## Quantum time talk today

*December 12th, 2009*

One of the members of my Macintosh programming SIG asked me if for today’s meeting I would talk about Quantum Time, which I was, of course, happy to do. There is nothing like explaining something to a bunch of intelligent listeners for getting it straight in your own head. And if you can get across some of the wonder & the weird that is modern physics, that’s even better!

I’ve got the slides online (see under talks). Summary:

- Relativity is strange. Time & space mix into each other. Taken seriously, this implies the highly counter-intuitive block universe picture: all time exists at once.
- Quantum mechanics is stranger. A particle can go thru two doors at once, and its paths will interfere, as if it were both wave and a particle. We can compute a wave function at a later time as the sum over all possible paths to get there from the starting wave function.
- Relativity & quantum mechanics do not mix well. In relativity time and space are interchangeable, but in quantum mechanics time is special (& boring): it marches forward a clock tick at a time. In quantum mechanics a particle’s position (in space only) is fuzzy, but in relativity particles have well-defined positions.
- The basic idea of “quantum time” is to
*assume*the positions of particles in time are fuzzy: so we not only don’t know*where*a particle is, we don’t know*when*it is either. Then we ask “what breaks”. - We start by taking the laboratory time, the time shown on clocks, as a given. Then at each tick of laboratory time, we
*assume*the particle is described by a wave function that extends in time as well as in space. - We use path integrals to work out how these extended-in-time wave functions change tick by tick.
- The expected effects are perhaps of order attoseconds, 1/billion billionth of second. (An attosecond is to a second as a second is to the age of universe.)
- Most of my effort (60 or 80% if not more) went into making sure I hadn’t broken anything, answering questions like: do we see conflicts with known experimental results? would we have seen this effect by accident? do we get the same energy levels for atoms? and so on. [Audience got a particular kick out of this point: programmers are familiar with spending most of their time making sure nothing is broken.]
- Of course, the effects of quantum time can’t be too unnoticeable or there is no point. We can see the effects of fuzziness in time as being like diffraction from edges of a shutter. If a beam goes thru a chopper, e.g. a camera shutter, & time is not fuzzy, the edges of the beam stay crisp. But if time is fuzzy, then beam will spread out into past & future – more than it otherwise should.
- In general, particles will be more spread out in time than otherwise. The effects should be measurable, under the right conditions.
- We discussed some experiments: the single slit in time, the double slit in time, & the Aharonov-Bohm in time. [New fortune cookie game: add “in time” to the end of your fortune.]
- I handed out a sheet with references, mentioning the Toomey and the Kaku as being particularly good places to get started.

There were lots of good questions. Typical:

- How can we sum all paths when the number of paths is infinite?
*Ans*. We cheat, using various methods. One way is to realize that most of the paths are centered on the average path, so do that first, then add in the rest as corrections. - Couldn’t all this quantum weirdness be explained somehow?
*Ans*. lots of people have thought so, but Bell’s theorem seems to have ruled out the most obvious hidden variable theories. - Can I use quantum fuzziness to explain to my boss why I am late?
*Ans*. So long as he or she doesn’t know what an attosecond is, yes.

It was a lot of fun: we didn’t go into depth on any topic, but it was clear people understood how weird all this stuff is & where to go for more information.

I’d like to thank the group for their attention, especially for something off-topic like this! And I particularly thank Chris Heimark for suggesting the talk in the first place & MLMUG and Mark Bazrod & Eugene Coggins for the space!

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