Are Real Numbers Really Real?

[Philip Thrift]

https://arxiv.org/abs/1803.06824

(V2: several mineurs changes ) !

Indeterminism in Physics, Classical Chaos and Bohmian Mechanics. Are Real Numbers Really Real?

Nicolas Gisin

(Submitted on 19 Mar 2018 (v1), last revised 31 May 2019 (this version, v3))

It is usual to identify initial conditions of classical dynamical systems with mathematical real numbers. However, almost all real numbers contain an infinite amount of information. I argue that a finite volume of space can't contain more than a finite amount of information, hence that the mathematical real numbers are not physically relevant. Moreover, a better terminology for the so-called real numbers is ``random numbers'', as their series of bits are truly random. I propose an alternative classical mechanics, which is empirically equivalent to classical mechanics, but uses only finite-information numbers. This alternative classical mechanics is non-deterministic, despite the use of deterministic equations, in a way similar to quantum theory. Interestingly, both alternative classical mechanics and quantum theories can be supplemented by additional variables in such a way that the supplemented theory is deterministic. Most physicists straightforwardly supplement classical theory with real numbers to which they attribute physical existence, while most physicists reject Bohmian mechanics as supplemented quantum theory, arguing that Bohmian positions have no physical reality.

Comments:	8 pages. Presented at the David Bohm Centennial Symposium, London, Octobre 2017 V2: several mineurs changes and additions
Subjects:	Quantum Physics (quant-ph); History and Philosophy of Physics (physics.hist-ph)
Cite as:	arXiv:1803.06824 [quant-ph]
	(or arXiv:1803.06824v3 [quant-ph] for this version)

@philipthrift

[John Clark]

I think it depends on if the Planck Length and Planck Time have physical significance, it they do then spacetime is not continuous and Real Numbers are not real; but if spacetime is smooth and continuous as the data from Gamma Ray Bursters seems to indicate then Real Numbers are real and there is no hope of ever developing a Quantum Theory Of Gravity.

John K Clark 

[Lawrence Crowell]

On Saturday, November 30, 2019 at 3:08:42 PM UTC-6, John Clark wrote:

I think it depends on if the Planck Length and Planck Time have physical significance, it they do then spacetime is not continuous and Real Numbers are not real; but if spacetime is smooth and continuous as the data from Gamma Ray Bursters seems to indicate then Real Numbers are real and there is no hope of ever developing a Quantum Theory Of Gravity.

John K Clark 

The Planck unit of length and time does not mean space or spacetime is discrete. All it means is this is the smallest scale one can localize a quantum bit of information. It does not mean that spacetime is somehow discrete.

LC 

[John Clark]

On Sat, Nov 30, 2019 at 4:36 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> The Planck unit of length and time does not mean space or spacetime is discrete. All it means is this is the smallest scale one can localize a quantum bit of information. It does not mean that spacetime is somehow discrete.

If discrete spacetime does not mean there is a smallest scale that a Qubit of information can be localized then what does "discrete spacetime" mean?

John K Clark

[Brent Meeker]

Discrete spacetime does mean there is a smallest scale at which things can be localized.  But that there is a smallest scale at which things can be located doesn't mean spacetime is discrete.

Brent

[Lawrence Crowell]

It is a form of quotient geometry. For 

1 →  G → H → K → 1

for G = U(1), H = U(N) and K = PSU(N) = SU(N)/Z_N this short exact sequence defines a discrete  gauge group. The projective Lie group is a Kleinian and for a manifold associated with SU(N), say AdS_5 = U(2, 2)/O(4,1) the quotient defines an underlying discretization. Of course to do this in greater generality we need to have a discrete system with polytopes that define cells. So G could be the Coxeter group for a polytope. Say for G the Coxeter group for the 4-dim icosian H the group O(3,2) ≈ AdS_4×O(3,1) then K would be this spacetime, with the Lorentz group, in a quotient with a lattice space.

LC

[Philip Thrift]

https://arxiv.org/pdf/1803.06824.pdf :

One may object that this view is arbitrary as there is no natural bit number where the transition from determined to random bits takes place. This is correct, though not important in practice as long as this transition is far away down the bit series. The lack of a natural transition is due to the fact that, in classical physics, there is no equivalent to the Plank constant of quantum theory. But this is quite natural, as the fact is that when one looks for this transition in the physical description of classical systems, one hits quantum physics.

In summary, physics with all its predictive and explanatory powers can well be presented as intrinsically non-deterministic. The dominant view according to which classical physics is deterministic is due, first, to a false impression generated by it’s huge success in astronomy and in the design of clocks and other simple mechanical (integrable) systems, and, second, to a lack of appreciation of its implication for (infinite) information density. Finally, an indeterministic world is hospitable to Res Potentia and to the passage of time.

https://arxiv.org/pdf/1709.03595.pdf

It is argued that quantum theory is best understood as requiring an ontological duality of res extensa and res potentia, where the latter is understood per Heisenberg's original proposal, and the former is roughly equivalent to Descartes' 'extended substance.' However, this is not a dualism of mutually exclusive substances in the classical Cartesian sense, and therefore does not inherit the infamous 'mind-body' problem. Rather, res potentia and res extensa are proposed as mutually implicative ontological extants that serve to explain the key conceptual challenges of quantum theory; in particular, nonlocality, entanglement, null measurements, and wave function collapse. It is shown that a natural account of these quantum perplexities emerges, along with a need to reassess our usual ontological commitments involving the nature of space and time.

@philipthrift 

[Bruno Marchal]

In First Order Logic, Real Numbers are the one which simplifies. The first order theory of the real is decidable, unlike the first order theory of the natural numbers. The digital, or discrete, reality is more complex than the reals, which fits all holes, and provides (in the complex extensions) all roots for the polynomials.

Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by “physical”), which requires a non Mechanist theory of mind.

With Mechanism, real number are phenomenological constructs by digital entities. It is real, but not ontologically real.

Bruno

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/8dd42147-b6ba-4716-9dfa-2a422964f79f%40googlegroups.com.

[Lawrence Crowell]

Quantum physics has complementaries that are both deterministic and nondeterministic. As a system of wave mechanics it is completely deterministic. However, the Fourier components are amplitudes that in polar form define probabilties for outcomes that occur by stochastic means. So how one frames QM, either deterministic or nondeterministic, is up to the choice of the analyst or how one performs an experiment or interprets the outcomes of an experiment.

LC 

[Philip Thrift]

On Monday, December 2, 2019 at 5:10:54 AM UTC-6, Lawrence Crowell wrote:

Quantum physics has complementaries that are both deterministic and nondeterministic. As a system of wave mechanics it is completely deterministic. However, the Fourier components are amplitudes that in polar form define probabilties for outcomes that occur by stochastic means. So how one frames QM, either deterministic or nondeterministic, is up to the choice of the analyst or how one performs an experiment or interprets the outcomes of an experiment.

LC 

Q: "So when you say that probability doesn’t exist, you mean that objective probability doesn’t exist."

A: "Right, it doesn’t exist as something out in the world without a gambling agent."

-- Christopher Fuchs [ https://quantamagazine.org/quantum-bayesianism-explained-by-its-founder-20150604/ ]

So there are those who think probabilities don't exist as fundamental, unreducible, objective physical entities out in the world having nothing to do with us, and those that do. I think the former is a kind of religious pining (as William James said).

@philipthrift

[John Clark]

On Mon, Dec 2, 2019 at 6:10 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

>> what does "discrete spacetime" mean?

> It is a form of quotient geometry.

Hawking said the Entropy of a Black Hole is one quarter of it's Event Horizon in areas of Planck Length squared, so Entropy is discrete. And Entropy is proportional to the logarithm of the microstates that made the Black Hole, so there are a discrete number of microstates.  And if there is also a smallest scale that a Qubit of information can be localized at then regardless of what quotient geometry and pure mathematics may say I'm having a hard time attaching physical significance to the statement that spacetime could still not be discreet. And if the recent results from Gamma Ray Bursts do not show that Spacetime lacks graininess then what do they show?

John K Clark

[Lawrence Crowell]

Spacetime does not really fundamentally exist. It is just a geometric representation for how qubits interact and are entangled with each other.

LC 

[Brent Meeker]

On 12/2/2019 12:41 AM, Bruno Marchal wrote:
> In First Order Logic, Real Numbers are the one which simplifies. The
> first order theory of the real is decidable, unlike the first order
> theory of the natural numbers. The digital, or discrete, reality is
> more complex than the reals, which fits all holes, and provides (in
> the complex extensions) all roots for the polynomials.

Do you know whether Gisin's "random" numbers produce a decidable structure?

Brent

[Philip Thrift]

On Monday, December 2, 2019 at 11:58:13 AM UTC-6, Lawrence Crowell wrote:

Spacetime does not really fundamentally exist. It is just a geometric representation for how qubits interact and are entangled with each other.

LC 

Or it could be the other way around: qubits come out of (stochastic) spacetime.

https://arxiv.org/abs/1612.04228

@philipthrift

[John Clark]

On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Spacetime does not really fundamentally exist. It is just a geometric representation for how qubits interact and are entangled with each other.

I agree it's possible Spacetime is not fundamental, it might be a composite and be constructed out of something else, but if that more fundamental "something else" is how Qubits interact and if there is a smallest scale at which a quantum bit of information can be localized then how can there be a one to one correspondence between the finite number of such localized areas and the infinite number of points in smooth continuous geometric spacetime that the Gamma Ray Burst results seem to indicate is the way things really are?

 John K Clark

[Lawrence Crowell]

Spacetime is an epiphenomenology of entanglement. There are several ways entanglement can happen. There is topological order that has no scaling, or where the entanglement occurs without any reference to space or distance. Then there are symmetry protected topological orders, where there is a locality. How these two are related is a matter of research, but it is a sort of quantum phase transition. 

An event horizon is a region where on either side there are entangled states. Close to the horizon there is are small regions on either side that are entangled. Further away these regions are larger. This has a sort of scaling and fractal geometry to it. As with fractals or chaos there are regions with regular dynamics where things are smooth and these are related to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime is the a manifestation of a condensate of symmetry protected states that construct a surface that is smooth.

LC

[Philip Thrift]

I don't see how this relates to stochastic metric spaces:

https://iopscience.iop.org/article/10.1088/2399-6528/aaa851

Stochastic Metric Quantization (SMQ)

In this work, a new quantization method based on the mathematical theory of probability is proposed. The concept is developed as follows: We consider the decay process of a given radioisotope. Because the probability of observing a decay during a unit of time is constant, the number of decays observed during a given time interval follows a Poisson distribution. Using this phenomenon, a clock in which the second hand advances each time a decay observed can be constructed; hereafter, this will be referred to as a Poisson-clock. We assume for simplicity that the Poisson-clock is designed to advance one tick per second on average. We then compare this clock to an ordinary mechanical clock, in which the time interval per tick of the second hand is constant. From the point of view of an observer using the mechanical clock, the second hand of the Poisson-clock seems to move randomly; however, this is of course a relative observation tied to the reference frame of the mechanical clock. If instead the time measured by the Poisson-clock is defined as the regular interval, the running of the mechanical clock becomes random. A distribution of 'one second' of the Poisson-clock, as measured by the mechanical clock, becomes an exponential distribution with an average value of unity. Following the central limit theorem, the deviation between the Poisson and the mechanical clock after n seconds will have a Gaussian distribution around zero with a variance of n. Using the mechanical clock to measure the time-of-flight of a free particle following a classical inertial path will result in a constant measured velocity. On the other hand, if the Poisson-clock is used, measurement becomes a stochastic-process based on the Wiener measure and can be expressed using a stochastic differentiation equation. It has been shown that such as expression agrees with the stochastic equation obtained by Nelson [6] that is used in stochastic quantization. Thus, classical mechanics with a Poisson-time measure results in QM, which suggests a new quantization method—Stochastic Metric Quantization(SMQ). This observation can be extended to spatial coordinates as well, and an equal treatment of space and time is necessary to apply this method to relativistic quantum field theories. A quantum field theory can be given on the stochastic metric space, not only for flat spaces such as Minkowski space, but also for highly curved spaces such as the surface of the black hole. As applications of this method, quantum effects in the early universe can be analyzed.

A main purpose of this work is to give a new framework of a quantum theory using mathematical tools of the stochastic metric space. In other words, a new stochastic quantization method is proposed in this work. A concept of our method is, in summary, that classical mechanics in the stochastic space is equivalent to quantum mechanics on the standard space time manifold. This concept can not answer a question why quantum mechanics requires a probabilistic interpretation (the Born rule), but it can answer what is an origin of a probabilistic nature. While our stochastic quantization gives consistent results to those from the standard method, it gives a new insight of quantum phenomenon. Moreover, a system which can not be quantized yet, e.g. gravitation, may be quantized using this stochastic quantization method.

@philipthrift 

[Bruno Marchal]

> On 2 Dec 2019, at 19:10, 'Brent Meeker' via Everything List <everyth...@googlegroups.com> wrote:
>
>
>
> On 12/2/2019 12:41 AM, Bruno Marchal wrote:
>> In First Order Logic, Real Numbers are the one which simplifies. The first order theory of the real is decidable, unlike the first order theory of the natural numbers. The digital, or discrete, reality is more complex than the reals, which fits all holes, and provides (in the complex extensions) all roots for the polynomials.
>
> Do you know whether Gisin's "random" numbers produce a decidable structure?

It certainly does not. Real numbers are logically much simpler than Natural Numbers (think about x^n + y^n = z^n in integer structure and with real numbers for example), but Gisin use QM, which adds the trigonometrical functions, or complex numbers, and this re-intrdouces the discrete structure and the integers in the picture (sin(2pi*x) = 0). Trigonometry, or waves, is what makes the continuum able to imitate the digital. Whatever physics can appear from arithmetic, it is described by a continuum, and it needs to be able to imitate the digital machines (or we would not be there (assuming Mechanism of course).

Bruno

>
> Brent
>
>> Also, Nicolas Gisin use the Aristotelian act of faith (defining “real” by “physical”), which requires a non Mechanist theory of mind.
>> With Mechanism, real number are phenomenological constructs by digital entities. It is real, but not ontologically real.
>>
>> Bruno
>
>

> --
> You received this message because you are subscribed to the Google Groups "Everything List" group.
> To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.

> To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/5cdc993a-d81f-2508-a970-6c62bcaba4b4%40verizon.net.

[Lawrence Crowell]

On Tuesday, December 3, 2019 at 2:40:27 AM UTC-6, Philip Thrift wrote:

On Monday, December 2, 2019 at 7:30:13 PM UTC-6, Lawrence Crowell wrote:

On Monday, December 2, 2019 at 2:52:05 PM UTC-6, John Clark wrote:

On Mon, Dec 2, 2019 at 12:58 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Spacetime does not really fundamentally exist. It is just a geometric representation for how qubits interact and are entangled with each other.

I agree it's possible Spacetime is not fundamental, it might be a composite and be constructed out of something else, but if that more fundamental "something else" is how Qubits interact and if there is a smallest scale at which a quantum bit of information can be localized then how can there be a one to one correspondence between the finite number of such localized areas and the infinite number of points in smooth continuous geometric spacetime that the Gamma Ray Burst results seem to indicate is the way things really are?

 John K Clark

Spacetime is an epiphenomenology of entanglement. There are several ways entanglement can happen. There is topological order that has no scaling, or where the entanglement occurs without any reference to space or distance. Then there are symmetry protected topological orders, where there is a locality. How these two are related is a matter of research, but it is a sort of quantum phase transition. 

An event horizon is a region where on either side there are entangled states. Close to the horizon there is are small regions on either side that are entangled. Further away these regions are larger. This has a sort of scaling and fractal geometry to it. As with fractals or chaos there are regions with regular dynamics where things are smooth and these are related to fractal geometry by the Feigenbaum number 4.669... . Classical spacetime is the a manifestation of a condensate of symmetry protected states that construct a surface that is smooth.

LC

I am not thinking of this. In fact this idea seems completely wrong headed. It might have been that people would have tried to capture QM by imposing stochastic Wiener processes and the like. 

[Philip Thrift]

On Tuesday, December 3, 2019 at 4:38:56 AM UTC-6, Lawrence Crowell wrote:

I am not thinking of this. In fact this idea seems completely wrong headed. It might have been that people would have tried to capture QM by imposing stochastic Wiener processes and the like. 

LC

 

There is a connection between

"The subject [of path integration in stochastic processes] began with the work of Wiener during the 1920's, corresponding to a sum over random trajectories, anticipating by two decades Feynman's famous work on the path integral representation of quantum mechanics."

(Path Integrals for Stochastic Processes: An Introduction, Horacio S. Wio) 

and the

"Path integral on the SLM[stochastic Lorentz metric]-space"

(Stochastic metric space and quantum mechanics, Yoshimasa Kurihara).

@philipthrift 

[John Clark]

On Mon, Dec 2, 2019 at 8:30 PM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> Spacetime is an epiphenomenology of entanglement. There are several ways entanglement can happen. There is topological order that has no scaling, or where the entanglement occurs without any reference to space or distance.

If there is no reference to space or distance in that sort of entanglement then where does the epistemological phenomenon of distance come from? Do 2 points in space less than a Planck Length apart correspond to 2 different entanglements, and is there any experimental evidence that could help us answer this question? It seems to me the Gamma Ray Burst results must be telling us something. 

 
And what about time, is it fundamental; it's right there in the Schrödinger equation and just takes it as a given.

 

> Then there are symmetry protected topological orders, where there is a locality.

But we know from experiment that Bell's Inequality is violated, so I don't see how that sort of entanglement could have produced the world we observe. 

 John K Clark

[Lawrence Crowell]

For symmetry protected quantum states, which are local entanglements, they are local because the symmetry or group action is generally covariant. This covariant property enforces what we think of as space and time.

LC

[Philip Thrift]

On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote:

For symmetry protected quantum states, which are local entanglements, they are local because the symmetry or group action is generally covariant. This covariant property enforces what we think of as space and time.

LC

It's reasonable that space and time precedes symmetry. We get symmetries from spacial measurements.

@philipthrift

[Lawrence Crowell]

An observer witnessing a black hole emit Hawking radiation discovers that while quantum states are approaching the event horizon they also appear as hawking radiation removed from the black hole. The entire notion of quantum states and events as localized in regions of space is not entirely applicable. What symmetries exist with these quantum states or field are then not tied to local geometry. Local geometry is something that emerges instead from the symmetries of quantum fields. This is because they are quantum gravitational. The quantum fields approaching the event horizon, or on the stretched horizon are pure Planck oscillator modes.

Two gravitons that scatter either do so as a 4 point interaction, similar to a φ^4 field theory, or they merge to form a black hole in a 3-point interaction so the quantum BH decays via a 3-point interaction into gravitons. There is no procedure for determining which of these amplitudes occurs, and in fact they both do. QM is odd that way. As a result there is no fundamental meaning to their being some point where a gauge action occurs.

As Arkani Hamed puts it, "Space must die."

LC

[John Clark]

On Wed, Dec 4, 2019 at 5:50 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

 

> The entire notion of quantum states and events as localized in regions of space is not entirely applicable. What symmetries exist with these quantum states or field are then not tied to local geometry.

OK, but if quantum states are to explain local geometry, and that is the entire point because that is all that experimenters can see, then the reverse can not be true, local geometry must be tied to quantum states. 

> Local geometry is something that emerges instead from the symmetries of quantum fields. This is because they are quantum gravitational.

So if the Gamma Ray Burst results hold up and spacetime really is smooth and continuous then, would it be correct to say there are a infinite (not just astronomically large) number of quantum symmetries and the Planck Length and the Planck Time have no physical significance, they are just numbers in units of time and space that for no particular reason happen to pop out when you mathematically play around with the constants of nature in certain ways?

> As Arkani Hamed puts it, "Space must die."

What about time, can space really be separated from it despite what Minkowski said? Time features prominently in Schrödinger's Equation, Dirac's Equation and even Feynman diagrams; you're going to have to go back to square one and rewrite the entirety of Quantum Mechanics without any reference to space or time, and that would be a massive job that I'm not certain could be done, I'm not even certain there would be any point in doing so, it would certainly make Quantum Mechanics far harder to use and its not exactly easy now.

 

> The quantum fields approaching the event horizon, or on the stretched horizon are pure Planck oscillator modes.

But a Planck oscillator is something that absorbs or emits energy only in amounts which are integer multiples of Planck's constant times the frequency of the oscillator, however frequency is the number of repeating events per unit of TIME.

 John K Clark

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 7:44:06 AM UTC-6, John Clark wrote:

On Wed, Dec 4, 2019 at 5:50 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

 

> The entire notion of quantum states and events as localized in regions of space is not entirely applicable. What symmetries exist with these quantum states or field are then not tied to local geometry.

OK, but if quantum states are to explain local geometry, and that is the entire point because that is all that experimenters can see, then the reverse can not be true, local geometry must be tied to quantum states. 

I guess this is not quite clear to me. Largely the quantum states that form spacetime are quantum gravitation states.

 

> Local geometry is something that emerges instead from the symmetries of quantum fields. This is because they are quantum gravitational.

So if the Gamma Ray Burst results hold up and spacetime really is smooth and continuous then, would it be correct to say there are a infinite (not just astronomically large) number of quantum symmetries and the Planck Length and the Planck Time have no physical significance, they are just numbers in units of time and space that for no particular reason happen to pop out when you mathematically play around with the constants of nature in certain ways?

The number of quantum states are Virasoro, which is in principle infinite. However, because the cosmological horizon can only bound a finite number of such states, as is the case with a black hole with entropy S = A/4ℓ_p^2, the number of physical states is bounded above. As a result the Virasoro algebra has high frequency modes that are mathematically possible, but not physically accessed. Virasoro states are those of the bosonic string and we may think of a black hole as a very large high mode string that wraps around the Planck region above the horizon. The largest a black hole could become is equal to all the mass in the observable universe. That in turn is finite because beyond the cosmological horizon mass can't be accessed. 

 

> As Arkani Hamed puts it, "Space must die."

What about time, can space really be separated from it despite what Minkowski said? Time features prominently in Schrödinger's Equation, Dirac's Equation and even Feynman diagrams; you're going to have to go back to square one and rewrite the entirety of Quantum Mechanics without any reference to space or time, and that would be a massive job that I'm not certain could be done, I'm not even certain there would be any point in doing so, it would certainly make Quantum Mechanics far harder to use and its not exactly easy now.

A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. Any unitary transformation between H_a and H_b defines a boundary if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for S_b. We have removed the off-diagonal terms. We then can define this as a boundary, aka holographic screen or horizon, between sets of entangled states. This then defines a form of geometry. The transformation between H_a and H_b can just as well be time evolution with a boundary that separates two temporal regions. The Taub-NUT spacetime has this characteristic as does the region between the spacelike region outside the inner horizon of a black hole and the mysterious region inside.

 

 

> The quantum fields approaching the event horizon, or on the stretched horizon are pure Planck oscillator modes.

But a Planck oscillator is something that absorbs or emits energy only in amounts which are integer multiples of Planck's constant times the frequency of the oscillator, however frequency is the number of repeating events per unit of TIME.

But this can be nonlocally correlated in both space and time as an observer finds quantum modes on the BH and outside as Hawking radiation.

LC 

 John K Clark

[Brent Meeker]

On 12/4/2019 2:50 AM, Lawrence Crowell wrote:

On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote:

On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote:

For symmetry protected quantum states, which are local entanglements, they are local because the symmetry or group action is generally covariant. This covariant property enforces what we think of as space and time.

LC

It's reasonable that space and time precedes symmetry. We get symmetries from spacial measurements.

@philipthrift

An observer witnessing a black hole emit Hawking radiation discovers that while quantum states are approaching the event horizon they also appear as hawking radiation removed from the black hole. The entire notion of quantum states and events as localized in regions of space is not entirely applicable.

Right.  So how can they "approach the event horizon"?  How can they move through space when they are not even localized?

Brent

What symmetries exist with these quantum states or field are then not tied to local geometry. Local geometry is something that emerges instead from the symmetries of quantum fields. This is because they are quantum gravitational. The quantum fields approaching the event horizon, or on the stretched horizon are pure Planck oscillator modes.

Two gravitons that scatter either do so as a 4 point interaction, similar to a φ^4 field theory, or they merge to form a black hole in a 3-point interaction so the quantum BH decays via a 3-point interaction into gravitons. There is no procedure for determining which of these amplitudes occurs, and in fact they both do. QM is odd that way. As a result there is no fundamental meaning to their being some point where a gauge action occurs.

As Arkani Hamed puts it, "Space must die."

LC

--
You received this message because you are subscribed to the Google Groups "Everything List" group.
To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.

To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/9887bb16-4158-490b-8229-fcf43bb62d05%40googlegroups.com.

[Brent Meeker]

On 12/4/2019 8:14 AM, Lawrence Crowell wrote:

But this can be nonlocally correlated in both space and time as an observer finds quantum modes on the BH and outside as Hawking radiation.

What can "nonlocal" in time mean?...at two different times, but the same place?  That's what "local" means.

Brent

[John Clark]

On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

>>> The entire notion of quantum states and events as localized in regions of space is not entirely applicable. What symmetries exist with these quantum states or field are then not tied to local geometry.

>> OK, but if quantum states are to explain local geometry, and that is the entire point because that is all that experimenters can see, then the reverse can not be true, local geometry must be tied to quantum states. 

> I guess this is not quite clear to me. Largely the quantum states that form spacetime are quantum gravitation states.

It seems to me if quantum gravitational states form spacetime, and if spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to show, then 2 distinct points that are less than a Planck Length apart must correspond to 2 distinct quantum gravitational states.  Am I wrong?

>> So if the Gamma Ray Burst results hold up and spacetime really is smooth and continuous then, would it be correct to say there are a infinite (not just astronomically large) number of quantum symmetries and the Planck Length and the Planck Time have no physical significance, they are just numbers in units of time and space that for no particular reason happen to pop out when you mathematically play around with the constants of nature in certain ways?

> The number of quantum states are Virasoro, which is in principle infinite. However, because the cosmological horizon can only bound a finite number of such states, as is the case with a black hole with entropy S = A/4ℓ_p^2, the number of physical states is bounded above. As a result the Virasoro algebra has high frequency modes that are mathematically possible, but not physically accessed.

Then although mathematically infinite as far as physics is concerned there are only a finite number of quantum gravitational states, but if quantum states produces spacetime then why does the Gamma Ray Burst results say spacetime is smooth and continuous? Can 2 points that are arbitrarily close to each other have any physical meaning, does physics need Real Numbers or not?  

 

> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. Any unitary transformation between H_a and H_b defines a boundary if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for S_b. We have removed the off-diagonal terms. We then can define this as a boundary, aka holographic screen or horizon, between sets of entangled states. This then defines a form of geometry. The transformation between H_a and H_b can just as well be time evolution with a boundary that separates two temporal regions. The Taub-NUT spacetime has this characteristic as does the region between the spacelike region outside the inner horizon of a black hole and the mysterious region inside.

You seem to be saying space may not be fundamental but time is. Would that be a fair representation of your views?

John K Clark

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 12:08:01 PM UTC-6, Brent wrote:

On 12/4/2019 2:50 AM, Lawrence Crowell wrote:

On Tuesday, December 3, 2019 at 8:32:43 AM UTC-6, Philip Thrift wrote:

On Tuesday, December 3, 2019 at 8:02:29 AM UTC-6, Lawrence Crowell wrote:

For symmetry protected quantum states, which are local entanglements, they are local because the symmetry or group action is generally covariant. This covariant property enforces what we think of as space and time.

LC

It's reasonable that space and time precedes symmetry. We get symmetries from spacial measurements.

@philipthrift

An observer witnessing a black hole emit Hawking radiation discovers that while quantum states are approaching the event horizon they also appear as hawking radiation removed from the black hole. The entire notion of quantum states and events as localized in regions of space is not entirely applicable.

Right.  So how can they "approach the event horizon"?  How can they move through space when they are not even localized?

Brent

The fields approaching the horizon are in a nonlocal superposition with itself far removed. The catch though is this persists even after a measurement meant to localize the particle-field. In a funny way the field is both in a superposition of two configurations and equivalently the entanglement of two field amplitudes.

LC

 

What symmetries exist with these quantum states or field are then not tied to local geometry. Local geometry is something that emerges instead from the symmetries of quantum fields. This is because they are quantum gravitational. The quantum fields approaching the event horizon, or on the stretched horizon are pure Planck oscillator modes.

Two gravitons that scatter either do so as a 4 point interaction, similar to a φ^4 field theory, or they merge to form a black hole in a 3-point interaction so the quantum BH decays via a 3-point interaction into gravitons. There is no procedure for determining which of these amplitudes occurs, and in fact they both do. QM is odd that way. As a result there is no fundamental meaning to their being some point where a gauge action occurs.

As Arkani Hamed puts it, "Space must die."

LC

--
You received this message because you are subscribed to the Google Groups "Everything List" group.

To unsubscribe from this group and stop receiving emails from it, send an email to everyth...@googlegroups.com.

[Lawrence Crowell]

On Wednesday, December 4, 2019 at 1:53:39 PM UTC-6, John Clark wrote:

On Wed, Dec 4, 2019 at 11:14 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

>>> The entire notion of quantum states and events as localized in regions of space is not entirely applicable. What symmetries exist with these quantum states or field are then not tied to local geometry.

>> OK, but if quantum states are to explain local geometry, and that is the entire point because that is all that experimenters can see, then the reverse can not be true, local geometry must be tied to quantum states. 

> I guess this is not quite clear to me. Largely the quantum states that form spacetime are quantum gravitation states.

It seems to me if quantum gravitational states form spacetime, and if spacetime is smooth and continuous as the Gamma Ray Burst evidence seems to show, then 2 distinct points that are less than a Planck Length apart must correspond to 2 distinct quantum gravitational states.  Am I wrong?

No it is not possible to know. If you localize a quantum bit to a Planck length it is in a black hole. If you try to localize two qubits arbitrarily closely they caon only be within 2 Planck areas, if on a horizon,or in two Planck volumes if in the bulk. A Planck volume is V_p = (4π/3)ℓ_p^3.So if you try to localize a field is less than two Planck volumes, or within a length 1.26ℓ_p there is a loss of any information about them.

 

>> So if the Gamma Ray Burst results hold up and spacetime really is smooth and continuous then, would it be correct to say there are a infinite (not just astronomically large) number of quantum symmetries and the Planck Length and the Planck Time have no physical significance, they are just numbers in units of time and space that for no particular reason happen to pop out when you mathematically play around with the constants of nature in certain ways?

> The number of quantum states are Virasoro, which is in principle infinite. However, because the cosmological horizon can only bound a finite number of such states, as is the case with a black hole with entropy S = A/4ℓ_p^2, the number of physical states is bounded above. As a result the Virasoro algebra has high frequency modes that are mathematically possible, but not physically accessed.

Then although mathematically infinite as far as physics is concerned there are only a finite number of quantum gravitational states, but if quantum states produces spacetime then why does the Gamma Ray Burst results say spacetime is smooth and continuous? Can 2 points that are arbitrarily close to each other have any physical meaning, does physics need Real Numbers or not?  

The gamma ray burst data just tells us that different wavelengths of photons have no dispersion. the G(p,p') = 1/(4π(|p - p'|^2 - m^2)) predicts different dispersons for different wavelengths of light. Over distances of billions of light years this would be significant. Nothing of this sort was observed. This means there is no "foaminess" or discreteness to spacetime. This is down to a scale of ℓ_p/50, the last I checked.

 

 

> A Hilbert space H that contains H_a and H_b is not equal to H_a×H_b. Any unitary transformation between H_a and H_b defines a boundary if we trace over one of these so S_a = tr_bS = -kTr_b[ρlog(ρ)] and similarly for S_b. We have removed the off-diagonal terms. We then can define this as a boundary, aka holographic screen or horizon, between sets of entangled states. This then defines a form of geometry. The transformation between H_a and H_b can just as well be time evolution with a boundary that separates two temporal regions. The Taub-NUT spacetime has this characteristic as does the region between the spacelike region outside the inner horizon of a black hole and the mysterious region inside.

You seem to be saying space may not be fundamental but time is. Would that be a fair representation of your views?

I tried to indicate that both space and time are emergent.

LC

 

John K Clark

[Philip Thrift]

But everything you wrote is in the vocabulary of space+time.

Even "wavelength".

@philipthrift 

[Lawrence Crowell]

This is in reference to the propagation of photons. It illustrates that spacetime is not made of chunks or finite elements. Spacetime is smooth. However, it is an epiphenomenology of quantum entanglement.

LC 

[Philip Thrift]

How does the mathematics of quantum entanglement imply that spacetime is smooth?

Or how does stochastic Lorentz metric space imply it isn't.

The Minkowski manifold equipping the stochastic metric is referred to as the

stochastic Lorentz metric space (SLM-space) hereafter. A distance between two points on the SLMspace will fluctuate around the geometric distance measured by the Lorentz metric, with the distance measured by the (non-fluctuating) Lorentz metric referred here as the geometrical distance. A distribution function is required to give the geometrical distance as an average value over a two-point ensemble on the SLM-space, with the variance of the distribution function set to be proportional to its geometrical distance. This distribution function makes a null vector (vector with zero length) without any fluctuation, a desirable characteristic for restraining a null photon mass after quantum corrections. Furthermore, to satisfy the causality condition the probability changing a sign of the length of a string stretching between two points must be zero.

https://arxiv.org/pdf/1612.04228.pdf

!philipthrift

[Lawrence Crowell]

As of yet the smoothness of spacetime as an emergent phenomenon is not clear. However, data does not point to there being this sort of stochastic processing metric. That would have had an effect that would show in the the dispersion of photons from distant sources. We might think of spacetime as a surface induced by the condensation of quantum states with an SU(2,2) symmetry. There are then in association with this quantum states with the same symmetry that are relatively separable states visa vie the condensate. These are the quantum gravitational states that represent the separation between an entropy surface and the horizon entropy. With Hawking radiation these two surfaces converge and this leads to the condition seen in the Page time.

LC

[Philip Thrift]

entropy surface

still merges quantum mechanics with geometrical mathematics  - which is what the stochastic metric  (SM) does.

And SM provides both the smoothiness of space and the probabilities of QM while keep ing space "real".

@philipthrift

[Lawrence Crowell]

No that is not the point. Quantum states on the entropy surface deviate from horizon states by the measure to which they are separable. There are no quantum metric fluctuations of a virtual nature.

LC

[Bruno Marchal]

I guess you meant “ontologically real”. That is a defect of SM, then, because it will eventually require the non computationalistic infinities to associate first and third person description. 

Note that something can be real, and emerge from something else. It just cannot be fundamentally real if they “something else” is judged more fundamental.

Bruno

@philipthrift

--
You received this message because you are subscribed to the Google Groups "Everything List" group.

To unsubscribe from this group and stop receiving emails from it, send an email to everything-li...@googlegroups.com.
To view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/e090b376-45c2-414e-849b-5a74036848fd%40googlegroups.com.

[Lawrence Crowell]

The sp

[Lawrence Crowell]

Overcomplete coherent states, such as laser states of light have a symplectic and Riemannian structure. This makes these states "classical-like " These are states in a huge quantum correlation, or a form of entanglement. This is the classical spacetime that has no quantum fluctuations. Quantum states that deviate are in a relative mixed or separable configuration.