Category: Quantum Time

Does the Heisenberg uncertainty principle apply along the time dimension?

Does the Heisenberg uncertainty principle (HUP) apply along the time dimension in the same way it applies along the three space dimensions? Relativity says it should; current practice says no. With recent advances in measurement at the attosecond scale it is now possible to decide this question experimentally. The most direct test is to measure the time-of-arrival of a quantum particle: if the HUP applies in time, then the dispersion in the time-of-arrival will be measurably increased. We develop an appropriate metric of time-of-arrival in the standard case; extend this to include the case where there is uncertainty in time; then compare. There is — as expected — increased uncertainty in the time-of-arrival if the HUP applies along the time axis. The results are fully constrained by Lorentz covariance, therefore uniquely defined, therefore falsifiable. And therefore we have an experimental question on our hands. Any definite resolution would have significant implications with respect to the role of time in quantum mechanics and relativity. A positive result would also have significant practical applications in the areas of quantum communication, attosecond physics (e.g. protein folding), and quantum computing.

Presented as a talk at International Association for Relativistic Dynamics 2020 Conference; currently in submission to the associated Journal of Physics: Conference Series: Proceedings of IARD 2020. 31 pages, 5 figures, 87 references

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!”

Philcon 2019 — Recap

Ultimately my “Time dispersion in quantum mechanics” is an attempt to answer Gisin’s question

Got some great questions during my talk at Philcon: lots of stuff I had not considered before. If quarks are high-energy beasts, and if high-energy means short time, and if short time means increased effects of time dispersion, shouldn’t you look at impacts on quark calculations. Should & will! And what of quantum computing: would dispersion in time provide additional bandwidth for quantum computing? Very probably! Not to mention additional insight into the bugaboo of the quantum computing, decoherence.

I also liked that the audience really picked up on why I centered the investigation on falsifiability: I wasn’t trying to prove that there is dispersion in time, I have presented a way to prove there is not. Falsifiability is what makes science science.

I have uploaded the Keynote, PowerPoint, and PDF versions of the talk.

My panels were, as usual, interesting.

Hildy Silverman did a great job moderating Dystopia Now! she kept the discussion focused & moving. Fellow panelist Hakirah D’Almah, a journalist with a focus on the Middle East, was particularly trenchant. Hard to find the bright side of Dystopia, but I think we did. 1984 is a deeply optimistic work: by writing it (Orwell’s last, he died shortly after completing it) Orwell helped us avoid it.

I will admit the Evolution of Mars panel, while interesting, drifted a bit (Wild Marses I Have Known would have been a more accurate description).

I was happy to be the moderator on Looking for Life in our Solar System: the great thing about being a moderator — especially when you are the least qualified person the panel — sit back & let your fellow panelists — Earl Bennett, Dr. H. Paul Shuch, John Skylar — do the heavy lifting. Which they did very well!

And I was also moderator on The Blurry Line between Cutting Edge and Pseudoscience. The panel was right after my talk, so made a nice seque. The best question came from an audience member: how do I tell, when I see stuff on the web, what level of credibility to give it? Just asking that question is the first step. The panelists suggested credentials of the author, links to it, and my personal favorite: does the author find the good in his/her opponent’s arguments, recognize the weak spots in his/her own?

Capclave 2019 — Recap

Alice & her dog examine the mysteries of time and quantum mechanics, slide from my talk at Capclave 2019.

Had a great time at Capclave. It’s one of the smaller cons — slightly north of 300 people — and doesn’t have some of the usual con stuff like an art show or cosplay. But for precisely those reasons, you tend to have more of those repeated one-on-one conversations that, for me, are the real life of a con.

Had a good time at the five panels I was on. All were energetic & held the audience.

Technospeed — is technology moving too far too fast? — was the first (Friday evening), with the smallest audience. It was hard to know what to do with the subject, a tad too broad I suspect. Much of the discussion focused on AI, a better subject. (I may take AI that for my big talk next year.) Not a bad panel, with that said: we had a lot of fun with Kurzweil’s Singularity and related topics.

My next two panels (both Saturday), The Coming Civil War & Failed SF Predictions, both had Tom Doyle as moderator. He did a great job, particularly with the Coming Civil War, where he asked the assembled panelists how they would treat present various scenarios from a fictional point of view. How would you tell the story of cities war with the country side? and so on. Kept the conversation from degenerating into what they thought of the [insert-derogatory-noun]-in-chief.

I had a bit of fun with Failed SF Predictions, bringing in some books of pulp age cover art: jet packs, menacing octopi, orbiting cities, threatening robots, giant computers, and attacking space fleets, … The role of women in SF in the days of the pulps is nothing like what it is in the real world today; a lot of the Failed SF Predictions chosen were about gender issues. Not even the first wave of feminist SF writers — LeGuin, Joan Vinge, Joanna Russ, … — fully anticipated how much the field would evolve.

Sunday my first panel was on Secrets of the Dinosaurs. The other three panelists were the GOH Robert Sawyer (author of the Far-Seer trilogy of dinosaur novels), Michael Brett-Surman (Collections Manager of the National Dinosaur Collection at the Smithsonian and co-author/editor of several dinosaur books with Dr. Thomas R. Holtz) and Dr. Thomas R. Holtz (who is the T. Rex of T. Rex scholarship). Being on a dino panel with these three was like being a small mammal in the Jurassic. The primary objective is to not get underfoot and squashed. All three are immensely polite & courteous individuals, who would never think to squash a small mammal who wandered on to the planet panel. I took advantage — as the designated amateur — to ask about dino parental care, how did hadrosaurs defend themselves against a T. Rex (rather easily — those tails are not just ornamental!), and my final q: if dinosaurs lived in groups & relied on visual & auditory display, did they have barn-dances?

My final panel was Exoplanets. My fellow panelists (Inge Heyer & Edward Lerner) were both expert & I had done a fair amount of swotting, so we had a good time going over rogue planets between the stars, planets made of diamond, life within the hidden seas, and various methods of finding new exoplanets — the total of confirmed exoplanets is 4000 & counting!

And my Time Dispersion in Quantum Mechanics talk went well (Saturday afternoon). I had a couple of practice run-thrus with a “volunteer” audience, which left it leaner, shorter, and easier to follow. Same content, but no math (except E=mc-squared, which is so familiar it doesn’t count). Talk went well, good audience and great questions: some I answered there, some I dealt with in the hall discussions, and one or two I had to admit “that’s one for the experimentalists!”

And my thanks to Brent Warner of NASA, who corrected — with great politeness — a couple of soft spots in the presentation. I will incorporate into the next iteration, in two weeks as it happens at Philcon.

And the next morning I got what I think is the best compliment I have ever received: the father of a 10th grader said his daughter was so inspired by my talk she is thinking of going into physics & quantum mechanics. “Here’s my email; tell her to feel free to follow up!” Yes!

Capclave 2019 — Talks & Panels

I’m appearing at Capclave this year (October 18th thru 20th), doing my talk on Time Dispersion in Quantum Mechanics (3pm on Saturday the 19th) and five panels, all great topics: Technospeed, Coming Civil War, Failure of SF Prediction, Secrets of the Dinosaurs, & Exoplanets. Prep for these will be a lot of fun. And the other panelists include a number of old friends and I’m sure some new ones.

Capclave — always one of the best organized cons — did a great job on the schedules, sliced & diced by time, track, & trouble-maker. I can’t improve on theirs for me:

Friday 9:00 pm: Technospeed (Ends at: 9:55 pm) Truman
Panelists:John AshmeadMartin Berman-GorvineBud Sparhawk (M), Christopher Weuve
Is technology moving too far? Too fast? What is coming up in the future? What happens to those left behind? Can people who never learned how to set the time on their VCRs handle what brain-implants and whatever else is coming next? Is this increasing the generation gap?
Saturday 10:00 am: Coming Civil War (Ends at: 10:55 am) Washington Theater
Panelists:John AshmeadTom Doyle (M), Carolyn Ives GilmanSarena UlibarriChristopher Weuve
Is the U.S. dividing again? Or are current difficulties just an historical burp? Why didn’t the US divide in the 1960s? What can be done to keep the Union together? Or would splitting be a good thing? Will the South rise again or will it be cities versus countryside?
Saturday 2:00 pm: Failure of SF Prediction (Ends at: 2:55 pm) Truman
Panelists:John AshmeadTom Doyle (M), Natalie LuhrsSarah PinskerK.M. Szpara
SF is not really supposed to predict the future but presents possibilities. Still, comparisons are inevitable. What did past SF writers get right and wrong about today? How can writers do a better job (or shouldn’t they even bother trying?)
Saturday 3:00 pm: Time Dispersion in Quantum Mechanics (Ends at: 3:55 pm) Truman
Panelists:John Ashmead (M)
John Ashmead gives a science talk on time dispersion. Is time fuzzy? In quantum mechanics space is fuzzy. And in special relativity time and space are interchangeable. But if time and space are interchangeable, shouldnt time be fuzzy as well? Shouldnt quantum mechanics apply — to time? Thanks to recent technical advances we can put this to the test. We ask: How do you get a clock in a box? How do you interfere with time? When is one slit better than two? And what happens at the intersection of time and quantum mechanics?
Sunday 10:00 am: Secrets of the Dinosaurs (Ends at: 10:55 am) Monroe
Panelists:Robert J. SawyerJohn AshmeadMichael Brett-SurmanThomas Holtz (M)
Did dinosaurs really have feathers? Why did people get it wrong for so long? What else did people believe about dinosaurs 50 years ago that is no longer true? Why did people think that then? What of our present knowledge about dinosaurs is most likely to also be incorrect?
Sunday 12:00 pm: Exoplanets (Ends at: 12:55 pm) Truman
Panelists:John AshmeadInge HeyerEdward M. Lerner (M)
What do we know about planets outside our solar system? How do we discover them? What are the implications for aliens Exobiology?

Time & QM at Balticon 2019

I did my “Time dispersion in quantum mechanics” paper as a popular talk at Balticon 2019 this last Saturday. Very energetic audience; talk went well. The audience had fun riffing on the time & quantum mechanics themes. And gave a round of applause to “quantum mechanics”. That doesn’t happen often. Post talk, I spent the next hour and a half in the hallway responding to questions & comments from attendees. And afterwards I ran into a woman who couldn’t get in because there was no standing room left. I think the audience liked the subject, liked the idea of being at the scientific edge, & was prepared to meet the speaker half way. So talk went well!

Thanks to Balticon for taking a chance on a very technical subject! and to all the attendees who made the talk a success.

So I’m hoping to do the talk for Capclave (DC science fiction convention) & Philcon (Philadelphia science fiction convention) in the fall.

My Balticon talk was basically a translation from Physics to English of my long paper of the same title, keeping the key ideas but doing everything in words & pictures, rather than equations.

Balticon will be publishing the video of the Balticon talk at some point. I developed the talk in Apple’s Keynote. I have exported to Microsoft Powerpoint and to Adobe’s PDF format. The advantage of the two slide presentation formats is that you can see the builds.

The long paper the talk was taken from was just published last week, by the Institute of Physics as part of their Conference Proceedings series. And the week before, I did a fairly technical version of the paper as a virtual (Skype) talk for the Time & Time Flow virtual conference. This is online on Youtube, part of the Physics Debates series.

Is time fuzzy?

Alice’s Past is Bob’s Future. And vice versa. Both are bit fuzzy about time.

“Time dispersion and quantum mechanics”, my long paper — long in page count & long in time taken to come to completion — has just been accepted for publication in the peer-reviewed Proceedings of the IARD 2018. This will be has been published as part of the IOP Science’s Journal of Physics Conference Series.

I had earlier presented this as a talk at the IARD 2018 conference in June 2018 in Yucatan. The IARD (International Association for Relativistic Dynamics) asked the conference participants if they would submit papers (based on the talks) for the conference proceedings. No problem; the talk was itself based on a paper I had just finished. Of course the paper had more math. Much much more math (well north of 500 equations if you insist).

Close review of the talk revealed one or two soft spots; fixing them consumed more time than I had hoped. But I submitted — on the last possible day, November 30th, 2018. After a month and a bit, the two reviewers got back to me: liked the ideas, deplored the lack of sufficient connection to the literature, and in the case of Reviewer #1, felt that there were various points of ambiguity and omission which needed attention.

And right they were! I spent a few rather pleasant weeks diving into the literature; some I had read before, some frankly I had not given the attention that must be paid. I clarified, literated, disambiguated, and simplified over the next six or seven weeks, submitting a much revised version on Mar 11th this year. Nearly ten per cent shorter. No soft spots. Still a lot of equations (but just south of 500 this time). Every single one checked, rechecked, & cross-checked. And a few fun bits, just to keep things not too dry. Submitted feeling sure that I had done my best but not sure if that was best enough.

And I have just this morning received the very welcome news it will be joining the flock of accepted submissions headed for inclusion in the conference proceedings. I am best pleased.

As to the title of this blog post, my very long paper argues that if we apply quantum mechanics along the time dimension — and Einstein & even Bohr say we should! — then everything should be just a little bit fuzzy in time. But if you title a paper “Is time fuzzy?”, you can say farewell to any chance of acceptance by a serious publication.

But the point is not that time might be fuzzy — we have all suspected something of the kind — it is that this idea can be worked out in detail, in a self-consistent way, in a way that is consistent with all experimental evidence to date, in a way that can be tested itself, and in a way that is definitive: if the experiments proposed don’t show that time is fuzzy, then time is not fuzzy. (As Yoda likes to say: fuzz or no fuzz, there is no “just a little-bit-fuzzy if you please”!)

In any case, if you are going to be down Baltimore way come this coming Memorial Day weekend I will be doing a popular version of the paper at the 2019 Baltimore Science Fiction convention: no equations (well almost no equations), some animations, and I hope a bit of fun with time!

The link at the start of this post points to a version formatted for US Letter, with table of contents & page numbers. The version accepted is the same, but formatted for A4 and without the TOC and page numbers (that being how the IOP likes its papers formatted). For those who prefer A4:

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.


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.

WordPress Themes