thinking covariantly about time (mathy and potentially confusing)

[yukoncpa]

[ QUOTE ]
The Schrodinger equation specifies an external mechanical time variable in which things evolve. But it does not tell you which direction is the past, and which direction is the future. The 2nd law of thermodynamics does tell you which direction is the past (low entropy), and which direction is the future (high entropy), but it assumes you already are working with a well-defined time variable (which is trivial in the case of the Schrodinger equation since you refer to a pre-defined external one, but it can be very non-trivial in certain covariant theories if you haven't identified which variable happens to be "playing the role of time"). There actually is no fully defined and completely general theory of "covariant statistical mechanics" -- it remains as mysterious in some ways as quantum gravity itself.



[/ QUOTE ]

Metric
I was just wondering. Could you please hurry up and come up with a complete theory of covariant statistical mechanics and while you’re at it, come up with an explanation for quantum gravity so that the rest of us can breathe a sigh of relief that the mysteries of the universe have been explained. [img]/images/graemlins/smile.gif[/img]

Is there an ETA as to when these ideas will be explained? Or are they simply beyond the human capacity for understanding.

I’m also wondering Metric, what do you think happens to us when we die? You’ve said that we will always exist in space time, but what does that mean to you? Is there any philosophy that can be gleaned from your knowledge? Should we have as much sex and drugs as possible so that throughout existence we will always be in a state of euphoria? What are your thoughts.

[Skidoo]

Would such a unitary state (with time as an internal parameter) exist in some other sort of time?

[Borodog]

That is one hellaciously awesome post.

You get a <font color="orange">Gold Star</font>.

[Piers]

Well I guess thats one way of putting it.

[Charon]

Great post (almost missed it).

A few questions though that popped in my head while reading it:

Is it ever possible to accurately describe the state of a singularity? So, in other words, are singularities incorporated in the state function of the universe?
If so, how can they be described?
And if not, how can one evolve a state that is not properly described? (And thus one cannot evolve the state of the universe, because one component of the state function should be the state function of the Big Bang for instance).

Maybe these questions dont make sense; havent thought it through yet.

Regards

[Metric]

Those are good questions. Singularities are problems in both pictures, and they arise from the use of a specific singularity-prone model under consideration -- not from the use of covariant dynamics, or the lack of the use of it.

In the non-covariant picture, singularities mean that there is some kind of breakdown of "U" -- it fails to give you sensible answers when you evolve certain states sufficiently far forward or back in time.

In the covariant picture, the problem manifests itself in your inability to adequately describe the whole state |PSI&gt;. Certain pieces of it are just "bad" and sometimes get arbitrarily "thrown out" by people who want to keep the part of the state that makes sense (but of course this doesn't really solve the problem -- if singularities show up, it's an indication that the model you are using simply goes bad under certain conditions).