Einstein’s theory of general relativity tells us that gravity is due to the curvature of space and time. But this theory is strictly speaking wrong. It is wrong because according to general relativity, gravity does not have quantum properties. I told you all about this in my earlier videos. This lacking quantum behavior of gravity gives rise to mathematical inconsistencies that make no physical sense. To really make sense of gravity, we need a theory of quantum gravity. But we do not have such a theory yet. In this video, we will look at the experimental possibilities that we have to find the missing theory.
But before I do that, I want to tell you why so many physicists think that it is not possible to test quantum gravity.
The reason is that gravity is a very weak force and its quantum effects are even weaker. Gravity does not seem weak in everyday life. But that is because gravity, unlike all the other fundamental forces, does not neutralize. So, on long distances, it is the only remaining force and that’s why we notice it so prominently. But if you look at, for example, the gravitational force between an electron and a proton and the electromagnetic force between them, then the electromagnetic force is a factor 10^40 stronger.
One way to see what this means is to look at a fridge magnet. The magnetic force of that tiny thing is stronger than the gravitational pull of the whole planet.
Now, in most approaches to quantum gravity, the gravitational force is mediated by a particle. This particle is called the graviton, and it belongs to the gravitational force the same way that the photon belongs to the electromagnetic force. But since gravity is so much weaker than the electromagnetic force, you need ridiculously high energies to produce a measureable amount of gravitons. With the currently available technology, it would take a particle accelerator about the size of the Milky Way to reach sufficiently high energies.
And this is why most physicists think that one cannot test quantum gravity. It is testable in principle, all right, but not in practice, because one needs these ridiculously large accelerators or detectors.
However, this argument is wrong. It is wrong because one does not need to produce a quantum of a field to demonstrate that the field must be quantized. Take electromagnetism as an example. We have evidence that it must be quantized right here. Because if it was not quantized, then atoms would not be stable. Somewhat more quantitatively, the discrete energy levels of atomic spectral lines demonstrate that electromagnetism is quantized. And you do not need to detect individual photons for that.
With the quantization of gravity, it’s somewhat more difficult, but not impossible. A big advantage of gravity is that the gravitational force becomes stronger for larger systems because, recall, gravity, unlike the other forces, does not neutralize and therefore adds up. So, we can make quantum gravitational effects stronger by just taking larger masses and bringing them into quantum states, for example into a state in which the masses are in two places at once. One should then be able to tell whether the gravitational field is also in two places at once. And if one can do that, one can demonstrate that gravity has quantum behavior.
But the trouble is that quantum effects for large objects quickly fade away, or “decohere” as the physicists say. So the challenge to measuring quantum gravity comes down to producing and maintaining quantum states of heavy objects. “Heavy” here means something like a milli-gram. That doesn’t sound heavy, but it is very heavy compared to the masses of elementary particles.
The objects you need for such an experiment have to be heavy enough so that one can actually measure the gravitational field. There are a few experiments attempting to measure this. But presently the masses that one can bring into quantum states are not quite high enough. However, it is something that will reasonably become possible in the coming decades.
Another good chance to observe quantum gravitational effects is to use the universe as laboratory. Quantum gravitational effects should be strong right after the big bang and inside of black holes. Evidence from what happened in the early universe could still be around today, for example in the cosmic microwave background. Indeed, several groups are trying to find out whether the cosmic microwave background can be analyzed to show that gravity must have been quantized. But at least for now the signal is well below measurement precision.
With black holes, it’s more complicated, because the region where quantum gravity is strong is hidden behind the event horizon. But some computer simulations seem to show that stars can collapse without forming a horizon. In this case we could look right at the quantum gravitational effects. The challenge with this idea is to find out just how the observations would differ between a “normal” black hole and a singularity without horizon but with quantum gravitational effects. Again, that’s subject of current research.
And there are other options. For example, the theory of quantum gravity may violate symmetries that are respected by general relativity. Symmetry violations can show up in high-precision measurements at low energies, even if they are very small. This is something that one can look for with particle decays or particle interactions and indeed something that various experimental groups are looking for.
There are several other ways to test quantum gravity, but these are more speculative in that they look for properties that a theory of quantum gravity may not have.
For example, the way in which gravitational waves are emitted in a black hole merger is different if the black hole horizon has quantum effects. However, this may just not be the case. The same goes for ideas that space itself may have the properties of a medium give rise to dispersion, which means that light of different colors travels at different speed, or may have viscosity. Again, this is something that one can look for, and that physicists are looking for. It’s not our best shot though, because quantum gravity may not give rise to these effects.
In any case, as you can see, clearly it is possible to test quantum gravity. Indeed I think it is possible that we will see experimental evidence for quantum gravity in the next 20 years, most likely by the type of test that I talked about first, with the massive quantum objects.
FYI, another recent proposal for experiment:
ReplyDelete"Sagnac Interferometer and the Quantum Nature of Gravity" (Chiara Marletto and Vlatko Vedral ) https://arxiv.org/abs/2001.02777
What about testing the quantum nature of gravity in the ultra low gravity state?
ReplyDeleteI am thinking about the cut-off point where MOND overtakes Newtonian dynamics and Verlinde's dark-matter theory.
First, MOND would have to beat Einstein and be accepted as a better theory...which isn't happening.
Delete"MOND would have to beat Einstein"
DeleteNot quite. The point of MOND is that there is curvature that has no "regular" mass counterpart.
Dark matter is one solution to that missing "mass". MOND claims that there are other ways to account for that extra curvature. Verlinde was even able to explain the extra curvature with a theory that implies a certain class of quantum-gravity theories.
Dr Bee has even published a blogpost on it:
https://backreaction.blogspot.com/2018/03/modified-gravity-and-radial.html
I suspect that this avenue of work targeting the ultra low energy limit might lead to some testable predictions about observables that, in turn could, guide theory development.
Sabine,
ReplyDelete"Einstein’s theory of general relativity tells us that gravity is due to the curvature of space and time. But this theory is strictly speaking wrong. It is wrong because according to general relativity, gravity does not have quantum properties."
I do not understand your position here. The idea of superdeterminism (which you endorse) is that QM is some sort of classical theory in disguise (hidden variables). Hidden variables are also required to solve the measurement problem. So, what does actually mean to say that "gravity does not have quantum properties"? Is GR not compatible with the hypothetical hidden variable interpretation of QM? How would you know that before having that theory in the first place?
"So, we can make stronger quantum gravitational stronger by just taking larger masses and bringing them into quantum states, for example into a state in which the masses are in two places at once. One should then be able to tell whether the gravitational field is also in two places at once. And if one can do that, one can demonstrate that gravity has quantum behavior."
I have three objections here:
1. As I have argued above, QM should be replaced with a hidden variable theory. In this theory superpositions would not be "real", they would reflect our incomplete knowledge about the system. So, an object would never be in two places at once.
2. Assuming that objects really are in two places at once, Born's postulate tells us that any measurement will find the object in one of the two positions, never in both. But a measurement of the gravitational field is a measurement of position in the same way a measurement of the electric field is a measurement of position. So, I would not expect to see the gravitational field pointing to both locations.
3. It should be impossible to prepare a superposition that requires an uncertainty greater than the one imposed by Heisenberg's principle. The critical assumption behind this type of experiments is that it is possible to completely isolate the system. Yet, one cannot shield gravity itself, so the position of the object can in principle be measured by placing a torsion balance outside the lab.
"The idea of superdeterminism (which you endorse) is that QM is some sort of classical theory in disguise (hidden variables)."
DeleteNo it is not. I do not know what makes you say so. Please read the paper that I recently wrote with Tim. It contains a definition.
With #3 what is impossible is an uncertainty less than the Heisenberg principle.
DeleteThere seems to be some disconnect here with what is a quantum superposition. For a System with energy E or the exoectation value E, quantum states may define a spectrum δE_i = E_i - E_{i-1} such that δE_i ≤ E. This is different from a classical system where δE_i << E, so the quantum states are tiny compared to an average energy. This is the world we normally experience.
In these experiments Sabine references a membrane has a set of vibrational modes. These are given by some complete set of orthogonal functions, such as Bessel functions. The vibration of a drumhead orcymbal is such an example. However, the vibration is given by a Fourier sum of terms with many modes that have a tiny amplitude at high frequency. However, if this membrane is in a coherent state or some condensate it will then vibrate with some large energy (high frequency) as a pure state. It this is quantization on the large with sufficient mass the argument can be made there will be a superposition of metrics if this pure state has two fundamental modes with an energy gap δE_i that is large compared to the energy of the system.
Sabine,
DeleteThe paper maintains that a superdeterministic theory is Psi-epistemic in the sense that "the wavefunction is emergent, for example as a statistical representation of a more fundamental theory". So, in order to conclude that GR must be wrong, one should provide evidence that GR is not compatible with that fundamental theory. Would you agree with this?
Lawrence Crowell,
Delete"With #3 what is impossible is an uncertainty less than the Heisenberg principle."
Sure, we all agree that one cannot get an "uncertainty less than the Heisenberg principle". However, I would also argue that assuming a higher uncertainty is unjustified. Clearly, the experiment Sabine proposes (superposition of a mg-sized object) would allow one to measure its actual position within the Heisenberg uncertainty bounds from outside the lab, regardless of how well the lab is isolated (the gravitational field cannot be shielded) using for example a torsion balance. So, the prepared superposition would be instantly collapsed. Not using a torsion balance is not a solution either because its role can be played by any object with mass. So, it seems to me, the experiment cannot be done.
Andrei,
DeleteThat it's psi-epistemic doesn't mean it's classical. Yes, that fundamental theory may be compatible with GR. (Though I don't think it is.)
I guess I am not following you. If there is a superposition in the configuration or position of a mass a measurement will collapse the wave function. Suppose this superposition of a mass position provides two paths for photons. We might consider a photon beam that reflects off the mass and a photon detected. We perform many experiments and find with the statistics find wave properties. Remember, we do not measure the wave directly in standard experiments but rather infer wave properties from many experiments. We might then carry this forward by considering a torsional mass that is influenced by the gravitation of the superposed quantum position of this quantized mass. If this torsional mass is also quantized in the large, then its position is in a superposition determined by this metric superposition. Then measurements of reflected photons will do this “collapse,” and the statistics of many such measurements used to infer wavy properties.
DeleteThe actual experiments in the paper I read last year is a bit different from this. It involves a moment arm coupled to a membrane in the superposed state. However, the idea is similar. I do not see anything impossible about this.
Why do you equate gravitational measurement and electromagnetic measurement? The usual pop science equivalence is metaphorical equivalence,not in an actual physical one. And that equivalence falls apart under scrutiny. Youre objection has no merit.
DeleteLawrence Crowell,
Delete"We perform many experiments and find with the statistics find wave properties. Remember, we do not measure the wave directly in standard experiments but rather infer wave properties from many experiments."
What would such an experiment tell us about gravity being quantized or not? The object will have wave properties, as predicted by QM, but those have nothing to do with gravity.
For example one can perform an electron interference experiment replacing the fluorescent screen (that is sensitive to the electron's EM fields) to some device that can detect the electron's gravitational field. I would certainly expect to observe the same pattern in both situations but I would not interpret this as evidence of gravity being quantized.
@ Westy: A weak gravity field is one where the squares of connection coefficients are near zero. So we drop them. A gravitational wave for a metric g_{ab} = η_{ab} + h_{ab}, with η_{ab} a flat Minkowski metric and h_{ab} a perturbation will obey a wave equation in vacuum
Delete∆ĥ_{ab} - ∂^2ĥ_{ab}/∂t^2 = 0,
for ĥ_{ab} the traceless transverse part of this metric perturbation and ∆ = sum_i ∂^2/∂^2x_i. This is a perfectly linear wave equation. This means the spatial deformations of the metric, sometimes written as h_{++} and h_{××}, are polarizations perpendicular to the direction of propagation. The occurrence of two polarization states is helicity = 2, or in a quantum sense there are two units of spin ħ, or s = 2ħ. So, this is remarkably similar to a HBT singlet entanglement of two photons. This is perfect for quantization with none of the nonlinear hoary problems faced in UV quantum gravitation.
So I should expect that at least weak field quantum gravitation exists in the standard form. It is when the gravitational field gets strong that I tend to find exceptions to most theory.
@ Andrei: The experimental set up would require a probe of the superposed metric. So, some sort of quantum optical set up is needed. In this way the quantum states of photons are entangled with the quantum superposition of the metric. From there we detect the quantum physics with the photons. A measurement apparatus works by entangling a “needle state” with the quantum system of interest, so the quantum phase in the superposition is transferred to an entanglement with the needle state. The experimenter then records the needle state, which is where the so-called collapse occurs.
∆ĥ_{ab} - ∂^2ĥ_{ab}/∂t^2 = 0,
for ĥ_{ab} the traceless transverse part of this metric perturbation and ∆ = sum_i ∂^2/∂^2x_i. This is a perfectly linear wave equation. This means the spatial deformations of the metric, sometimes written as h_{++} and h_{××}, are polarizations perpendicular to the direction of propagation. So this is remarkably similar to a HBT singlet entanglement of two photons. This is perfect for quantization with none of the nonlinear hoary problems faced in UV quantum gravitation.
So I should expect that at least weak field quantum gravitation exists in the standard form. It is when the gravitational field gets strong that I tend to find exceptions to most theory.
@ Andrei: The experimental set up would require a probe of the superposed metric. So, some sort of quantum optical set up is needed. In this way the quantum states of photons are entangled with the quantum superposition of the metric. From there we detect the quantum physics with the photons. A measurement apparatus works by entangling a “needle state” with the quantum system of interest, so the quantum phase in the superposition is transferred to an entanglement with the needle state. The experimenter then records the needle state, which is where the so called collapse occurs.
@Andrei, is it possible that these "hidden variables" are mere fluctuations of space caused by omnipresent (background) gravitational waves of very high frequencies?
DeleteIn that case I don't expect contradiction between GR and QM.
Nice article.
ReplyDeleteSome typos:
1) "we can make stronger quantum gravitational stronger by" -> "we can make stronger quantum gravitational effects by"
2) "That doesn’t heavy" -> "That doesn't sound heavy"
But overall nice article. Looking forward to the discovery of quantum gravity, 20 years seems like quite a survivable time span!
Ugis,
DeleteThanks for spotting this, I have fixed it.
Could you explain this idea of "neutralization" of non-gravitational force a bit more? Don't larger magnets exert stronger attraction to the fridge door?
ReplyDeleteWhat she means is that the Universe contains almost same amounts of positive and negative electric charges. Hence, on average, their electromagnetic effects cancel out. This is not the case for gravitational/inertial mass, where "positive mass charge" is clearly dominant.
Deletebks,
DeleteYes, but (as Julius said) the remaining long-distance fields are almost zero. We do see magnetic fields on long distances, but they're nowhere near as strong as the long distance gravitational fields.
These experiments to test quantum gravity require a Planck mass in a quantum superposition of states or two or more such masses in entanglements. The Planck mass is 2.176×10^{−8} kg and the mass of a proton is 1.67×10^{−27} kg. So for a system made of atoms with several tens of AMUs this means around 10^{15} to 10^{16} atoms must be in some coherent state, condensate or otherwise a form of single quantum state. This does at least approximately occur, and some techniques with quantization on the large with vibrating systems are pushing this boundary. Once this reaches Planck mass scales it should then be possible to detect physics associated with a superposition of the metric.
ReplyDeleteIt is though possible to look at extremely high energy. Black hole coalescence. Within a region of 10^{-15}m of the event horizon of a black hole there is a form of "quantum hair." This hair involves gauge quantum numbers associated with QCD and QFD (weak force) and in the tiny fraction of a second before coalescence, around 10^{-24}sec, this quantum hair is excited and it produces gravitons. These should then be detected as a form of gravitational memory. This quantum hair will generate BMS symmetry transformations. Further, while the time period is very small, the tortoise coordinates expand the time domain for detecting this. This detection is an indirect detection of gravitons.
I have for 2-1/2 years been working on this, and using the moduli curve theory Mirzikhani developed for orbits in hyperbolic spaces. This has been a quite a mathematical challenge.
With detecting gravitons it is best to let nature do the heavy lifting. There is no conceivable way we humans could even build a system that could slam particles at the Planck energy.
Newsflash: Bee changes stance, endorses building a larger particle accelerator after all! ;)
ReplyDeleteNewsflash clarification: Bee recommends building a new collider the size of the Milky Way!
DeleteNewsflash:
DeleteAs Sabine’s galaxy size accelerator nears completion, the physicists and engineers in charge of the project realize that workers on the opposite side of the 100,000 light year in diameter machine have been using error-filled blueprints and it will take more than 100,000 years to get them the corrected ones.
Newsflash 2:
After many tests have been performed with the galaxy size accelerator, it has now been deduced that in order to fully understand the “new particles” being discovered in the tests, an accelerator the size of the universe will need to be built.
Newsflash 3:
“Ach du lieber!!!” exclaims one of Sabine’s descendants.
After many tests have been performed with the universe size accelerator, it has now been realized that the accelerators themselves were literally creating the particles being “discovered.”
Sabine, even though it may sound like I’m joking here,...
(and at the risk of me and my ideas being pilloried by you or PhysicistDave)
...nevertheless, in reference to the search for hypothetical gravitons, isn’t one of the abiding mysteries of quantum mechanics implied in the fact that the very way in which we configure our measuring devices is what seems to assign certain attributes to quantum entities?
For example, if we create a device designed to measure an electron for position, it will display position. And if we create another device to measure that same electron for angular momentum, it will display angular momentum.
However, allegedly (according to the Copenhagen Interpretation), just prior to measurement,...
(say, for instance, while it is in superposition in the double slit experiment)
...an electron possesses none of those particular attributes, and only acquires them after the measurement is made.
In which case, wouldn’t the same also apply to gravitons?
What I am getting at is that if we do somehow manage to “discover” a graviton appearing within the context of our measuring devices, aren’t we simply self-creating the results of what we see by reason of the experimental means that we have arbitrarily chosen and devised to look for it?
The point is that if any of that is even remotely possible, then my questions are:
1. Do you think that gravitons truly exist and are simply waiting for us to discover them?
Or...
2. Are we simply going to invent some uniquely configured measuring device that in turn will create the “appearance” that gravitons exist, when, in fact, they do not exist?
Or...
3. Is it possible that what we are actually encountering with quantum mechanics is the inherent ability of the underlying substance from which reality is created to transform itself into displaying whatever attributes our measuring devices are designed to look for (as per the abovementioned Copenhagen example)?
(Not that anyone cares, but my money is on #3.)
@Lawrence Crowell:
ReplyDelete"There is no conceivable way we humans could even build a system that could slam particles at the Planck energy."
What makes colliding particles mandatory, though?
Why not collide micro-objects (which have Planck mass), like a Railgun, instead?
(Imagine, if 2 (super (hyper?) powerful) railguns were firing at each other!)
A quanta of black hole has a mass m = 2×10^{-5}g, about equal to a 1/1000 ths of a flee. If converted to energy that would be equal to around 40 liters of petrol or a full tank of gasoline. That is a lot of energy. So, if I detonate 10 gallons of gasoline do I get quantum gravity or a unit of quantum black hole? Of course not. The energy density is what counts, for in order to get a quantum black hole unit that needs to be in a region 10^{-33}cm in length. That is where things get tough. A collider capable of sending protons to 10^{19} times their mass in energy, or a Lorentz gamma factor γ = 10^{19}, the LHC has γ = 10^4, would convert two colliding protons into a quantum black hole that would then decay in a huge gemish or particles.
DeleteBTW, my son wanted to see a gallon of petrol or gasoline explode. So, I eventually conceded to his wish and rigged an electric starter to a gallon of fuel. It was impressive. Imagine a particle detector that must detect daughter particles flying out with that sort of explosive energy!
To excite quanta of black hole you need this energy on a particle scale. If you want to generate gravitons you similarly need a fair amount of energy to get them to couple to a detector. The coupling constant between curvature and energy is 8πG/c^4 and I leave it to the reader to input numbers to see how very small this is. Even though the coalescence of two black holes produces more energy than billions of supernovae, these waves couple so weakly they are not easy to detect.
@Lawrence Crowell:
DeleteI remember, when LHC was getting build, there were a lot of fears about it creating a micro-BH!
Imagine, if someday physicists start building a (linear/circular) collider, that is specifically designed to produce a micro-BH! :-)
But, IMHO, that is exactly what needs to be done!
To finally learn everything about BHs & finally truly complete SM (by adding (what is called) Planck particle)!
& to finally get all data needed for the true theory of Quantum-Relativity!
Of course, the biggest problem for it would be how to handle the explosion (the decay of Planck particle (micro-BH)) afterwards!
(So the collisions can be repeated as many times as needed!)
The fears over black holes coming out of the LHC were silly. This also goes with concerns over strangelets. The Earth and other planets are bombarded by cosmic rays that have up to a million times the energy the LHC musters. If there were some planet destructive high energy process it would have happened a long time ago.
DeleteA quantum black hole would decay in a few Planck times of 10^{-43}sec. The production of a quantum black hole this way is the ultimate scattering experiment. The black hole does not exist long enough to grow by gravitational accretion of matter.
The concern with a black hole in the LHC stemmed from ideas of extra large dimensions. This was an idea that by various means the Planck scale turns out to be expanded to a much larger scale at the electroweak scale. It was really a bit of a desperate idea that somehow we could do quantum gravitation with the LHC.
There was also from the RHIC at Brookhaven some physics of quark-gluon plasmas that are analogous to black holes. This has the title of QCD-BH equivalence, or because black holes have AdS equivalencies QCD-AdS. Asymptotic freedom and IR confinement have some similarities to the physics of black holes. The low energy "gluon bag" confines quarks and QCD color charge in a way analogous to how event horizons conceal the interiors of black holes. The RHIC found some physics along these lines, and the ALICE detector at the LHC has probed some of this as well.
Lawrence,
DeleteThose fears were not silly. Given how many papers were published about it, it was very reasonable to check what the risk is associated with such an experiment. The argument you quote about cosmic rays is entirely non-trivial because for cosmic rays you basically have a fixed target experiment, and not, as for the LHC, a com system that's in rest with the planet.
Also note that to produce black holes at the LHC the Planck energy has to be lowered, so the typical decay time is 10^-23 (in a naive estimate), ie, you are 20 orders of magnitude off.
I was thinking of the standard Planck scale; agreed the decay time would expand if there were these large dimensions.
DeleteI think the topic of rouge black holes eating up Earth was fueled to quelle a popular narrative and concern. Even if the black hole was generated in a lab frame instead of a center of mass frame by cosmic ray event the black hole would still go through Earth and eat out a tube of material. With the Planck scale expanded by 20 orders of magnitude in extra large dimension the black hole would also be slowed down.
Lawrence,
DeleteWithout the lowered Planck scale you can't make them to begin with, so the two issues are not unrelated. In fact the decay time is basically just the inverse of the lowered Planck energy: 1/TeV is something like 1 fm/c that comes out to be about 10^-23 s, take or give an order of magnitude.
"Even if the black hole was generated in a lab frame instead of a center of mass frame by cosmic ray event the black hole would still go through Earth and eat out a tube of material. With the Planck scale expanded by 20 orders of magnitude in extra large dimension the black hole would also be slowed down."
Indeed, and as it eats up material, it increases in mass which decreases the temperature, making it less likely that the black hole decays. Now you have to ask yourself what is the probability that the initial momentum of the black hole is so small that it keeps on oscillating around the center of the earth and keeps on growing in that process? And that doesn't even take into account that the 10^-23s second estimate is off by 2-3 orders of magnitude if you use the correct thermodynamical ensemble (which Hawking didn't).
And, yes, the media fueled the concern beyond the reasonable and yes, that was irresponsible, but that doesn't mean it was silly to ask what the risk is associated with that given that so many people believed the story with the extra dimensions.
(What was silly here really was the idea that the lowered Planck scale should be at the TeV scale, which is, believe that or not, the same argument from naturalness that my book is about. I probably don't need to tell you that adding spatial dimensions to a quantum field theory does not exactly improve its convergence properties.)
Wow, that was a rapid response with length! Agreed about the time frame.
DeleteThe idea of extra-large dimensions only seemed to make sense if there were some sort of renormalization of the Planck scale. I had thought that maybe with overcomplete coherent states or some form of squeezed vacuum state might the Planck scale be rescaled 10^{-33} cm to 10^{-17}cm or so. I found it implausible the Planck scale was ordinarily rescaled to such a large value without the gravitational field being much stronger.
“I found it implausible the Planck scale was ordinarily rescaled to such a large value without the gravitational field being much stronger.”
DeleteLawrence, unless I’m misunderstanding what you’re saying, I thought it was the other way around. In the seminal ADD paper of 1998: “The Hierarchy Problem and New Dimensions at a Millimeter”, it’s argued that gravity is weak due to its “dilution” in a hypothesized extra dimensional space. Since nothing was found in that energy regime to support such a contention, it seemed like it was case closed, not to mention the difficulty of reconciling such a concept with quantum field theory, as Sabine pointed out.
However, ever the future technology optimist, if not grounded in a deep understanding of quantum theory, I found myself intrigued by the recent (2017) US Navy disclosure of top gun pilot encounters with anomalous objects off the Baja California coast in 2004. In the words of Commander David Fravor, as he and his wingman circled above an estimated 40 foot long, tic-tac shaped object just above the ocean surface: “This thing would go one way to another, similar to if you threw a ping-pong ball against a wall”. In an interview he expanded on this describing its movements as highly erratic and extremely rapid.
The point I wish to make is this description, and others like it, reminded me of the behavior of fundamental particles, like electrons, as detailed in a subsection of chapter 7 of the book “Schrodinger, Life and Thought”, by Walter Moore. On page 257 it’s stated: “…and thus one has the picture of an electron undergoing a rapidly oscillating Zitterbewegung [trembling motion] which is superimposed on the center of the wave packet representing the free electron.” It’s almost as if ‘someone’ has developed a technology corresponding to quantum behavior writ large; that is, projected up to the macro-scale. Other eyewitness accounts, which I won’t detail for brevity, suggested to me that extra dimensions might be involved.
Of course these are personal opinions/observations that hopefully are OK to mention in a professional blog setting. Whether extra dimension models are currently compatible with the framework of the Standard Model is quite honestly beyond my knowledge. You, Sabine, and others are vastly more qualified than I am to gauge whether such a speculative extension of the Standard Model is at all viable.
I was thinking of the Planck length ℓ_p = √{Għ/c^3}, and where if this increased by 20 orders of magnitude then G must increase by 10 orders of magnitude. With extra-large dimensions it was argued that for gravitation in larger dimensions, say n, that the potential would be V = -GM(ℓ_p^{n-3}/r^{n-2}), where for n = 2 this is a logarithmic formula. This was argued to be why gravity was strong at certain small scales. Say for r → ℓ_p then V = -GM/ℓ_p, which would be enormous. However, gravitation with 1/r potential means these dimensions are closed off. Then if the Planck length were at the scale of say the standard model then gravitation would be weaker at this scale. The idea with a Gauss’ law argument was that flux lines were escaping into these other dimensions.
DeleteThis is sort of messy in a way. It implies that gravitation at somewhat larger scales obeys standard Newtonian rules, but then at smaller scales it transitions into being a 1/r^8 or 1/r^9 potential. There were ideas of experiments at the submillimeter scale to determine if some increased gravitation strength was present. There were also expectations that this would manifest itself in the LHC. Nothing has occurred to my knowledge,
On building a galaxy-sized particle accelerator, even if the resources were available to construct such an accelerator, detection of gravitons would still be problematic, because the background radiation of neutrinos and possible dark matter would overwhelm any detection of gravitons, and any attempt to construct a barrier to such radiation would result in the entire system collapsing into a black hole. So it isn't even possible in principle to detect a graviton directly.
ReplyDeleteHopefully the theory where "mathematical inconsistencies" are resolved ("according to general relativity, gravity does not have quantum properties") is one based on some stochastic calculus, like
ReplyDeleteStochastic metric space and quantum mechanics
Yoshimasa Kurihara
https://iopscience.iop.org/article/10.1088/2399-6528/aaa851
Because then I might be able to understand it.
This lacking quantum behavior of gravity gives rise to mathematical inconsistencies that make no physical sense.
ReplyDeleteI've been looking for papers that focus on this issue, but unfortunately they are all too old and behind paywall. If anyone got a good reference, that would be appreciated (I'm trying to know if there is anything else than the singularity issue).
For instance, one can make a thought experiment where particles are entangled and show this leads to inconsistencies if you insert gravitational waves, but the original article is behind a paywall. I can only see summaries and other articles that reference it.
Regarding methods of testing quantum gravity beside the first one listed, it seems to me they all depends on specific peculiarities of how GR and QFT are mixed, and probably get published mostly because the effect happens to be observable in principle, or in conditions that are postulated to perhaps exist. Since at most one of these theories can be the right one, and since conditions that can mathematically exist are in general not realized in nature (ex: wormholes), I'm fairly sure none of these expected observations will ever be made.
Or rather, if they are indeed observed, we will just have discovered some new astrophysical effect 100% explained with standard physics.
“Einstein’s theory of general relativity tells us that gravity is due to the curvature of space and time.”
ReplyDeleteI admit this makes no sense to me. I understand that the curvature of space does a great job describing the path objects take moving under the influence of gravity, but mere curvature of itself seems inadequate to explaining the force that causes motion in the first place.
I am familiar with the “deformed rubber sheet” explanation and even seen physical demonstrations of it. But it still seems incomplete; objects follow the rubber sheet because gravity is pulling them down. So the thing being “modelled” (gravity) is included in the model of gravity; what plays the role of gravity in the theory? Some “ur-gravity”?
I can’t make sense of that yet: how curvature of space/time induces motion or acceleration.
sean s.
If you are interested, two recent journal articles that may help clarify: "Gravity and warped time, clarifying conceptual confusions in general relativity," by Magdalena (Physics Education, vol 55, 2020) and "Interactive animations as a tool in teaching general relativity to upper secondary school students," by Ryston (Journal of Physics: Conference, 2019). Both published by Institute of Physics Publishing, both are free to access. Hope they are useful to you.
DeleteThank you, Gary. I will look for those.
Deletesean s.
Sean:
DeleteIn GR there is no such thing as a gravitational "force". Objects always travel in a "straight" line, like force-free objects in Newtonian physics. Only that, because of the curvature of space-time, a "straight" line in GR (called a geodesic) is actually a curved path.
It's like an ant walking on a balloon. It travels along a curved line, not because of any force, but simply because the surface it's walking on is itself curved.
I am familiar with the “deformed rubber sheet” explanation and even seen physical demonstrations of it. But it still seems incomplete; objects follow the rubber sheet because gravity is pulling them down. So the thing being “modelled” (gravity) is included in the model of gravity; what plays the role of gravity in the theory? Some “ur-gravity”?
DeleteHelbig's internet theorem: for every interesting question in a blog comment, there is a web comic which is the perfect answer. In this case, at xkcd.
sean s. said:
Delete>> “Einstein’s theory of general relativity tells us that gravity is due to the curvature of space and time.”
> I admit this makes no sense to me. I understand that the curvature of space does a great job describing the path objects take moving under the influence of gravity, but mere curvature of itself seems inadequate to explaining the force that causes motion in the first place.
sean s.:
This motion can be explained if you look at particle physics. Einstein’s curvature of space (exactly: of space-time) is assumed to describe the curvature of light moving in a gravitational field. If we now look at the internal circular motion in particles, which was called “Zitterbewegung” by Erwin Schrödinger, we have the solution. Also this motion is subject to this curvature. The curvature causes an elementary particle to be accelerated (i.e. to spiral down) towards the direction of stronger gravity. And this applies for every object as every object is built by elementary particles.
If this acceleration of a particle is deduced from the curvature, the result is Newton’s gravitational acceleration: a = G*M/r^2. This is an algebraic result and so applicable for every situation.
So, if I understand it correctly (from Gary Allen's links, please pardon the informal language):
Delete1. All particles/objects are in motion; whether by travel or mere vibration. Nothing is still.
2. When a particle moves “downhill” time slows for it. When a particle moves “uphill” time speeds up for it.
3. When a particle moves “downhill” some distance X, time is slower for it the steeper the local gravitational ‘slope’. Since the slope increases steadily as the particle moves into the gravitational well, and time slows; the particle is moving distance intervals in “less” and “less” time; it’s accelerating. And the opposite when particles are moving “uphill”.
Is that about right?
sean s.
re: Phillip Helbig's xkcd comic example.
DeleteIn physics, there is nothing outside the \TeX [math environment].
You are completely right: Space curvature is nothing more than hand waving.
DeleteA "curvature of space" is not detectable within the space since all is in the same way affected: all measures, all lines, rulers, all beams and all length. So you cant detect "space curvature" and it has no effect on that what is contained in the space.
I know: the specialists will come know with inner or outer curvature. Hand waving.
Think of flatland. There is no effect on the flatlander if you crumple the paper on which the flatlanders live.
weristdas,
Delete"A "curvature of space" is not detectable within the space since all is in the same way affected: all measures, all lines, rulers, all beams and all length. So you cant detect "space curvature" and it has no effect on that what is contained in the space."
This is bluntly wrong, as even the most basic textbook on differential geometry would explain to you. I will not approve further comments that are equally ill-informed. It boggles my mind how people as ignorant as you fail to notice they don't have the faintest clue what they are talking about.
(And please stop trying to post links to personal websites. I don't approve those either.)
Based on prior comments; more questions occur to me.
Delete1. is there properly a “gravitational force”? Or is gravity merely an effect caused by space/time curvature? Is there really a sensible difference?
2. would a graviton represent an incremental value of space/time curvature? If not a quanta of force.
3. if gravity is “caused” by the mass of particles or objects, would not every fundamental particle be associated with its own graviton whose mass would be determined by the space/time curvature created by the particle in question?
4. if gravitons exist and have mass, do they have their own separate subtype of gravitons?
There is so much I don’t know. Mea culpa.
sean s.
Sean,
Delete1. Gravity is an effect caused by the curvature of space-time that in certain approximations can be described as a force.
2. No, a graviton is not an incrementaal value of curvature. A graviton is loosely speaking something like a tiny gravitational wave whose energy is quantized. Please do not take this literally. It is a math-thing and that's the best I can do converting math into English.
3. No, there is no reason every particle has its own graviton, for the same reason there is no reason every particle has its own photon. They all couple to the same graviton/photon. The difference is that all particles couple to gravitons while not all particles couple to photons.
4. No, see 3.
OK, I think I understand. (I may be mistaken, but ... !)
Delete“It is a math-thing and that's the best I can do converting math into English.”
I’m sure your math-to-English is much better than mine!
What I’m trying to get at is whether the curvature of space/time is quantized. It appears that gravitons are waves in space/time (and presumably quantized) but it is the curvature that causes the effect of gravity. If gravity is quantized, but the curvature is not, that seems counter-intuitive.
sean s.
sean,
DeleteI understand your problem of force in gravity, which is a problem of imagination. What about the following understanding:
Take an object that moves in a gravitational field, for instance a particle passing the sun. This object moves on a curved path. This curvature does not need a force, as this object merely follows the curvature of space. And this means, seen from the outside, an acceleration towards the gravitational source. And so it is obvious that the acceleration in a gravitational field is not caused by a force.
But if you now wish to keep an object at a fixed position in this field, you have to cause a counter-acceleration to cancel the gravitational acceleration. This counter-acceleration now needs indeed a force according to Newton’s law. And this is the force which we see on a balance, when the object rests on it.
I think that this is accessible to our imagination, and by the way it again yields the correct physical result. And further it explains why the gravitational acceleration does not depend on the mass of the falling object.
sean s.
DeleteIf gravity is quantized, space-time curvature is also quantized. Let me mention however that many people erroneously think quantization means discretization. This is not necessarily the case. Quantization, I am afraid I have to say this once again, is a mathematical term for a certain procedure that doesn't have a good linguistic description. In some cases (think of energy levels) quantization results in discretization. Best,
Sabine
When you say "quantize gravity" a lay person understands "show that gravity is discrete". I think you mean "develop a theory of gravity that is consistent with quantum mechanics, and find experimental evidence for it". Is there even a requirement of quantum gravity that the gravitational field be discrete? Would that be the same as saying that spacetime is discrete?
ReplyDeleteAlso practical question, if we put objects in superposition that are large enough to have observable gravity, won't they decohere by gravitational interactions with the environment?
No, quantization means "make it a quantum theory" and not "make it discrete". You can have non-quantum theories that are discretized.
DeleteSabine, if others have pointed out this small error, please ignore my response: "participle accelerator"
ReplyDeleteThanks for spotting this, I have fixed this!
Delete
ReplyDeleteIf gravitation could be quantified, it seems to me that it would be similar to the electromagnetic quantum that has a wide spectrum of energy; in low energy it is only capable of slightly changing the symmetry of space; but in high energy it can oppose weak energy and fuse matter; perhaps the mechanism of explosion of a supernova is due to the contraposition of the weak and gravitational field; rapid transition from nuclear density to atomic density. If it could be quantified, each of the other forces would serve as a measurement scale.
I have already filed the printed versions of your earlier blog articles on Quantum Gravity:
ReplyDelete- Researchers propose experiment to measure the gravitational force of milli-gram objects, reaching almost into the quantum realm.
and
- How can we measure quantum gravity?
But anyway, thanks for repeating and updating the topic.
I have a layman's question that proves I know nothing about Physics. However other amateurs might be similarly puzzled. The hypothesis is that gravity is quantized therefore particle mediated, the problem is the immense energy required to create such a particle. But as I sit here I am subject to gravity, therefore shouldn't there be large numbers of mediating particles actively mediating? I.e. shouldn't gravitons be ubiquitous, like photons?
ReplyDeleteTim,
DeleteYou do not need large energies to create a graviton. You are right in thinking that we constantly create gravitons. At low energies the problem is it's not possible to measure one of them individually to demonstrate that gravity is quantized.
Also note that I did not say you need large energies to produce a graviton. I said "you need large energies to create a measurable amount of gravitons." The thing is that with higher collision energies, gravity becomes increasingly important, until you get to a point where the probability of producing a graviton is similar to the probability of (say) producing a photon. You would notice that even if you can't detect the graviton because it would carry away energy. Strictly speaking this also sometimes happens at lower collision energies. But the effect is way too small. The point is that it becomes non-negligible at collision energies of about the Planck energy, which is where the huge collider estimate comes from.
"with higher collision energies, gravity becomes increasingly important". Is it an assumption, or a consequence of GR, or a consequence of QM, or a consequence of quantum gravity?
DeleteIt is a consequence of the perturbative quantization of gravity, but it goes back directly to the most important property of gravity: It couples universally to all kinds of energy.
DeleteIt couples universally to all kinds of energy.
DeleteThis gives me a recurring headache.
Because feelings imply selectivity. For example, electrons don’t feel the strong force, neutrinos don’t feel electric charges... What is not felt is as important as what is felt. There would be no fundamental plurality in nature without such selectivity among feelings. One of the most - if not the most - important and general rule about feelings is modal selectivity. To exist is to differ.
But gravity does not work like that. There is no selectivity.
But is it a feeling in the first place?? After all, there is no need to feel anything to follow the curvature of space-time, you just need to be included in it.
And as you said, the other interactions are neutralized on average. But not gravity. These two apparent features of gravity are a mystery for my little brain.
Maybe I have to understand that this deep uniformity present at the heart of nature cannot be separated from the advent of plurality...
Another question on the graviton : is there such a thing in loop quantum gravity ?
ReplyDeleteYes, there is, and Google could easily have answered this question for you. The next time before you ask a question, please make some effort to answer it yourself first, thanks.
DeleteAs I had free time, I spent it researching the question "Is there such a thing as a graviton in loop quantum gravity ? " First, I turned to my 2004 copy of Rovelli's Quantum Gravity (the index provides for 'graviton' on only two pages: 272 and 398). Surprisingly, the question is not there--or, if the answer is there, I do not understand it. Next, I did a search on arXiv employing the combined terms 'graviton' and 'LQG.' It returned five papers. I failed to locate an unambiguous answer in perusal of those papers. There appears to be an issue in obtaining the correct full graviton propagator. Rovelli: "Low energy limit--one component of the graviton propagator (or the Newton law) appears to be correct, to first orders in λ." Rovelli and Alesci: In a previous article we have shown that there are difficulties in obtaining the correct graviton propagator from the LQG dynamics defined by the Barrett-Crane vertex amplitude. Here we show that a vertex amplitude that depends nontrivially on the intertwiners can yield the correct propagator. We give an explicit example of asymptotic behavior of a vertex amplitude that gives the correct full graviton propagator in the large distance limit." Ultimately, a meaningful, unambiguous, answer to the question "Is there such a thing, as a graviton, in loop quantum gravity ? proves elusive.
Delete@Sabine
ReplyDeleteThere are two things I really don't understand:
1. " if [the EM field] was not quantized, then atoms would not be stable. ". Why? The Schrodinger equation with the Coulomb potential of the nucleus predicts stable electron orbits with the corresponding energy eigenvalues. You do not need to quantize the field.
2) "we can make quantum gravitational effects stronger by just taking larger masses and bringing them into quantum states, for example into a state in which the masses are in two places at once".
If you think of two charged particles in a quantum superposition, you do not need to quantize the EM field to describe such superposition. All would be well even if the field were not quantized. Again, you do need anything more than the Schrodinger equation to describe such situations. Same for gravitational interactions.
opamanfred:
Delete1. I already answered this question above.
2. No, not all would be well if the gravitational field was not quantized, but that's not the point of the sentence which you quote. The point of the sentence is that you can experimentally test which mathematical description describes reality.
There are a couple of things that might need clarifying. Gravitons in a weak gravity limit are a linear theory and similar to a diphoton in a triplet state. Such occurs with the Hanbury Brown-Twiss effect or photon bunching. This weak form of quantum gravitation is probably a decent IR limit of quantum gravitation. So I don't think it is entirely right to say we know nothing about quantum gravitation. What we do not understand is the the full UV limit of strong field quantum gravitation, such as what might happen with a black hole singularity.
ReplyDeleteThese proposed experiments with superposed masses and metric correspondence will produce a linearized weak field graviton with the "collapse" of the wave function. This is similar to the metric back reaction from the emission of Hawking radiation. The quantum phase of the superposed metric is, if we consider qubits conserved, carried off in this elusive graviton. Of course this graviton is far to weak to consider measuring it. For starters the graviton would have a wavelength far larger than the lab, and the experiment is done in the near field region analogous to the same in EM theory.
These experiments as a result would not really tell us much about the deep structure of quantum gravitation. All they would tell us is that in the weak and linear field limit that gravitation is quantized similarly to electromagnetism. Mind you, this would be enormous progress! However, it would be only the beginning.
What odds would you give the proposition that, while matter/energy is clearly quantized, spacetime and gravity are not?
ReplyDeleteThe reason gravity is so different is that it isn't a boson-mediated force. There are no gravitons. It's strictly a spacetime effect.
Any hope at all for such a hypothesis?
Gauge fields are interior symmetries, which means the space of the symmetry is not space or spacetime itself. This means that nonlinear waves due to the nonabelian structure of the gauge field is workable. While the internal symmetry is nonlinear the configuration of the wave, determined by field amplitudes acting on a Fock space basis, is linear. So we can do quantum theory with QCD.
DeleteGravitation is an exterior symmetry, which means the nonlinear structure is manifested in space or spacetime. Also the group structure is pseudoEuclidean, which means the group is not compact with an orbit space of curves or moduli that have Cauchy convergence. The moduli space is nonHausdorff and complicated to work with a linear wave theory such as QM. This does make things difficult. However, weak gravitation is linear for the nonabelian terms sufficiently small, so an approximate linear field is quantizable.
However, classical gravitation and spacetime may be a form of condensate or large N entanglement of quantum states. Laser states of light are such quantum mechanical systems that have a classical structure. Laser coherent states have both Riemannian and sympletic metric structure. A wave function is of the form
ψ(x;q,p) = π^{-1/4}exp{-ipq/2 – ipx – (x – q)^2/2}
This is a state common in the Wigner quasi-probability distribution. The overlap of states is the,
⟨ q_2,p_2|q_1,p_1⟩ = exp{-i(q_1p_2 – p_1q_2)}exp{-[q_2 – q_1)^2 + (p_2 – p_1)^2]}
Where the first of these is generated by a symplectic metric q_1p_2 – p_1q_2 and the second is generated by a Riemannian metric (q_2 – q_1)^2 + (p_2 – p_1)^2. Spacetime is then quite possibly a manifestation of large N entanglement and an epiphenomenology.
It is worth pointing out that with N qubits the number of possible entanglements is given by the integer partition. This is the number of ways one can form the integer N with addition of smaller integers. An approximate form is given by the Hardy-Ramanujan formula, and the exact theory by Duncan, Griffin and Ono et al etc. The integer partition function is a way of computing the density of states in string theory and also the set of possible ways that quantum states may be partitioned on a stretched horizon of a black hole.
There are reasons to think that QM and GR do have some relationship with each other. That relationship might however not be what most physicists have usually thought.
Thank you, Lawrence Crowell, for taking the time to answer, but being neither a mathematician nor a trained physicist, I'm afraid your answer went pretty far over my head. :(
DeleteDo I take it your answer to my question is, "Maybe. Maybe not."
If you read some of my posts above on quantization of weak gravity fields, in particular gravitational waves, I lay a case for saying in this case there should be a straight forwards quantization. The gravitation is essentially linear and the problems with nonlinearity and quantization are negligible.
DeleteIt would be strange or almost schizophrenic of nature if it should turn out there is no relationship between gravity and quantum mechanics. Of course experiments have to be the final arbiter of this. These sorts of measurements involving quantization of large masses will test for weak field quantum gravitation. That should be very linear and quantized in a pretty straight forwards manner.
“... relationship between gravity and quantum mechanics.”
DeleteIf you are fighting all the “time” you also have a relationship - non-quantized and non-linear versus quantized and linear. And spacetime is the battle field.
@Lawrence Crowell: Thank you, that's an answer that's much more my speed. I wish I did speak math at that level, but I'm still struggling to understand tensors and partial derivatives.
DeleteIt sounds like you confirm what I take to be the consensus: It is most likely gravity (and I assume spacetime) are quantized, and any hope for smooth spacetime is a faint one. But a faint hope can exist without contradiction?
There are tensions in physics, for example, between wave-like and particle-like behavior, or between conjugate pairs locked in Heisenberg's embrace. I am attracted to the idea there could be a tension between smooth spacetime and quantized matter/energy.
Even if that's a very faint hope. :)
Ward Smythe wrote:
Delete> I wish I did speak math at that level, but I'm still struggling to understand tensors and partial derivatives.
Ah, but knowing that you are struggling is the beginning of wisdom!
It is those who will not admit that they are having difficulty grasping something who are really in trouble.
This really is true, by the way, even of truly brilliant people, from contemporary Nobel laureates all the way up to Einstein, who documented his own tortuous path to understanding General Relativity in great detail.
If you are having trouble grasping partial derivatives, then I assume you understand ordinary derivatives? A partial derivative is then just an ordinary derivative along one specific direction, usually one of the coordinate directions (x, y, z, etc.).
There are several different ways to think about tensors: the old-fashioned way is to think of them as if they were a multi-dimensional array of numbers that, for one reason or another, transform as if they were products of vectors. I myself found that approach very difficult to wrap my head around.
Misner, Thorne, and Wheeler's classic textbook Gravitation explain tensors as "machines" that take several vectors as input and spit out a number as output. (The "machines" have to be linear in each input.)
The “machine” approach happens to be equivalent to the old-fashioned approach, but I found it much easier to grasp. (MTW is not the best book to learn GR from, but I did find their discussion of what a tensor is to be helpful.)
Of course, the "machine" approach can be proven mathematically to be equivalent to the old-fashioned multi-dimensional array of numbers approach.
Probably the best way to understand tensors is to learn about specific tensors: the most important one in General Relativity is the "metric tensor." If you know about polar coordinates vs. Cartesian coordinates in the plane, you actually already know about the metric tensor, just not by that name. It's not that hard.
And, beyond the metric tensor... well, the basics of General Relativity can actually be presented without going into the higher-order tensors (Riemann tensor, Ricci tensor, etc.). I’m working on a write-up of how to derive the Schwarzschild solution working only with the metric tensor without ever having to deal directly with all those more complicated tensors. The needed background for the approach I am taking is laid out in Chapter 42 of Volume II of the Feynman Lectures.
I strongly recommend reading the Feynman chapter: you will notice that he never explicitly mentions tensors.
I favor a slightly different approach in which the focus is not on the radius excess (Feynman’s eq. 42.3) but rather on the tidal distortion of a little ball of dust that is in free fall: again, though, there is no need to mention (or deal mathematically with) “tensors.” And, with this approach, you can derive General Relativity all the way through to the Schwarzschild solution.
So, don’t let tensors flummox you: the real physics can be explained without getting heavily into the math of tensors. (I should add that to truly get deeply into General Relativity, at the level of cutting-edge research, of course you would have to master tensor calculus. But for most practical purposes, it is really not needed.)
All the best,
Dave
“... how to derive the Schwarzschild solution working only with the metric tensor ...”
DeleteAnd partial derivatives of the metric in the form of Christoffel symbols, I guess.
So, you will be back on the battle field.
“As you see, the war treated me kindly enough, in spite of the heavy gunfire, to allow me to get away from it all and take this walk in the land of your ideas.” Schwarzschild wrote to Einstein.
"Newton had his plague and Schwarzschild his heavy gunfire" is a section in here (unfortunately not on display - neither way)
Reimond wrote to me:
Delete>[Dave]“... how to derive the Schwarzschild solution working only with the metric tensor ...”
>[Reimond]And partial derivatives of the metric in the form of Christoffel symbols, I guess.
Well... at some level, you are really calculating the Ricci tensor, of course.
But, you can do "Einstein-style" reasoning (falling elevator and all that) where you never go through all the algebra to calculate the Christoffel symbols, the Ricci tensor, etc.
At some abstract level, you are taking advantage of the spherical symmetry and the fact that everything is static in time so that lots of the quantities are zero.
But, in practice, the math looks like freshman-level calculus. The vertical derivative of g00 (ordinary derivative, since g00 only depends on r) gives you the acceleration starting from rest, the geometry gives you tidal forces, you can take the non-trivial grr term into account by noting that a non-trivial grr term basically gives a geometry like a thin slice through a cone, and so on.
You do not really even need partial derivatives!
Of course, you have to think carefully about the actual physical effects, but I think that is a good thing. Too many people learn the math of relativity (e.g., all the differential geometry behind General Relativity) but cannot explain in simple terms, for example, why Einstein's value for light deflection by the sun is twice Newton;s value.
So, actually, I can get everything without any of the standard apparatus, even partial derivatives. And, of course, I can state the field equations without using any of that. The basic starting point is indicated in Taylor and Wheeler's Spacetime Physics in their final chapter on General Relativity: see in particular their Section 9.6 and, specifically, Box 9.1.
I've been lecturing our non-STEM friends here on how you cannot understand physics without using math, but I have always been interested in what the truly minimal math is that is required to grasp some physics -- often less than we realize.
Of course, it is the extraordinary symmetry of the Schwarzschild problem that makes this possible: it would be hard to get the Kerr-Newman solution this way, and impossible to model, say, colliding black holes.
I have all the analysis worked out on this, but my current priority is the monograph that gives an updated version of Rosser's Classical Electromagnetism via Relativity. So, it may be a while before I get a manuscript done for GR and the Schwarzschild problem. I'd like to think of it as the "volume 2" of Spacetime Physics that was never written (and, yes, I do know about their book on black holes), but no doubt I do not write as well as they do.
All the best,
Dave
It is worth highlighting that a second-edition of "Exploring Black Holes" (2018) is free for pdf-download from Edwin Taylor's webpage (Edwin F. Taylor, John Archibald Wheeler
Deleteand Edmund Bertschinger).You find this: "Einstein’s equations are most economically expressed in advanced mathematics such as tensors, and deriving a global metric from them is a bit tricky. In contrast, the global metric expresses itself in differentials, the working mathematics of most technical professions, and leads directly to measurable quantities: wristwatch time and ruler distance. We choose to start with the directly useful." (page 79).
In my mind, the existence of gravitational waves proves gravity IS quantum. Light is both a particle and a wave. Ergo, gravity is both a wave and a particle. All that's left is to figure out how it works. And Sabine is right, we are closer than we may think.
ReplyDeleteIn my mind, the existence of gravitational waves proves gravity IS quantum.
DeleteNo, it does not. This is not a matter of opinion, the statement you make is wrong.
OK, thank you for the clarification. I shall correct myself henceforth.
DeleteQuantum gravity against Einstein's theory of relativity is monism against pluralism.
ReplyDeleteCopy editor here:
ReplyDelete> does not neutralize and therefore add up
should be
does not neutralize and therefore adds up
Estimating the uncertainty scale of gravity leads to the conclusion that we handle with the scale of galaxies.
ReplyDeleteAlso we have dark matter in the same scale. What if the dark matter would be in fact nonlocal-like(bosonic) energy of gravitational change signaling "medium"? No need for trying to measure conventional mass "in two places at once" but only dark matter quanta some way if they were in the scale of several light years or several thousands ly or so...
ReplyDeleteNow I have a question; if the gravitational field reaches such an energy that it can lose its long range ?; Would the gravitational formula change drastically for a black hole?
Luis,
DeleteI have no idea what it means for a gravitational field to "lost its long range".
The principle to see: the force to be quantized is not the force of gravity but the force of gravitational change.
ReplyDeleteHello, "One should then be able to tell whether the gravitational field is also in two places at once". which kind of effect are you talking about ? i heared about experiments trying to obtain a double slit interference with massive objects ... but it was to check whever the two parts of the wave function (through the two slits) may gravitationally attract each other resulting in a more focused interference pattern and in that case it would actually not be evidence for quantum gravity, but just the contrary : rather a kind of semiclassical theory of gravity would be favoured by this kind of observation as far as i can remember...
ReplyDeleteHello,
DeleteYes, you can test a hypothesis by trying to falsify it. You may have heard of that. It's not exactly a new idea.
Lee Smolin, 2003: "Gambini, Pullin, and others calculated how light travels in a quantum geometry and found that the theory--loop quantum gravity-- predicts that the speed of light has a small dependence on energy. Photons of higher energy travel slightly slower than low-energy photons. The effect is very small, but it amplifies over time. Two photons produced by a gamma-ray burst 10 billion years ago, one redder and one bluer, should arrive on Earth at slightly different times. The time delay predicted by the theory is large enough to be detectable by a new gamma-ray observatory called GLAST (for Gamma-ray Large Area Space Telescope), which is scheduled for launch into orbit in 2006. We very much look forward to the announcement of the results, as they will be testing a prediction of a quantum theory of gravity." (edge.org). Lee Smolin writes "What are we missing in our search for quantum gravity ? " (arXiv:1705.09208).
ReplyDeleteSabine,
ReplyDeleteExcellent article as usual.
The third link you posted (the one to this blogpost of yours: http://backreaction.blogspot.com/2016/03/researchers-propose-experiment-to.html ) is a Youtube redirect.
Andrea
I’ve long hoped that there could be an end run around these exceptionally delicate and precise experiments attempting to detect the superposition of a milligram sized mass, that might be attainable in the coming decades, to prove the graviton’s existence. Specifically I’m referring to outlandish claims involving experiments with high temperature superconductors by a very controversial figure in the decade of the 90’s and beyond. On the face of it these claimed experimental results could be interpreted as resulting from the production of gravitons at an abundance and energy level many magnitudes beyond what standard physics would allow. Of course extraordinary claims require extraordinary proof as Carl Sagan reminds us, and that proof is not there, at least not yet.
ReplyDeleteNot being one prone to discouragement, I elected to run my own experiments with some commercially available yttrium-barium-copper-oxide (YBCO), 1 inch diameter discs. This involved discharging some 600 volts through these YBCO chips, while monitoring for acceleration signals with an accelerometer shielded from EMP’s within a metal budbox. I had some false positives from acoustic ‘pops’ as the liquid nitrogen expanded with the passage of about 1.2 megawatts through the superconductor chip. Now the experiment is configured so that the hoped for ‘graviton burst’ that would propagate at light speed, is readily separated on the scope display from any acoustic signal. All the YBCO runs resulted in null results.
Some time ago I purchased some surplus niobium-titanium alloy rod, a type-1 superconductor requiring liquid helium temperatures. Cutting off a 2 inch section and drilling/tapping the ends for 4-40 screws, my intent is to repeat the YBCO experiments, with hopefully an improved signal-to-noise ratio due to the 10-fold higher density of cooper pairs that niobium has over YBCO. But liquid helium is not something an amateur can work with in a basement workshop. Fortunately, numerous universities are within driving distance of my home, where liquid helium is routinely used in their physics labs. These include Yale, Harvard, Worcester Polytechnic, MIT (where my late dad graduated in chemistry, 1931), and others. I’ve procrastinated for literally years on this plan, but should I ever get around to it, and one of these facilities allows these experiments on their premises it could either rule out these far-fetched claims, or lead to an interesting discovery.
Dave,
ReplyDeleteThanks for your very helpful explanation of tensors and partial derivatives. I am one of those guys who while having an intuitive understanding of mechanical systems, flunked college physics because I could not do the math. At 77 years of age trying to understand what you guys are talking about and trying to get a better grasp of the math is tremendously good exercise for my mind.
Proving the fact of quantum gravity seems rather like LIGO proving the existence of gravitational waves. Yes, very important, and almost certainly Nobel Prize territory.
ReplyDeleteHowever, the simple fact of existence only has us confirming what we assumed was probably the case all along. Again like LIGO we surely have to look further as to what type of result may lead us to new Physics. And could any of the suggested techniques ever be sufficiently sensitive as to show gravity is not quantised, which would of course be far more profound.
MikeS,
DeleteThis is not a good comparison. We have had a theory for classical gravity for a long time before LIGO measured gravitational waves. LIGO tested a prediction of an existing theory. But we do not have have a theory of quantum gravity. Finding evidence for quantum gravity would be enormously important to develop such a theory to begin with. It would be both more interesting and more relevant for progress in quantum gravity than the detection of gravitational waves has been for general relativity.
The Heisenberg uncertainty principle sais that either the momentum or the position of a quantum particle cannot be measured with arbitrary certainty. It seems to me that quantum gravity is A BIT IN THERE already: The position is uncertain. So somehow the space is quantized already, isn't it?
ReplyDeleteHow about look at the quantum gravity problem as an "uncertainty of theories": If gravity is certain than the position of the particle is not. Gravity as the "other side of the coin" of quantum mechanics? Is it possible to formulate a theory of quantum gravity by assuming classical behavior of objects in an unknown, yet-to-be-descibed quantum space(-time)?
We have used sound (called phonons) to simulate such quantum phenomena as the evaporation of black holes, where one of the virtual pairs exists beyond the event horizon while the other virtual particle exists outside the event horizon. Perhaps we can come up with a simulation of quantum gravity using phonons. While it’s not actually using gravitons, I think it may be possible to design a simulation of quantum gravity in this manner - after all the use of phonons was instructive in studying black holes, another gravity related phenomenon.
ReplyDeleteThis could be a big experimental result. Measurements of wave function collapse with gamma radiation sources finds no correction that would be attributed to a role for gravitation. This may throw ideas such as Penrose's in doubt. This is a copy of what I wrote in the entry on singular limits
ReplyDeletehttps://www.sciencemag.org/news/2020/09/one-quantum-physics-greatest-paradoxes-may-have-lost-its-leading-explanation