matter whether we had a theory; the experiment itself would tell us whether gravitational wave measurements obey the HUP or not.
Tanks, PeterDonis.

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  • #26
lightarrow said:
the Gedankenexperiment I described

I should clarify, in the light of the comments @Vanadium 50 has been making, that I agree with him that you have not actually defined a specific experiment. You have just given a very general hand-waving description of a category of possible experiments, along the lines of "use gravitational waves to measure something about a quantum particle in a similar way to how we would make an analogous measurement with EM waves". Everything I have said applies to any possible experiment in that category, which is why I've gone ahead and responded even though no specific experiment has been described. As far as I can tell, the same applies to what @vanhees71 has said as well.
 
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  • #27
PeterDonis said:
I should clarify, in the light of the comments @Vanadium 50 has been making, that I agree with him that you have not actually defined a specific experiment. You have just given a very general hand-waving description of a category of possible experiments, along the lines of "use gravitational waves to measure something about a quantum particle in a similar way to how we would make an analogous measurement with EM waves". Everything I have said applies to any possible experiment in that category, which is why I've gone ahead and responded even though no specific experiment has been described. As far as I can tell, the same applies to what @vanhees71 has said as well.
I believed you all know the "Heisenberg microscope gedankenexperiment":
https://en.m.wikipedia.org/wiki/Heisenberg's_microscope
Am I so old? 🤔

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  • #28
lightarrow said:
I believed you all know the "Heisenberg microscope gedankenexperiment":

Us all knowing it is not the same as us knowing that that is the gedankenexperiment you were talking about. You need to give such references explicitly, not make other people guess what you mean.
 
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  • #29
It's not clear how that relates to gravity.
 
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  • #30
Vanadium 50 said:
It's not clear how that relates to gravity.

Substitute gravitational waves, in the geometric optics approximation, for the light rays in the Heisenberg microscope setup.
 
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  • #31
PeterDonis said:
Substitute gravitational waves, in the geometric optics approximation, for the light rays in the Heisenberg microscope setup.

I don't see how this can possibly work. You have a gravity wave source, a gravity wave detector and a target. All three of them are subject to the rules of QM. You will not violate the HUP - assuming that's what we are trying to discuss now - because every element you build your experiment out of is subject to it.
 
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  • #32
Vanadium 50 said:
I don't see how this can possibly work.

In principle, setting up the experiment should be the same as for the corresponding experiment with EM waves. Of course that's way beyond our present technical capabilities, but I don't see why it would be impossible in principle.

Vanadium 50 said:
You have a gravity wave source, a gravity wave detector and a target. All three of them are subject to the rules of QM.

We don't know that for certain because we don't have a theory of quantum gravity and we have no capability at present of probing any quantum aspects of gravity (or more precisely of spacetime geometry) experimentally. Most physicists believe that we will sooner or later discover a theory of quantum gravity that works and confirm it experimentally; but until it actually happens, it's a belief, not a proven fact. Of course if the belief is correct then the theoretical prediction of what would happen in such an experiment would be exactly as you describe. Hopefully someday we'll be able to actually test it and see.
 
  • #33
But for this you don't need quantum gravity but just the semiclassical approximation, i.e., electron quantized the gravitational field classical. It's exactly analogous to the em. case, and indeed there's no way to violate the Heisenberg-Robertson uncertainty relation. Ironically Heisenberg's first paper is wrong. It has been corrected by Bohr immediately after its publication ;-)).
 
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  • #34
PeterDonis said:
We don't know that for certain

Of course we do. Our generator, to pick one element, is some contraption of masses and springs (perhaps with high spring constant, like a rod) and some energy source to push them around, Those components behave according to QM. Their behavior does not change just because our intent is now to use them to study gravity.

This is obscured because the OP has steadfastedly refused to provide a description of what he is suggesting. So long as we are talking about black boxes one can implicitly ascribe to them all sorts of non-physical behavior. Even if there were some funny business going on with gravity, we would not be able to tell because our tools to study it are all subject to the HUP.
 
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  • #35
Vanadium 50 said:
This is obscured because the OP has steadfastedly refused to provide a description of what he is suggesting.
"In principle, setting up the experiment should be the same as for the corresponding experiment with EM waves. Of course that's way beyond our present technical capabilities, but I don't see why it would be impossible in principle".
PeterDonis, who wrote this, seems to have understood what I meant. The same for vanhees.
Of course you didn't mean to ask me to describe in all details such an experiment, since:
1. It's highly speculative.
2. I'm not an experimental physicists and not even theoretical, I don't even have a degree in physics.
3. If I had in mind an experiment with full details I wouldn't have described it here but in a research paper.

Obviously all (or almost) of us are good in answering a perfectly described question.
But questions are asked, mostly, because we don't know well the subject, isn't it?

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  • #36
Vanadium 50 said:
Even if there were some funny business going on with gravity, we would not be able to tell because our tools to study it are all subject to the HUP.

Gravitational waves are a (potential future) tool as well; the question would be whether they are subject to the HUP. If they aren't, something different would have to happen when they interact with, say, an electron (possibly in a different experimental setup than the "Heisenberg microscope", based on the comment by @vanhees71), even if every other experiment we've done with electrons shows that they are subject to the HUP.

Or, to put it another way, if it is really the case that there is no way for us to ever observe HUP violations with gravitational waves (or any other gravitational phenomenon) because all of our other measuring tools obey the HUP, that is the same, physically, as saying that gravity does obey the HUP. If violations are intrinsically unobservable, then as far as physics is concerned, they aren't there. But we won't know whether or not violations are observable until we can actually make an observational test.
 
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  • #37
vanhees71 said:
for this you don't need quantum gravity but just the semiclassical approximation, i.e., electron quantized the gravitational field classical. It's exactly analogous to the em. case, and indeed there's no way to violate the Heisenberg-Robertson uncertainty relation.

So basically this means that, while there might be some way of testing whether gravitational waves have quantum aspects, or whether they can violate the HUP, the gravitational wave analogue of the Heisenberg microscope experiment cannot provide such a test?
 
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  • #38
PeterDonis said:
Gravitational waves are a (potential future) tool as well; the question would be whether they are subject to the HUP. If they aren't, something different would have to happen when they interact with, say, an electron (possibly in a different experimental setup than the "Heisenberg microscope", based on the comment by @vanhees71), even if every other experiment we've done with electrons shows that they are subject to the HUP.
I think, what you are after is even more ambitious, i.e., you don't want to use gravitational waves (in the sense of classical ones, i.e., based on standard GR) but you even want to see quantum-gravitational effects, i.e., field quantization.

Take the analogy with em. waves: There the direct experimental confirmation of field quantization is already pretty difficult. The first indirect hint was of course already black-body radiation when treated in the kinetic approach by Einstein (1917): There you necessarily need not only the classical notions of stimulated emission (em. waves emitted by accelerated charges, where the acceleration is due to the em. field itself, e.g., the electrons/nuclei in the walls of a cavity) and absorption but also spontaneous emission, which is a generic quantum effect and due to the vacuum fluctuations of the em. field.

Now for the gravitational field it's hard to imagine how to achieve an analogue of gravitational black-body radiation or, in quantum language, a graviton gas in thermal equilibrium.

Then more direct hints at field quantization in the em. case are not so easy to find. The usual QED-tree-level results like the photoelectric effect or Compton scattering are equivalent to the semiclassical treatment, i.e., with the particles involved (here mostly electrons) treated quantum-mechanically and the em. field/waves as classical.

Since the most simple case for truly quantum effects of the em. field is the impossibility to split a photon of given frequency somehow, you need to prepare true single-photon Fock states to use quantum optical measures to demonstrate field quantization. AFAIK the first experiment on the "indivisibility of photons" is the one by Grangier, Roger, and Aspect (1986). They used an atomic cascade to have heralded single photons and demonstrated the anticorrelation effect using the heralded single photon in a beam splitter. To really see this anticorrelation, it's important that the single photon is heralded, i.e., a utmost dimmed coherent state won't do. Today of course a more convenient way is to use parametric downconversion as a heralded-single-photon source. All this is technically available for about 30 years only, and it's hard to imagine how long it will take to devolop the gravitational analogue, i.e., to produce "heralded true single-graviton states".

All these speculations of course also assume that this analogy with the electromagnetic field and its quantization somehow applies to the gravitational field too, which is not so clear. Though of course you can quantize the (free) gravitational field formally, there's still not a satisfactory quantum theory of gravitation including interactions (interactions of the gravitational field with matter as well as the self-interaction of the gravitational field, because as non-abelian gauge theory gravitons should be self-interacting at tree level if the analogy with standard-field quantization holds).

Another puzzling question is, in how far one has to take the geometrical reinterpretation of the gravitational field as spacetime geometry as is standard in the formulation of classical GR since Einstein's original forumulation seriously, i.e., in how far is spacetime itself quantized and what does this really mean on an operational and observational level.
 
  • #39
PeterDonis said:
So basically this means that, while there might be some way of testing whether gravitational waves have quantum aspects, or whether they can violate the HUP, the gravitational wave analogue of the Heisenberg microscope experiment cannot provide such a test?
I don't think so, because you just have a classical gravitational wave which is scattered by the electron and you infer information from the scattered wave. Of course that's impossible to detect in reality since the gravitational waves emitted from a wiggling electron are very weak. One should note that the typical interaction strength between em. interactions and gravitational interactions is ##10^{40}##.
 
  • #40
vanhees71 said:
I think, what you are after is even more ambitious, i.e., you don't want to use gravitational waves (in the sense of classical ones, i.e., based on standard GR) but you even want to see quantum-gravitational effects, i.e., field quantization.

Yes, agreed. Which means, as you note, that experimentally testing for this will be extremely difficult even compared to ordinary GW experiments, just as experimentally testing for quantization of the EM field is more difficult than testing classical EM behavior.
 
  • #41
Sure, don't forget that the observational direct discovery of gravitational wave is just 5 years old and consider, how long it took from the discovery of em. waves (Hertz ~1890) to the ability to prepare true (heralded) one-photon states (Aspect ~1985)!

In addition, it's not so clear to me, whether one can really draw this analogy between GWs and em. waves concerning quantization for the reasons given above. In the 1980ies when true single-photon states were realized for the first time, the experimentalists had a clearly developed QFT for the em. interaction, QED and it was well understood in theory how to prepare single-photon states. If I remember right, Aspect used atomic cascades, which was well understood. Nowadays it's standard to have much better single-photon sources from parametric downconversion thanks to the developments in laser technology and in non-linear optics (again on the quantum level).
 
  • #42
It's not clear to me how one could create a single graviton state.

But going back to the original question (or at least what I infer the original question was), what exactly is the HUP? It's a statement that the commutator of a variable and its canonical conjugate is non-zero (in fact, it's -iħ).

If one wants to argue "maybe it's different", one needs to specify what conjugate pair one is looking at, and how one interacts with the measuring system, as well as if and how the environment interacts with the measuding system. If you can't do any of these, I don't see how one can move past "maybe it's different".
 
  • #43
The HUP says for any two operators and any (pure or mixed) states
$$\Delta A \Delta B \geq \frac{1}{2} |\langle [\hat{A},\hat{B}] \rangle|.$$
I understood the OP such that he's looking at the usual position-momentum uncertainty relation
$$\Delta x_j \Delta p_k \geq \frac{\hbar}{2} \delta_{jk}.$$
 
  • #44
lightarrow said:
Summary:: Would using gravitational waves to measure position and momentum of an electron disprove HUP since grav. waves are not "made of" particles?

Would using gravitational waves to measure (it's obviously a gedankenexperiment!) position and momentum of, say, an electron in a specific state, disprove HUP since the quantum of energy of grav. waves does not exist? Would it be possibile to have an arbitrarily small uncertainty in position measurement, and in momentum measurement (e. g. with arbitrarily small wavelenght and arbitrarily small amplitude of the wave)?

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lightarrow
This is a rather complex question. Contained within the question itself are a number of assumptions. Controlling all the variables to obtain the answer would be an interesting project, as the experiment unfolded. Just the words, "gravitational waves," have presumptions. By the way, are gravitational waves continuous or are they continual?
 
  • #45
Alex Ford said:
By the way, are gravitational waves continuous or are they continual?

What's the difference?
 
  • #46
Continuous means no breaks are allowed. Continual means they are. (e.g. daylight is continual)
 
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  • #47
Alex Ford said:
This is a rather complex question. Contained within the question itself are a number of assumptions. Controlling all the variables to obtain the answer would be an interesting project, as the experiment unfolded. Just the words, "gravitational waves," have presumptions. By the way, are gravitational waves continuous or are they continual?
If "continuous" means "never ending" while "continual" means "starts at t1, proceeds without jumps and then stops at t2", how they couldn't be the second?

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  • #48
Alex Ford said:
Just the words, "gravitational waves," have presumptions.

What presumptions are you referring to?
 
  • #49
lightarrow said:
g. w. have to be quantized
Or QT relativized or a new theory beyond both...
 
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