State of "matter" of a singularity

[Mitcher]

On 9/24/2022 at 12:42 AM, Markus Hanke said:

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.

On this diagram a photon ds = cos(pi/2) = 0 and sin(pi/2) = 1 = maximum spatial extension, while for the observer on the x axis it is the contrary, his translation in time is maximally extended as per cos(0) = 1 = his proper time by definition.

On 9/23/2022 at 10:33 PM, Markus Hanke said:

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.

If we talk about the geodesic of a single photon one has to think not in terms of dynamics but as a quantic event with emission and absorbtion being simultaneous. So it is really a hypersurface of constant time : once we have shot a laser pulse in space we will never been able to see it again not only because it is speeding away in space but also because we are also speeding away in time from that event.

On 9/24/2022 at 3:22 PM, joigus said:

How to translate observables that make sense in the bulk to observables that make sense on the horizon.

Do you mean like say, a unit of mass in the bulk would leave an inprint of surface unit on the surface ? And for each mass unit added one would have an increase of surface and entropy ?

[joigus]

1 hour ago, Mitcher said:

Do you mean like say, a unit of mass in the bulk would leave an inprint of surface unit on the surface ? And for each mass unit added one would have an increase of surface and entropy ?

Not exactly or necessarily. I understand these things only in a very very qualitative way, so I can't help you much. Let's say I'm just an assymptotic observer  .

From what I understand, this dictionary has to be built with a lot of guesswork for each case. Doing a quick google search, and after filtering non-related stuff, you can find papers and seminars under titles like,

AdS₂ Holographic Dictionary

Holographic dictionary for generic asymptotically AdS black holes

Building a Gauge-Invariant Holographic Dictionary

etc.

I learnt about the holographic dictionary on Jacques Distler's blog, Musings. He's a mathematical physicist, string theorist, bitter enemy of Lee Smolin and the LQG people, so much/most of what he says goes right over my head.

But it's interesting to take a look at what people with irreconcilable views say. You take a look at one, take a look at the other, and maybe the homotopy that connects both enlightens your mind.

In a theory that's invariant under deformations, ascertaining what the observables are is no piece of cake, because coordinates don't mean anything much, and you have to find (bulk/interior) invariants --like the ones that Markus talked about many posts ago--, and relate them to invariants on the boundary. Or, perhaps, if the boundary theory is well-behaved, the other way around. I'm well out of my depth here.

Edited September 25, 2022 by joigus
minor correction

[Mitcher]

On 9/26/2022 at 1:29 AM, joigus said:

Not exactly or necessarily. I understand these things only in a very very qualitative way, so I can't help you much. Let's say I'm just an assymptotic observer  .

From what I understand, this dictionary has to be built with a lot of guesswork for each case. Doing a quick google search, and after filtering non-related stuff, you can find papers and seminars under titles like,

AdS₂ Holographic Dictionary

Holographic dictionary for generic asymptotically AdS black holes

Building a Gauge-Invariant Holographic Dictionary

etc.

I learnt about the holographic dictionary on Jacques Distler's blog, Musings. He's a mathematical physicist, string theorist, bitter enemy of Lee Smolin and the LQG people, so much/most of what he says goes right over my head.

But it's interesting to take a look at what people with irreconcilable views say. You take a look at one, take a look at the other, and maybe the homotopy that connects both enlightens your mind.

In a theory that's invariant under deformations, ascertaining what the observables are is no piece of cake, because coordinates don't mean anything much, and you have to find (bulk/interior) invariants --like the ones that Markus talked about many posts ago--, and relate them to invariants on the boundary. Or, perhaps, if the boundary theory is well-behaved, the other way around. I'm well out of my depth here.

ok, thank you.

[Markus Hanke]

Sorry everyone for not replying to your comments - my focus is currently on things related to my real-life vocation, so I’m not online much. 

On 9/26/2022 at 8:05 AM, Mitcher said:

emission and absorbtion being simultaneous

In whose frame?

 

On 9/24/2022 at 11:22 PM, joigus said:

Could it be the case that this "approximation" can be made valid once a surface is chosen, but not extrapolated to be valid globally?

What do you have in mind when you say “surface”? As in, a 3D surface in spacetime?

On 9/24/2022 at 11:22 PM, joigus said:

Most fundamental static field equations have the form (schematically):

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

(delta)F=S

I remember that MTW takes a very different approach to justifying the form of the EFE - that is, via topological principles, specifically the fact that the boundary of a boundary is zero, which leads to the automatic conservation of certain quantities. I will have to review my notes on this first though, as I’ve grown a bit hazy on the details. This may be relevant here though.

[joigus]

4 hours ago, Markus Hanke said:

What do you have in mind when you say “surface”? As in, a 3D surface in spacetime?

Sorry, I didn't mention that. I meant 2D surfaces. Once a time-like foliation is chosen, it would be a matter of choosing Sx[t₁,t₂] to consider the "objects" trapped inside the surface in terms of histories.

The point is: Could it be that the different theories (classical field theory, quantum, and beyond) were related to the choice of local charts in the field variables?

IOW, could it be that field variables are also inevitably affected by choice of charts in their field-variable phase space, each chart being a different domain, representing a different field-theory approximation? Something like what I'm trying to schematically represent in the following sequence of pictures:

The orange circles represent the 2D-surfaces I'm talking about.

5 hours ago, Markus Hanke said:

I remember that MTW takes a very different approach to justifying the form of the EFE - that is, via topological principles, specifically the fact that the boundary of a boundary is zero, which leads to the automatic conservation of certain quantities. I will have to review my notes on this first though, as I’ve grown a bit hazy on the details. This may be relevant here though.

OK. I'll keep re-cycling myself on these questions too, as I'm a bit hazy as well.

[Mitcher]

7 hours ago, Markus Hanke said:

In whose frame?

In photon's frame, which i understand is not a valid reference frame, however one writes ds = 0 = simultaneous.

[Markus Hanke]

4 hours ago, Mitcher said:

In photon's frame, which i understand is not a valid reference frame

That’s right.

4 hours ago, Mitcher said:

however one writes ds = 0 = simultaneous

This doesn’t mean simultaneity (which is a meaningless concept since there’s no valid frame for photons). It means that, if you choose arc length as your parametrisation on the geodesic, then the overall spacetime interval between two neighbouring points on that curve is zero. IOW, the time and space parts within the line element are of equal magnitude.

6 hours ago, joigus said:

IOW, could it be that field variables are also inevitably affected by choice of charts in their field-variable phase space, each chart being a different domain, representing a different field-theory approximation?

I think I know what you mean, and it makes perfect sense. The question then becomes what the chart (or: the choice of surface - same thing?) itself physically represents. If you schematically equate a choice of charts with a choice of scale, you’d recover our usual hierarchies of QFT-QM-Classic. But that’s not enough, we’d need to know the precise physical meaning.

The reminds me suspiciously of the concept of emergence, tbh.

[Mitcher]

23 hours ago, Markus Hanke said:

This doesn’t mean simultaneity (which is a meaningless concept since there’s no valid frame for photons). It means that, if you choose arc length as your parametrisation on the geodesic, then the overall spacetime interval between two neighbouring points on that curve is zero. IOW, the time and space parts within the line element are of equal magnitude.

Let's do a thought experiment à la Einstein and imagine that you would be emitted from a laser on Earth and absorbed on the Moon 1.3 second later. But for you it would seem that the trip was instantaneous, and that's not meaningless. Then how the lenght of an arc comes in play here ? Why not a line, like the sinus of pi/2 to describe both the time and space parts in equal magnitude ? Then cos of pi/2 = 0 for the geodesic.