Category: Relativity

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!”

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 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.

Invisibility: Theory & Practice

I’ve posted my talk on the Theory & Practice of Invisibility  to ShareShare.  I’ve given the talk at Balticon, FOSSCON, & Capclave, & will be giving it at Philcon in a few weeks.

At Capclave, NASA asked if I would give it at their Goddard Space Center, once the sequester is lifted.  Nice to be asked!

Balticon records the talks in the science track, so at some point a video record should be online.  The last page on SlideShare has the references; I’d start there.

I’m not really sure why I decided to do invisibility for Balticon; Miriam Kelly, who organizes the science track at Balticon, asked me what I was going to talk about this year, & the next morning I woke up knowing the title.  Then there was the awkward few weeks while I tried to attach a talk to the title.

It’s a great subject; the main problem was really to throw enough out that the rest would fit into a 50 minute hour.  Seemed to go OK, lots of questions during the talk & afterwards in the halls.  That’s the real test.

One thing I like about the subject is that it leads in so many directions, among which:

  1. It’s about the math.  One of the limiting factors is just getting enough control over the mathematics of bending light to create the appropriate cloaking effect.  Any subject that borrows math from general relativity in the interests of simplifying itself is complex!
  2. It’s about the money.  The more money, the more transparency! In general, you can make things invisible from specific angles, over specific frequency ranges, to a certain level of quality.
  3. It’s not about the media:  the general approaches for making something invisible are the same for visible light, for radar, for sound waves.  One application under discussion is to make cities invisible from earthquakes:  arrange for the seismic shocks to pass around the city for instance.
  4. The hype to results ratio is still pretty high.  This is normal when an area is just starting; longer term, the most important uses are likely to be ones we haven’t even dreamt of.
  5. Making  things invisible & making them visible are two sides of the same coin, like attack & defense in war, to master either we must master both.
  6. And, finally, while the future of invisibility may not be clear, our motives in studying it are transparent: it’s interesting, potentially profitable, and fun.

 

 

WordPress Themes