Einstein's field equations

[Alan Grayson]

Where do the several postulates of GR imply that the field equations fail to apply at some small dimensions of space and time? It's commonly claimed that GR does not apply at the microscopic level, but I see nothing in the several postulates of GR that imply this result. AG

[Philip Thrift]

On Saturday, October 26, 2019 at 3:19:03 PM UTC-5, Alan Grayson wrote:

Where do the several postulates of GR imply that the field equations fail to apply at some small dimensions of space and time? It's commonly claimed that GR does not apply at the microscopic level, but I see nothing in the several postulates of GR that imply this result. AG

They don't imply that. The EFE is the wrong mathematics to match phenomena at the quantum scale. 

So in that sense EFE is wrong (as a "universal" theory).

@philipthrift 

[Alan Grayson]

You haven't answered my question -- which is WHY the EFE don't apply at the quantum scale. AG 

[Brent Meeker]

What creates the problem at microscopic level is that the stress-energy tensor on the right hand side will be due to the wave function of a quantum particle and so would only have a probabilistic interpretation.  We an do semi-classical computations by replacing the wave function by it's expected value at each point.  But that avoids the point that the metric stuff on the left hand side needs to be represented by a probabilistic function to match the right hand side.

Brent

On 10/26/2019 1:19 PM, Alan Grayson wrote:

Where do the several postulates of GR imply that the field equations fail to apply at some small dimensions of space and time? It's commonly claimed that GR does not apply at the microscopic level, but I see nothing in the several postulates of GR that imply this result. AG

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[Philip Thrift]

Because Nature is a bitch?

@philipthrift 

[Philip Thrift]

On Saturday, October 26, 2019 at 3:57:01 PM UTC-5, Brent wrote:

What creates the problem at microscopic level is that the stress-energy tensor on the right hand side will be due to the wave function of a quantum particle and so would only have a probabilistic interpretation.  We an do semi-classical computations by replacing the wave function by it's expected value at each point.  But that avoids the point that the metric stuff on the left hand side needs to be represented by a probabilistic function to match the right hand side.

Brent

That's an interesting way to express it.

@philipthrift 

[Alan Grayson]

In effect, what Brent is getting at, is that GR is a classical theory, which assumes a classical space-time field. But if you assume a classical field at the microscopic level, will GR give answers which are contradicted by measurements? AG

[Lawrence Crowell]

Brent has a part of the problem laid out. The semiclassical approach to physics is that T_{ab} - ½Rg_{ab} = 8πG<T_{ab}>, and the curvature stuff on the left is nonlinear. Quantum mechanics is not good with nonlinear operators. If we try to make the Ricci curvature an operator, the nonlinearity of the operator causes troubles. The only way to fix this is to impose Wightman conditions that quantum oscillators for the field are localized to a point and independent on spatial manifolds. General relativity has problems with this because curvature is evaluated by a loop in spacetime and is the field through that area. Gravity is then more nonlocal. There is another problem that spacetime has with quantum physics. Putative operators for gravitation are evaluated on a metric signature (+,-,-,-), which results in negative probabilities. 

Are there ways around this? I think so. For one thing quantization only makes sense on event horizons, where the area curvature is evaluated on is dual to a point. So we can with holography I think quantize gravitation on horizons and then compute amplitudes in the bulk. The negative probability problem can be worked around with coherent states, such as those with laser physics. The gravitational quantum states are then a condensate or massive entanglement of states. The maximally mixed states that are an apparent problem then have probability p = 1/N, for N modes, and we can evaluate a relative entropy S(ρ*|ρ) = N + S(ρ) for  ρ* and ρ the density operators for maximally mixed states and the coherent states on the horizon.

In this way the states on the horizon are near Planck energy oscillators, and the mixed states the Hawking radiation. This relative entropy is then a dualism between the UV fields on the horizon and the IR fields beyond, or in the bulk. This is then

UV-fields of quantum gravity = IR-fields of gauge interactions and fermions

If you think about it this is a way of writing the Einstein field equation.

LC

[Alan Grayson]

If one wants to quantize GR, one would have to quantize the underlying classical field of space-time. But what would pop out of the quantized field when a measurement occurs? I couldn't be a photon as in QED. What would be the quantized measurement? A graviton? AG 

[Brent Meeker]

On 10/26/2019 7:15 PM, Alan Grayson wrote:
>
> If one wants to quantize GR, one would have to quantize the underlying
> classical field of space-time. But what would pop out of the quantized
> field when a measurement occurs? I couldn't be a photon as in QED.
> What would be the quantized measurement? A graviton?

It should be an eigenvector of whatever operator you applied to the wave
function of the metric field.  That's why Lawrence was worried about
what a Ricci tensor operator would return.

Brent

[Lawrence Crowell]

As I said, I think the gravitational field that might be quantized fully is on event horizons. In the bulk with one dimension larger the quantized gravitational field would be gravitons that are very red shifted. These gravitons are then weak and asymptotically linear. The only possible quantization would then, at least within what I think is a foreseeable quantum gravitation theory, is a weak field graviton. In that setting it would be linearized. A linear graviton that is a weak perturbation on the background metric would be similar to a diphoton or HBT entangled photon pair. To "climb" the ladder to some measure of nonlinearity would require some perturbation series. A full quantum gravitation of the spacetime bulk may really be impossible. In fact it may not really even exist. This is then a substructure that would support an asymptotic quantum gravity in the bulk similar to Weinberg's asymptotic safe q-gravity.

LC

[John Clark]

On Sat, Oct 26, 2019 at 5:24 PM Alan Grayson <agrays...@gmail.com> wrote:

 > GR is a classical theory, which assumes a classical space-time field.

General Relativity assumes space and time are continuous and infinitely divisible, Quantum Mechanics assumes it is not, hence our 2 best physical theories are incompatible and that makes physicists unhappy.     

 > But if you assume a classical field at the microscopic level, will GR give answers which are contradicted by measurements?

Every time we've tested General Relativity it has easily passed the test, but nobody has made a measurement at the singularity in the center of a Black Hole where spacetime is infinitely curved, at that point General Relativity breaks down and can no longer tell us what's going on.

 John K Clark

 

[Lawrence Crowell]

On Sunday, October 27, 2019 at 8:05:47 AM UTC-6, John Clark wrote:

On Sat, Oct 26, 2019 at 5:24 PM Alan Grayson <agrays...@gmail.com> wrote:

 > GR is a classical theory, which assumes a classical space-time field.

General Relativity assumes space and time are continuous and infinitely divisible, Quantum Mechanics assumes it is not, hence our 2 best physical theories are incompatible and that makes physicists unhappy. 

Quantum mechanics makes no particular prediction on the continuity of spacetime. If one equates the Schwarzschild radius with a Compton wavelength you get the Planck scale of 1.6x10^{-35}m. However, this really just tells us one is not able to locate a qubit in a region smaller than this scale. The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

LC

[Philip Thrift]

Emergent 4-dimensional linearized gravity from spin foam models

https://arxiv.org/pdf/1812.02110.pdf 

In this paper, we show for the first time that smooth solutions of 4-dimensional Einstein equation emerge from Spin Foam Models (SFMs) under an appropriate semiclassical continuum limit (SCL).

@philipthrift 

[John Clark]

On Sun, Oct 27, 2019 at 12:04 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

I've heard that too but how solid is the evidence? I ask because it seems to me if it's true that would be a HUGE discovery, finding out that the Planck Length and Planck Time have no physical significance would be far more important than finding the Higgs Particle, but it doesn't seem to have made much of a splash. In trying to resolve the contradictions between Quantum Mechanics and General Relativity most leave Quantum Mechanics alone and try monkeying around with Quantum Mechanics; but if the evidence holds up and spacetime really is smooth then maybe they should do it the other way around, leave General Relativity alone and monkey around with Quantum Mechanics.

 John K Clark

[Brent Meeker]

On 10/27/2019 3:23 PM, John Clark wrote:

On Sun, Oct 27, 2019 at 12:04 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

I've heard that too but how solid is the evidence? I ask because it seems to me if it's true that would be a HUGE discovery, finding out that the Planck Length and Planck Time have no physical significance would be far more important than finding the Higgs Particle, but it doesn't seem to have made much of a splash.

I think there is very strong evidence:

DOI: 10.1103/PhysRevD.83.121301
arXiv:1109.5191v2 [astro-ph.CO] 18 Apr 2012

But there are loopholes in assumptions about how photons interact with discrete spacetime structure.

Brent

In trying to resolve the contradictions between Quantum Mechanics and General Relativity most leave Quantum Mechanics alone and try monkeying around with Quantum Mechanics; but if the evidence holds up and spacetime really is smooth then maybe they should do it the other way around, leave General Relativity alone and monkey around with Quantum Mechanics.

 John K Clark

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[Alan Grayson]

On Sunday, October 27, 2019 at 10:04:42 AM UTC-6, Lawrence Crowell wrote:

On Sunday, October 27, 2019 at 8:05:47 AM UTC-6, John Clark wrote:

On Sat, Oct 26, 2019 at 5:24 PM Alan Grayson <agrays...@gmail.com> wrote:

 > GR is a classical theory, which assumes a classical space-time field.

General Relativity assumes space and time are continuous and infinitely divisible, Quantum Mechanics assumes it is not, hence our 2 best physical theories are incompatible and that makes physicists unhappy. 

Quantum mechanics makes no particular prediction on the continuity of spacetime. If one equates the Schwarzschild radius with a Compton wavelength you get the Planck scale of 1.6x10^{-35}m. However, this really just tells us one is not able to locate a qubit in a region smaller than this scale. The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

LC

You're out of my depth here. If the Schwartzshild radius has one value, and the Compton wavelength has another value, why would anyone want to equate them? AG

[John Clark]

On Sun, Oct 27, 2019 at 12:04 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Quantum mechanics makes no particular prediction on the continuity of spacetime. If one equates the Schwarzschild radius with a Compton wavelength you get the Planck scale of 1.6x10^{-35}m. However, this really just tells us one is not able to locate a qubit in a region smaller than this scale.

If you can't put a particle or a wave or a qubit in less than 1.6x10^{-35}m then what can you put in there, and in what sense is it meaningful to say spacetime is smooth?

 John K Clark

[Philip Thrift]

It still is a problem being worked on.

https://arxiv.org/abs/1812.11450

Spin-Spacetime Censorship

Jonathan Nemirovsky, Eliahu Cohen, Ido Kaminer

(Submitted on 30 Dec 2018 (v1), last revised 7 Oct 2019 (this version, v2))

Quantum entanglement and relativistic causality are key concepts in theoretical works seeking to unify quantum mechanics and gravity. In this article, we show that the interplay between relativity theory and quantum entanglement has intriguing consequences for the spacetime surrounding elementary particles with spin. Classical and quantum gravity theories predict that a spin-generated magnetic dipole field causes a (slight) bending to the spacetime around particles, breaking its spherical symmetry. Motivated by the apparent break of spherical symmetry, we propose a very general gedanken experiment that does not rely on any specific theory of classical or quantum gravity, and analyze this gedanken experiment in the context of quantum information. We show that any spin-related deviation from spherical symmetry would violate relativistic causality. To avoid the violation of causality, the measurable spacetime around the particle's rest frame must remain spherically symmetric, potentially as a back-action by the act of measurement. This way, our gedanken experiment proves that there must be a censorship mechanism preventing the possibility of spacetime-based spin detection, which sheds new light on the interface between quantum mechanics and gravity. We emphasize that our proposed gedanken experiment is independent of any theory and by allowing spacetime to be quantized its purpose is to be used for testing present and future candidate theories of quantum gravity.

@philipthrift 

[John Clark]

On Mon, Oct 28, 2019 at 3:45 AM Philip Thrift <cloud...@gmail.com> wrote:

> It still is a problem being worked on.

https://arxiv.org/abs/1812.11450

 "by allowing spacetime to be quantized its purpose is to be used for testing present and future candidate theories of quantum gravity".

If spacetime is quantized then it's not smooth,

John K Clark

 

[Lawrence Crowell]

On Sunday, October 27, 2019 at 6:56:37 PM UTC-6, Alan Grayson wrote:

On Sunday, October 27, 2019 at 10:04:42 AM UTC-6, Lawrence Crowell wrote:

On Sunday, October 27, 2019 at 8:05:47 AM UTC-6, John Clark wrote:

On Sat, Oct 26, 2019 at 5:24 PM Alan Grayson <agrays...@gmail.com> wrote:

 > GR is a classical theory, which assumes a classical space-time field.

General Relativity assumes space and time are continuous and infinitely divisible, Quantum Mechanics assumes it is not, hence our 2 best physical theories are incompatible and that makes physicists unhappy. 

Quantum mechanics makes no particular prediction on the continuity of spacetime. If one equates the Schwarzschild radius with a Compton wavelength you get the Planck scale of 1.6x10^{-35}m. However, this really just tells us one is not able to locate a qubit in a region smaller than this scale. The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

LC

You're out of my depth here. If the Schwartzshild radius has one value, and the Compton wavelength has another value, why would anyone want to equate them? AG

This equality is the elementary condition for a quantum unit of black hole.

LC

[Bruno Marchal]

On 26 Oct 2019, at 22:56, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:

What creates the problem at microscopic level is that the stress-energy tensor on the right hand side will be due to the wave function of a quantum particle and so would only have a probabilistic interpretation.  We an do semi-classical computations by replacing the wave function by it's expected value at each point.  But that avoids the point that the metric stuff on the left hand side needs to be represented by a probabilistic function to match the right hand side.

Yes. We could say that both theories (EFE and SWE) works well at both scales (microscopic, macroscopic).

The problem is that they are different and logically incompatible, at both scale.

So, scale is not the problem, except that EFE equation are needed for the macroscopic, and the quantum is needed for the microscopic. Many heuristics can combine them, like when working on black hole, but we have just no theory making them fitting together coherently. 

Put in another way, the problem is that EFE, (GR) resist to quantisation. Two impressive attempts do exist (Loop Gravity, which follows GR logic, and quantise the whole space time structure), and string theory, which consider the particles to be strings, and explains quickly the graviton. But both attempts get into very mathematical and physical difficulties.

Bruno 

Brent

On 10/26/2019 1:19 PM, Alan Grayson wrote:

Where do the several postulates of GR imply that the field equations fail to apply at some small dimensions of space and time? It's commonly claimed that GR does not apply at the microscopic level, but I see nothing in the several postulates of GR that imply this result. AG

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[John Clark]

On Sun, Oct 27, 2019 at 8:56 PM Alan Grayson <agrays...@gmail.com> wrote:

On Sunday, October 27, 2019 at 10:04:42 AM UTC-6, Lawrence Crowell wrote:

Quantum mechanics makes no particular prediction on the continuity of spacetime. If one equates the Schwarzschild radius with a Compton wavelength you get the Planck scale of 1.6x10^{-35}m. However, this really just tells us one is not able to locate a qubit in a region smaller than this scale. The Fermi and Integral spacecraft data on arrival times of different wavelengths of radiation from burstars indicates spacetime is smooth to two orders of magnitude smaller than the Planck length.

> You're out of my depth here. If the Schwartzshild radius has one value, and the Compton wavelength has another value, why would anyone want to equate them? AG

The Compton wavelength of a particle is just the wavelength light would have if the mass of the particle were converted to energy. As the wavelength gets smaller the energy gets larger, at some point the energy gets so high and the distance so small it turns into a Black Hole; that distance is the Planck length the time it takes light to move that distance is the Planck Time and the amount of mass required is the Planck Mass which is about the mass of a flea egg. The most acceleration anything can have is the Planck Acceleration, it is the amount of acceleration needed to move something from a speed of zero to the speed of light in the Planck Time, and the hottest that things can get is the Planck Temperature (1.4*10^32 Kelvin) because anything hotter would start radiating Black Holes instead of Blackbody Radiation. Or at least that's what Quantum Mechanics says, but if the evidence from the Fermi and Integral spacecraft holds up and spacetime really is smooth then something is wrong with this picture.

John K Clark

[Philip Thrift]

That's the quantum space agenda: How does a quantumized space "appear" like it's a smooth thing?

@philipthrift 

 

[Lawrence Crowell]

That is basically it. The Planck scale does not say that spacetime is sliced and diced up into chunks. It just says that if you try to localize a qubit onto a region smaller than √(Għ/c^3) ~ 1.6×10^{-35}m one gets a quantum of black hole that conceals the qubit for a tiny time interval √(Għ/c^5) ~ 5×10^{-44}sec before it explodes into a huge number of low mass particles. It is a sort of Heisenberg microscope argument. 

The LQG machers were forced into a frantic fix on their loop theories that had spacetime chopped up near the Planck scale. The data very much appears to indicate that spacetime is not built up from chunks, but instead it may be built from nonlocal quantum entanglements. So rather than spacetime being a highly localized structure, with it might be added a lot of fine tuning of variables, it is more an emergent phenomenon due to nonlocaly of QM and entanglements. 

LC

[Philip Thrift]

Of course space being made of "variables" vs. foam is a more mathematically Platonistic view.

[Lawrence Crowell]

I downloaded this and I am aware of these ideas. I still prefer holographic quantum entanglement. It really is much simpler because the fundamental physics is on a lower dimensional manifold. I will try to read this before too long however.

LC 

[Bruno Marchal]

Me too. It is by far more coherent with digital mechanism, but I cannot judge from the paper here.(I mean in any wish way, as I have to study it first, …).

Bruno

It really is much simpler because the fundamental physics is on a lower dimensional manifold. I will try to read this before too long however.

LC 

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