Re: How many things can happen in a single instant?

From: Igor Khavkine (igor.kh_at_gmail.com)
Date: 12/20/04 

Date: Mon, 20 Dec 2004 16:03:02 +0000 (UTC)

On Sun, 19 Dec 2004 12:48:24 +0000, Mike Helland wrote:

> This seems to be a standard assumption people have:
>
> "If time did not exist, no event occurred."
>
> As you may know this the opposite of how I view things. Instead I would
> say:
>
> "If no event occured, time does not exist."

You are free to say whatever you wish. However, merely stringing together
a few words does not guarantee meaning. This is a common mistake.

The general idea that you seem to be presenting is not new. However, you
are falling into the common pit extracting philosophy from it before any
physical predictions. The examples that you are presenting are too ill
defined, too crude, and too far from anything realistic to be able to
produce any physical predictions. Moreover, neither of the statements you
give above is used in the derivation of the transformation equations of
special relativity, hence you are neither contradicting nor reinforcing
the statements made by relativity.

Everything in physics goes back to measurements. The ideas of space
and time arise from the fact that we can measure space distances and time
intervals. When discussing a general enough theory of the world, one
eventually has to include a description of the apparatus that allows us to
make these measurements. Then outcomes of these measurements become
subject to theoretical prediction and are no longer specified externally.

Realizing that a clock and a meter stick are significantly distinguished
as physical systems, as neither are stars, clouds, or volcanoes, one comes
to the conclusion that time intervals and space distances must be
consequences of correlations between physical observables. Loosely
speaking, time and distance separation between different events can be
calculated from the values that physical fields take on. In our universe,
these physical fields would be matter fields, radiation fields, and the
gravitational metric field.

Upon some reflection this idea seems very beautiful and rather natural.
And given an opportunity to explain it to someone one may try to justify
it by concocting various simple examples or by pointing out that it is
philosophically appealing. However, for an idea to survive, its usefulness
must extend beyond mere popularization.

The holy grail application of this idea would be to take a background
independent theory (a universal theory of the type I described above) and
to derive from it in some physically plausible regime a theory with an
explicit time parameter, such as Newtonian mechanics or even quantum field
theory. This problem is still open and is known as the "problem of time"
in quantum gravity and more generally in background independent theories.
Rovelli has done some work on this problem. He talks about his attempts at
a solution in

C. Rovelli, in Conceptional Problems in Quantum Gravity, ed. by A.
Ashtekar and J. Stachel (Birkhauser, Boston, 1991), p. 126 C. Rovelli

"What is observable in classical and quantum gravity?", Class. Quant.
Grav. 8, (1991), 1895

C. Rovelli, "Partial Observables", Phys. Rev. D65, (2002), 124013

And also in the first few chapters of his recent book "Quantum Gravity".

Igor

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