Category: Interpretations of Quantum Mechanics

Time dispersion in time-of-arrival measurements

I will be presenting a paper “Time dispersion in time-of-arrival measurements” at the International Assocation for Relativistic Dynamics this coming Wednesday (6/3/2010). The conference was originally scheduled to be held in Prague but has been moved online because of COVID-19. It may still be held as a physical conference as well, we will see.

My own paper is a follow up to my “Time dispersion in quantum mechanics“, published last year as part of the Institute of Physics Conference Series. That took the hypothesis: the quantum wave function should extend in time as it does in space & worked out the implications. The new paper is about experimental tests of the hypothesis: how would we determine if this hypothesis is true. Since it is real science however I turned the question around & made it “how do we prove that the wave function does not extend in time”.

In the new paper I shift focus to the Heisenberg uncertainty principle (HUP), specifically to the Heisenberg uncertainty principle in time and energy. Einstein & Bohr both held it was true, in fact essential if quantum mechanics was to be consistent with relativity. Bohr’s demonstration that it was was the end of Einstein’s direct attempts to falsify quantum mechanics.

Note that the formulation “the Heisenberg uncertainty principle applies to time/energy as it does to space/momentum” is loosely equivalent to “the wave function extends in time as it does in space”. If the wave function extends in time, then we would get the HUP in time/energy as a side-effect. And the most direct tests of the wave function extending in time are really tests of the HUP in time/energy.

The test I primarily focus on is that if the wave function extends in time all measurements in the time dimension would be just a bit fuzzier. In particular, if you are measuring when a particle is detected, if you are measuring the time-of-arrival, then if the wave function is extended in time you expect to see it both sooner & later than otherwise expected.

The advantage of this as a test is that the additional fuzziness if present at all must be present everywhen. Any time-varying experimental setup can potentially serve as a test.

The main problem — somewhat to my surprise — was that we really don’t know how to predict the time-of-arrival in standard quantum mechanics, let alone quantum mechanics with time in play as well! I’m trying to make a pincer attack on time: left jaw — standard quantum mechanics (SQM), right jaw — quantum mechanics with time (TQM). I was focused on the right jaw, but found that actually it was the left jaw that was weak. So I had to backtrack & deal with this problem. Interesting. And this turned out to be the single trickiest bit in the paper.

After getting the left jaw in better shape, good enough to take a punch anyway, I did a recap of TQM. This was probably the 2nd trickiest bit of the paper: how do you describe a hypothesis that took over a hundred pages and nearly five hundred equations to work out in a just a few pages? I found the core ideas coming a bit clearer in my own head at least. That’s gotta be worth something.

Then the payoff bit, the actual tests, is only the last quarter of the paper. And after working out how the additional fuzziness in time plays out, I got to my favorite test: the single slit in time. This is the single cleanest test of the idea. Not an easy experiment however.

Really the best part of tests of TQM is that if it is proved true, great. But if it proved false it will be taking down one or two of its neighbors with it. TQM is built by applying the quantum rules to relativity (or applying relativity to the quantum rules). If it is false, one (or both) of those two has a problem. And that in turn means there are really no null experiments.

And if I know my experimentalists, there is nothing they like more than proving a bunch of theorists wrong. If I have setup the arguments correctly — we’ll see — then they are sure to break something. As the well-known quantum experimentalist Nicholas Gisin said to me a long time ago (I paraphrase, it was quite a long time ago) “Look, I don’t care what your theory of time is. Just give me something I can prove wrong!”

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! 

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

Quantum Mechanics, Reality, & You at Philcon

Did my Quantum Mechanics, Reality, & You talk at Philcon this last weekend.  Had a very energetic & engaged audience. My thanks to Ed Bishop, Tom Purdom, Ron Bushyager, Ferne Welch, Walt Mankowski, & lots of others for great questions! Did five panels as well.  Full schedule:

Fri 8:00 PM in Plaza III (Three) (1 hour)
LOVECRAFT’S SUCCESSORS (1107)

[Panelists: John Ashmead (mod), Darrell Schweitzer, Marvin Kaye,
A.C. Wise, Neal Levin]

Is anyone writing good cosmic horror today? What new directions has
cosmic horror been taken in
Fri 9:00 PM in Crystal Ballroom Two (1 hour)
COSMOLOGY AND ITS DISCONTENTS (981)

[Panelists: Paul Halpern (mod), John Ashmead, Dr. H. Paul Shuch,
Robert Kauffmann]

The Standard Cosmological Model is the history of the universe as
arrived at over decades of observation and experiment and accepted
by the majority of scientists. It includes the Big Bang, Cosmic
Expansion, Inflation, Dark Matter, Dark Energy, etc. However, there
are real problems with the SM, and real (non-crank) scientists who
disagree with parts of it. What are the issues with Standard
Cosmology, and what alternative ideas are currently being discussed
Sat 12:00 PM in Plaza II (Two) (1 hour)
QUANTUM MECHANICS, REALITY, AND YOU (1319)

[Panelists: John Ashmead (mod)]

Behold the weird! Wigner and his panel of babies! The case of the
highly charged cat! The collapse of the collapse of the wave
function! And quantum chess! What’s new with quantum mechanics &
what does it all mean
Sat 1:00 PM in Plaza III (Three) (1 hour)
TIME TRAVEL FOR THE MILLIONS (1115)

[Panelists: John Ashmead (mod), Andrew C. Murphy, Gail Z. Martin,
Michael F. Flynn, Glenn Hauman]

If everyone could do it, how would this affect daily life? What are
the most frivolous uses of time travel we can think of? What would
be a time traveler’s practical joke
Sat 7:00 PM in Plaza II (Two) (1 hour)
FICTION ABOUT ITSELF: METAFICTION (1200)

[Panelists: John Ashmead (mod), Gregory Frost, April Grey, Neal
Levin, Alexis Gilliland]

Metafiction is when the story and the text becomes interchangeable,
each a part of the other. What are the roots and nature of this kind
of fiction
Sun 1:00 PM in Crystal Ballroom Three (1 hour)
EXOPLANETS AND SCIENCE FICTION (1124)

[Panelists: John Ashmead (mod), Eric Kotani, Inge Heyer, Walter F.
Cuirle]

We now know that planets are as common as stars. Over 500 are known,
nearly 20,000 are suspected.
What impact has this enormous expansion of the known universe had on
science fiction?

 

 

Quantum Mechanics, Reality, & You

I’ll be doing my talk “Quantum Mechanics, Reality, & You” tomorrow at Capclave, the DC SF Convention.  I have the latest slides up on slideshare.

Enjoyed putting the talk together.  I go thru the interpretations of quantum mechanics — some spectacularly silly — and then argue that quantum mechanics is real, you & I — not so much.  🙂

Also doing panels at Capclave on Hot Steamed Punk, Practical Uses of Faster-Than-Light Travel, Choose Your Own Apocalypse, & Great Cthulhu:  Threat or Menace?

 

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).

Temporal Paradoxes Talk Online

I had a lot of fun putting my NASA talk Temporal Paradoxes together.  The feedback I got from the assembled multitude at the Radnor Library last week was extremely helpful, leading to a near complete rework of the talk, in the interests of making it clearer.   Thanks!

The pdf & keynote versions are now online.

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