Quantum entanglement and the big bang

Prior to the Big Bang all matter was compressed into a point of high density. Why isn't all matter already entangled?

• This is actually a complicated and subtle problem in cosmology. All observations say that the universe looks far more "stirred" than it rationally should be, given that regions of the sky out of causal contact with each other appear to have nearly the same density and temperature. – Jerry Schirmer Jun 19 '15 at 13:56
• – John Rennie Jun 19 '15 at 14:42
• It's not even clear if there was matter at the beginning of the big bang and what kind of properties it had. Of course the entire quantum state of the universe (in your light cone) is entangled, but it doesn't matter for individual measurements any more than the entanglement matters individually for Alice and Bob in an entanglement experiment. – CuriousOne Jun 19 '15 at 18:20

Let $|\Omega\rangle$ be the quantum state that describes the whole universe. Certainly it doesn't make sense to talk about the entanglement of $|\Omega\rangle$ with something else, since $|\Omega\rangle$ describes everything. However, we can meaningfully discuss the entanglement of the marginals of $|\Omega\rangle$: \begin{equation} \rho_a=\text{Tr}_{a'}\left(|\Omega\rangle\langle\Omega| \right) \end{equation} and
\begin{equation} \rho_b=\text{Tr}_{b'}\left(|\Omega\rangle\langle\Omega| \right) \end{equation} Here I have defined these two marginals by tracing out a part of the state-space (i.e. ignoring a part of the universe). Therefore,$\rho_a$ and $\rho_b$ are sub-systems of $|\Omega\rangle$: i.e. they may describe a "smaller" part of the universe. Now the notation of bi-partite entanglement can used to discuss the entangelment and/or separability of $\rho_a$ and $\rho_b$.

So to answer your question succinctly: some matter is indeed entangled with other matter, but everything in general is not entangled. This can be experimentally verified.

A particle can only be maximally entangled with exactly one other particle.

If it helps, you can think of being maximally entangled as having a perfect relationship between two particles rather than either particle having a perfect property in the slightest.

If you had a perfect spin up (in a particular direction) then obviously you could have some (that direction) correlation with anything and everything to the degree that the other particle has a probability of giving spin up in that direction. But that is 100% not what entanglement is. Entanglement is having the correlation instead of the two things having there own properties.

When you are maximally entangled, then every measurement gives every result equally likely so measurements reveal nothing about what you were, they just force a particular actualization of the relationship between the two particles into existence, and once that actualization is actualized, they are not entangled any more.

So an entanglement is an ability to actualize a relationship along a yet to be determined basis (you can measure in many different directions). The measurement causes the relationship to appear along the directions measured, so that's want entanglement is.

And you can be partially entangled with many particles, but when you are measured your entanglement with everything else is realized and then gone (and you become maximally entangled with the measurement device, because measurements actually create new maximal entanglement).

I actually happen to believe that they can be, and not only that but I think it would be very likely that all particles in the universe were entangled prior to, during and after the big bang. The problem would be verifying this entanglement in experiments as I can see no way of deducing which particle any given particle would be entangled with.

Entanglement has been proven in the lab but can only be done so with a high level of quantum coherence which is unfortunately lacking in nature. If you were to observe a particle in nature change the direction of its spin spontaneously you could put it down to entanglement, or to its interaction with other particles in its environment. Otherwise I can't see why this notion of entanglement at the beginning wouldn't be possible if not somewhat likely.