I've been reading about quantum cosmology and how it doesn't have a universal time variable so-to-speak. Instead it uses certain fields as clocks with which to compare other fields.

Now, it got me thinking. Does any of physics really need time?

For example time is measured by clocks and clocks are made of certain configuration of fields (or particles). So to measure how a field (or particles) changes with time really you are just comparing fields (or particles) with other fields (or particles).

If you had three particles $x_1, x_2, x_3$ and knew their positions at some instant, then if they wander randomly in a quantum mechanical way you could use the distance between two particles (which would tend to increase) as a clock which you could compare the distances of the other particles with conditional probabilities. e.g. $P((D_{13},D_{23}) | D_{12})$. There would be some statistical correlation between the three distances which you could base your theory on instead of the time variable.

Even in classical physics if you know the positions and momenta of two particles, you would not need a time variable since the distance between the two particles gives the time.

Has quantum there been any formulations of quantum field theory that are independent of time? (Or is this something that only occurs in quantum cosmology?)

How would you formulate something like a Schrodinger equation without time? If you just compare fields with other fields at some 3 dimensional slice?

  • $\begingroup$ Short answer: QFT is usually considered in the presence of the background Minkowski geometry, which gives you a unique notion of time (and thus, unitarity). What you suggest lies outside of the scope of ordinary QFT. Try reading about background independent quantum gravity, those guys try to fully embrace these ideas in the quantum theory. The most famous background independent approach is Loop Quantum Gravity. $\endgroup$ – Prof. Legolasov Mar 20 '18 at 1:31

As Einstein emphasised, "time" is the quantity measured by a clock.

But what is a clock? Its just another system (lets call it C) which we use as a reference to study change in our system of interest (S). C might simply be some dial moving around a circle. So we are correlating variables in S with the dial position in C.

So this relational viewpoint is already there in classical physics and it is taken over in quantum physics, as long as you have some external reference system you can call C.

In quantum cosmology there is no 'external' reference frame C, so you have to choose to study some system variables with reference to some other variable of the same system.

You can push the quantum cosmology point of view back to classical physics as you suggest, and do away with external clocks. This has been pursued by Julian Barbour, see eg this essay.

In quantum theory there have been several attempts to do away with the external time parameter, eg see this.

But it seems to me that the timeless approach isn't catching on because, except for maybe some philosophical niceities, it doesn't seem to provide any benefits for practical applications.

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  • $\begingroup$ Thanks for the links. I also found some more articles about "Jacobi's principle" and the problem of time. $\endgroup$ – zooby Mar 19 '18 at 18:37

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