Local dynamic brane variables in higher dimensions fix the arrow of time

The Arrow of Time Points to Very Large Extra Spatial Dimensions

Entropy breaking the time symmetry of the equations of the FLRW metric is an idea that is just a crutch for a theory without a basis to affect space-time.

Consider a FLRW metric in 3+1 dimensions. Consider a particular universe filled with non-interacting pressureless and frictionless dust. Lets say that the universe has enough dust that it will collapse back into itself. Then for every time, τ, in the co-moving frame, there exists a time that is symmetric to it found by reflecting time across the universe’s half age.

All information of the state of the universe is encoded into the constant parameters of the model (Ωₘ , H₀, k) and the single variable τ. But there exist no local dynamic variables in this model that can tell the universe what it should do from any given moment τ. One simply has to dial τ forward from zero.

In other words there exists no local measurement in such a space time that can used to identify the arrow of time.

If I were a temporary observer into this universe I could look out and see the dust moving away during the early phase of the universe and in the later phase I would see dust approaching me again. But I would have to look far out to see that. There are no microscopic variables that I could use to measure whether the universe was expanding or contracting. So how does any local portion of this universe, which is supposed to respect local Lorentz Invariance, know what to do?

OK, well let’s say we embed the universe into a 4th physical dimension and say that our FLWR metric is on a brane. The brane has a local extrinsic curvature that is locally measurable, although it might be close to flat. This type of universe is called a Randall-Sundrum universe.

If I where an observer, not on the brane, but close to it, I would be able to tell if I were above it or below it, from its local curvature. Not only that, but I could measure its local expansion or contraction because I would know if I am above or below it and whether it was moving toward me or away from me. The local velocity of the brane is a dynamical variable measurable from the bulk.

That breaks the local time symmetry because now I can use local measurements of dynamical variables to determine what state the universe is in. The universe does need the global parameter τ to tell it what to do.

Well, you say, we don’t need to do all of that extra-dimension nonsense because we have entropy and that is enough to determine the arrow of time. The real universe has friction and all of the effects needed to generate entropy. And entropy is something you can measure locally, just by watching matter, even if you might need a lot of it to do that.

But I argue that for the universe to be self-consistent, the added effects of radiation and stellar evolution that come with frictional effects must be accidental or apparent only in breaking time symmetry.

Nobody has ever shown that a fundamental, local, space-time symmetry breaking arrow of time can be derived from thermodynamics. Its borderline mysticism to think that and its taken a long time for me to get that thought out of my head.

Thermodynamics is not even a quantum process. It only has to do with large collections of particles that reside in space-time and do not generate space-time.

In fact, thermodynamics and talk about entropy breaking the time symmetry of the equations of General Relativity is a crutch for a theory without a basis to affect space-time. The only thing that is fundamental to space-time is space and time itself, therefore only an answer that utilizes space-time itself as a solution can be the solution.

I believe that this is enough of a proof that at least one extra extremely large physical dimension exists and that that we live stuck to a brane for which none of the known forces of nature, not even gravity, can leave.