CSflim

Well with that amount of knowledge, it should be reasonably easy to explain.

Just one thing "wave function collapse" is just a fancy way of saying "making an observation" or "measuring". It is also sometimes referred to as state vector reduction.

First of all, as you approach light speed, time appears to slow down for you. At faster than light speed, it will seem that a signal will propagate backwards in time.

Suppose we have a person at A, who sends a faster than light signal to B, who then returns that message to A, again at faster than light speed, A will receive this message before he sends it....a very obvious paradox.

Now, we have to ask the question, can we arrive at the same paradox using the instantaneous wave function collapse (obviously faster than light).

Well, first we have to explain, exactly what the wave function is, and what it means to "measure it".

Some people see this as being a purely subjective matter. The wave function is nothing more than a mathematical description of our knowledge of the system. As time passes, our knowledge of this system reduces, and so the wave function grows. Each possible "state" for the system gets superimposed together into one big state.
So if we don't know if a system is in state A, or B, we refer to it as being in the linear superposition of A (+/-) B.
When we "measure" the system, and we determine that the system is in fact NOT in A, but is in B, we have reduced the state vector to just B.
There is no objective reality to the wave function, or its collapse. They are both merely mathematical abstractions of our knowledge of said system.

This is not how I choose to interpret it. As I explained above, I see the wave function as being something very definite and objective, and I also see the "measurement" of a system being something definite.

Anyway, we can try and use this wave function to send a signal.

What we can do is let a particle decay into two photons. The overall spin of the original particle was W. As spin is conserved, we know that the spin of particle A (Y) plus the spin of the other particle B (Z) adds up to W. For simplicity, we'll say W = 0, so Y=-Z.

At the moment however, both particles are in an undefined state. We don't know the actual values of the spins, but we know their sums. As such, by measuring one, we can know the other.

We keep particle A with us, and we send particle B to a further location.
We now wish to send our message.
Particle A is in an undefined state |Y>.
We don't know the angle of Y.
We can't actually "ask" the particle the question "what is your angle of polarization", we can only ask yes/no questions, such as "is this your angle of polarization"?

We test particle A for an angle of ß.
We will have a 50/50 chance of getting a YES to this angle.

However, once this measurement is made, B will automatically JUMP to the orthogonal state.

In other words, suppose we measure A for an angle of ß, and we are given a YES.
We will now know with certainty, that B will give a NO for a test of ß.
Somehow B now "knows" that A has been measured! This "knowledge" has travelled an arbitrarily long distance, instantaneously.

But the question is, can we send a signal with it?
Well actually, no we can't.
At Bs end, all we will get is either a YES or a NO.
We can get the signal, only through "comparing notes" with the results from particlae A.
So, if we repeated the experiment a number of times, we might observe the following results:

Results for B:
YES, YES, NO, YES, NO.

and when we correlate them with A, we will see the "signal"

Results for A:
NO, NO, YES, NO, YES.

so, we get no problems with causality there!

Now you might take the approach that maybe A and B's spin we not actually undefined, but rather simply unknown? This is of course the most obvious reaction. However, this too can be proven wrong...

..but maybe later. I'm tired! I'll post again later!

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