## 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:

1. 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.
2. 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.
3. 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.
4. 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”.
5. 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.
6. We use path integrals to work out how these extended-in-time wave functions change tick by tick.
7. 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.)
8. 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.]
9. 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.
10. In general, particles will be more spread out in time than otherwise. The effects should be measurable, under the right conditions.
11. 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.]
12. 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:

1. 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.
2. 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.
3. 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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