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Gravity of objects in superposition won't teach us anything

LHC data fully charged: In this week, the CMS published the first paper (about B-mesons) with the full data collected up to now (there will be a pause for several years for upgrades), a whopping 140/fb of data. Via CERN. With this dataset, about 4x 35/fb, all the "numbers of sigma" may double relatively to the previous wave of papers!

For the first time during her full-blown campaign to ban both theoretical and experimental particle physics, Sabine Hossenfelder told her readers what she imagines to be her alternative. In her text When gravity breaks down, she concluded with a wish:
I hope to see experimental evidence for quantum gravity in my lifetime.
You can easily see why she was elected the new chairwoman of the International Movement Against Solid Physics. Yes, both Smolin and Woit have been dethroned a few years ago. According to this lady, it is impossible for a \(100\TeV\) collider to see new non-gravitational particle physics. But to see effects that are associated with the Planck scale, \(10^{19}\GeV\) (which is some 14 orders of magnitude higher), is doable in her lifetime.

"A Little Apple" by Kristína. Does the apple actually appear in the song? Even if it doesn't, the video is a good enough example of beauty in physics. If you don't understand Slovak, imagine that the lyrics is a translation of the blog post below. ;-)

Great. Just to be sure, every high school student who has some understanding of modern physics knows that Hossenfelder's plan to find new physics through "experimental quantum gravity" is vastly less likely than the plan she considers unlikely.

You know, Max Planck calculated the Planck energy, Planck length, and other Planck-things more than a century ago. During the subsequent decades, and it's more than half a century ago by now, physicists increasingly understood the correct interpretation of those constants of Nature. For example,\[

\ell_{\rm Planck} = \sqrt{ \frac{\hbar G}{c^3} } \approx 1.6 \times 10^{-35}\,{\rm m}

\] is the Planck length and expresses the typical length of patterns in an experiment that is sensitive to a nontrivial combination of quantum and gravitational phenomena. The reason is that when the distances are much longer, \(L \gg \ell_{\rm Planck}\), it must be true that either the \(\hbar\to 0\) or \(G\to 0\) approximations are adequate to describe what is going on.

Every physicist sort of knows that "you cannot experimentally test quantum gravity". So what can she possibly mean? The paragraph near the very end summarizes her random remarks:
In summary, the expectation that quantum effects of gravity should become relevant for strong space-time curvature is based on an uncontroversial extrapolation and pretty much everyone in the field agrees on it.* In certain approaches to quantum gravity, deviations from general relativity could also become relevant at long distances, low acceleration, or low energies. An often neglected possibility is to probe the effects of quantum gravity with quantum superpositions of heavy objects.
Now, all the new research directions that she considers "promising" are clearly fringe physics – but they are fringe physics to different extents.

First, yes, quantum gravity becomes relevant at strong spacetime curvature. But how strong should the curvature be? Well, very very strong. The radius of curvature should be about the Planck length discussed above – i.e. one in the Planck units. The curvature tensor itself scales like \(1/a^2\) with the length. To compare, what is the curvature created by Earth's gravitational field in the Planck units? The curvature scales like \(M/a^3\). The distance from the center of Earth is some \(10^7\) meters or \(10^{42}\) Planck lengths. Take the minus third power to get \(10^{-126}\). OK, you may figure out how much insufficient the Earth's mass well below \(10^{40}\) Planck masses is to bring this number close to the unity.

We just can't make the curvature so strong. The high-energy colliders that Hossenfelder wants to abolish are clearly the most promising gadgets to create conditions that are effectively equivalent to these high values of curvature. But they're still insufficient. They're similarly "much below the Planck curvature" as their energy is "well below the Planck energy".

The only known loopholes involve the surprising and unlikely claim that the relevant Planck length we should substitute is much longer than \(10^{-35}\) meters. How it could be much longer? Only if there are additional large or warped extra dimensions – associated with scenarios by Arkani-Hamed et al. and Randall et al., two people and two research directions that Hossenfelder counts among the main targets of her populist anti-science campaign. The likelihood of the large (ADD) and warped (RS) dimensions isn't the same but let's not discuss these "relative details" here.

Too bad, without the pictures with extra dimensions of one kind or another (where the weakness of gravity is partially explained by the large enough size of the extra dimensions in which the originally stronger gravity is "diluted" – or where it escapes to some other brane), we may really prove that none of the experiments that are doable produce a sufficiently high curvature to measure the effects of quantum gravity. In the Randall-Sundrum scenario, one could have a chance to see quantum gravity, e.g. the evaporation of small black holes that could be experimentally produced. It's unlikely but assuming that RS is irrelevant for all experiments, there's no chance.

Aside from the "high curvatures" which are a correct regime for quantum gravity but an impossible one experimentally, she mentions "long distances" and "low energies" – in a somewhat bizarre order in which "low accelerations", which are a completely different issue, get in between "long distances" and "low energies" which are nearly equivalent. Too bad, all papers claiming some generic "quantum gravity effects" in the regime of long distances or low energies belong to the broken physics category. Long distances and low energies is exactly where the normal separated theories of gravity and non-gravitational forces work well – that's where they have been tested.

In this triplet of conditions, only "low accelerations" has a chance for surprises. I do think it's plausible – but the probability is something like 0.01% – that the dark matter phenomena may actually be explained by a specific version of MOND theories where a "low acceleration" is a natural quantity that decides whether the new surprising effects kick in. I have proposed a novel holographic/interference justification for such unusual physics myself. But even if this is how the galactic curves etc. are explained, there is virtually zero chance to reconstruct these effects by man-made experiments.

If the acceleration is below a tiny constant, the gravitational force could be a bit stronger than what is predicted by Newton. But which acceleration should we exactly substitute to the previous sentence for the rule to make sense? Do new effects exist if the total acceleration relatively to some freely falling frame is tiny? Or is it enough for individual terms to be tiny? Or should we measure that acceleration relatively to some frame that is not freely falling?

These questions haven't been coherently answered – there is no persuasive, mathematically coherent theory of the MOND kind that would also make new predictions for man-made experiments. Moreover, I think that every possible answer to those questions either produces a theory that has already been falsified (e.g. by tests of the equivalence principle); or a theory whose newly predicted effects for man-made experiments are negligible so that no new physics could be measured in this way. If you reached a different conclusion, please tell us about a whole derivation of yours.

But what is most characteristic for her identity as a talking head preferring pseudoscience is the last option:
An often neglected possibility is to probe the effects of quantum gravity with quantum superpositions of heavy objects.
I have discussed these misunderstandings in Why "semiclassical gravity" isn't self-consistent (2012) and Quantum character of gravity doesn't need to be "tested" (2015), aside from other places. And I would like not to write very similar things again. I hate to do things repeatedly – while demagogues like Hossenfelder clearly enjoy it because a lie repeated many times "becomes" the truth.

What she wants to see is experiments going "beyond semiclassical gravity". She approvingly quotes about four papers. A theoretical one, Kuo-Ford 1993, and three recent experimental ones: Schmöle et al. 2016, Bose et al. 2017, and Marletto-Vedral 2017. I have discussed the emptiness of the Marletto-Vedral physics in Summer 2017.

You know, she seems obsessed with the semiclassical gravity, an approximation in which the gravitational field is considered classical and it is driven by the "expectation value" of the stress-energy tensor derived from the matter. But the matter itself is treated quantum mechanically. Einstein's equations say\[

R_{\mu\nu}-\frac{1}{2} R g_{\mu\nu} = \frac{8\pi G}{c^4} \left\langle \hat T_{\mu\nu} \right\rangle_{\ket\psi}

\] in this framework. This approximation is a usable approach to deal with the co-existence of gravity and quantum matter in the practical situations. Quantum mechanics is normally confined to short distances so it doesn't affect the motion of the macroscopic objects. But only macroscopic objects influence gravity which makes it sensible to assume that only some "classical approximation" drives the gravitational field.

But the formula above is completely inconsistent with the basic rules of quantum mechanics. It is non-linear in \(\ket\psi\). More gravely, it promotes \(\ket\psi\) into a set of classical degrees of freedom – because the evolution of some other classical degrees of freedom, the metric tensor, directly depends on \(\ket\psi\). That's too bad because in this picture, \(\ket\psi\) is no longer probabilistic, it is a classical degree of freedom, exactly what it shouldn't be.

In particular, when \(\ket\psi\) collapses due to the measurement, the collapse immediately manifests itself by the response of the metric tensor according to the version of Einstein's equations above. That's too bad because the precise moment of the collapse shouldn't matter – and if there were a precise moment, the collapse is only simultaneous in one reference frame. That's why this preferred reference could be measured by the response of the metric tensor – and the Lorentz covariance (or basic rules of the theory of relativity) would be broken.

This just doesn't happen in the real world. And while the approximation above may often be assumed – because the gravitational relevant matter is heavy and therefore "approximately classical" – every good theorist knows that the equation above, or semiclassical gravity, isn't like the Standard Model. What I mean is that it is not a state-of-the-art theory or the best theory that we have that is describing some phenomena. Instead, it is just a somewhat practical but otherwise scientifically dirty approximation to a theory that actually is the state-of-the-art theory.

So even if an experiment saw some "violation of semiclassical gravity", and the parameters of those aforementioned proposed experiments are still many orders of magnitude away from that goal, it would represent no discovery of new physics whatsoever.

You know, genuine good theorists are using the phrase "semiclassical approximation" often but they mean something else. They mean the semiclassical approximation of any quantum mechanical theory which is basically a generalization of the Bohr-Sommerfeld condition from the old quantum theory. The integral \(\oint p\,dq\) is quantized in integral multiples of \(h\) and things like that. This isn't just a thesis in an obsolete predecessor of quantum mechanics. It's a picture that is basically equivalent to the WKB approximation in the "new" theory of quantum mechanics – the same WKB approximation I recently discussed in the context of Michael Mann's cheesy claims.

In the semiclassical approximation – as used by big shot physicists (which is largely equivalent to one-loop approximation in Feynman diagrams) – there is no rule "how the gravitational field should be treated" because the approximation isn't about gravity at all. And if they talk about the "semiclassical approximation" in the context of theories with gravity, they still allow gravitons – the quantum mechanical treatment of perturbations of the gravitational field, on top of a classical background. You may distinguish good quantum physicists from the bad ones by their usage of the word "semiclassical". If they find it obvious that they mean things like the WKB approximation, they're closer to good physicists – at least good ones to do research of things that depend on quantum mechanics; if they imagine things like "semiclassical gravity", they are not good.

What do you have to do to violate the assumptions of semiclassical gravity in experiments? Well, because the stress-energy tensor – which is an operator in the full theory, like every other observable – is being replaced by its expectation value, the "violation of the semiclassical approximation" clearly involves situations in which the quantum mechanical uncertainty of the stress-energy tensor (the uncertainty encoded in the wave function for that tensor) becomes large enough to have observable consequences.

Is it hard? Well, if you only want the wave function to be spread, it's not hard. Just extend the Schrödinger's cat experiment. A random quantum process, such as the decay of a radioactive nucleus, decides whether a cat is killed. And to make things dramatic, we don't just kill a cat by some invisible poison. Instead, we kill the cat by a huge hammer whose gravitational field may be measured.

In this straightforward way, the random decay of the nucleus brings the hammer – and its gravitational field – to a superposition of two or many states, just like Schrödinger's cat is brought into a superposition. Much like Erwin Schrödinger himself, the laymen have an impossible psychological problem with "big objects" in superpositions but real quantum physicists don't have this problem. Real physicists know that quantum mechanics – and superpositions – apply to all objects, including the big ones. They apply to the gravitational fields, too. Any object in the Universe that may be in many states may also be in their superposition. This is an absolutely universally valid postulate of quantum mechanics, the linearity postulate. If you think that this fact forces quantum mechanics to make invalid predictions, then you have completely misunderstood how the quantum mechanical predictions are actually made and what they say – you have probably been persuaded by not so real scientists in the media with their idiotic whining how "weird" quantum mechanics is. In reality, there's no contradiction.

Fine. So the gravitational field of the large hammer that killed the cat evolves into a superposition. In practice, we think that the hammer is either here or there and it's enough to use classical physics to describe the "or". But physicists know it's just an approximation. This approximation is viable because the relative phase between the states "innocent hammer" and "homicidal hammer" is unobservable. It's unobservable because of decoherence that is normally fast enough for objects like hammer.

Can you slow it down? It's very hard to protect quantum coherence, especially for objects that are heavy enough for their gravitational field to be experimentally observable. Even if you succeeded, there's one problem: the leading decoherence is almost certainly due to non-gravitational interactions. Why? I think we could reduce it to our Weak Gravity Conjecture. Gravity is the weakest force – and in some proper counting, it will also mean that it gives the weakest contribution to the decoherence.

So if some experiments succeed in cooling down the hammer etc. to observe the quantum coherence between its states – which correspond to different profiles of the gravitational field – it won't be a gravitational experiment. The last effects they will have to struggle with are non-gravitational interactions that cause most of the decoherence. When the decoherence is fast enough, only the squared absolute values of the wave function are experimentally observable in practice.

But if such experimenters succeeded and measured some "relative phase" of the pieces of the wave function "innocent hammer with the innocent gravitational field" and "homicidal hammer with the homicidal gravitational field" – two options whose names describe what the hammer did to the cat (note that the death of the cat is completely unnecessary in that experiment, the experimenters are cruel) – state-of-the-art theories of physics do predict what will happen and there exists no known plausible alternative theory that would be compatible with the known experiments but that would also imply something "new" for these experiments with "heavy objects in superpositions" etc.

If you follow Hossenfelder's recommendations, the chance of finding something that genuine good physicists would consider "new physics" is basically zero. Well, there may always be surprises. But scientists generally don't look for surprises totally randomly – deeply religious people who look for God in public bathrooms may be better for that. Scientists must have at least rough theories or scenarios that are feasible. Those exist for the FCC collider but they don't exist for Hossenfelder's scenarios.

A few paragraphs ago, I discussed how folks like Hossenfelder use the word "semiclassical" differently than the good physicists do. Well, at least in that case, there was a semi-meaningful definition of the phrase "semiclassical gravity". In the case of "quantum gravity", there isn't one. She uses the phrase "quantum gravity" completely incorrectly and connects this phrase with lots of completely wrong statements.

(I think that other pop science writers, including Ethan Siegel, suffer from the same problem. For example, in this 2018 text, he correctly shows that a simple experiment shows that we need a theory of quantum gravity. Well, he has only shown that our world involves both quantum and gravitational phenomena, that's enough for the proof that we need a consistent theory involving both. But he's wrong in his implicit or explicit statement that we don't know and we can't predict what will happen in his simple experiment and other experiments that combine quantum mechanics and gravity in an "innocent" way. We – meaning the competent professional physicists in the field, not the laymen [what the laymen know is a matter of education, not science] – know what will happen. We do have a practically good enough theory combining QM and GR. The "quantum gravity" that remains mysterious or unpredictable requires much more extreme or more esoteric experiments.)

Good physicists know that just by seeing superpositions of heavy objects and their gravitational fields, you just don't test any quantum gravity. It's still a mundane low-energy physics. Our approximate effective quantum field theories – which do allow the incorporation of gravitons and their Fock space including all the superpositions (just like they incorporate photons and the Fock space of the electromagnetic field) – are perfectly sufficient for predicting what actually happens in doable experiments even if both the gravitational force and quantum interference appear somewhere in these experiments.

The real problem is that Hossenfelder doesn't actually understand the state-of-the-art physics. So she doesn't know what our established theories predict. What she wants professional physics to be replaced with is some kind of schoolgirls' physics (it can be schoolboys' physics but it's more likely to be schoolgirls' physics). In that kind of physics, people aren't actually discovering new phenomena. Instead, they are discovering old phenomena and once the teacher asks the schoolgirls to be impressed (because the observations disagree with the prediction based on some ideas that aren't very good or correct – but those people don't care), schoolgirls say that they are impressed and they get a good grade for that.

But real physicists won't be surprised by the detection of heavy objects in quantum superpositions because that's how our Universe has been known to work for more than 90 years – and they may actually make all these predictions and have virtually no doubt that these predictions work and have to work.

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