I include here my favourite part: John discusses how gravitational waves might be the mechanism for pilot wave mechanics.

I hope I’m not the one bombarding him with emails!

]]>While the physics media, popular opinion and generally accepted lecturers says things like ‘GR is wrong because singularities’, the physical and theoretical facts suggest very strongly the opposite.

In a black hole merger we have a well defined, simple to describe, and definitely calculable scenario. To summarize: a black hole – black hole merger releases a few percent of the total mass energy into gravitational waves, the aspects of which have been calculated to high precision.

Consider the electromagnetic equivalent. If two macroscopic (well any mass) charged, massive point particles do the same thing – orbit each other, the equations of Maxwell break down – infinite energy is predicted to be emitted in an ultraviolet catastrophe (Raleigh-Jeans). OK says everyone – that’s why we need quantum mechanics! But QED – which covers orbiting massive particles (say positronium, H atom) has huge renormalization problems and is ‘dippy‘.

GR handles this ultraviolet catastrophe – indeed it does not have one – much better than Maxwell or QED. Standard ‘simple’ QED is a mess (according to its authors). Of course QCD and canonical quantum gravity have much more immediate problems with complexity and are harder/impossible to get working, even with the normal merely dippy renormalization. Indeed if one were to quantize gravity then one might presumably end up with a quantum gravitational ultraviolet catastrophe!

First, the above arguments only hold for black holes (but they can be of any mass, even the mass of a proton). Since most physicists think that naked singularities can’t exist, it only makes the above argument stronger. Let’s also not forget that merging black holes will end up with merged singularities. *Gravity is fine when you only consider gravity*.

Tom Andersen, 2021

.Black hole mergers are well behaved and calculable, while the ‘best theory in the world’ – QED struggles with renormalization and more. QCD is incalculably worse and let’s not get started on quantum theories of gravity

So how about back to the original question? Are singularities a problem for Einstein’s gravity?

I’ll talk to a few things here: Naked Singularities ( EG Kerr solution with a > m) and also how these overextreme Kerr solutions would interact.

The Kerr solution to the Einstein equations contains a parameter, ‘a’ that is a measure of the angular energy in the black hole (or naked) Kerr object. If this parameter is over the mass of the hole (m) then (supposedly) all hell will break loose as a naked singularity will be visible. Having a > m is of more than dry theoretical concern, as for instance a wheel spinning on your car when driving at even 20km/hr has a > m (but it’s not the size of a molecule so the Kerr solution does not apply). More to the point, basically every black hole discovered has a spin > 0.1m, so we know astrophysical real Kerr solutions are already dangerously close to being naked. A little scandalous!

- Naked singularities could cause a quantum explosion of particles.
- Naked singularities will cause General Relativity to be wrong, as predictions break down.
- See this Wikipedia Naked Singularity article.
- Roger Penrose said they are impossible.

- General Relativity on its own does just fine with them. The Kerr solution with a > m is not ‘weird’ math.
- We don’t have a quantum theory of gravity (so arguments invoking QM are moot).
- The Cosmic Censorship Hypothesis is likely wrong: As the same Wiki article points out.
- My own theory is that both QM and EM are built from GR, but that is not needed for this article.
- “Evaporating black holes are naked singularities since they are not fully concealed by their event horizon.”
- Even Roger Penrose can make a mistake.

By Avi Loeb on May 3, 2020

Instead of finding reasons to avoid naked singularities, we should cherish the opportunity to find them as a path for exploring new physics. Of course, the crucial unknown in this regard is: “What do naked singularities look like?” Owing to the extreme curvature of spacetime in their vicinity, naked singularities might produce high-energy particles in a powerful fireball of energy. Do we observe such fireballs on the sky? Is it possible that we have already detected naked singularities but misinterpreted their nature?

https://blogs.scientificamerican.com/observations/in-search-of-naked-singularities/

One can do the orbiting spinning black hole calculation for Kerr solutions with a ~ m. See the references below etc.

The only reason that it has not been done for a > m is in my opinion that a > m is taboo in numerical relativity circles.

Horizons are a global – not local phenomena – so why would things change from a = 0.9999m to a = 1.0001m? In other words how is the other black hole to ‘know’ that a > m? In order to measure a > m requires being well outside the black hole. On merge, it’s not the horizons that merge, but rather the singularity structures, even in a normal a < m black hole merger. Think of a (planar spins +z) collision of two black holes, each with a = 0.9999m. Also imagine them to be huge – two light hours across. There is no feasible way that the black holes can tell a=0.9999m from a = 1.0001m – the bits that hit each other first will be barely concealed singularities (the horizon is very close to the singularity at a ~m).

Play with a single Kerr here!

“fast == overextreme (a > m)” Note that in the Visualizing Aspects of the Kerr Metric you can get a to 2 (where m is assumed m=1). Also see the entire https://analyticphysics.com/ – a really great site.

An interesting circumstance not discussed in O’Neill’s book is that the ergosphere remains for a fast Kerr black hole.

Note that a > m is not usually specifically talked about, mostly due to technical (numerical code and excise regions need changes) and (according to my reading of the physics community) taboo reasons. Looking at the papers – one can see that there is nothing special at a = m. For instance empirically developed formulas in some of the papers have no dependence on (a – m), etc.

See it on Twitter at https://twitter.com/knobsturner/status/1434586301119012864

]]>So my admittedly personal view is that matter cannot exist on its own. One hydrogen molecule will start to sleep if it’s not near other atoms. How near? The thought is that dark matter densities can tell us.

Matter cannot exist on its own, isolated. It needs a certain density of quantum waves or energy to bathe in. Otherwise the entire mechanism of both electromagnetism, quantum mechanics (and maybe nuclear forces) simply dies, the interactive particles (quarks and electrons) that form matter relax into sleeping versions of themselves, likely with virtually all of the mass intact. When in the presence of normal matter or the density of sleeping matter goes up to maybe something like an extremely diffuse gas cloud, the matter wakes up, and starts to take part in electromagnetic interactions. Indeed, the nuclear forces of this sleepy matter do not have to sleep, as we can’t see sleeping nucleons. Perhaps just the EM interaction drops off. This article explores some predictions and consequences of the Sleepy Matter Model.

Dark matter is sleepy matter, and dark energy is the ‘quantum energy’ – the dark energy is released when matter ‘goes to sleep’.

Dark matter is just plain matter, but it has ‘spun down’ due to being lonely. This effect happens at about the maximum density of dark matter ever found, or about the density of the most diffuse clouds of gas ever found (which are about equal).

There are a number of problems with the ΛCDM model (Lambda cold dark matter).

I will refer to as normal dark matter as Dark Matter.

Wikipedia is a good place to start for most of these problems. One can see the Bullet cluster below, which is both a problem and a victory for Dark Matter. That’s where we sit.

Dark Matter Problem | Problem | Sleepy Matter solution |

Satellite galaxies | Models of DM predict lots of Satellite galaxies. More are being found, but they tend to be equatorial to the galaxy, which is another problem. | Sleepy matter interacts with density rise on galactic plane and gets stuck there as the core of a satellite galaxy. Should be able to model this. |

Baryonic Tully Fisher relation | The mass of a galaxy is correlated to the fourth power of the rotation velocity of the outermost stars. Why would Dark Matter, which ignores regular matter obey this rule? | Sleepy matter wakes up when the density gets high, turning into normal matter. This normal matter interacts, limiting density, etc. There is only so much sleepy matter to fit in. Should be able to model this. |

Renzo’s rule | “For any feature in the luminosity profile there is a corresponding feature in the rotation curve and vice versa.” | This is simple with sleepy matter. Stars are born when sleepy matter wakes up, condenses. |

Bullet Cluster | Galactic velocities are too high. | The braking friction power of dark matter is lost as the sleeping matter can’t get near luminous matter to put the brakes on. |

Core-Cusp | No dark matter found (via gravitational searches) in the cores of galaxies. | The sleepy matter comes in, get woken up, interacts, and thus does not sink into the centre. |

Why Dark Matter | No reason for it, its just another set of parameters. | Sleepy matter is an experimental prediction of both matter and fields arising from the Einstein’s ether, and thus is predicted. |

Any new solution to the dark matter problem would hopefully not touch the success of the dark matter paradigm

Dark Matter Victory | Explanation | Sleepy matter comment |

Galaxy Clusters | The virial theorem says galactic clusters have dark matter holding them together. Lots of it. | Not a problem, since this intergalactic sleepy matter behaves just like dark matter. |

Einstein rings, gravitational lensing | The pretty pictures of Einstein rings, carefully measured, show much more mass around a galaxy than is in it that we can see. | Not a problem, as the sleepy matter is at low densities when the entire halo is taken into account. |

Early universe 2nd peak and all that. | The explanations of the CMB multipole work well with Dark Matter. | One might think that at early universe times, all the matter was awake, which would not be good for the model, but on the other hand, BBN troubles in the early U combined with a much different interaction scheme for matter and dark energy would change things. A 20 parameter LCDM cosmological model with 1000 PhDs and tens of thousands of papers will fit anything. |

Bullet Cluster | The dark matter from two colliding galaxies sailed right through each other. The gravitational field shows 1) lots of dark matter and 2) It did not interact like the regular stuff to the collision. | Sleeping matter can run right through each other, as long as the critical density is missed. So one gets both the correct density profile and lots of star formation, etc. |

Here are some predictions for sleepy matter. Some of the tests can be done today with ‘only’ a literature search and some graphing tools. Others require labs that likely can’t be built on earth or in the near future.

Prediction | Details | Test |

Sleepy matter can’t be detected in current experiments. | The sleeping matter is ~all woken up by the time it gets to a lab on earth. | More negative results looking for WIMPs, Axions, etc etc. So far 30 years of bright people have looked for dark matter, mostly by going deep into the earth. |

Sleepy matter might be detectable in a new kind of experiment. | Perhaps we can simply watch matter fall apart. | Maybe a (deep space?) lab with a large, cold dark room can make a rarefied gas sleep. Could be detected by lighting up a gas at some emission line as it’s pumped down in pressure. Maybe the matter will start to sleep as the pressure drops. Make a graph of pressure as measured by some direct method, and pressure measured by the emission of the atoms in the gas on excitation pulses at one per hour. |

Clouds of dark matter have a maximum density. | Maybe ordinary matter gas clouds have a minimum observed density already? | Extensive literature search for gas densities measured around our galaxy, combines with literature search for dark matter densities. Do the distributions overlap? I am thinking they don’t overlap, to within the statistics of astronomy. |

Sleepy matter on waking up might have some emission | Perhaps on waking up/sleeping the spinup produces some sort of weak photon emission, maybe in infrared or radio, or even higher frequencies. | Unexplained sky maps showing emission of photons in at places where the dark matter density is high. |

Sleepy matter going to sleep raises the dark energy level. | Planck – Supernovae Hubble tension. | The effect may be subtle, but overall it would seem that more matter is becoming sleepy than the other way around. This releases energy into space. The energy was bottled up as some part of matter, then it gets released. Perhaps most of the dark energy came from matter going to sleep, in which case we would need a huge mass/energy drop of like 90% for sleepy matter. But maybe the sleepy matter energy exchange is only a small part of the dark energy story. |

Is Sleepy Matter worthwhile? I like it, but it will take some more effort to put it into the ‘this contributes’ category. I have looked for papers on the density of DM vs the density of gas clouds, but I don’t think there are any. The gas cloud people and dark matter density people run in different circles.

I am going to try and dig up the references/papers I can find on dark matter and gas cloud density measurements.

Dark matter density tops out at about 10 GeV/cm^3 in the Milky way according to Figure 1 in

**Determination of the local dark matter density in our Galaxy**

*M. Weber and W. de Boer *

Is dark matter any more dense anywhere else?

**The dark matter density of the Universe**

Also see this:

Unfolding the Laws of Star Formation: The Density Distribution of Molecular Clouds

Note this image:

Wikipedia

Note that I just of something: Say some sleepy matter condenses out, then gets moved away condensed into new stars, etc. There would be gas clouds lighter than the dark matter limit.

]]>** The recent experimental proposals by Bose et al. and Marletto et al. (BMV) outline a way to test for the quantum nature of gravity by measuring the gravitationally induced differential phase accumulation over the superposed paths of two **∼

*This work predicts the outcome of the BMV experiment in Bohmian trajectory gravity – where classical gravity is assumed to couple to the particle configuration in each Bohmian path, as opposed to semi-classical gravity where gravity couples to the expectation value of the wave function, or of quantized gravity, where the gravitational field is itself in a quantum superposition. *

*In the case of the BMV experiment, Bohmian trajectory gravity predicts that there will be quantum entanglement. This is surprising as the gravitational field is treated classically.*

There have been a few papers written over the years modelling Einstein’s ether as an elastic solid. I have been reading these papers:

https://doi.org/10.1007/s12043-020-01954-5

http://arxiv.org/abs/1603.07655

http://arxiv.org/abs/1806.01133

So – lots of stuff about the ether as a solid.

A few problems with this approach – you can see one paper coming up with Young’s modulus varying with frequency (McDonald), and others struggling with how to even support transverse waves in this elastic medium. A key measure of a substance is its Poisson’s ratio – which is an elasticity measure. The semi consensus is that this ratio is 1 for the ether, which is not like any normal material (but OK spacetime is not a normal material!).

One thing about materials is that they in general support two kinds of waves ‘P-waves’ (pressure waves) and ‘S-waves’ (shear waves). Choosing Poisson’s ratio as 1 leads to P-waves having a speed of 0! Which is ‘required’ as everyone knows that p-waves can’t exist in general relativity. I agree that p-waves can’t be made in GR using normal matter moving around, but see this paper http://arxiv.org/abs/astro-ph/0309448 to get an idea of how one might generate monopole wave action.

There seems to be a lot of hand waving going on in these papers about thin plates, absolute length scales (Planck length chosen), and more just to get things to work out.

Since I’m an optimist at heart, I decided to look at this from another direction. What if Einstein’s ether was more like a fluid? Fluids have Poisson’s ratio of about 1/2, and only support shear waves if there is viscosity to the fluid. So lets let our fluid have a Poission’s ratio of just shy of 0.5, say one part in 10^14 away from 0.5, and a see what happens.

Here is what happens: Faster than light effects – the fluid of spacetime is extremely incompressible, and has a very small Young’s modulus.

I’ll quote a section of the Tenev-Horstemeyer paper here:

Run the calculations for *µ* and *M*, we get *µ* = Y/3 and *M* = 10^14 times *Y*, so the pressure waves in this fluid ether would travel at 10^7 (square root) times faster than c. (There is no experiment or theory describing the viscosity of Einsteins ether at this point, the 10^14 delta is for illustration only).

This huge pressure wave speed would not be seen in experiments as the paragraph points out – all known waves that propagate in real space are transverse. I think that the paper makes the mistake of assuming that because all we have measured are transverse waves, that those are the only kind that exist! Pressure waves in general relativity would be hard to generate it would seem, since one would have to pulsate spacetime.

So how would we generate these monopole waves? If we simply shoot matter on and off a planet, we will generate ‘dragged along’ monopole waves, which would travel at light speed (or less) with the matter.

One way to make superluminal p-waves is of course with the physicists favourite friend, the magic wand. Magic wands have been used in theoretical physics to create extra dimensions, multi-universes, etc. Here I only invoke it to make matter disappear, in a periodic pattern. For a concrete example, assume fundamental particles are varying in mass (imagine some worm hole mechanism) at their Compton frequency. Then we would have these pressure waves at fantastic velocity around them, exchanging information with their surroundings, in a de -Broglie or Madelung way. This would help quantum mechanics emerge from spacetime, something I have been searching for over several decades.

I don’t think that this is a possible idea simply because I wish there to be a way to communicate at velocities above c, or that it helps with a realistic model for quantum mechanics, I also think its a simpler way to look at Einstein’s ether than with the ‘closely packed’ layers of manifolds that the solid models quoted above mostly assume.

It seems that this bulk modulus pressure wave velocity being orders of magnitude faster than c might mean that there is a preferred frame for p-wave speed in the Universe. Lorentez transformations and the constancy of the speed of light measurements would presumably stay the same as they are now, as this fluid would simply be a way to generate the Einstein field equations.

Could a bulk modulus and Poisson’s ratio allowing for super-luminal p-waves replace inflation? One of the big reasons for inflation is that the universe is too smooth – given the paltry speed of light, places far from each other should have different temperatures, etc. https://www.newscientist.com/term/cosmic-inflation/

There are many people who think inflation is a silly crutch.

Here is a new story in Scientific American about ‘strange results’ from Nanograv. Could these be signs of longitudinal gravitational waves? The arXiv papers referenced point out that the observed signal has no quadropole signature, which is part of the ‘weird’ results. https://www.scientificamerican.com/article/galaxy-size-gravitational-wave-detector-hints-at-exotic-physics/

https://arxiv.org/abs/2009.04496

Does Pizzella’s experiment violate causality?

https://iopscience.iop.org/article/10.1088/1742-6596/845/1/012016

The idea about electromagnetic interactions being

composed of both instantaneous (bound) and retarded (radiation) parts is not new. It was

repeatedly expressed theoretically [3, 4, 5], and electromagnetic superluminal effects were seen

in experiments as well [6, 7, 8].

Measuring Propagation Speed of Coulomb Fields – http://arxiv.org/abs/1211.2913 ,

Arend Lammertink https://www.researchgate.net/post/Did-I-actually-measure-a-superluminous-signal-thus-disproving-the-relativity-theory

]]>It doesn’t work. Or rather has not worked.

Since it’s virtually impossible to prove that something can’t be done in physics (see von Neuman’s ‘no hidden variables proof’ as an example), we are left with hundreds of PhDs per year being granted trying to add another brick to a wall that is sinking in mud, hoping that the mud is only so deep, so that another few thousand postdocs life efforts piled up will hit the rock bottom.

It won’t. It’s pure folly.

An alternative is what I present on this site, namely that one can and indeed must build on General Relativity – that in a very real sense all future successful theories will be phenomena inside the ** Riemannian** manifold controlled by the Einstein Equations that we live in.

Examples provided on this site show how one can make electric fields, quantum waves and particles from nothing more than GR. Of course, it’s a minority viewpoint, one I’m willing to stand on.

In this essay I argue for the case of simply trying, in the sense of a toy model, to build parts of the universe out of nothing more than 4D, standard Einstein General Relativity. Its already the norm for a postdoc to spend a decade looking at some 2D toy model of a field that is known not to be able to work, just because it’s easier to do some calculations.

But apparently doing the same thing with a model (4D GR) that we know works extremely well is, well wrong, boring and silly.

I don’t think so.

Physics needs new trial balloons. To the fundamental physics establishment – you can’t actually pop a balloon unless you at least get it in front of you.

]]>**Abstract**. The recent experimental proposals by Bose et al. and Marletto et al. (BMV) outline a way to test for the quantum nature of gravity by measuring gravitationally induced differential phase accumulation over the superposed paths of two ∼ 10−14kg masses. These authors outline the expected outcome of these experiments for semi-classical, quantum gravity and collapse models. It is found that both semi-classical and collapse models predict a lack of entanglement in the experimental results. This work predicts the outcome of the BMV experiment in Bohmian trajectory gravity – where classical gravity is assumed to couple to the particle configuration in each Bohmian path, as opposed to semi-classical gravity where gravity couples to the expectation value of the wave function, or of quantized gravity, where the gravitational field is itself in a quantum superposition. In the case of the BMV experiment, Bohmian trajectory gravity predicts that there will be quantum entanglement. This is surprising as the gravitational field is treated classically. A discussion of how Bohmian trajectory gravity can induce quantum entanglement for a non superposed gravitational field is put forward.

This paper is a result of a talk I gave at DICE2018. The trip and the talk allowed me to sharpen the math and the arguments in this paper. I’m convinced that the results of a BMV like experiment would show these results – namely that gravity violates QM! Most physicists are of course on the opposite side of this and would assume that QM would win in a BMV experiment.

For those of the main camp, this paper is still important, as it describes another way to approximate quantum gravity – one that works better than the very often used Rosenfeld style semi-classical gravity. Sitting through talks where researchers use the semi-classical approximation in order to do sophisticated quantum gravity phenomenology has convinced me that often the results would change significantly if they had of used a Bohmian trajectory approach instead. The chemists figured this out a while ago – a Bohmian approximation is much more accurate than semi-classical approximations.

]]>In some sense semi-classical gravity seems more complicated than Bohmian trajectory gravity, as in semi-classical gravity the gravitational field has to somehow integrate the entire position space of the wave function (a non local entity) in real time (via the Schr ̈odinger – Newton equation), in order to continuously use the expectation value as a source for the gravitational field. In Bohmian mechanics, the gravitational field connects directly to an existing ’hidden’ particle position, which is conceptually simpler.

I am attending GR22 in Valencia Spain, to present a poster and also take part in the talks. I will be presenting a poster based on this paper (soon to be published) from a talk I gave at DICE2018.

What the paper and poster argue is that in the BMV experiment, observing entanglement is *not* enough to show that gravity is quantum. I do this by showing that a classical gravitational field coupled to the Bohmian trajectories of the individual particles will show entanglement.

The conference looks like its going to be interesting to attend.

The image at the top shows 4 runs of the BMV experiment, with all 4 Bohmian particle trajectory combinations shown. There is entanglement generated 1/4 of the time, when the experiment happens to look like the 2nd diagram from the left.

The poster is 90 x 200cm, available in real 3D, if you visit Valencia From July 7-12 2019 :-)

The BMV experiment sets out to show that gravity is quantized. If gravity is quantized, we expect to be able to form a gravitational field into a superposition, so that fundamentally the gravitational field is not certain at one spacetime point. Trying to come up with a theory of gravity that can be in a quantum superposition, while still working for all present tests of Einstein’s General Relativity has proved impossible so far, despite thousands of very smart people working over 50 years on the problem.

Perhaps gravity cannot be quantized. With Bohmian trajectory gravity, gravity is not quantized and has a well-defined connection to the sub-atomic particles.

If gravity is not quantized, all sorts of assumptions about quantum mechanics suddenly fail, as an unquantized gravity allows one to cheat behind the back of quantum mechanics. This is a large part of the reason why many people think gravity must be quantized. I’m not in the gravity must be quantized group, mostly because I think it just won’t work.

]]>Consider the following facts.

- The experimental record shows that the Lorentz transformations and special and general relativity all work remarkably well, from galaxies and indeed the structure of the Universe on down to scales probed by CERN.
- Locality is demonstrated in virtually all experiments conducted to date. This holds across fields such as fluid dynamics, radiation fields, etc. We have local causality.
- Quantum experiments such as those done by Aspect and later show that not everything is local – we have non-local effects. The wavefunction collapse is instant, etc. This worried Einstein.

Given the above facts, the simplest spacetime I can come up with looks roughly like this:

So this spacetime, which is not new, ( Wheeler had similar ideas), seems to cover our knowledge about the logical structure of quantum mechanics and general relativity. Until someone comes up with something better, this is what I use.

- Spacetime is locally casual. Einsteins equations show us how things need to touch (with light or gravity waves, etc) in order to interact.
- Locality is therefore local in nature only.
- non-signalling holds today, but there seems to be no reason for it. We have a connection, we just need to figure out how to use it.
- Spacetime is multiply connected, which means it is not globally localized. Events can interact outside of their past light cones.

This is how our universe operates: we feel everything locally causal. But experiment shows some non-local (in the global sense) connections.

Therefore, the phase shift of this interferometer is not determined by the local acceleration along a single populated trajectory, demonstrating that the atomic wavefunction is a nonlocal probe of the spacetime manifold [34].

Thus they have experimentally shown that wave functions feel gravity pretty much where they ‘are’ in real space ( try not to think of configuration space at this point! ). No one really doubted this would happen. Still, it leads one to wonder what about the other side – the backreaction – to this. Do the atoms in the Asenbaum experiment source gravity in the same way they detect it? It would seem obvious that they should, but no one has done an experiment to verify this (see later in this article).

A proposal in the opposite spirit to the above results is given by Kafri, Taylor, and Milburn (KTM) in A classical channel model for gravitational decoherence. KTM posits a way for the gravity to be sourced as follows:

That is, the gravitational centre of mass coordinate,x_{i}, of each particle is continuously measured and a classical stochastic measurement record, J_{k}(t), carrying this information acts reciprocally as a classical control force on the other mass.

In other words in the KTM model, the source and detection channels for a particle are both as in semi-classical gravity. The expectation value of the particle’s is the mass location for both source and detection.

You can sense that the Asenbaum experiment shows KTM does not work – the experiment shows that atom, which is in a dual humped wave function with a separation of *centimeters* cannot be seeing only the average field – the wave function senses the curvature. The paper by Altamirano, Corona-Ugalde, Mann, and Zych Gravity is not a Pairwise Local Classical Channel , confirm these feelings about KTM – like theories. They don’t work.

Here we show that single-atom interference experiments achieving large spatial superpositions can rule out a framework where the Newtonian gravitational inter-action is fundamentally classical in the information-theoretic sense: it cannot convey entanglement. Specifically, in this framework gravity acts pairwise between massive particles as classical channels, which effectively induce approximately Newtonian forces between the masses.

So gravity is not truly semi-classical. No surprise to me, or to the quantum gravity workers (LQG, String Theory, etc). What many/most quantum gravity people like to think, however, is that KTM or similar (Diosi – Penrose), Rosenfeld like semi-classical gravity basically exhaust the spectrum of classical gravity theories.

The papers describing the BMV experiments by Bose et al., Marletto and Vedral, and Christodoulou and Rovelli.

These proposed experiments are in some ways similar to the Asenbaum experiment described above, but instead of atoms, small particles like micro diamonds are prepared in position-dependent superpositions, and instead of a huge mass of lead, two diamonds are dropped near each other, so they can feel the gravitational effect of the other also in a position superposition diamond. The promise of these experiments is tremendous – if successful they might show that gravity is quantized: Christodoulou and Rovell state

...detecting the [BMV] effect counts as evidence that the gravitational field can be in a superposition of two macroscopically distinct classical fields and since the gravitational field is the geometry of spacetime (measured by rods and clocks), the BMV effect counts as evidence that quantum superposition of different spacetime geometries is possible, can be achieved..

A problem I see in these BMV papers is that they all use the predictions of semi-classical theories (not KTM but semiclassical as a source only) as a classical test case, without much thought to the predictions of other ‘classical’ theories of gravity. The possibilities are many and the experimental consequences are not simple.

There have been some papers over the years touting the usefulness of the Bohmian trajectory viewpoint as a better approximation to classical field – quantum system interaction. Usually, the case for using Bohmian trajectories is one of computational or conceptual efficiency, but as Ward Struve in Semi-classical approximations based on Bohmian mechanics puts it:

Finally, although we regard the Bohmian semi-classical approximation for quantum gravity as an approximation to some deeper quantum theory for gravity, one could also entertain the possibility that it is a fundamental theory on its own. At least, there is presumably as yet no experimental evidence against it.

The interpretation of the BMV experiment if one assumes Bohmian trajectories are ‘real’ results in the following conclusions:

- Each run of the experiment has particles in any one of 4 configurations, – the trajectories.
- There is no superposition of gravitational fields – each run has a different gravitational field configuration.
- The resulting experimental statistics show entanglement – even though gravity is classical throughout.

The last point is the most surprising. We look at why an experimenter will see entanglement with Bohmian trajectories.

At the heart of the argument is the fact that while these Bohmian trajectories look very classical, they are actually quantum – more clearly *sub*quantum aspects of (Bohm/de Broglie) quantum theory. So we have a situation where we can get behaviour very similar – ( i.e. showing entanglement ) to quantum gravity for the BMV experiment by using classical gravity coupled to Bohmian trajectories, where there is a superposition of gravitational fields – but only in the boring classical histories of the experiment viewpoint. Since the experimenter has only histories to look at, showing that the gravitational field was in a superposition requires more than merely observing some level of entanglement in the BMV experiment.

]]>