## The Other Shoe Drops

I’ve just finished the cross checks on my dissertation “Quantum Time“.

The dissertation asks “what happens if measurements in the time dimension are fuzzy, just as we know they are in the space dimensions”? Another way to put this is “what if particles are spread out in time, not just fixed in the present instant, but extending a bit into future and past”?

The question is motivated by relativity: From relativity we know that time and space are interchangeable. Even if a particle should happen to be flat in one frame, with no extension into past or future, in another frame it will have such an extension. Therefore it is simplest to assume any particle is always extended a bit in time, just not so much that we notice it.

But to work out specific predictions from this is tricky: how do you give an experimentalist something to chew on?

I was able to work out the rules for this by rewriting quantum mechanics in a way that doesn’t favor space over time. But even with that part done, it was still tricky to apply these rules to specific experimental cases and be confident that I had used the rules consistently and correctly.

Eventually what I hit on is a set of principles (aside from being as careful as possible about the algebra!): when the extension in time goes to zero, we should get exactly the standard result. And every experiment should morph smoothly into its neighbors. For instance, if we are working on a double slit experiment, and we separate the two gates far enough, the results should look like those for two separated single gates.

I’ve spent the last two months working on this & as of yesterday the analysis seems complete.

In general, of course, everything gets fuzzier in time. If you send a particle through a “chopper”, a gate in time, then the pattern it leaves in time at the detector will be more spread out if time is fuzzy.

There were some surprises of course. For instance, the classic double slit experiment normally produces an oscillating comb-like pattern at the detector. If time is fuzzy, not only does each tooth of the comb get wider (we knew that was coming) but the teeth get more spread out. And shorter. So there are three different effects to look for.

All three effects are subtle, so it is possible that the effects of quantum time have already been seen, but racked up to experimental noise.

I’m letting the latest version of the paper cool off for a week, then giving it a quick double check & submitting it to the physics archive next weekend.