"ER = EPR" and the never-ending triumph of string theory I've just heard about the latest craze in string theory, or to be more precise, in American science journalism. This is called "ER = EPR". A paper by Maldacena and Susskind, that, apparently, already deserves
its own Wikipedia page. (But then, many pop song hits also have their own Wikipedia pages...)
So, what is this about? Quoth Wikipedia:
They proposed that a nontraversable wormhole (Einstein-Rosen bridge) is equivalent to a pair of maximally entangled black holes.
...
This conjecture is an extrapolation of the observation by Mark van Raamsdonk[2] that a maximally extended AdS-Schwarzschild black hole, which is a nontraversable wormhole, is dual to a pair of maximally entangled thermal conformal field theories via the AdS/CFT correspondence.
...
This conjecture sits uncomfortably with the linearity of quantum mechanics.While I can still recall the meaning of these technical terms, let me offer a translation into plain English:
Wormhole - a special configuration of gravity that cannot actually exist, according to known physics. If a wormhole could exist, it might enable fast long-range space travel and/or time travel.
Nontraversable wormhole - a configuration of gravity that does not admit any signals to travel through it, so there aren't any observable effects of the presence of the "other side" of the wormhole (and it still cannot exist anyway).
Maximally entangled black holes - a configuration of gravity that has the maximum allowed value of a certain quantity (the quantum-mechanical entanglement). This configuration cannot be created out of actual black holes, if only because it is impossible in reality to attain the maximum degree of entanglement. Actually, nobody has ever managed to produce or observe a pair of
pinheads that were
at all quantum-mechanically entangled, let alone
maximally entangled, let alone
black holes that are
maximally entangled.
AdS spacetime - an imaginary spacetime that has interesting mathematical properties but cannot exist because its structure violates causality. Causality is a basic assumption of physics: you should be able to predict future events if you know enough about events at the initial time. If AdS spacetime existed around us, we would be unable (
even in principle) to predict any future events at later times, even if we knew
everything in the entire space at the initial time. (Solutions of wave equations in AdS are not unique after a global Cauchy horizon, even if initial conditions are fixed in the entire infinite space.)
AdS-Schwarzschild black hole - a black hole that is imagined to be present in an AdS spacetime (which cannot exist).
Thermal conformal field theories - mathematical theories that have interesting mathematical properties (e.g., conformal symmetry) but do not actually describe the known fundamental physical phenomena. In other words, these theories are
not applicable to gravitons, photons, electrons, quarks, Higgs bosons, or any other fundamental particles of matter that we know about, - in particular, because known matter does not obey conformal symmetry.
AdS/CFT correspondence - a 1997 conjecture by Maldacena that certain mathematical features of the AdS spacetime will satisfy the same mathematical equations as some features of thermal conformal field theories. The AdS/CFT correspondence, sometimes also called the "AdS/CFT duality" and the "holographic principle", is a
conjecture because it has not yet been demonstrated to be correct.
Linearity of quantum mechanics - a basic law of all fundamental quantum-mechanical systems. It says that any two states of quantum systems can be linearly added (with coefficients), which always yields another allowed state. This law was discovered about 80 years ago and has been experimentally verified with great precision. There is no experimental data that contradicts it. Engineers nowadays make devices that are designed using this law. In other words,
all known matter obeys the law of QM linearity.
Now we are ready to translate the statement of the "ER=EPR" from Wikipedia into plain English. For brevity, let us introduce this notation:
X = "
maximally extended AdS nontraversable wormhole"
Y = "
a pair of maximally entangled thermal conformal field theories"
Z = "
the quantum-mechanical law of linearity"
So, here goes:
"Consider X and Y - two theories that are fundamentally unable to describe anything in our real, physical world, and actually weren't ever proposed as realistic physical theories. It is now conjectured that maybe some aspects of the mathematical description of X and Y are exactly similar to each other. If this similarity were true (which has not been actually demonstrated!) then it is claimed that Z will not hold for X and Y. Here, Z is a well established law that has been experimentally confirmed to hold without exception for all physical systems."
The real triumph of string theory is the fact that there is now a separate Wikipedia page devoted to the above statement, and that hundreds of people have been studying various properties of X and Y and making statements like this for the last 20 years or so, while calling themselves "physicists".
P.S.
Actually, it occurred to me that the claim "If the AdS/CFT conjecture holds for X and Y, we can refute Z" is mistaken on at least two levels:
First, the refutation of Z is based on the assumption that if there is an entangled state of two black holes then there is a wormhole connecting them. In other words, it is assumed that the
physical existence of something described by Y will lead to the
physical existence of something described by X, - despite the fact that both X and Y are admittedly unphysical theories that do not describe our observed reality. Even if X and Y were physically realistic, it is merely some
mathematical properties of X and Y that are conjectured to coincide. The physical existence of any objects described by X has nothing to do with the physical existence of any objects described by Y.
Second, the theories X and Y are themselves
quantum field theories, that is, they are based on quantum mechanics and must assume that the fundamental quantum property Z holds. If a conjecture that uses X and Y were to refute Z, it would automatically also refute X and Y themselves, leading to a logical contradiction.
So, it follows that either the AdS/CFT conjecture is false, or the property Z is not refuted by applying the AdS/CFT conjecture to X and Y.