Quantum Measurements with Gravitational Waves

[PeterDonis]

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.

 

[PeterDonis]

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?

 

[vanhees71]

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.

 

[vanhees71]

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 $10^{40}$.

 

[PeterDonis]

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.

 

[vanhees71]

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).

 

[Vanadium 50]

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".

 

[vanhees71]

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
$$\Delta x_j \Delta p_k \geq \frac{\hbar}{2} \delta_{jk}.$$

 

[Alex Ford]

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?

 

[PeterDonis]

By the way, are gravitational waves continuous or are they continual?

What's the difference?

 

[Vanadium 50]

Continuous means no breaks are allowed. Continual means they are. (e.g. daylight is continual)

 

[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?

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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lightarrow

 

[PeterDonis]

Just the words, "gravitational waves," have presumptions.

What presumptions are you referring to?

 

[physika]

g. w. have to be quantized

Or QT relativized or a new theory beyond both...