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In relativity, each observer experiences their own proper time as normal, even though time can pass at different rates when compared between frames—due to either velocity (special relativity) or gravitational potential (general relativity).

In quantum field theory, we know that certain physical quantities—like mass and coupling constants—can vary depending on the energy scale of the interaction. Could proper time itself exhibit some kind of scale-dependence as well?

For example, quantum-scale processes often seem incredibly fast to us, while cosmic-scale processes seem extremely slow—yet for observers within those domains, time presumably feels normal.

Is there any theoretical or experimental work exploring whether time might behave differently across physical scales (from quantum to cosmic), even if it always ticks at one second per second locally? Or is time’s behaviour across scale considered invariant by definition?

Navel-gazer
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1 Answers1

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In quantum field theory, we know that certain physical quantities—like mass and coupling constants—can vary depending on the energy scale of the interaction. Could proper time itself exhibit some kind of scale-dependence as well?

Proper time is defined by

$$c^2\text d\tau^2=g_{\mu\nu}\text dX^\mu\text dX^\nu$$

for the metric $g$ and gradients of coordinates $\text dX^\mu$ and the speed of light $c$. None of these are thought to run with the energy scale ($c$ certainly not, $\text dX$ probably not) except for the metric, which might deal with quantum-scale fluctuations.

This wouldn’t be the same as coupling constant running, if the metric really does have quantum fluctuations (we don’t have quantum gravity, so we’re not sure); it would be more of a “normal” quantum effect, like being in a superposition of locations or momenta.

For example, quantum-scale processes often seem incredibly fast to us, while cosmic-scale processes seem extremely slow—yet for observers within those domains, time presumably feels normal.

This is just because at the quantum scale even slight forces will push things great distances and to great speeds—not because of any special quantum effect, but because when the measuring rod is short things seem to take less time to cross it at the same speed. Same for cosmic-scale events. It’s not related to coupling constant running or any other such “scale”-related events.

Be careful not to conflate the quantum mechanical or general relativistic “observers” with conscious entities. It is a common mistake, and it will lead to many false results. I can always change units at any scale to make any process seem to run at any rate I want.

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