Posts tagged: Quantum Mechanics

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

Philcon 2019 — Precap

Lagrange's tightrope, balancing kinetic & potential energy
Working out the effects of quantum mechanics on time requires a delicate balancing between kinetic & potential energy; Lagrange showed the way

The Philcon 2019 schedule is up. I’m doing my Time Dispersion in Quantum Mechanics talk — the tightrope walker is one of the slides, gives you a sense of the style of the whole, balancing ideas against math, time against space, classical against quantum, … — and four panels, all interesting. The con runs from Friday 11/8/2019 through Sunday 11/10. Details:


Fri 8:00 pm. John Ashmead (mod), Earl Bennett, Dr. H. Paul Shuch, John Skylar. What’s the latest evidence that we’ve found? Where are the best places to look?


Sat. 4:00 PM. John Ashmead. We know from quantum mechanics that space is fuzzy- that particles don’t have a well-defined position in space — and we know from special relativity that time and space are interchangeable. So shouldn’t time be fuzzy as well? Thanks to recent technical advances in measurements at “short times” we can now put this to the test. Discuss!


Sat 5:00PM. John Ashmead (mod), Charlie Robertson, Rebecca Robare, Dr. H. Paul Shuch, Carl Fink, Lawrence Kramer. Niels Bohr famously said, “Your theory is crazy but it’s not crazy enough to be true”. How do we keep an open mind but not one so open that our brains fall out? A look at how to tell strange-yet-true science from weapons grade balonium.


Sat 7:00 PM Darrell Schweitzer (mod), John Ashmead, Tom Purdom, James L. Cambias, Earl Bennett. How have depictions of Mars changed in SF from the imaginings of Burroughs and Bradbury to the Mars we know now from studying its surface?


Sat 9:00 PM Hildy Silverman (mod), John Ashmead, Karen Heuler, B. Lana Guggenheim. No one should be surprised that climate change, technological over-reach, and political anxieties have translated themselves into a bumper crop of contemporary dystopian fiction. How coherent are their messages — and how good are the stories? Is there a way to make such a work more than a cautionary tale about the present era’s problems?

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!

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.

Why quantum time?

Why quantum time?

A few years ago I was looking for an interpretation/formalism for quantum mechanics which would be manifestly symmetric between time and space. The first question I had was:

Is time already quantized?

Is time treated using the same quantum rules as space is? can quantum mechanics be written in a way which is manifestly covariant?
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The Block Universe

fmany of

‘Can a cube that does not last for any time at all, have a real

Filby became pensive. ‘Clearly,’ the Time Traveller proceeded, ‘any
real body must have extension in _four_ directions: it must have
Length, Breadth, Thickness, and–Duration. But through a natural
infirmity of the flesh, which I will explain to you in a moment, we
incline to overlook this fact. There are really four dimensions,
three which we call the three planes of Space, and a fourth, Time.
There is, however, a tendency to draw an unreal distinction between
the former three dimensions and the latter, because it happens that
our consciousness moves intermittently in one direction along the
latter from the beginning to the end of our lives.’Clearest.

‘Clearly,’ the Time Traveller proceeded, ‘any real body must have extension in four directions: it must have Length, Breadth, Thickness, and–Duration. But through a natural infirmity of the flesh, which I will explain to you in a moment, we incline to overlook this fact. There are really four dimensions, three which we call the three planes of Space, and a fourth, Time. There is, however, a tendency to draw an unreal distinction between the former three dimensions and the latter, because it happens that our consciousness moves intermittently in one direction along the latter from the beginning to the end of our lives.’

– H. G. Well’s The Time Machine

This is still the best single explanation of the idea of the  “block universe”, though Well’s Time Traveller does not use that term. As Julian Barbour puts it his The End of Time: “The objective world simply is, it does not happen. Only to the gaze of my consciousness, crawling upward along the life line of my body, does a section of this world come to life as a fleeting image in space which continuously changes in time.”
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References on Time & Time Travel

Updated 12/2/2009

Recommended popular books on time. All of the authors know their physics; none are mortal enemies of the English language.  Enjoy:
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Five Popular Talks

Over the last ten or fifteen years I’ve done a number of slide talks at Balticon, Philcon, & Farpoint, three local science fiction conventions. A number of these have been relatively heavy on the physics – within the context of a science fiction convention of course – and I thought it might be fun to post them. As Rod Sterling might have put it, presented for your consideration:
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