Recent content by PeterDonis

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In physics is that you are using a model that predicts a random distribution of outcomes. If your model predicts the same outcome every single time, it's not "chance" as far as physics is concerned. I'm referring to the definition in physics. See above. I'm not sure because I'm not sure what...

You're welcome! :smile:

Briefly: An invariant is a quantity that is independent of any choice of coordinates. A scalar is an invariant that is simply a number--or rather, a number at each point of spacetime, i.e., a scalar function on spacetime.

The definition of "chance" prevents it. That isn't something specific to QM.

Because we have other ways of inferring what the properties of the universe were before it became transparent to radiation. For example, we measure the relative abundances of light elements in our present universe, and we apply our knowledge of nuclear reactions to infer what the density and...

QM doesn't say there is an "interaction" between the two entangled particles. Certain QM interpretations do, but not all of them.

"Pure chance" wouldn't make it happen every single time. No, because "chance" would mean you would get different results on different runs. That's the definition of "chance". If you get opposite results every single time, that's not "chance".

That isn't the way cluster decomposition is presented in the literature, though. There's no claim that it breaks down for measurements that are spacelike separated, but not far enough. I'm also not sure that cluster decomposition is really a necessary principle. The really necessary principle...

This would need to be experimentally tested. They don't give any specific numbers, but there are experiments showing Bell inequality violations in measurements at, IIRC, kilometer distances now.

That's an invariant which is due to the invariant expansion scalar, yes.

This paper basically seems to be saying that the correlations that break factorizability don't vanish when you look at the correct measurement operators--the ones that describe measurements at the spatially separated locations where they're actually made.

Yes, when @jbriggs444 said "nothing is moving", he was (implicitly) using a comoving coordinate system. That's the most common coordinate system used to describe our models of the universe, but it's still a choice of coordinates, not something absolute. The scale factor is a function of...

Not really no. The viewpoint that "nothing is moving through space, but space itself is expanding", and the viewpoint that "objects are moving apart", are not two different ways things could be. They're two different descriptions of the same underlying physics.

You can't make this statement without specifying a coordinate chart. There is no such thing as "moving" or "not moving" in any absolute sense in relativity. Comoving worldlines are "not moving" relative to comoving coordinates. But they are moving relative to other coordinates. For example...