State of "matter" of a singularity

[Mitcher]

On 9/15/2022 at 11:19 PM, joigus said:

Something that, in my mind, is extremely peculiar is that Planck's length and time are unfathomably small, while Planck's mass is roughly the size of an amoeba.

Thank you for your extremely interesting answers. Most of this discussion interest for me comes from examining Dirac's large numbers and holographic theories. I consider the Planck's lenghts and times as physical absolute limits while the Planck's mass is right in the middle of the wider mass spectrum, that's all. That's why the entropy of a BH cannot go to zero by the way, it is limited by Planck's surfaces. And probably in physical singularities too. I say probably but I'am personnaly 100% sure of it. Haramein has a good theory about the inside of a BH from that perspective. It is also interesting that spins cannot be expressed in terms of momenta since h dimensions are those of an angular momentum, what am I missing ? And just wondering here : if we had enough energy to downsize to the Planks's lenght, would we reach a substrate equivalent to the inside of BH's ? The repercussions would be staggering, that substrate would be ubiquitous and universal. I seem to be going obliquely here, but perhaps not that much.

21 hours ago, Markus Hanke said:

You’re still missing the point here - the light cone is not meant as a way to visualise trajectories of anything, which is why the question is somewhat misplaced. In some sense it does indeed show how light travels on a time vs distance plot, but that’s not its purpose.

I'am sorry I make you repeat all those explanations, I do not express myself right sometimes. I mean I totally understood, and since long ago, the causal boudaries of the light cone concept but I try to get a clear-cut answer about which part EXACTLY stands the light path within this diagram. It has to be either along the cone's 3D surface representing a 4D space-time, OR on the 2D surface of the pond representing our 3D space. It cannot be both ways. If, according to this image, light follows the pond's surface then I totally agree with it.

Edited September 17, 2022 by Mitcher
typo

[studiot]

[Mitcher]

On 9/15/2022 at 11:19 PM, joigus said:

Spin is a good example. In quantum mechanics you have orbital angular momenta --things like xp_y-yp_x

Everything moves in the Universe, gaz clouds contracting will start rotating, then this rotation will increase when stars collapse. Around a BH, due to frame-dragging even spece and time will rotate while matter will whirl to around 95% of c, and then what ? There can be no classical BH, that's only for the class room. But what I mean is that even in the Q realm rotations are still some velocities of some sort.

14 minutes ago, studiot said:

Absolutely correct by the way, it would be the hell of a mess.

On 9/15/2022 at 11:19 PM, joigus said:

This is known as Klein's paradox --well, the solution to it, to speak more properly.

Could we consider the Universe radius as a large gravitational potential?

[NTuft]

"I think I can... say that nobody understands Quantum Mechanics." Save perhaps for other Quantum Mechanics. Thanks for this discussion.

On 9/16/2022 at 3:07 PM, joigus said:

Suppose a civilisation more familiar with both BH's and entropy than our scientist ancestors have been for centuries, and didn't know QM, came to study BH's very much like physicists of the 19th century came to study the black-body radiation. The Planck of this civilisation solves a puzzle for a generation of these physicists. What is their puzzle?: all calculations of a BH's entropy give infinity! Let's call it the ultra-entropic catastrophe, in close analogy to the ultraviolet catastrophe that gave rise to QM.

The solution to the puzzle comes in the form of regularising the entropy by means of quantising the action variables on the denominator so that the entropy doesn't come out infinite. That's what the HB formula for the BH seems to be suggesting.

Now that's what I find very surprising. What is that infinite entropy that the quantum equation is suggesting if we "classicalise" the BH by doing h-> 0?

What are these classical variables, all scrambled up, that QM needs to regularise?

"Formula for black hole entropy
How to express the black hole entropy in a concrete formula? It is clear at the outset that black hole entropy should only depend on the observable properties of the black hole: mass, electric charge and angular momentum."

I posit that trying to bring into the same occupying space like* charges implies an entropic increase because of the inordinate potential force that they be ejected far away and into any other possible degree of freedom but I do not understand entropy.

Edited September 18, 2022 by NTuft
like not opposite

[joigus]

15 hours ago, Mitcher said:

It is also interesting that spins cannot be expressed in terms of momenta since h dimensions are those of an angular momentum, what am I missing ?

The fact that a spin 1/2 cannot be expressed in terms of position and momenta has nothing to do with dimensions. Dimensional analysis is very useful sometimes, but doesn't give you all the answers by any means.

It's to do with the general properties of the Hilbert space of position-momentum.

First time people realised you need a quantum mechanical operator of angular momentum that generalises orbital angular momentum was because of splitting of spectral lines in hydrogen (anomalous Zeeman effect) that had nothing to do with the orbits, but must be something "rotational" because it was a coupling to a magnetic field.

Then they went back to the QM's drawing board and formulated the general properties of an angular momentum, and discovered that there was room for this subspectrum that jumps in half-units of \( \hbar \).

[Mitcher]

10 hours ago, joigus said:

Then they went back to the QM's drawing board and formulated the general properties of an angular momentum, and discovered that there was room for this subspectrum that jumps in half-units of ℏ .

Is this why you said earlier than the quantity that QM points to is a surface ? What about the omnipresence of the number i as almost always associated with h by the way ? Could it point to a Complex reality plane ?

[joigus]

On 9/17/2022 at 7:28 PM, Mitcher said:

And just wondering here : if we had enough energy to downsize to the Planks's lenght, would we reach a substrate equivalent to the inside of BH's ? The repercussions would be staggering, that substrate would be ubiquitous and universal. I seem to be going obliquely here, but perhaps not that much.

Planck's length and time are so incredibly small that I don't think we will ever be anywhere near what would be necessary to start seeing anything interesting coming from perturbative approaches, at least.

Non-perturbative approaches are a different matter though. Non-perturbative approaches are non-incremental. So, who knows...

I may be going wildly speculative here, but the fact that the mass Planck is neither here no there between elementary-particle scale and cosmic scale, seems to suggest something about information, levels of organization, etc. That kind of thing. But again, who knows. As @Markus Hanke has pointed out before --here or somewhere else, I don't remember now-- we probably need a quantum theory of gravity, the idea that bridges both, a metatheory of which both regimes are but an approximation. This again is, at least to me, a big "who knows."

[Mitcher]

21 minutes ago, joigus said:

I may be going wildly speculative here, but the fact that the mass Planck is neither here no there between elementary-particle scale and cosmic scale, seems to suggest something about information, levels of organization, etc.

I think you are absolutely right here. It one also take the arithmetic mean between the radius of the Universe and the Planck's scale we get about one or two hundreth of a millimeter, which is the size of a red cell. The most basc forms of life are inatvertently right in the middle of a gigantic span of - 35 to 26 = +-60 orders of magnitude.

[joigus]

1 hour ago, Mitcher said:

Is this why you said earlier than the quantity that QM points to is a surface ? What about the omnipresence of the number i as almost always associated with h by the way ? Could it point to a Complex reality plane ?

Not exactly. The combination of QM and GR seems to suggest a surface because of Maldacena's AdS-CFT correspondence principle, which I do not completely understand. It says that a pure-gravitation theory whithin a certain closed "bulk" of a space is equivalent to a corresponding gauge theory (a generalisation of electromagnetism) on the surface of that space (the boundary.)

Why complex variables become necessary to describe micro-physics? I don't know.

I'll give you my best guess: Maybe the whole thing is a problem with local charts for covering the field variables. Example: If you want to chart a sphere* with one global coordinate chart, it's impossible. You have to take at least a second local chart to map the pole that you've left out.

Maybe what quantum mechanics is telling us [?] is something like: It's topologically impossible to map all of reality with one Cartesian/spherical-polar, etc., chart. If you insist on going "Cartesian cartographer" on something like an electron, you need to use a complex chart at some range, and then the problem of describing the "north pole" (where the electron is) becomes a probabilistic problem.

Why does it become probabilistic? I don't know, and that does strike me as strange.

* I really do believe that we should once and for all drop the dream of explaining everything with one parametrisation, and become humbler, like the cartographers of old did. We're nothing but cartographers, aren't we?

[NTuft]

1 hour ago, joigus said:

Maybe what quantum mechanics is telling us [?] is something like: It's topologically impossible to map all of reality with one Cartesian/spherical-polar, etc., chart. If you insist on going "Cartesian cartographer" on something like an electron, you need to use a complex chart at some range, and then the problem of describing the "north pole" (where the electron is) becomes a probabilistic problem.

Why does it become probabilistic? I don't know, and that does strike me as strange.

It has appeared to me that  is reduced to  either when the momentum operator is multiplied by itself in the operator method of deriving the Hamiltonian for the Schrodinger equation or when squaring (normalizing?) the probability amplitude a la the Born rule under Copenhagen. In the first case I think -i*-i is resolved to -1, and in the second multiplication by the complex conjugate simplifies the complex number.

The interpretation I've read says that the azimuthal  of the wave we're left with a description of is constantly varying on that line unlike any other wave form, but the interpretations of probabilistic clouds of potential locations fits that.

[Mitcher]

On 9/18/2022 at 11:59 PM, joigus said:

Not exactly. The combination of QM and GR seems to suggest a surface because of Maldacena's AdS-CFT correspondence principle, which I do not completely understand. It says that a pure-gravitation theory whithin a certain closed "bulk" of a space is equivalent to a corresponding gauge theory (a generalisation of electromagnetism) on the surface of that space (the boundary.)

Why complex variables become necessary to describe micro-physics? I don't know.

I'll give you my best guess: Maybe the whole thing is a problem with local charts for covering the field variables. Example: If you want to chart a sphere* with one global coordinate chart, it's impossible. You have to take at least a second local chart to map the pole that you've left out.

Maybe what quantum mechanics is telling us [?] is something like: It's topologically impossible to map all of reality with one Cartesian/spherical-polar, etc., chart. If you insist on going "Cartesian cartographer" on something like an electron, you need to use a complex chart at some range, and then the problem of describing the "north pole" (where the electron is) becomes a probabilistic problem.

Why does it become probabilistic? I don't know, and that does strike me as strange.

* I really do believe that we should once and for all drop the dream of explaining everything with one parametrisation, and become humbler, like the cartographers of old did. We're nothing but cartographers, aren't we?

Agreed on everything here. I could add that the holographic scenery looks very promising but the string theory has not resulted in anything for the last 30 or so years and looks more and more like a hopeless lane. Similarly it is possible that the complex plane would not be a simple mathematical trick to force results but an essential substrate to reality and perhaps able to explain action at a distance or probabilistic trajectories. At least the chartographers knew very well what the oceans they sailed on looked like.

[joigus]

On 9/19/2022 at 1:35 AM, NTuft said:

It has appeared to me that  is reduced to  either when the momentum operator is multiplied by itself in the operator method of deriving the Hamiltonian for the Schrodinger equation or when squaring (normalizing?) the probability amplitude a la the Born rule under Copenhagen. In the first case I think -i*-i is resolved to -1, and in the second multiplication by the complex conjugate simplifies the complex number.

The interpretation I've read says that the azimuthal  of the wave we're left with a description of is constantly varying on that line unlike any other wave form, but the interpretations of probabilistic clouds of potential locations fits that.

Sorry, I don't follow. The azimuthal angle leads to a description that's constantly varying on a line? One angle disappears because you can only use one direction to provide a set of operators to express angular momentum. It's a convention that we use the angle that represents rotation around the z-axis. J_x, J_y and J_z do not commute with each other, so we only get to pick one. Is that what you're trying to say?

20 hours ago, Mitcher said:

Agreed on everything here. I could add that the holographic scenery looks very promising but the string theory has not resulted in anything for the last 30 or so years and looks more and more like a hopeless lane.

Superstring theory has produced some intuitions or concepts that strike me as potentially revealing: dualities, unexpected symmetries... It has the flavour of a Copernican turn. But the landscape of possibilities it opens up is too complicated to be predictive. I'd say I'm in two minds about it, but it's more like I'm in 10⁵⁰⁰ minds, or whatever the number of ways to compactify the manifolds there were.

 

20 hours ago, Mitcher said:

Similarly it is possible that the complex plane would not be a simple mathematical trick to force results but an essential substrate to reality and perhaps able to explain action at a distance or probabilistic trajectories. At least the chartographers knew very well what the oceans they sailed on looked like.

This is what I think truly underlies John Bell's concept of beables: A set of commuting operators that expand the internal space of elementary particles. We would have to drop the requisite that everything relevant "inside the particle," so to speak, is amenable to parametrisation with real numbers and Hermitian operators --observables. Maybe the condition that every relevant parameter be an observable is too strong, and only a human constriction. Maybe that's the path to tackle the problem of singularities. Expressing measurable consequences of that idea may be a taller order though.

Edited September 21, 2022 by joigus
minor correction

[Mitcher]

4 hours ago, joigus said:

This is what I think truly underlies John Bell's concept of beables: A set of commuting operators that expand the internal space of elementary particles. We would have to drop the requisite that everything relevant "inside the particle," so to speak, is amenable to parametrisation with real numbers and Hermitian operators --observables. Maybe the condition that every relevant parameter be an observable is too strong, and only a human constriction. Maybe that's the path to tackle the problem of singularities. Expressing measurable consequences of that idea may be a taller order though.

It's more the arena itself of the observables that i have in mind, like the Complex plane ameanable to an extra dimension so to speak. Consider for instance the two functions y = 1/x and y = 1 - x not like two independant systems S1 and S2 but rather like a global one {S1 + S2} whose elements are symbolically intricated. The rectangular hyperbola is also composed of 2 apparently distinct elements by the way. To realize that intricated state one force the equality 1/x = 1 - x which result in both equations x^2 - x + 1 = 0 and 1/x + x - 1 = 0,  both with the same complex roots as solution so the image of that parabola might represent the system {S1 + S2}. When the straight line cuts across the hyperbola the solutions are obvious observables but when it is somewhere in between its two branches there are no apparent csolution anymore, however we still have complex solutions somewhere beyond the realm of our space. So it's not so much that there are hidden variables but more like about hidden dimensions, where particles could operate incursions at will.

[NTuft]

On 9/18/2022 at 2:21 AM, joigus said:

Then they went back to the QM's drawing board and formulated the general properties of an angular momentum, and discovered that there was room for this subspectrum that jumps in half-units of ℏ .

At the risk of preaching to the choir,

 

Quote

 

"1. Electron spin /2 and spin magnetic moment.

How did the concept of "electron spin" appear in physics, moreover, of such a relatively huge magnitude as /2? Why huge? And what is ? Let's look at all this in detail:

A physical constant , the Planck constant, is the quantum of action, central in quantum mechanics. Planck's constant divided by , =/ is called the reduced Planck constant (or Dirac constant). Both these parameters, h and , are fundamental constants of modern physics.
In magnitude, the constant  is exactly equal to the orbital moment of momentum (or angular momentum or rotational momentum) of the electron in the first Bohr orbit, according to the Rutherford-Bohr atomic model, and is a quantum of this moment:
  (1.1)

where  is the electron mass,  is the first Bohr speed of the electron moving around a proton in the hydrogen atom,  is the radius of the first Bohr orbit.

In quantum mechanics, there is no concept of the trajectory of the electron motion and, correspondingly, there are no circular orbits along which electrons move. Accordingly, there is no concept of speed of motion along orbits, just as there is no concept of the radii of such non-existent orbits.

Moreover, in quantum theory, according to the uncertainty principle, conjugate variables such as the particle speed v and its location r cannot be precisely determined at the same time. Therefore, the above two parameters cannot be presented together in the corresponding equations of the given theory.
For the reasons stated above, formula (1.1) and the formular for h,
h=  (1.2)
do not make sense in quantum physics and are practically not mentioned.

It should be noted that in the spherical field of an atom the product of the orbital raidus r_n and angular velocity v_n of the electron is the constant value v_nr_n=const. Accordingly,

=v_nr_n

The true, classical origin of the constants  and h is simply hushed up.

However, the history of introducing the concept of electron spin is associated with the rotational momentum  (1.1). And everything began with the Einstein and de Haas experiments on the determinaton of the magnetomechanical (gyromagnetic) ratio (1915). They adhered to the Borh model of the atom [...]"

 

Quote

 

On 9/21/2022 at 10:55 AM, joigus said:

Sorry, I don't follow. The azimuthal angle leads to a description that's constantly varying on a line? One angle disappears because you can only use one direction to provide a set of operators to express angular momentum. It's a convention that we use the angle that represents rotation around the z-axis. J_x, J_y and J_z do not commute with each other, so we only get to pick one. Is that what you're trying to say?

It is within formulating the operator method for developing the Schrödinger wave equation. In "the transition from the complex basis into the real one...". Instead of the power series expansion, the operator method creates a wave value number, k, in the Schrödinger equation:

; a quantity that varies continuously in the radial () direction. Hence our woowoo probability superposition?

 

On 9/20/2022 at 2:10 PM, Mitcher said:

Similarly it is possible that the complex plane would not be a simple mathematical trick to force results but an essential substrate to reality and perhaps able to explain action at a distance or probabilistic trajectories. At least the chartographers knew very well what the oceans they sailed on looked like.

Can you please elaborate?

On 9/21/2022 at 10:55 AM, joigus said:

This is what I think truly underlies John Bell's concept of beables: A set of commuting operators that expand the internal space of elementary particles. We would have to drop the requisite that everything relevant "inside the particle," so to speak, is amenable to parametrisation with real numbers and Hermitian operators --observables. Maybe the condition that every relevant parameter be an observable is too strong, and only a human constriction. Maybe that's the path to tackle the problem of singularities. Expressing measurable consequences of that idea may be a taller order though.

Dope...

On 9/21/2022 at 3:58 PM, Mitcher said:

It's more the arena itself of the observables that i have in mind, like the Complex plane ameanable to an extra dimension so to speak. Consider for instance the two functions y = 1/x and y = 1 - x not like two independant systems S1 and S2 but rather like a global one {S1 + S2} whose elements are symbolically intricated. The rectangular hyperbola is also composed of 2 apparently distinct elements by the way. To realize that intricated state one force the equality 1/x = 1 - x which result in both equations x^2 - x + 1 = 0 and 1/x + x - 1 = 0,  both with the same complex roots as solution so the image of that parabola might represent the system {S1 + S2}. When the straight line cuts across the hyperbola the solutions are obvious observables but when it is somewhere in between its two branches there are no apparent csolution anymore, however we still have complex solutions somewhere beyond the realm of our space. So it's not so much that there are hidden variables but more like about hidden dimensions, where particles could operate incursions at will.

Combined, dopest thing I've read in a long time. I basically wrote about this to someone in an email but was calling that space in between (on the hyperbolic complex plane) a time interval... I guess you elaborated on hidden variables/FTL(action at a distance) here in a way already.

I want to link @Mitcher to @joigus post here:

 

, #comment-1218003, on gauge invariance b/c it too is super doped and he could perhaps make sense of it or weigh in over there. I lost the mustard I had to try and lay on consistent histories there, like anti-solipsistic QM to me, but I do not understand QM.

[Markus Hanke]

On 9/17/2022 at 8:07 AM, joigus said:

as much as the fact that a classical BH would have an entropy at all,

I’m afraid I don’t quite follow you - you cannot derive the entropy of a BH in any way from either the Einstein equations or QFT alone; you need to assume the validity of both GR and QFT at the horizon. The existence of entropy (and Hawking radiation) is a consistency condition that must hold for these two to play nice together.

So BH entropy is fundamentally a semi-classical result. Within GR alone, the concept of entropy is meaningless.

 

On 9/18/2022 at 3:28 AM, Mitcher said:

I try to get a clear-cut answer about which part EXACTLY stands the light path within this diagram

I haven’t been online much lately, so haven’t been following along with this thread. I’ll try to explain it again:

The horizontal plane represents space at time t=0, being the instant of emission - we suppress one dimension here, to be able to draw the diagram at all. The vertical axis is time. 

Saying that the light propagates on the plane within that diagram isn’t really correct, because that’s a snapshot of space at a single instant in time. So there are of course no dynamics on that plane itself. To see how light moves, you can draw another plane further up at, say, t=1 - that’s also a snapshot of space at a single instant, but the wavefront will now be at a different spatial position, some distance away in all directions. You can keep doing this, and draw a whole stack of such planes, which gives you a sense of how the wavefront expands away from the emitter over time. The continuum limit of this plot will be the cone itself of course.

So, to be precise, the position of the wavefront at a given time t is at the intersection of the light cone with the hypersurface of simultaneity corresponding to t; meaning it would appear as a circle on a plane that is parallel to the base plane for t=0. For all intents and purposes the light cone itself is thus a schematic depiction of how the wavefront would propagate through space over a period of time, with one spatial dimension omitted.

Bear in mind here though - and this is important - that all angles and distances on this diagram explicitly depend on the metric. In curved spacetimes, then, a light cone is a purely local object, and light cones at different events will be tilted and distorted with respect to each other.

[joigus]

4 hours ago, Markus Hanke said:

I’m afraid I don’t quite follow you - you cannot derive the entropy of a BH in any way from either the Einstein equations or QFT alone; you need to assume the validity of both GR and QFT at the horizon. The existence of entropy (and Hawking radiation) is a consistency condition that must hold for these two to play nice together.

So BH entropy is fundamentally a semi-classical result. Within GR alone, the concept of entropy is meaningless.

 

Sorry. I wasn't clear.

I totally agree with you that a classical BH has no entropy. The no-hair theorem guarantees that there are only three parameters that characterise a static BH: mass, charge, and angular momentum. IOW, there is only one state. IOW probability(Q,M,J)=1, and the probability of any other state is zero because there is no other state.

Therefore,

\[ S_{\textrm{CBH}}=-1\ln1=0 \]

On the other hand,

\[ S_{\textrm{QBH}}(A)=\frac{c^{3}A}{4G\hbar} \]

and,

\[ \lim_{\hbar\rightarrow0}\frac{c^{3}A}{4G\hbar}=+\infty \]

So, considering a classical BH, "dressing" it with entropy, and trying to get to the classical version by (perhaps simplemindedly) having h go to zero, doesn't make a lot of sense.

I'm willing to admit I may be just chasing shadows here.

Edited September 23, 2022 by joigus
minor re-phrasing

[Mitcher]

18 hours ago, NTuft said:

I lost the mustard I had to try and lay on consistent histories there, like anti-solipsistic QM to me, but I do not understand QM.

Speaking about dope head....

11 hours ago, Markus Hanke said:

I’m afraid I don’t quite follow you - you cannot derive the entropy of a BH in any way from either the Einstein equations or QFT alone; you need to assume the validity of both GR and QFT at the horizon. The existence of entropy (and Hawking radiation) is a consistency condition that must hold for these two to play nice together.

So BH entropy is fundamentally a semi-classical result. Within GR alone, the concept of entropy is meaningless.

 

I haven’t been online much lately, so haven’t been following along with this thread. I’ll try to explain it again:

The horizontal plane represents space at time t=0, being the instant of emission - we suppress one dimension here, to be able to draw the diagram at all. The vertical axis is time. 

Saying that the light propagates on the plane within that diagram isn’t really correct, because that’s a snapshot of space at a single instant in time. So there are of course no dynamics on that plane itself. To see how light moves, you can draw another plane further up at, say, t=1 - that’s also a snapshot of space at a single instant, but the wavefront will now be at a different spatial position, some distance away in all directions. You can keep doing this, and draw a whole stack of such planes, which gives you a sense of how the wavefront expands away from the emitter over time. The continuum limit of this plot will be the cone itself of course.

So, to be precise, the position of the wavefront at a given time t is at the intersection of the light cone with the hypersurface of simultaneity corresponding to t; meaning it would appear as a circle on a plane that is parallel to the base plane for t=0. For all intents and purposes the light cone itself is thus a schematic depiction of how the wavefront would propagate through space over a period of time, with one spatial dimension omitted.

Bear in mind here though - and this is important - that all angles and distances on this diagram explicitly depend on the metric. In curved spacetimes, then, a light cone is a purely local object, and light cones at different events will be tilted and distorted with respect to each other.

ok so you are saying light does not translate exclusively on its space axis but simultaneously on the time one. Hence it follows the surface of the cone. For some reasons you seem to agree to that but also refuse to say it loud. Or is it impossible to draw the light path on the light-cone diagram ?

7 hours ago, joigus said:

So, considering a classical BH, "dressing" it with entropy, and trying to get to the classical version by (perhaps simplemindedly) having h go to zero, doesn't make a lot of sense.

How h could possibly go to zero ? It's a constant.

[Markus Hanke]

7 hours ago, joigus said:

So, considering a classical BH, "dressing" it with entropy, and trying to get to the classical version by (perhaps simplemindedly) having h go to zero, doesn't make a lot of sense.

You’re absolutely right, it doesn’t make a lot of sense - but I think in the absence of a quantum gravity model, this semi-classical approach is pretty much the best we can do.

I do find it encouraging, however, that it is in fact possible to have both GR and QFT be valid simultaneously on the horizon while still producing sensible results. To me this indicates that our quest for quantum gravity hopefully won’t be in vain.

57 minutes ago, Mitcher said:

ok so you are saying light does not translate exclusively on its space axis but simultaneously on the time one.

Yes, of course. Null geodesics are geodesics in spacetime, just like all geodesics are. You cannot have dynamics of any kind on a single hypersurface of constant time - the wavefront will just appear as a static circle there. Only if you combine many such surfaces into a stack, does the cone appear.

59 minutes ago, Mitcher said:

For some reasons you seem to agree to that but also refuse to say it loud.

This seems to me so basic and obvious that it never occurred to me that it needs explicit mentioning. The light cone diagram has space and time axis, after all. But I concede it could be my fault - I’ve been doing GR for a long time, so I tend to take some things for granted that mightn’t be immediately obvious to others. One becomes a bit complacent.

I suspect the confusion might be due to my earlier example of ripples on a pond? If so, I apologise - it was meant only as an analogy, and perhaps I didn’t explain myself properly at the time, thereby causing confusion.

1 hour ago, Mitcher said:

Or is it impossible to draw the light path on the light-cone diagram ?

The light cone is a valid representation of the propagation of light waves away from some source (at the origin of the diagram), where the cone itself would be the set of all possible null geodesics. However, as it is usually drawn, the diagram only works for flat Minkowski spacetime. For curved spacetime, these diagrams only make sense locally, in a small and thus nearly flat region. If you need to depict light propagation through larger regions, then light cone diagrams are wholly unsuitable; you’d instead choose specific boundary conditions that are of interest, and draw out the worldlines of individual photons - which would just be a single trajectory in spacetime. For example:

This is just a random example of how to plot null geodesics around a Schwarzschild BH. If you want to still use light cone, you have to draw several of those in different places, to visualise the metric (=causal structure) of spacetime. For example:

[Mitcher]

12 hours ago, Markus Hanke said:

In curved spacetimes, then, a light cone is a purely local object, and light cones at different events will be tilted and distorted with respect to each other.

 

Edited September 23, 2022 by Mitcher
Had not seen previous answers

[joigus]

1 hour ago, Mitcher said:

8 hours ago, joigus said:

 

How h could possibly go to zero ? It's a constant.

What we mean by that is the action (frequently named S) is enormous in comparison to h.

This generally works fine when you take the solutions of the equations and make an expansion in powers of (h/action) or action+ h(something of order 1) etc. It's not to be applied directly to the equations of motion, for example. The Schrödinger equation would be meaningless.

So it's something to do at the end, after having solved a problem, or in intermediate steps, but more carefully --like in the WKB (semiclassical) approximation, where you ignore terms in powers of h only when the powers are high enough.

[Mitcher]

27 minutes ago, Markus Hanke said:

I suspect the confusion might be due to my earlier example of ripples on a pond? If so, I apologise - it was meant only as an analogy, and perhaps I didn’t explain myself properly at the time, thereby causing confusion.

In fact you explained very carefully and the pond example was easy. Going back to the origin of this discussion then, we differ on the point of the actual path followed by light in space-time and a different type of diagram could be used, with the fixed observer proper time on the X axis. If space is supported by the Y axis then a photon emited at (0,0) would follow Y and arrive at (0,1) simultaneously when the observer arrives in (1,0). IOW light would stay behind in respect to the time of the observer as it carries an instant of his past. The zone outside the influence of the observer would then be in the left quadrant. The velocity of a mobile object having also passed by (0,0) can also be represented by v = sin (a), with cos(a) representing the relativistic factor 1/gamma. In addition, dt, dx and ds can be easily represented on this type of diagram.

45 minutes ago, joigus said:

What we mean by that is the action (frequently named S) is enormous in comparison to h.

In your equation S does not represent the dimentionless entropy ?

1 hour ago, Markus Hanke said:

To me this indicates that our quest for quantum gravity hopefully won’t be in vain.

I suspect we need a complete change of paradigm to reach that goal, so powerfully that even basic notions need to be metamorphosed.

[joigus]

37 minutes ago, Mitcher said:

In your equation S does not represent the dimentionless entropy ?

Yes. Sorry. Same letter, different things. It's tradition, plus too few letters in the alphabet.

[Markus Hanke]

34 minutes ago, Mitcher said:

we differ on the point of the actual path followed by light in space-time and a different type of diagram could be used

I’m not sure we differ on this - I completely agree that you can choose whatever type of diagram in whatever coordinate system is most useful for the particular problem at hand. There’s no right or wrong way, only usefulness and its opposite. That’s precisely the beauty of GR - the physics do not depend in any way on how you label and depict events in your spacetime. Labels don’t have physical significance, only the relationships between them do.

There are just two points that need to be borne in mind:

1. A choice of coordinate system generally (not always) corresponds to choosing a particular observer, so it will reflect how that specific observer evaluates the situation using his own local clocks and rulers. This is very important, since notions of space and time are purely local, so different observers will differ on these without creating any physical paradoxes. They’re bookkeeping devices - like accountants using different currencies may come up with different-looking books for the same company. In particular, Schwarzschild coordinates (irrespective of where you place the origin) physically correspond to a far-away observer at rest, and will thus reflect the far-away stationary notion of clocks and rulers. For obvious reasons, if you plot null geodesics on a chart using these coordinates, they will never reach or intersect the horizon on that diagram (!!!). I’m highlighting and exclamation-marking this to point out that such a diagram is observer-specific and reflects only what this particular observer calculates using his own local clocks and rulers.

2. There is no rest frame associated with photons, so, unlike is the case for time-like geodesics, you cannot parametrise photon geodesics by arc length (=proper time), since ds=0 by definition. Instead you can use an affine parameter of your own choosing.

59 minutes ago, Mitcher said:

I suspect we need a complete change of paradigm to reach that goal, so powerfully that even basic notions need to be metamorphosed.

I completely agree, especially since we already know that our usual paradigms don’t work for this. In particular, I suspect that any notions of smooth and regular space, time, spacetime with well-defined causal structures, and fields on spacetime will become meaningless in the realm of quantum gravity. Physics there will deal with dynamical quantities that are very different from those of ordinary classical physics, or even those of quantum physics, which will likely change the way we think about reality in very fundamental ways. 

I hope I will get to see it in my lifetime, but it’s possible that we are still a long way from such a model. There’s no way to tell, really.

[NTuft]

 

6 hours ago, Mitcher said:

In fact you explained very carefully and the pond example was easy. Going back to the origin of this discussion then, we differ on the point of the actual path followed by light in space-time and a different type of diagram could be used, with the fixed observer proper time on the X axis. If space is supported by the Y axis then a photon emited at (0,0) would follow Y and arrive at (0,1) simultaneously when the observer arrives in (1,0). IOW light would stay behind in respect to the time of the observer as it carries an instant of his past. The zone outside the influence of the observer would then be in the left quadrant. The velocity of a mobile object having also passed by (0,0) can also be represented by v = sin (a), with cos(a) representing the relativistic factor 1/gamma. In addition, dt, dx and ds can be easily represented on this type of diagram.

Preferred reference frame? is this like dt² = ds² + dx² + dy² + dz², or Lorentzian ether theory?

6 hours ago, Mitcher said:

In your equation S does not represent the dimentionless entropy ?

waht, is it J/J now? or is that some weird natural units. action, quanta , relevent to bh

6 hours ago, Mitcher said:

I suspect we need a complete change of paradigm to reach that goal, so powerfully that even basic notions need to be metamorphosed.

9 hours ago, Mitcher said:

How h could possibly go to zero ? It's a constant.

What is there was variation in the speed of light? Or, if in your preferred reference frame, everything was moving? Further,

Quote

A Wick rotation changes the Lorentz-Minkowski 4- dimensional geometry into a 4-dimensional Euclidian geometry. With this change, a quantum mechanical theory becomes a statistical mechanical theory with  playing the role of the temperature. The only difference between the Wick rotated LMG and the PTG is that the PTG makes the 4th dimension cyclic, while a Wick rotation keeps it unbounded. In actual practice with Lattice Gauge theory, even this difference is eliminated as their simulations are done with all four dimensions cyclic. The implication is that  should be interpreted as the temperature of background fluctuations in space-time.
The Proper Time Geometry - Carl Brannen

 

6 hours ago, Markus Hanke said:

2. There is no rest frame associated with photons, so, unlike is the case for time-like geodesics, you cannot parametrise photon geodesics by arc length (=proper time), since ds=0 by definition. Instead you can use an affine parameter of your own choosing.

oh, haha, no aether for you.

[joigus]

16 hours ago, Markus Hanke said:

You’re absolutely right, it doesn’t make a lot of sense - but I think in the absence of a quantum gravity model, this semi-classical approach is pretty much the best we can do.

I agree through and through. What seems peculiar to me is that, if you insist on forcing the maths tell you something, and try to get S(entropy)=0, which would be sensible for a classical approach, you end up getting S(entropy)=infinity!, pointing to a, perhaps misleading --maybe just an artifact of the approximation--, "entropic catastrophe," instead of an entropy-less picture.

16 hours ago, Markus Hanke said:

I do find it encouraging, however, that it is in fact possible to have both GR and QFT be valid simultaneously on the horizon while still producing sensible results. To me this indicates that our quest for quantum gravity hopefully won’t be in vain.

I do too. What I find intriguing in the holographic approach is that, quantities that make sense in the bulk, perhaps do not in the complementary of the bulk* (the exterior bulk, STS,) but have a counterpart on the horizon. This, of course, must have to do with the hyperinteresting question of the holographic dictionary: How to translate observables that make sense in the bulk to observables that make sense on the horizon.

This takes me back to mutterings that I've suffered for years now, and I will express here. What if Einstein's equations are valid locally** in the exterior of a certain compact surface, but not globally? Most fundamental static field equations have the form (schematically):

[2nd-order differential operator](fields with assymptotic constraints)=(coupling constant)x(sources)

(delta)F=S

In the case of Einstein, delta is the non-linear combination of 2nd-order derivatives that constitutes the Einstein tensor G when acting on g (the metric, say the field), formally constructed in such a way that covariant differentiation D produces an identity:

D(delta)g=DG=0

and,

DS=0

In the case of Laplace, delta is the Laplacian, F is the electrostatic field, and S (the source) is the charge density. This makes sense for smooth charge distributions with spatial extension, but gets dramatically silly when S is a point charge.

Could it be the case that this "approximation" can be made valid once a surface is chosen, but not extrapolated to be valid globally? (shrinking the surface to one point so as to express the field everywhere, as the singularity is suggesting.)

* Maybe they do. I don't know enough to know.

** Or even only on charts.