Category: Theories of 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?

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 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.

StarGates Jump to FossCon — The Free & Open StarS Convention!

9/3/2017: I have just posted the slides from Fosscon on slideshare.  Comments, questions, problems, & buildable blueprints, all very welcome!

This coming Saturday I’ll be doing the latest revision of my StarGates talk at FossCon, the Free & Open StarS Convention!

(Pay no attention to those who assert this is the Free & Open Source Convention, that is a mere cover story.)

The convention is at International House in Philadelphia, starting at 9am, and is free.  As to my talk:

“Call them Stargates, Jumpgates, Fargates, Hypergates or just an invitation to every pest from the far reaches of the Galaxy to visit, they would be invaluable in helping mankind break free of this solar system.

Are StarGates only a convenient plot device — or could they actually be built? Accordingly to Einstein’s Theory of General Relavity, they are possible — at least in principle.

We will discuss how to glue black holes together to build a wormhole, how to avoid the dangers of spaghettification, radiation poisoning and paradox noise, and just what would it take to build one in practice.”

My talk’s at 1pm.  Hope to see you there!

And there I have you seen!  There was a nice turnout (in the South America room at International House) with a lot of questions.  We finished with a few minutes for additional questions, including my favorites:

What happens if you drag a wormhole through a wormhole?

I congratulated the questioner on the question & he just pointed at his young son sitting next, a lad clearly with a bright future as a scientist!

I had to admit I wasn’t sure, but I suspect it would be bad news for all concerned:  both wormholes, and any spaceships, space stations, or space-persons nearby!

How do you think this might actually be done?

I focused on wormholes because that is far & away the most popular of the approaches.  But if some sort of stargate were ever actually to come to fruition, I suspect a combination of the Einstein-Rosen-Podolsky (EPR) effect and the ideas behind the Krasnikov tube would be at work.  The EPR effect is the spooky-action-at-a-distance Einstein objected to; the Krasnikov tube is an idea of — curiously enough — Krasnikov for laying out a tube of warped spacetime behind your slower-than-light spacecraft.  You’d have to go slower-than-light while laying out the tube, but could use it for faster-than-light thereafter. And as I said in the talk, negative energy & vortices are pretty sure to be involved.



Time to the Power of Tim

Three Time Travel Tales by Tim Powers

Three Time Travel Tales by Tim Powers

This year the guest of honor at Capclave was Tim Powers. (Capclave is the Washington DC Science Fiction convention.) Tim is not only the author of many fine science fiction novels, but a very nice guy.

This turned out to be a good thing, as the initial proposal was to have Tim & I appear together and do something physic-y about his novels.  I have never done a talk with a live author before (dead authors are no problem, I have that down cold), so I was a bit nervous about the whole thing.

But it worked out well:  Tim was very helpful & gracious and when the audience asked him if one of my theories about the time travel in his novel The Anubis Gates was correct he said, essentially, “Now it is.” 🙂

I focused on three of his novels, The Anubis Gates — his first big success (with romantic poets & time-traveling Jackel Gods), Three Days to Never — something like the bastard child of John Le Carre & H. P. Lovecraft, and Medusa’s Web — who can resist the Time Spyders?

One of the distinctive features of Tim Powers working method is that he starts with a place and a time, researches it looking for the curious facts, bizarre details, & strange omissions that point to an unknown but dark reality, then gradually teases out the true story of whatreallyhappened!

“I made it an ironclad rule that I could not change or disregard any of the recorded facts, nor rearrange any days of the calendar – and then I tried to figure out what momentous but unrecorded fact could explain them all.”

So Tim builds his novels from the bottom up. As a result, they tend to differ wildly from each other.  Other authors, once they have got a setting that works, tend to reuse it, Tim builds anew each time.  No ten volume trilogies here!

And he also works out the timelines of all of his critical characters.  At each moment, he knows where each of his on and off stage characters are & what they are up to.  His notes on this are a kind of secret history of the secret history!

He has 20 or more novels out, so I focused on just three, all involving time travel.  And in each the theory of time travel was radically different!  I had a lot of fun linking each up to the corresponding physics and going back & forth about all this with my stage-mate Tim. 🙂

The talk, minus alas, the actual talking, is now up on slideshare.  Download if you will & any questions/comments please let me know!  thanks!



Stargates: The Theory & Practice

Doors and Portals and Stargates, Oh My!

Call them Stargates, Jumpgates, Fargates, Hypertubes or just an invitation to every unwanted pest from the far reaches of the Galaxy to visit, they are absolutely necessary if we are to have the glorious Science Fiction action we desperately need.  But could they actually be built?  We look at what modern physics has to say:  how to glue black holes together to build a wormhole, how to avoid the dangers of spaghettification, radiation poisoning, and paradox noise, and just what it would take to build one in practice.

This was a talk I did at the last Philcon, went over well.  And I had a lot of fun doing it.  I’ve got it up as a talk on slideshare.  And I may do variations on this at the 2017 Balticon & also Capclave.

It is the kind of subject you can go anywhere with!


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