Abstract:
Some physicists surmise that gravity lies outside of quantum mechanics. Thus theories like the standard semiclassical theory of quantum to gravity coupling (that of Rosenfeld and Møller) are possible real models of interaction, rather than a mere approximation of a theory of quantum gravity. Unfortunately, semiclassical gravity creates inconsistencies such as superluminal communication. Alternatives by authors such as Diósi, Martin, Penrose, and Wang often use the term ’stochastic’ to set themselves apart from the standard semiclassical theory. These theories couple to fluctuations caused by for instance continuous spontaneous localization, hence the term ’stochastic’. This paper looks at stochastic gravity in the framework of a class of emergent or ontological quantum theories, such as those by Bohm, Cetto, and de Broglie. It is found that much or all of the trouble in connecting gravity with a microscopic system falls away, as Einstein’s general relativity is free to react directly with the microscopic beables. The resulting continuous gravitational wave radiation by atomic and nuclear systems does not, in contrast to Einstein’s speculation, cause catastrophic problems. The small amount of energy exchanged by gravitational waves may have measurable experimental consequences. A very recent experiment by Vinante et al. performed on a small cantilever at mK temperatures shows a surprising non-thermal noise component, the magnitude of which is consistent with the stochastic gravity coupling explored here.
If we take values of a strain of 15 orders of magnitude lower than LIGOs sensitivity, and a frequency of the Compton frequency, we get levels of energy flux and density that are very surprising. No one talks about this, though, since HFGWs are ‘known’ not to exist. I posit that we should not assume anything about gravitational waves at this point. Its an obvious place for experimentalists to work in. Are there any experiments that can detect gravitational radiation at millions of watts per square meter and nuclear frequencies? This is something that experiments should decide.
Just think about it – there is no way we can tell – there may be billions of watts of gravitational wave energy passing through your body right now. They may be there, waiting for us to find them.
The comments on dark energy and dark matter in the calculator are to be interpreted as follows:
Dark Matter is measured as an excess of mass/energy – as it’s presence is determined by gravitational effects on regular matter. In fact- experimentally, dark matter is too tied to matter – one can predict the amount of dark matter in a galaxy or galaxy cluster, etc by simply writing down the total mass distribution of baryons! What we know of dark matter is that it’s weakly coupled to matter and that it’s much denser than the level of dark energy that is spread throughout the universe.
Dark Matter is gravitational waves associated with matter. Call it DarkGW. It looks like the presence of matter controls the amount of dark matter present and DarkGW interacts very weakly with matter (perhaps not in a linear fashion?), perhaps even violatiing the rules of quantum mechanics – after all there is no quantum theory of gravity yet.
In this scenario, dark energy is the ‘leaking’ of this DarkGW into intergalactic space. Thus there is a source for DE and it does not have to have a transcendental source. Its ‘just’ regular radiation – radiation that does not redshift as the Universe ages, as the redshifted bits are replaced on a continual basis by the DarkGW.
This tells us why the amount of DarkGW is related to the amount of Dark Energy (why are they within a factor of two of each other?). As the DarkGW has leaked out, the Universe has expanded. Once the galaxies start to get cold and far apart (say in 200billion years) – the dark energy would start to redshift, and the Universe would approach a ‘balance point’ universe instead of a runaway expansion as in modern LCDM.
Riess says that it could be caused by hypothetical “sterile neutrinos”, interactions with dark matter, or a strengthening over time of dark energy (which accelerates the universe’s expansion).
Sterile Neutrinos are a last ditch effort to keep dark energy as a parameter (Lambda) in Einstein’s equations. Its clear to me that the best answer is that dark energy is getting stronger over time. Dark Energy is on the right side of the Einstein equations, not the left. Lambda was a mistake. Its zero.
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What about a field associated with every nucleon that saturates at some level, called S here. (its saturated near dense matter like here on Earth or in the Milky Way plane, while when protons/neutrons get below a certain density, the field then eventually drops as the density of matter drops.
This solves the cuspy galaxy core problem, it also makes the BTFR (Baryonic Tully Fisher Relation) work, it also seems it would work on the bullet cluster, galactic clusters, etc.
The Baryonic Tully Fisher Relation is one of the most accurate relations in cosmology. It’s a huge thorn in the side of LCDM cosmology, since dark matter and regular matter are not supposed to be in lockstep with one another. See Stacy McGaugh
THE SMALL SCATTER OF THE BARYONIC TULLY–FISHER RELATION
With the S field presented here, there is a saturable field associated with every nucleon. When nucleons are about a mm apart or less on average, the S field is at some standard strength, then as the density lowers more, the S field maintains its density (or slowly loses density) until at some limiting low matter density this saturable field S starts to drop. By the point this happens there is ~100x more energy in the saturable field S than the baryonic density.
This effect can explain the BTFR as dark matter is present in quantities as a function of baryonic mass in some fashion.
The bullet cluster poses a problem for MOND like theories – there seems to be excess dark matter causing lensing. So dark matter really exists, it seems. The S field solves this nicely. No one thinks that the lensing areas of the Bullet cluster are completely free of matter, it’s just that the dark matter is not located where the bulk of the matter is.
Clusters of galaxies would not hold together without about 5 times the mass of the individual galaxies available between the galaxies to hold the galaxies together. See Galaxy clusters prove dark matter’s existence as an intro by Ethan Siegel .
The mechanism is clear – the intergalactic dust and gas provide the framework to energize a large S field which keeps the cluster gravitationally bound.
The S field is associated with matter and has a limiting high density. At low densities (ie halo galactic densities) the field has a mass of up to about 10 (or 100?) times the mass of a nucleon, per nucleon.
Where does the energy come from? It’s dark energy – just clumped. So S is dark energy. There is always a flow of it running around, and its pulled from dark energy as needed to saturate around matter.
What is the form of the field?
What is the minimum energy density in say GeV/m^{3} ? Dark Energy has an energy density of about 0.5 GeV/m^{3} .
The max is determined by the maximum density measured for dark matter which is about 0.5 GeV/cm^{3} (note the centimeter scale used by astronomers when dealing with matter clouds) see my earlier related post Is Dark Matter merely Inactive Matter? so about 100^{3} or a million times the density of dark energy.
Thus the S field saturates at a density of ~ 5e5 GeV/m^{3} and is present all around us.
The S field density is then some function of the matter density. It turns out that it’s a cumulative effect from all matter enclosed inside ‘R’.
Stacy S. McGaugh and Federico Lelli
Consequently, the dark matter contribution is fully specified by that of the baryons. The observed scatter is small and largely dominated by observational uncertainties. This radial acceleration relation is tantamount to a natural law for rotating galaxy.
From http://stacks.iop.org/0004-637X/836/i=2/a=152?key=crossref.21cde6b778a1e42d6160598a6ba24e03
Start at Equation 22:
Then use and simplify to
Thus the quantity of DM inside a certain radius is wholly dependent on the amount of baryonic matter inside that radius. The S field is a cumulative effect of density of regular baryons.
When I use this on density I get
This equation states that the density of dark matter depends only on the enclosed average density of baryonic matter.
Calculating the acceleration at R , given a 35kPc distance R, and a density of baryons of 1GeV per cm^{3 }gives = 1.2×10-10 m/s2 – ie which is the Milgrom acceleration. So that’s the cut where dark matter starts to be apparent, as the denominator starts to take off.
Of course, this density equation has limits on both ends. The dark matter S field has a maximum density of about a GeV per cm^{3} and once the density goes down to about dark energy levels one no longer calls it dark matter. Don’t forget my density version of the equation requires the average density inside R for the galaxy/gas cloud/cluster.
In my mind this S field is HFGW, but it’s not important what is the nature of the field, vs the mass of the field.
It seems to me that battling it out as MOND vs LCDM is perhaps not the best way to approach the problem as there are obviously more models around that might work. One just has to throw out some part of standard model physics!
Looking at the above more, I’m not convinced that sticking exactly to the MOND formula for mass and density is the way to go with this S field idea. I’m hoping there is a function where the density of DM is only given by the local density of matter, but perhaps that will not work. Perhaps there is something happening where DM depends on the total SUM of all all the matter interior to the radius R.
]]>MOND (MOdified Newtonian Dynamics) is one explanation for the Tully-Fisher relation. It posits that the force towards the centre of a galaxy at large distances is not simply that of Newton, but is modified with the a_{0} of 1.2×10^{-10}m/s^{2} in all galaxies in addition to the usual force predicted by standard Newton or General Relativity’s gravity. LCDM Dark matter is a clumsy explanation for the BTFR, as it needs fine tuning for every galaxy (or every galaxy type) in order to make that straight line be so, well, straight.
There is another way to generate an inward acceleration.
We need a force on each nucleon that changes with how much matter is inside the radius where the particle is. It somehow ‘knows’ the gravitational potential at R, and has a force that depends on that!
What I have so far on this is something to do with dark energy being more concentrated in galaxy cores, so the particle feels this dark energy slope and responds to it.
NOTE: This needs to include a dependence on the enclosed M (ie enclosed Dark Energy inside R). I call this emission based acceleration ‘Anomalous radial nucleonic radiation’ (ARNR). MOND tells us that particles in the galactic halo can ‘weigh’ the galaxy. They have that information. So there must/might be something like dark energy concentrated in the galaxy and the particles react to this, pushing radiation outward and reacting inward. Note in the galactic core the divergence of the DE is 0 – so no extra force on the particle in the middle of the galaxy.
It might seem strange to have this concerted outward radiation pattern though! Here are some possible explanations for an outward constant radiation by the halo constituents.
People don’t generally like the MOND theories because general relativity (GR) in its usual form is so well tested and accurate. LCDM is disliked by many because of the fine-tuning required in order to get everything to match observations. ‘Anomalous radial nucleonic radiation’ (ARNR) allows GR to exist as is.
If nuclei really do radiate continuously, (perhaps in violation of quantum – mechanics) then there will be experimental consequences. These consequences may be largely hidden from earth-based experiments, as the emission would be isotropic and take place in some field (such as gravitational waves) that is hard to detect with current instruments.
There may be other places where cosmological or galactic cluster observations might note this energy output.
In other posts, I have wondered if dark matter is ‘sleeping regular matter‘ and I still think that it may be a viable option, but it seems like any explanation in terms of dark matter may need to be fine-tuned to match observations.
Also, see:
http://backreaction.blogspot.ca/2016/10/what-if-dark-matter-is-not-particle.html
https://tritonstation.wordpress.com/2016/09/26/the-third-law-of-galactic-rotation/
https://tritonstation.wordpress.com/category/dark-matter/
at http://iopscience.iop.org/article/10.1088/0004-637X/802/1/18/pdf
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I attended in 2015. The event has the byline – the 4th International Symposium about Quantum Mechanics based on a »Deeper Level Theory«. Its mission this year is
Towards Ontology of Quantum Mechanics and the Conscious Agent David Bohm Centennial Symposium
When I first really understood what quantum mechanics really was – in second-year undergrad at the University of Toronto, I immediately read all sorts of books and papers by and about Bohm’s theories. He made quite a change in my outlook of physics in general. I became convinced in 1985 that quantum mechanics was incomplete and that something along the lines of Bohm’s theory was the way to go. That makes the conference more special for me, and I’m sure many other attendees share the same view.
I am presenting a poster which I’m still polishing that up right now (the abstract at least was well received!). Its based on a paper called ‘Fully Classical Quantum Gravity (see link)‘. I have renamed the poster to Stochastic Gravity and Ontological Quantum Mechanics and rewritten most of it.
The poster describes the results of a paper by Vinante et al. :
Improved noninterferometric test of collapse models using ultracold cantilevers . If the results hold up, they are quite breathtaking as they state:
The finite intercept, clearly visible in the inset of Fig. 3 implies that the data are not compatible with a pure thermal noise behavior, and a nonthermal ex-cess noise is present.
The paper details the careful procedures followed to chase down possible experimental problems. The analysis is carefully thought out. The paper claims the results show a possible signature of Adler’s Continuous Spontaneous Localization (CSL), but to me it seems like if the results hold up that its simply a great puzzle to solve! My take (in line with the ‘Fully Classical Quantum Gravity‘ paper) is that this noise is caused by the continuous emission and/or absorption of gravitational waves at nuclear frequencies.
Gravitational waves are notoriously hard to see, and these high-frequency ones (HFGWs) even more so. Indeed, since gravitational wave power goes with the square of frequency, truly tiny values of the gravitational wave strain ‘h’ (h == 0 in flat space and h < 1) make for large energy fluxes. The LIGO observations saw gravitational waves with . The formula for the flux of a gravitational wave is:
So LIGO can see gravitational waves with a flux of about , while at nuclear frequencies like , the same formula yields an incredible – another way to look at that flux is that it represents 400+ kg! of mass per square meter per second! I propose that results like this suggest that matter itself can be made of nothing but elaborate patterns of gravitational structures. Clearly, high-frequency gravitational structures can hold an incredible amount of energy.
Another way of thinking about this result is that anytime a better telescope is built, or one is built that looks at a new wavelength, field or pattern of signals, those signals are not only discovered, they produce deep new insights about our universe. The fact that HFGWs are hard to detect does not mean that they are not there! Indeed, instead of calculating what the flux of HFGWs might be around us, we should instead admit our ignorance and calculate what we don’t know. Huge amounts of gravitational wave energy could be whipping by everything right now and we would not know a thing about it.
It’s going to be a quick few days in London!
–Tom
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Which of course is what I have been saying all along. Of course Susskind’s paper is actually ‘of course’ not about QM emerging from GR, which is what I believe, and have good reason to follow up on.
Instead Susskind says:
Dear Qubitzers, GR=QM? Well why not? Some of us already accept ER=EPR [1], so why not follow it to its logical conclusion? It is said that general relativity and quantum mechanics are separate subjects that don’t fit together comfortably. There is a tension, even a contradiction between them—or so one often hears. I take exception to this view. I think that exactly the opposite is true. It may be too strong to say that gravity and quantum mechanics are exactly the same thing, but those of us who are paying attention, may already sense that the two are inseparable, and that neither makes sense without the other.
The ‘paper’ (perhaps letter is a better name), has made the rounds/ Not Even Wrong,
Instead of that happening, it seems that the field is moving ever forward in a post-modern direction I can’t follow. Tonight the arXiv has something new from Susskind about this, where he argues that one should go beyond “ER=EPR”, to “GR=QM”. While the 2013 paper had very few equations, this one has none at all, and is actually written in the form not of a scientific paper, but of a letter to fellow “Qubitzers”. On some sort of spectrum of precision of statements, with Bourbaki near one end, this paper is way at the other end.
While Woit’s nemesis Lubos Motl,
Susskind also says lots of his usual wrong statements resulting from a deep misunderstanding of quantum mechanics – e.g. that "quantum mechanics is the same as a classical simulation of it". A classical system, a simulation or otherwise, can never be equivalent to a quantum mechanical theory. The former really doesn't obey the uncertainty principle, allows objective facts; the latter requires an observer and is a framework to calculate probabilities of statements that are only meaningful relatively to a chosen observer's observations.
Sabine Hossenfelder put it visually on Twitter:
My take is about the same as these popular bloggers. Don’t really think much of it.
Except the title. QM can, I believe, emerge from Einstein’s General Relativity, in much the same way that Bush and Couder’s bouncing drops can display quantum behaviour.
My research gate page has more.
Its ridiculous that 11 dimensions and sparticles have hundreds of times more study than fundamental emergent phenomena. Emergence is the way to go forward. You don’t need a new force/particle/dimension/brane to make fundamentally new physics from what we already have in electromagnetism and general relativity.
See the search links on the side of this blog for some recent papers in these areas.
]]>Singularities, de Broglie and emergent quantum mechanics comes to mind for me.
The interaction causes a wave to propagate. After a time equal to the period of a wave on the ring, it separates into two.
https://file.scirp.org/pdf/ACES_2013100819104983.pdf
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by
The hardcover is out – for example here: Amazon.com or at Springer – but its coming out in paperback soon – Amazon.ca . Its not coming in paperback, so I just bought the hard cover. Its ok if a paperback comes later but I can’t wait!
So what I’m saying is that I’m cheap enough to wait for the paperback, so I actually have not read the book, but it looks like its going to be a real addition to the field. Its aimed at people with at least a science background.
The book takes the discovery (by for example Couder/Bush) that quantum-like behaviour is not solely reserved to atomic particles one step further. If electrons are modelled as vibrating droplets instead of the usually assumed point objects, and if the classical laws of nature are applied, then exactly the same behaviour as in quantum theory is found, quantitatively correct! The world of atoms is strange and quantum mechanics, the theory of this world, is almost magic. Or is it? Tiny droplets of oil bouncing round on a fluid surface can also mimic the world of quantum mechanics. For the layman – for whom the main part of this book is written – this is good news. If the everyday laws of nature can conspire to show up quantum-like phenomena, there is hope to form mental pictures how the atomic world works.
Here is an excerpt from the Preface to the book: (other tidbits can be downloaded from Springer)
To begin with a warning: the contents of this book may be controversial. The readers the author had in mind when writing this book are interested laymen, typically the kind of reader who searches bookshops for the latest popular-scientific books on developments in cosmology, on recently found fun- damental particles, or on the ever more magical findings of quantum physics. These readers presumably have some background of classical school physics (although most of it may have been forgotten). It is the kind of reader who does not like to be bothered with formulae or is even allergic to them, but who has the interest and tenacity to read sentences twice if necessary. But complete novices in the matters of the atomic world should be warned: the stories told in this book are not the same as usually found in books about quantum phenomena. This book does not give the conventional explanations. In order to read the usual stories, it is better to start in one of the many other popular-scientific books. What then is this book about? This book certainly does not pretend to contain a new theory of quantum mechanics, nor does it have the intention. Quantum theory in its present form is an almost perfect tool to calculate the behaviour of elementary particles. But the theory is “strange”, it is not something that intuitively can be understood. What this book tries to add are visualisations or mental pictures, closer to the intuition, because they are based on classical physics. However, the mental pictures in this book are not just half-baked analogies or metaphores, they are solidly founded on a large body of mathematical theory (for the diehards: the theory can be found in the appendix). This aspect makes this book different from other popular-scientific books.
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An observer far away from a black hole sees photons of normal infared or radio wave energies coming from a black hole (i.e. << 1eV). If one calculates the energies that these photons should have once they are in the vicinity of the black hole horizon, the energy is becomes high – higher than the Planck energy, exponentially so. Of course if we ride with the photon down to the horizon, the photon blue shifts like mad, going ‘trans-Planckian’ – i.e. having more energy than the Planck energy.
Looked at another way: if a photon starts out at the horizon, then we won’t ever see it as a distant observer. So it needs to start out just above the horizon where the distance from the horizon is given by the Heisenberg uncertainty principle, and propagate to us. The problem is that the energy of these evaporating photons must be enormous at this quantum distance from the horizon – not merely enormous, but exponentially enormous. A proper analysis actually starts the photon off in the formation of the black hole, but the physics is the same.
Adam Helfer puts it well in his paper. Great clear writing and thinking.
My take is simple. After reading Hefler’s paper plus others on the subject, I’m fairly convinced that black holes of astrophysical size (or even down to trillions of tons) do not evaporate.
Let’s get things straight here: the math behind Hawking evaporation is good: Hawking’s math for black hole evaporation is not in question.
It should be emphasized that the problems uncovered here are entirely physical, not mathematical. While there are some technical mathematical concerns with details of Hawking’s computation, we do not anticipate any real difficulty in resolving these (cf. Fredenhagen and Haag 1990). The issues are whether the physical assumptions underlying the mathematics are correct, and whether the correct physical lessons are being drawn from the calculations.
Yet Hawking’s prediction of black hole evaporation is one of the great predictions of late 20th century physics.
Whether black holes turn out to radiate or not, it would be hard to overstate the significance of these papers. Hawking had found one of those key physical systems which at once bring vexing foundational issues to a point, are accessible to analytic techniques, and suggest deep connections between disparate areas of physics. (Helfer, A. D. (2003). Do black holes radiate? Retrieved from https://arxiv.org/pdf/gr-qc/0304042.pdf)
So it’s an important concept. In fact it so important that much of not only black hole physics but quantum gravity and cosmology all use or even depend on black hole evaporation. Papers with titles like “Avoiding the Trans-Planckian Problem in Black Hole Physics” abound.
There are so many theories in physics today that rely on an unreasonable extrapolation of the efficacy of quantum mechanics at energies and scales that are not merely larger than experimental data, but exponentially larger than we have experimental evidence for. Its like that old joke about putting a dollar into a bank account and waiting a million years – even at a few per cent interest your money will be worth more than the planet. A straightforward look at history shows that currency and banks live for hundreds of years – not millions. The same thing happens in physics – you can’t connect two reasonable physical states through an unphysical one and expect it to work.
The trans-Planckian problem is replicated perfectly in inflationary big bang theory.
The trans-Planckian problem seems like a circle the wagons type of situation in physics. Black hole evaporation now has too many careers built on it to be easily torn down.
Torn down:
To emphasize the essential way these high–frequency modes enter, suppose we had initially imposed an ultraviolet cut–off Λ on the in–modes. Then we should have found no Hawking quanta at late times, for the out–modes’ maximum frequency would be ∼ v′(u)Λ, which goes to zero rapidly. (It is worth pointing out that this procedure is within what may be fairly described as text–book quantum field theory: start with a cut–off, do the calculation, and at the very end take the cut–off to infinity. That this results in no Hawking quanta emphasizes the delicacy of the issues. In this sense, the trans–Planckian problem may be thought of as a renormalization–ambiguity problem.)
Some may argue that other researchers have solved the trans-Planckian problem, but its just too simple a problem to get around.
One way around it – which I assume is what many researchers think – is that quantum mechanics is somehow different than every other physical theory ever found, in that it has no UV, IR, no limits at all. In my view that is extremely unlikely. Quantum mechanics has limits, like every other theory.
If there is a limit on quantum mechanics – that QM is like any other theory – a tool that works very well in some domain of physical problems, then many many pillars of theoretical physics will have to tumble, black hole evaporation being one of them.
March 2018 update: Ok – upon reading this paper by Steven B. Giddings
Where does Hawking radiation originate? A common picture is that it arises from excitations very near or at the horizon, and this viewpoint has supported the “firewall” argument and arguments for a key role for the UV-dependent entanglement entropy in describing the quantum mechanics of black holes. However, closer investigation of both the total emission rate and the stress tensor of Hawking radiation supports the statement that its source is a near-horizon quantum region, or “atmosphere,” whose radial extent is set by the horizon radius scale.
So after I wrote this I am not convinced that holes don’t radiate.
Adam’s argument is below. Basically in order for Unruh’s/Giddings ‘saving’ of black hole radiation to work, there has to be enough ‘source space’ around the black hole to generate the Hawking radiation. There might be.
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It (I will call the paper WZU) has been discussed at several places:
Sabine Hossenfelder at the Backreaction blog,
Reddit ,
So why talk about it more here?
Well because its an interesting paper, and I think that many of the most interesting bits have been ignored or misunderstood (I’m talking here about actual physicists not the popular press articles).
For instance here are two paragraphs from Sabine Hossenfelder
Another troublesome feature of their idea is that the scale-factor of the oscillating space-time crosses zero in each cycle so that the space-time volume also goes to zero and the metric structure breaks down. I have no idea what that even means. I’d be willing to ignore this issue if the rest was working fine, but seeing that it doesn’t, it just adds to my misgivings.
So with the first paragraph, Sabine is talking about the a(t, x) factor in the metric (see equation 23 in the paper). I think that she could be a little more up front here: a(t, x) goes to zero alright, but only in very small regions of space for very short times (I’ll come back to that later). So in reality the average of the a(t,x) over any distance/time Planck scale or larger determines an almost flat, almost Lambda free universe -> average(a(t,x)) –> the a(t) as per a FLRW metric. I guess Sabine is worried about those instants when there are singularities in the solution. I agree with the answer to this supplied in the paper:
It is natural for a harmonic os- cillator to pass its equilibrium point a(t,x) = 0 at maximum speed without stopping. So in our solution, the singularity immediately disappears after it forms and the spacetime continues to evolve without stopping. Singularities just serve as the turning points at which the space switches. ...(technical argument which is not all that complicated)... In this sense, we argue that our spacetime with singularities due to the metric becoming degenerate (a = 0) is a legitimate solution of GR.
As I said, more on that below when we get to my take on this paper.
The second paragraph above from the Backreaction blog concerns the fact that the paper authors used semi classical gravity to derive this result.
The other major problem with their approach is that the limit they work in doesn’t make sense to begin with. They are using classical gravity coupled to the expectation values of the quantum field theory, a mixture known as ‘semi-classical gravity’ in which gravity is not quantized. This approximation, however, is known to break down when the fluctuations in the energy-momentum tensor get large compared to its absolute value, which is the very case they study.
They are NOT using a classical gravity coupled to the expectation values of the quantum field theory. Indeed, according to WZU and the mathematics of the paper they say:
In this paper, we are not trying to quantize gravity. Instead, we are still keeping the spacetime metric a(t, x) as classical, but quantizing the fields propagating on it. The key difference from the usual semiclassical gravity is that we go one more step—instead of assuming the semiclassical Einstein equation, where the curvature of the spacetime is sourced by the expectation value of the quantum field stress energy tensor, we also take the huge fluctuations of the stress energy tensor into account. In our method, the sources of gravity are stochastic classical fields whose stochastic properties are determined by their quantum fluctuations.
So I think that she has it wrong. In her reply to my comment on here blog she states that its still semiclassical gravity as they use the expectation values of the fluctuations (they don’t as you can see by the quote above or better by looking at the paper. See how the equation 29 talks about expectation values, but the actual solution does not use them ). She concludes her comment: “Either way you put it, gravity isn’t quantized.” I think that’s also fair appraisal of the attitude of many people on reading this paper many people don’t like it because gravity is treated classically.
I think its interesting as their approach to connecting gravity to the quantum world is basically identical to my Fully Classical Quantum Gravity experimental proposal – namely that gravity is not quantized at all and that gravity couples directly to the sub-quantum fluctuations. Wang and co-authors apologize for the lack of a quantum theory of gravity, but that appears to me anyway as more of a consensus-towing statement than physics. Indeed, the way its shoved in at the start of section C seems like it is an afterthought.
Singularities are predicted by many or (even all?) field theories in physics. In QED the technique of renormalization works to remove singularities (which are the same as infinities). In the rest of modern QFT singularities are only perhaps removed by renormalization. In other words quantum field theory blows up all by itself, without any help from other theories. Its naturally bad.
The Einstein equations have a different behaviour under singular conditions. They are completely well behaved. Its only when other fields are brought in, such as electromagnetism or quantum field theory that trouble starts. But all on their own singularities are no big deal in gravity.
So I don’t worry about the microscopic, extremely short lived singularities in WZU at all.
We have WZU metric equation 23
ds2 = −dt2 +a2(t,x)(dx2 +dy2 +dz2)
a(t,x) oscillates THROUGH zero to negative, but the metric depend on a^2, so we have a positive definite metric that has some zeros. These zeros are spread out quasi periodically in space and time. If one takes two points on the manifold (Alice and Bob denoted A & B), then the distance between A and B will be equivalent to the flat space measure (I am not looking at the A and B being cosmic scale distances apart in time or space, so its almost Minkowski). Thus imagine A and B being 1 thousand km apart. The scale factor a(t, x) averages to 1.
Here is the exciting bit. While an arbitrary line (or the average of an ensemble of routes) from A -> B is measured as a thousand km, there are shorter routes through the metric. Much shorter routes. How short? Perhaps arbitrarily short. It may be that there is a vanishingly small set of paths with length ds = 0, and some number of paths with ds just greater than 0, all the way up to ‘slow paths’ that spend more time in a > 1 areas.
Imagine a thread like singularity (like a cosmic string – or better a singularity not unlike a Kerr singularity where a >> m). In general relativity such a thread is of thickness 0, and the ergo region around it also tends to zero volume. One calculation of the tension on such a gravitational singularity ‘thread’ (I use the term thread as to not get confused with string theory) come out to a value of about 0.1 Newtons. A Newton of tension on something so thin is incredible. Such a thread immersed in the WZU background will find shorter paths – paths that spend more time in areas where a << 1, these paths being much more energetically favoured. There are also very interesting effects when such gravitational thread singularities are dragged through the WZU background. I think that this might be the mechanism that creates enough action to generate electromagnetism from pure general relativity only.
So these thread singularities thread their way through the frothy WZU metric and as such the distance a single such thread may measure between Alice and Bob may be far far less than the flat space equivalent.
It seems to me that one could integrate the metric as given in WZU equation 23 with a shortest path condition and come up with something. Here is one possible numerical way: start out with a straight thread from A to B. Then relax the straight line constraint, assign a tension to the thread, and see what the length of the thread after a few thousand iterations, where at each iteration, each segment allows itself to move toward a lower energy state (i.e. thread contraction).
This opens up:
Realist, local quantum mechanics is usually thought of requiring on having some dependency on non-local connections, as quantum experiments have shown. This shortcut path may be an answer to the need for non-local connections between particles, i.e. a mechanism for entaglement, a mechanism for Einstein’s “spooky action at a distance”.
Its always fun to see if there are realistic methods where one might beat the speed limit on light. It seems that worm hole traversal has been one of the favourites to date. I think that the WZU paper points at another mechanism – the fact that there exist shorter paths through the sub-quantum general relativistic froth of WZU. How might one construct a radio to do this? Entangled particles, particles that follow the zeros of a(t, x) preferentially, etc etc. One could imagine a brute force method to test this where huge pulses of energy are transmitted through space at random intervals. Perhaps a precursor signal could be measured at the detector, where some of the energy takes a short path through the WZU metric.
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