Hořava - Lifshitz gravity is a possible realization of the most sought after improvement on Einstein's theory.
In this Note I write what I understand so far about it.
We have a change in the Idea of change, from Newton, to Einstein, to Hořava. With the last one similar to the first. Time and space separate, spacetime related, to time and space separate again. Newton ->Einstein->Hořava.
I don't know about you, but time mystifies me.
I am succinct here, Newton had to invent a metaphor. Time flows like a river, independently of everything, it is then absolute. All clocks are synchronized, maybe by a prime force at the moment of creation. All clocks, somehow know about all clocks, as if connecting with infinite velocity information signals.
Einstein thought that 299 792 458 m/s was a better number for this velocity. Now our current Natural Philosopher in residence at UC Berkeley has reasons to believe that in the beginning time was more like Newton thought.
Theoretical Physics is a mathematical game, whatever gives you the results of other games, you believe will appear more like the real thing. Here we are talking about a computer game. Ambjørn, Jurkiewicz and Loll invented Causal Dynamical Triangulation. They play it in a computer.
If they don't separate space and time, they get into a mess, so they do. For his own reasons the Berkeley Professor, Hořava. Had done the same trick, but he was more thorough. He fill in more details. When the computer model gave something close to what Hořava-Lifshitz got previously, he felt vindicated, and believes the computer discovered the same tricks independently.
I believe the new Idea of change is based on these elements. The problem of time, critical phenomena, and acceleration of the Universe. Somehow one must get rid of time at the beginning, otherwise the math gets non-sense. What is done in the H-L theory is to vanish it slowly, one goes from four dimensions, to a kind of two dimensional primeval soup. The heat must do something to time, in this sense is not at all like Newton's river that won't evaporate. It becomes fractal. He calculates a fractal dimension for time-space and gets the beautiful formula:
ds = 1 + D/z
When z = 3 and D = 3, ds = 2. When z= 1 we are back in our immediate neighborhood, the Earth, with ds =4.
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Or time simply restarts every time that the plank scale gets breached by a big bang. If I'm understanding this correctly, all clocks somehow know about all clocks because a universe that has certain volume when it has a big bang is causally connected, which also resolves the horizon problem without the necessity of extra-ordinarily rapid inflation.
PS: I left you a note in your history of math thread.
Robert Brandenberger has a paper with a bounce. Time restarts. Somehow this H-L theory avoids entropy disruptions for multiple beginnings.
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