Comments on: The Black Hole War

By: String Theory and the Multiverse - Christian Forums

String Theory and the Multiverse - Christian Forums — Sat, 13 Jun 2009 22:31:45 +0000

[…] of my favorite books is The Black Hole War. The Black Hole War | Cosmic Variance | Discover Magazine __________________ To view links or images in signatures your post count must be 10 or greater. […]

By: Where Does the Entropy Go? | Cosmic Variance | Discover Magazine

Where Does the Entropy Go? | Cosmic Variance | Discover Magazine — Mon, 12 Jan 2009 18:10:42 +0000

[…] is “How does the information get out?” An increasing number of physicists believe that the evaporation of black holes conserves information, but they don’t know precisely how the details of the state which created the black hole get […]

By: Lawrence B. Crowell

Lawrence B. Crowell — Tue, 12 Aug 2008 03:00:18 +0000

It gets a little deeper than this. The fields on a three dimensional space, or space plus time in four dimensions are determined by fields which are on a slice within a two dimensional null congurence. This relationship between fields in this manner involves some subtle matters of Lagrangians on a full space and the Chern-Simons Lagrangian on a subchain or cycle. This can lead to ways of constructing a “mass” for black holes from gauge charges, similar to BPS black holes. In this way it leads to a 3 + 2 dimensions which is dual to the CFT on S^5.

Lawrence B. Crowell

By: collin237

collin237 — Mon, 11 Aug 2008 19:58:42 +0000

By “3+2 dimensional” do you mean that the two interpretations (internal and external) are interpolated by a parameter that behaves like an extra time-like dimension? (As if the internal and external observers are looking at the surfaces of bread surrounding a 5-dimensional sandwich?)

By: Lawrence B. Crowell

Lawrence B. Crowell — Mon, 11 Aug 2008 17:59:02 +0000

The black hole duality indicates that an exterior observer, at “infinity,” will see fields which have entered a black hole according to harmonic oscillator modes (or string vibrations) on a membrane a Planck unit length above the event horizon. The Russian for a black hole is a frozen hole, where because of time dilation nothing is ever seen to cross the r = 2M. Then as the black hole decays away these modes end up being radiated away in three space (or 4-dim spacetime). Conversely for an observer which enters the black hole their quantum information is not seen pinned to the event horizon, but taken in by the singularity, or some type of quantum-mawl in the interior.

This is the matter of black hole complementarity, which is that the observers outside and inside a black hole observe the same field amplitudes, but in complementary forms. Loosely put, the exterior viewpoint has fields on this membrane above the horizon, similar to a type of D2-brane, equivalent to fields in space removed from the black hole. So there is a 3 + 2 dimensional perspective on fields as measured outside the black hole. The interior is given by a D5-brane, and the duality says that the amplitudes on the two are equivalent.

Lawrence B. Crowell

By: collin237

collin237 — Sun, 10 Aug 2008 19:53:43 +0000

I mean how can an interior field be controlled from a surface it can’t classically communicate with?

If the surface is the cosmological horizon, this is clearly not a moot point. Without a non-relativistic causality, it would mean everything we observe has already been decided billions of years ago.

By: Lawrence B. Crowell

Lawrence B. Crowell — Sun, 10 Aug 2008 14:17:30 +0000

It looks like I messed up the tex on that equation. Ng’s fluctuation equation for a volume of length scale L bounded by an area is

$latex
\Big(\frac{\delta L}{L}\Big)^3~ge~\Big(\frac{L_p}{L}\Big)^2
$

L. C.

By: Lawrence B. Crowell

Lawrence B. Crowell — Sun, 10 Aug 2008 12:48:15 +0000

I am not sure what is meant by inner or outer causality.

If the holographic theory is correct then metric fluctuations of spacetime should manifest themselves on a scale larger than the Planck length. Y. Jack Ng has shown that the fluctuations in a three dimensional volume are equated to those on a two dimensional bounding region by

$latex
\(Big(delta L}{L}\Big)^3~\ge~\Big(\frac{L_p}{L}\Big)^2, L_p~=~\sqrt{G\hbar/c^3}
$

and so by solving for the delta L fluctuation these occur on a scale considerably larger than the tiny Planck length L_p.

The AdS/CFT is largely a stringy result. However, aspects of string theory shows up in a number of forms — such as sphere packing and quantum codes. It also sneeks its way into Jordan exceptional algebras in loop quantum variables. So physics probably has both stringy and loopy aspects to it.

Lawrence B. Crowell

By: collin237

collin237 — Fri, 08 Aug 2008 23:44:27 +0000

Isn’t that just replacing the “inner causal” with an “outer causal”?

And what validity does it have for a non-stringist like me?

By: Lawrence B. Crowell

Lawrence B. Crowell — Fri, 08 Aug 2008 20:32:05 +0000

The holographic principle has connections with the S^5 ~ AdS duality in superstring theory. It on lower dimensions tells us that field amplitudes in three dimensional space at a given “time” are projections from fields pinned to event horizons.

Lawrence B. Crowell