Category: Quantum Time

Time and Quantum Mechanics

I’ve submitted an extended abstract for my paper “Time and Quantum Mechanics” to the Center for Philosophy of Science’s workshop on Quantum Time. I’m not sure what the odds are of my getting in, but at a minimum prepping the abstract for the center has been a big help getting the paper organized, working out what is essential to the argument, and what can be let go.

Note the abstract is more extended than abstract, about two pages:

CFP-abstract-extended

Talks now on Slideshare

I’ve uploaded a number of my more recent talks to Slideshare.  Physics, with occasionally a wee bit of speculation admixed:

  1. Thought experiments – talk done 1st April 2012 for the Ben Franklin Thinking Society.  Role of thought experiments in history, use by Galileo & by noted violinist, how they can turn into real experiments.
  2. Not Your Grandfather’s Gravity – done last year (2011) on the latest developments in the suddenly hot area of gravity.  The stuff on faster-than-light neutrinos is, alas, already out of date:  boring won:  looks as if the FTL neutrinos were due to experimental error.   But Verlinde’s entropic gravity is still one of the most promising lines of attack.
  3. Temporal Paradoxes – physics talk given at NASA’s Goddard Space Center 2011.  A slightly NASA-fied version of a talk I’d given at several SF conventions in 2010.
  4. Quantum time – physics talk given at Feynman Festival in Olomouc in 2009.  I did popular versions of that talk as well.
  5. How to build a (real) time machine – talk given at several SF conventions in 2009.
  6. Life, the Universe, & the Second Law of Thermodynamics.  Or, the Infinite Probability drive.  About the role of entropy in the universe, complete with Babelfish.  2008.
  7. Faster Than Light – talk on faster than light travel:  theory, practice, applications. Given at several SF conventions in 2007.
  8. Confused at a Higher Level – arguably one of the funniest talks ever given about problems in quantum mechanics. OK, competition not that fierce.  Given at several SF conventions in 2004.
  9. The Physics of Time Travel.  Review of time, with respect to the bending, stretching, folding, & tormenting thereof.  Given at Philcon & Balticon (in various versions) in 2003.
  10. The Future of Time Travel – mostly about the science fiction thereof.  Probably 2002.

These are not all of my talks — I’ve probably done 20 or 30 SF talks over the last 20 years, at least one per year — these are just the ones done using Keynote or Powerpoint.  The 2005 & 2006 talks have gone walkabout.  If they reappear, I will upload.  I generally talk at Balticon, Philcon, & more recently Capclave.  I’ve spoken twice at Farpoint, but that is really more of a media convention, not as good a fit.

Talks before 2002 were done with Word & overheads. Overheads are easier to make than slides, but have a tendency to get bent, flipped, out of order, or in one especially memorable talk:  burnt.  That talk I was doing at the Franklin Inn Club: the projector failed at the last minute & I had to rent another from a nearby camera shop.  The rented projector ran hot. If I stayed on a specific slide for more than 60 seconds, the slide began to smoke.  Literally.  Colored smoke of course, wafting in strange tendrils towards the ceiling. Taught me a lot about pacing, mostly to make it faster.
By the way the word you are looking for, in re me & time travel, is not obsessed, it is focused.  Let’s just be clear about that.

Other talk(s), marginally less speculative:

  1. Overview of Backbone – talk on the jQuery library Backbone, given at PhillyCoders. April 2012.
  2. How to Destroy a Database – talk on database security.  October 2007.  Wile E. Coyote & other experts on correctness & security are enlisted to help make key points.
  3. Getting started with MySQL – talk given at PACS and my Macintosh programming group in 2006. Manages to work in the Sumerians, the Three Stooges, a rocket-powered daschhund, some unicorns, and – of course – dolphins (the totem animal of MySQL).

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.

Finally

Quantum Time now up on the physics archive.

Dissertation complete

I’ve finished re-checking the dissertation:  629 equations, 188 references, 110 pages, 83 input files, 48 lists, 36 footnotes, 28 quotes, 17 figures, 6 chapters (counting the appendix), 5 requirements, 1 idea.  It should be up on the physics archive in a day or two.

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.

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:
Read more »

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?
Read more »

“Quantum time” slightly less fuzzy: clean copy up.

I’d like to thank Ferne Welch and Arthur Tansky for copy-editing the previous version of “Quantum Time“.  It bears a significantly greater resemblance to English now!

And I would like to thank Jonathan Smith and also Mark West and Ashleigh Thomas for help in getting setup at University of Pennsylvania.

If anyone knows a bibtex style that handles electronic references well, please let me know.   If no suggestions, then I think I will warm up learning Old Kingdom hieroglyphs, then tackle bibtex.

All comments on Quantum Time are very welcome.  I’m planning to fold such into the great work of time as appropriate, then, if not too discouraged, push Quantum Time to the archive.

Thanks!

John Ashmead

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