Category: Quantum Time

Is time an observable? or is it a mere parameter?

I’ve just put my long paper “Time dispersion and quantum mechanics” up on the physics archive.   If you are here, it is very possibly because you have at one point or another talked with me about some of the ideas in this paper and asked to see the paper when it was done.  But if you just googled in, welcome!

The central question in the paper is “is time fuzzy? or is it flat” Or in more technical language, “it time an observable? or is it a mere parameter?”

To recap, in relativity, time and space enter on a basis of formal equivalence. In special relativity, the time and space coordinates rotate into each other under Lorentz transformations. In general relativity, if you fall into a black hole time and the radial coordinate appear to change places on the way in. And in wormholes and other exotic solutions to general relativity, time can even curve back on itself.

For all its temporal shenanigans, in relativity everything has a definite position in time and in space.  But in quantum mechanics, the three space dimensions are fuzzy.  You can never tell where you are exactly along the x or y or z positions.  And as you try to narrow the uncertainty in say the x dimension, you inevitably (“Heisenberg uncertainty principle”) find the corresponding momentum increasing in direct proportion. The more finely you confine the fly, the fiercer it buzzes to escape. But if it were not for this effect, the atoms that make us — and therefore we ourselves in turn — could not exist (more in the paper on this).

So in quantum mechanics space is complex,  but time is boring. It is well-defined, crisp, moves forward at the traditional second per second rate.  It is like the butler Jeeves at a party at Bertie Wooster’s Drone’s Club:  imperturbable, stately, observing all, participating in nothing. 

Given that quantum mechanics and relativity are the two best theories of physics we have, this curious difference about time is at a minimum, how would Jeeves put it to Bertie?, “most disconcerting sir”.

Till recently this has been a mere cocktail party problem: you may argue on one side, you may argue on the other, but it is more an issue for the philosophers in the philosophy department than for the experimenters in the physics department.

But about two years ago, a team led by Ossiander managed to make some experimental measurements of times less than a single attosecond.    As one attosecond is to a second as a second is to the age of the universe, this is a number small beyond small.

But more critically for this discussion, this is roughly about how fuzzy time would be if time were fuzzy.  A reasonable first estimate of the width of an atom in time is the time it would take light to cross the atom — about an attosecond.

And this means that we can — for the first time — put to experimental test the question:  is time fuzzy or flat? is time an observable or a parameter?

To give the experimenters well-defined predictions is a non-trivial problem. But it’s doable. If we have a circle we can make some shrewd estimates about the height of the corresponding sphere.  If we have an atomic wave function with well-defined extensions in the three space dimensions, we can make some very reasonable estimates about its extent in time as well.

The two chief effects are non-locality in time as an essential aspect of every wave function and the complete equivalence of the Heisenberg uncertainty principle for time/energy to the Heisenberg uncertainty principle for space/momentum.

In particular, if we send a particle through a very very fast camera shutter, the uncertainty in time is given by the time the camera shutter is open. 

In standard quantum mechanics, the particle will be clipped in time.  Time-of-arrival measurements at a detector will show correspondingly less dispersion. 

But if time is fuzzy, then the uncertainty principle kicks in.  The wave function will be diffracted by the camera shutter. If the uncertainty in time is small, the uncertainty in energy will be large, the particle will spread out in time, and time-of-arrival measurements will show much greater dispersion. 

Time a parameter — beam narrower in time.  Time an observable — beam much wider in time.

And if we are careful we can get estimates of the size of the effect in a way which is not just testable but falsifiable.  If the experiments do not show the predicted effects at the predicted scale, then time is flat.

Of course, all this takes a bit of working out.  Hence the long paper.

There was a lot to cover:  how to do calculations in time on the same basis as in space, how to define the rules for detection, how to extend the work from single particles to field theory, and so on. 

The requirements were:

  • Manifest covariance between time and space at every step,
  • Complete consistency with established experimental and observational results,
  • And — for the extension to field theory — equivalence of the free propagator for both Schrödinger equation and Feynman diagrams.

I’ve been helped by many people along the way, especially at the Feynman Festivals in Baltimore & Olomouc/2009; at some conferences hosted by QUIST and DARPA; at The Clock and the Quantum/2008 conference at the Perimeter Institute; at the Quantum Time/2014 conference Pittsburgh; at   Time and Quantum Gravity/2015 in San Diego; and most recently at the  Institute for Relativistic Dynamics (IARD) conference this year in Yucatan.  An earlier version of this paper was presented as a talk at this last conference & feedback from the participants was critical in helping to bring the ideas to final form.

Many thanks! 

If you get a chance to look at the paper and have some comments to make, please send! 

Particularly interesting are ideas for experimental tests that are within the reach of current technology.

PS The paper has been submitted to the IOP Conference Proceedings series.  The copy on the archive is formatted per their requirements so is formatted for A4 paper, and with no running heads or feet.  I have formatted for US Letter here.


Time Dispersion in Quantum Mechanics

If a quantum wave function goes through a single slit in time is it diffracted or clipped?

I will be speaking at the  2018 meeting of  the IARD — The International Association for Relativistic Dynamics  this afternoon.  Had a nice chat with the organizers & some early arrivals last night over coffee:  my talk clearly a good fit to the conference.

The decisive test is what happens if you send a quantum wave function through a single slit in time, say a very fast camera shutter.  If quantum mechanics does not apply (current generally accepted view), the wave function will be clipped — and the dispersion at a detector arbitrarily small.  If quantum mechanics does apply (proposal here), the wave function will be diffracted — and the dispersion at a detector arbitrarily great.

I’ve uploaded the talk itself  in several formats Time Dispersion in Quantum Mechanics – KeynoteTime Dispersion in Quantum Mechanics – Powerpoint, and Time Dispersion in Quantum Mechanics – PDF.

I’ve incorporated feedback from the IARD conference into the underlying paper Time Dispersion in Quantum Mechanics.  I’ve submitted this to the IOP Conference Proceedings series & have also uploaded it to the physics archive.  I hope it will be a useful contribution to the literature on time and quantum mechanics.

Your comments very welcome!

Time and Quantum Mechanics accepted at IARD conference

The physics paper I’ve been working on for several years, Time & Quantum Mechanics, has been accepted for presentation at a plenary session of the 2018 meeting of  the IARD — The International Association for Relativistic Dynamics. I’m very much looking forward to this:  the paper should be a good fit to the IARD’s program.

Abstract:

In quantum mechanics the time dimension is treated as a parameter, while the three space dimensions are treated as observables.  This assumption is both untested and inconsistent with relativity.

From dimensional analysis, we  expect quantum effects along the time axis to be of order an attosecond.  Such effects are not ruled out by current experiments.  But they are large enough to be detected with current technology, if sufficiently specific predictions can be made.

To supply such we use path integrals.  The only change required is to generalize the usual three dimensional paths to four.  We treat the single particle case first, then extend to quantum electrodynamics.

We predict a large variety of testable effects.  The principal effects are additional dispersion in time and full equivalence of the time/energy uncertainty principle to the space/momentum one.  Additional effects include interference, diffraction, resonance in time, and so on.

Further the usual problems with ultraviolet divergences in QED disappear.  We can recover them by letting the dispersion in time go to zero.  As it does, the uncertainty in energy becomes infinite — and this in turn makes the loop integrals diverge.  It appears it is precisely the assumption that quantum mechanics does not apply along the time dimension that creates the ultraviolet divergences.

The approach here has no free parameters; it is therefore falsifiable.  As it treats time and space with complete symmetry and does not suffer from the ultraviolet divergences, it may provide a useful starting point for attacks on quantum gravity.

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.

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