Time - Mobius Dimension?

Neo

Is it possible for time to be a "Mobius dimension," with its non-linear topology and simultaneous one-way linear direction, as described by relativity theory?

selfAdjoint

What do you mean by Mobius dimension? Is it a reference to Mobius coordinates?

Haelfix

I imagine some mathematician has probably solved the field equatiosn for a metric using Mobius coordinates. AFAIR I don't think it was interesting though, as it doesn't seem to have relevance to the real world.

I thought about that a bit as an undergrad, kinda in the 'wouldn't this be cool'.

Neo

Well imagine a "Mobius dimension" based on the concept of a Mobius strip. What are the properties of the strip? Namely:

1. Non-linear topology
2. One-way linear direction due to only one "side"

Now time based on relativity:
1. Non-linear topology due to time-space curvature
2. One-way linear direction due to entropy

Is it possible that time is a "Mobius dimension"?

Neo

What is AFAIR? As far as I remember? (Sorry, I'm new here) Theoretically, it corresponds to reality fairly accurately. The shape of time based on relativity is undeniably quite similar to that of a Mobius strip. Do you disagree?

selfAdjoint

The R in AFAIR could be remember or recall.

Time in relativity does not resemble a mobius strip at all. The mobius strip is a compact manifold - basically that means it's finite so every infinite point set on it converges. But time in Minkowski space in linear, and contains nonconverging point sets. As for the twist, the relationship of time to space in relativity is different than a mobius twist.

Neo

Time grows linearly right now. Did it always grow linearly? What about during the Big Bang? Could it be possible that time expanded faster (the opposite of time dilation) at the time of explosive spatial growth if time is intricately connected to space in an inseparable continuum?

Take Einstein’s (Temporal) Relativity Theory:
The faster something is moving, the "slower" time is moving for it. So if space is expanding explosively, is time growing because it is in a continuum with space or is it dilated because space is moving so quickly?

selfAdjoint

This isn't so. Something is moving faster only with respect to something else. Possibly by moving faster with respect to one thing, it's moving slower with respect to something else. And every massive object experiences its own rest frame, in which it isn't moving at all. And the time of this object, as physically experienced in these three frames is different in each one. In the rest frame time is not dilated at all.

It is these facts, and not mobius twists, that you should strive to learn about relativity.

chroot

Also, please try to learn some mathematics while you're at it. The phrases "non-linear topology" and "one-way linear" are meaningless. The Mobius strip is a compact, non-orientable manifold. That's really all that one can say about it.

Off to Theory Development this one goes...

- Warren