Category: Introduction

Not your grandfather’s gravity

Talk tomorrow at the Baltimore Science Fiction Convention:

Several possible modifications to Einstein’s theory have been proposed & may even have some experimental support; in addition to string theory & loop quantum gravity, is gravity a thermodynamic effect? Astronomers are looking hard at gravity waves in search of clues as to the origin of the universe (or even as to whether the universe had an origin), and …!

I’ve just finished the talk — main problem, too many interesting possible side channels — and have uploaded it as pdf,  keynote, power point, & html.  Comments welcome!

Physics of Paradox

This talk — scheduled for the Library of Congress & for Capclave next week — is now up.

It was a lot of fun to put together:  I discuss time in relativity & quantum mechanics, kinds of time, some possible time machines, the three kinds of paradox (grandfather, bootstrap, & freewill), the Hawking & Novikov consistency conditions for avoiding paradox, some ways to implement those conditions, paradox noise, what the world might look like if paradox avoiding time travel were possible, and of course why this is likely.

I’ve got the talk on line as Keynote (for Mac users), PowerPoint (for PC users), PDF in slides-only and also annotated forms.

I’m doing a practice run on the talk in two days at the Radnor Memorial Library in the Winsor room from 6pm to 8pm (when we have to be out).  I start the actual talk about 6:30pm.  This is a dry run (well more of a wet run really) for the talks next week.

If you are not too far from Wayne, PA & have an interest in time & paradox (but then if not why are you reading these words?) please feel free to come!

Time and quantum mechanics at the Chestnut Hill Book Festival

Spoke at noon yesterday (July 10th, 2010) at the Chestnut Hill Book Festival; in spite of heavy rain a nice crowd.
This was my Balticon Time & Quantum Mechanics talk, adjusted for a general (rather than a science fictional) audience.  I covered over a hundred years of physics in less than an hour — a lot — but the audience survived & even seemed to prosper, asking some good questions!
I’ve uploaded the power point and keynote versions of the talk so you can see the animations of the double slit experiment, if you have power point and/or keynote.  You may have to tell your browser how to handle .ppt and/or .key files, for all parts to work with maximum smoothness. I’ve also uploaded the pdf and html versions.
The references — several asked after them — are on slide 36.  Enjoy!
I’d like to thank Oz Fontecchio for organizing this, Ferne Welch for moral & practical support, Bob Rossberg (sp?) for critical help on the AV, & the Chestnut Hill Book Festival for providing the venue!

Next step for time & quantum mechanics

“When you come to a fork in the road, take it!” — Yogi Berra, Quantum Philosopher

I’ve been wondering what to do with quantum time.  I’ve gotten a certain amount of feedback on the original paper, ranging from “hard but interesting” to “interesting but hard”.
There are really two directions I would like to take this project at this point:

  1. Do the calculations in a more transparent way, to leave us, hopefully, just with “interesting”.
  2. Extend the ideas to the multi-particle case, which is needed for the analysis of all but the most trivial cases. For instance, we need this even to compute bound state wave functions.

In the spirit of quantum mechanics, it seems best to do both. I look at each in turn.

I noticed when I talked in Baltimore last month that the animations were really the most transparent part of the talk.  But the only way to develop them is to use numerical methods.  I’ve done a bit of numerical work in the past, mostly to calculate charged particle orbits around a black hole (when I was a grad student at Princeton).  From this I learned two things:

  1. Numerical calculations are tricky.  I learned this the hard way. I had thought — ah youth — that the smaller you make the step size, the more accurate the results. But I found this was true only up to a point; below a certain step size the calculations would produce obvious nonsense: at small enough step sizes, round-off errors dominated the results, sending the particles either into the black hole or out into space. [No real particles were harmed in the course of this experiment.] Ultimately, I had to completely rewrite the equations in a non-linear but stabler way to get something meaningful.
  2. If you don’t have a reliable source of physical intuition, tricky can quickly escalate into nonsense.  With anything involving time this is particularly a problem, largely because our usual intuition about time is so compelling that it is hard to move past it.  And if we do move past it, where do we get a “reliable source of physical intuition”?

Consequently I’ve been a bit chary of doing numerical work.  But while researching my Baltimore talk, I came across a work, Advanced Visual Quantum Mechanics, by Bernd Thaller, where the problem was solved, at least for low dimensional cases. Bernd Thaller worked primarily with Mathematica, a higher level language, but used a C program written by Manfred Liebmann for the low level numerical work.  This was a dissertation paper by Liebmann. A quick scan of the table of contents was enough to confirm my intuition that the problem is non-trivial.

I’ve spent a few hours with Liebmann’s dissertation.  It is written in German but apparently my high school German, Google translate, and a fair knowledge of the subject area [plus checking the references as I go] is enough to let me stumble thru it. The basic approach is essentially path integrals done a step at a time, in such wise as to minimize the numerical error at each step. This I can manage. Approximate proudly!

The second problem is how to extend quantum time to the multi-particle case.  The main problem here is how to generalize the single particle results to the multi.  After some mulling, and in the spirit of “approximate proudly” I’ve decided that using the usual Feynman rules but with the standard propagator replaced by the slightly fuzzier quantum time propagator is a reasonable first step.  When we are only looking for first order corrections, we don’t need an elaborate theoretical framework.

What to use for the “slightly fuzzier” is a bit of a question. Our single particle action is:

The most obvious generalization to the field theoretical case looks like:

This won’t do.  It is dimensionally wrong.  We need to multiply τ by something with dimensions of mass. But we can’t use the mass of any specific particle, as that would be to prefer one over another. We will instead insert a factor κ, defined as something with dimensions of mass/energy:

This will give us [insert hand-waving here] a propagator looking like:

If we are looking at a Feynman diagram we will wind up convoluting over the laboratory time:

Which makes most of our integrals look like products of the Laplace transform of the propagator:

Compare to the usual Feynman propagator:

Modulo an overall dimensional factor of κ [the sort of thing that comes out in the wash], they look much alike — in the limit of small κ.  As small κ corresponds loosely to large τ and as we expect to get standard quantum theory back in the long time limit of quantum time, this is fine.

The next question is where did κ come from?  We don’t need to sort that out entirely up front, but we do need to know we have at least one viable answer.

If we want to take an aggressively Machian view of quantum mechanics, then there is nothing to the universe but its wave function:  space and time are mere ensemble averages over the wave function of the rest of the universe.  κ then can be a measure of how much energy stored in the local vacuum fluctuations, small but not zero:

So, that is the plan for the multi-particle case:  use the κ-ified propagator with the Feynman rules, require we get standard quantum theory back in the large τ/small κ limit, see the testable inferences in re quantum time/multiple particle case as the first order corrections due to non-zero κ and/or small dispersions along the time dimension.

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:
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Why quantum time?

Why quantum time?

A few years ago I was looking for an interpretation/formalism for quantum mechanics which would be manifestly symmetric between time and space. The first question I had was:

Is time already quantized?

Is time treated using the same quantum rules as space is? can quantum mechanics be written in a way which is manifestly covariant?
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Quantum time – Overview

In relativity time and space are treated symmetrically but in quantum mechanics the treatment of time is very different:  in quantum mechanics time enters as a parameter, not an observable.

In my dissertation, I bridge this gap from the quantum mechanics side by quantizing time using the same rules as for space and then seeing what happens.
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