Determinism, Free Will and Paradox

[Alex K]

There is not the time in relativity, so the question is meaningless unless you prescribe which time you are interested in.

You're stealing my line. I'm saying that the universe as a whole has no reference framework to compare against.

That's true in the simplified case of special relativity, but not in reality: the fact that we have nonzero temperature left over from the big bang gives us an absolute rest frame, as measured by the CMB dipole



You see here the blueshift and redshift of the cosmic microwave background due to the movement of earth relative to the heat bath left over from the big bang. You might be able to imagine a hypothetical universe of zero temperature with no special frame though.

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Okay, I'm trying to determine what happens to calculations when there's no reference frame. In the case of a photon traveling very far (say a million light years by Earth measurements), you have one frame of reference in which no time has passed at all, and one in which a million years have passed. Who's "right"? Both/neither/meh whatever.

There is not right or wrong concerning choice of reference frames, or more generally, coordinates - in the same way that one cannot from a modern point of view claim that the earth moves around the sun or vice versa, without imposing additional conditions. There are better and worse choices of coordinates, but if you do things correctly, in the end the physics conclusions may not depend on the choice of reference frame.

The reference "rest" frame of the photon, where no time passes, is a pathological limiting case where the entire universe sits in a 2 dimensional plane of infinite density. That mainly tells you that it's a very bad reference frame to do calculations. Time obviously passes for all non-singular rest frames while the photon travels.

I'm saying for "change" to occur in any measured sense, you must have not only a reference, but a subjective reference, to "pin down" what it means for something to happen at a particular rate.

You can always define the rate of a process as the time it takes in the rest frame of the process. Of course you need one physical system to give you a timing reference, otherwise there is indeed no notion how quickly time passes.

Without this reference point, all you really have is interrelated data-- but do events play out infinitely fast, or infinitesimally fast, without that subjective reference point? What's the "rate of unfolding" of universal events?

As I said above, in our realistic universe, the big bang gives us an absolute timing information via the temperature - that's why it objectively makes sense to say that the big bang was 13.7 billion years ago - as seen from the CMB rest frame.

In a deterministic universe, that subjective reference is discarded as an irrelevant byproduct of mechanistic interactions. The problem is that in this model there's now no standard by which the "rate" of change in the universe could meaningfully be measured. Time ceases to have any meaning, and so, therefore, does causality.

I don't agree - not having an absolute time scaling standard does not mean that there is no causality; special relativity alone has no absolute time standard, but has a strict separation of so-called light cones which preserves causality

1. two events either have a defined time ordering (when they have so-called "time-like" or "light-like" distance), and that's exactly the case in which one event can influence the other, or

2. they have "space-like" distance, in which case they have no defined ordering of before and after, because it depends on the observer which comes first, but precisely in this case they cannot influence each other.

Basically, without anyone there to witness the measured relationships in timed events, time collapses into a singularity.

Again, as I said above, the geometry of special relativity has a defined causal structure even if there is no absolute standard of time scale, and I think this collapse to a singularity is merely an artifact of choosing a mathematically divergent coordinate system

en.wikipedia.org/wiki/Spacetime