Whether time "moves" or "stays exactly where it is" is a metaphysical question: you can't make an experiment that distinguishes the two possibilities. Thus it's just a matter of how we explain things to ourselves.
There is some evidence of time's asymmetry, and hence the "arrow of time" in particle physics. It is known as t non-invariance, and is the process by which a particular meson may be observed to decay into several other particles, but this process may not be reversed as in Feynmann's theory of opposite particles travelling in different directions in time. These processes are distinct to a particular subatomic particle, but nevertheless they indicate that there is some definite direction to time. Whereas most subatomic particles have an opposite number (electrons and positrons, protons and antiprotons) (t-invariance), T non-Invariance has been observed only in the weak decay of neutral kaons.
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