Physics distinguishing future from past

[Alex K]

Surgenator already said it, in classical physics, the arrow of time arises as a statistical phenomenon. The classical laws of physics are time reversal invariant. If you look at a system of masses moving according to newtonian laws, and play it backwards, you will again see a system of masses moving according to the same newtonian laws, but with different initial conditions. Incidentally, Surge, it is exactly the choice of inital conditions which tells you whether to use retarded or advanced potentials (since they are both perfectly fine Greens functions of the wave equations).

My favourite example is as follows: imagine an otherwise empty space with only two masses which attract each other with newtonian gravity for example. They will have some mutual kepler orbit. If you let run time backwards in this system, you will not be able to tell that it's backwards. There is no arrow of time.

If you add one more mass, the situation already changes: if you start with a constellation of three gravitationally bound masses and let the system run, it can happen that one of the masses gets a lot of kinetic energy by accident and is ejected from the system. If you look at this film backwards, you will see a particle coming from infinity and hitting a two body system at just the right energy to get integrated in it.

You'd see that and say: what are the odds!

And that's exactly the point, as soon as you have a more complicated system, the arrow of time is defined by going from less to more likely states. And that's what entropy is.
The analogy in electromagnetism: if you calculate the emissions of a radio antenna using advanced potentials, you'll get a radio programme coming in from the infinities of space and hitting the antenna at just the right point and moment to correspond to the electrons moving in the antenna. A very unlikely scenario.

If you have physics going on depending on a time parameter, future is the direction of increasing total entropy. If you have a minimum of entropy at some point and it goes up in both directions, you have two universes in which time runs the opposite way, which are connected at their temporal origins. Cool, huh.

Now, there are two more things that boggle my mind: first of all, quantum mechanical measurements in the copenhagen interpretation break this invariance as far as I understand it, because the wave function collapse happens only when going to the future. In the MWI, there is no problem afaik, it's again perfectly invariant under time reversal.

Secondly, the weak interactions have a term which violates time reversal, but it's extremely weak and can't possibly be the source of the arrow of time now. However, it could have something to do with the reason why a low entropy state was created.

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1) 2nd law of thermodynamics.
2) Retarded potential (<-- not a joke, that is what it is actually called)

"Retarded potential" is my middle name.
I'll look it up and see if I understand it... thanks.

The retarded potential is given as that solution of maxwells equations where a movement of charges produces a wave which moves away as time progresses. The advanced potential is the opposite: a wave comes in and cancels with the movement of the charges. The retarded potentials are needed to describe the usual situation of an antenna emitting something.

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I was wondering if this relates to causality somehow? If the universe is completely deterministic, would there be a way to distinguish future from past or cause from effect?

To answer that question, yes, also via entropy

I'm thinking about the "first cause" argument for God. Some Gnostics believed that God was a "unity". What would entropy and thermodynamics suggest as the starting point - a single bit?

The first cause argument for God is nonsense anyway. You'd first have to do their work for them and come up with a proper definition of God which allows you to say something about its thermodynamics