Black hole information : Holographic theory question.

[Justice Hunter]

Question!

So Alice falls into a black hole, instead of the volume increasing for the black hole, it actually increases proportional to it's area. Thus one can draw the conclusion that 3 dimensional information can be fully explained by the information encoded on the surface area at the boundary of a system.

Can the same be said to encode all 2 dimensional information of a system onto it's perimeter (1 dimensional line)?

and can all 1 dimensional information on a line be encoded at all by a 0 dimensional point?

 

[phinds]

Question!

So Alice falls into a black hole, instead of the volume increasing for the black hole, it actually increases proportional to it's area.

Do you realize that you just said "instead of increasing it increases" ? I assume you left out part of your intended sentence here.

Leonard Susskind knows far more physics than I will ever know but I find his holographic theory VERY hard to believe.

 

[WannabeNewton]

Leonard Susskind knows far more physics than I will ever know but I find his holographic theory VERY hard to believe.

Regardless of whether or not you "believe" it, the AdS/CFT correspondence is firmly established mathematically and verified explicitly in various toy models such as the 2+1 BTZ black holes.

To the OP, yes it works in lower dimensions. A 2+1 (that is, 2 spatial dimensions and one time dimension) geometry (the "bulk") is dual to a 1+1 boundary, roughly speaking.

 

[phinds]

Oh, I'm used to finding things in cosmology and QM that I find hard to believe

 

[Justice Hunter]

To the OP, yes it works in lower dimensions. A 2+1 (that is, 2 spatial dimensions and one time dimension) geometry (the "bulk") is dual to a 1+1 boundary, roughly speaking.

Ah cool! That's really interesting, Thanks!

 

[Topolfractal]

okay so black hole holography works in the following manner. The relativistic perspective states for Alice and Bob , that if Bob falls toward a black hole ,then he wouldn't notice anything different as he passes the event horizon. From general relativity it's just a harmless point of no return. Now the quantum view states that black holes are subject to quantum fluctuations. Therefore little pieces of the black hole break off until eventually a shell covers the event horizon, containing colliding ,flying bits of a black hole. This shell becomes super heated plasma and interacts with the hawking pair production to become even hotter. Now when Bob falls in from the quantum perspective he eventually is burnt up when he reaches the plasma shell , He and his atoms are ionized and spread across the horizon and don't end up actually crossing the event horizon. There is no contradiction at all.

 

[PeterDonis]

little pieces of the black hole break off until eventually a shell covers the event horizon

This is not correct; "little pieces of the black hole" doesn't even make sense. The black hole is not an object that can break into pieces. It's spacetime geometry.

This shell becomes super heated plasma and interacts with the hawking pair production to become even hotter.

No; the shell of hot particles near the horizon is the particles from Hawking pair production.

Now when Bob falls in from the quantum perspective he eventually is burnt up when he reaches the plasma shell

This is a speculation which may or may not pan out; as I understand the current state of the "firewall" controversy, it is not currently looking very likely. In what currently looks like the most likely scenario, there is no "firewall", and the shell of hot particles near the horizon is only detectable by accelerated observers who are "hovering" near the horizon; observers like Bob, who are freely falling through the horizon, would not detect them.

 

[Topolfractal]

Both perspectives are completely true and there is no contradiction is the slogan of susskind's black hole complementarity. Try to come up with a situation where a contradiction is discovered. Now excuse me on my sloppiness concerning the first two quotes in your message, you are right , but the complementarity is true and an application of the holographic principle. The firewall is a mathematically proven facet of black hole physics. Also it's not whether the observer feels he is passing through it but in connection with an outsider it looks like he was burned up. The complementarity concerns the two perspectives of an outsider and a "faller" and states that the firewall perspective of an outsider is true and the insider perspective of passing through a harmless point of no return is true to, both are the true. Try to come up with a situation where a contradiction can be reached between the outsider and the insider.

 

[Topolfractal]

I apologize I was being sloppy.

 

[PeterDonis]

The firewall is a mathematically proven facet of black hole physics.

Please give a reference for this statement. I strongly suspect you have misinterpreted something.

 

[Topolfractal]

Leonard Susskind's book black hole wars.

Please give a reference for this statement. I strongly suspect you have misinterpreted something.

 

[PeterDonis]

The complementarity concerns the two perspectives of an outsider and a "faller" and states that the firewall perspective of an outsider is true and the insider perspective of passing through a harmless point of no return is true to, both are the true.

Yes, this is Susskind's claim. However, it is not consistent with this previous statement of yours:

when Bob falls in from the quantum perspective he eventually is burnt up when he reaches the plasma shell , He and his atoms are ionized and spread across the horizon and don't end up actually crossing the event horizon.

This is not Susskind's position. His position is that the infaller's atoms do cross the event horizon, and that the infaller sees no "firewall"; but the quantum information contained in the infaller's atoms gets copied just outside the horizon and is contained in the Hawking radiation that the hole emits. The issue with this claim is its apparent violation of the quantum no-cloning theorem: the quantum state of the infaller has to be cloned just before he crosses the horizon. Susskind's position is that this is not a problem because no experiment will ever be able to compare the infaller's original quantum state and its clone to verify that they are identical.

 

[PeterDonis]

Leonard Susskind's book black hole wars.

That is not a scientific reference; it's a pop science book. I am asking for a scientific reference--a peer-reviewed paper or a textbook--that supports your claim.

 

[Topolfractal]

Also Gerard t' Hooft's dimensional reduction in quantum gravity is the first paper stating the holographic principle.