Lawrence B. Crowell

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

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.

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

L. C.

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

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

Lawrence B. Crowell

$latex
U(\theta) = exp(i\sigma_a\theta_a)
$

for the index around the axis to be rotated.

Susskind’s black hole complementarity and holographic principle indicates that states which are identifiable on a membrane which wraps the black hole horizon are dual to states inside the black hole. This does suggest some deep connections with quantum gravity, for it the black hole becomes very small the horizon might become “blurred” by quantum fluctuations and the fields associated with the horizon and those in the interior will exhibit new physics.

Lawrence B. Crowell

Lawrence B. Crowell

Any attempt to deduce the structure of a black hole from the laws of physics is a total waste of time.

I then make a measurement of the state I want to teleport and find one of the four outcomes

1. Why would you find mixtures like that?
2. I assume “rotation” refers to an SU2xSU2 group. Is that correct?
3. Are the x, y, and z axes only an isospin basis, or do they have actual directions in a physical frame?
4. What is a zero rotation?

Lawrence B. Crowell

Suppose that you and I have a quantum state which are in an entangeled state. Say these states are due to the decay of a spin-0 boson, and which decay into two fermions. You and I are separated by some considerable distance. So we both then have this Bell state. Now suppose that I have another state |Y> = a|+) + b|-) that I want to teleport to you. So I then entangle this state with the Bell state so I have |Y)|B). By such an entanglement since you hold part of the EPR pair your state is similarly entangled. I then make a measurement of the state I want to teleport and find one of the four outcomes

|+)|-) – |-)|+)

|+)|-) + |-)|+)

|+)|+) – |-)|-)

|+)|+) + |-)|-)

What I do is then communicate each of these possible outcomes with the numbers 1, 2, 3, 4 as classical information. If you then take your Bell state and perform the following operations:

1: 0 rotation

2: pi rotation about the z axis

3: pi rotation about x axis

4: pi rotation about y axis

you will reconstruct the state I am intending to transmit because of its entanglement with your part of the EPR pair.

The point of going through all of this is that without the classical information you will not beable to reconstruct the state properly. Further, the total information communicated involves 2 bits, but from that the state you find exists in the whole H^4 state space or points on the Bloch sphere.

Lawrence B. Crowell