It's About Time
Quantum Time Conference
March 2829, 2014
::: More photos
::: Conference page
The opening talks of a conference are usually the ones that lift my thoughts above mundane annoyances into the subject of the conference. It was not to be that way with our conference on time in quantum mechanics. The evening and morning prior to the conference were filled with time in relativity and quantum mechanics. By the start of the conference my head was already wellelevated.
The process began the previous evening with an event run by the Department of History and Philosophy of Science. Each year the Department invites an alumnus or alumna to return in triumph to give a talk. It is a proud moment for everyone. This year's speaker was Tim Maudlin and his topic was "Topology and the Structure of SpaceTime."
His idea is a simple and intriguing one. We normally set up a spacetime theory by starting with a manifold of point events. That is just a set of events that have been assembled loosely into somewhat amorphous neighborhoods ("open sets"). That assembly takes no notice of which direction in the manifold will be time and which will be space. The division comes later.
That indifference is what bothered Tim. The assemblages should be chosen at the start to reflect something physical in spacetime, he insisted. Why not assemble the events into lines that will later reflect the spacetime trajectories of points moving in space?
That simple idea seeded the rebuilding of spacetime theories using linear structures, as opposed to the familiar manifolds.
This description so far is of a dry technical gadget in mathematics. It quite masks the raw enthusiasm of Tim's presentation. He was not just relating a simple modification to spacetime theories. Tim was recounting a great journey of personal discovery and his astonishment as slight, but natural, modifications to his linear structures unexpectedly delivered key elements of relativistic spacetime geometry.
Perhaps the most exciting of these was his recognition that fixing the temporal structure is sufficient to return the spatial structure of spacetime in the relativistic case.
Time is fundamental.
The following morningthe morning of the conferenceis all about time again. It is Tom Pashby's dissertation defense in the Department of History and Philosophy of Science. His topic is time in quantum mechanics.
If you have never been to one, it is easy to imagine a dissertation defense as a moment of life or death. The name already suggests mortal conflict. We have a doctoral student who has labored for years to produce a great work or, perhaps, something less. That is what is to be decided.
The work is presented humbly to a lofty committee whose charter is to assail it, to test it, to weigh it, while the candidate defends. The event is public and has been advertised. Anyone can walk into the room to watch. It begins to sound like the ceremonial testing of an accused witch. She is thrown into the water. If she floats, the water has rejected her and she is a witch. If she drowns, well, good... she was no witch.
Of course real dissertation defenses are not such precarious affairs. No supervising committee with any humanity allows a candidate to proceed to a defense if there are serious doubts. A failing defense would be an embarrassment for both the candidate and the committee.
We all know this, but the importance of the moment is hard to ignore. The previous evening, at Tim's talk, I'd been looking for Tom, just to make sure he was ready. He was nowhere to be found. One of the graduate students reported that he was still preparing and promised to bring him in on time.
The defense itself was lively. After Tom's warmup speech, John Earman announced he had fifteen questions. That is as many as I've heard him ask in all the defenses of the last decade. ("Shall we send out for coffee?" I quipped.) Whether a scripted ritual or not, Tom really must defend. And he did, with great thoroughness. He passed without reservation from the committee.
It is no accident that Tom's dissertation topic coincides with the conference topic. There has been an explosion of work on time in quantum mechanics. Tom's work and, a few year's before him, Bryan Roberts' work have been Pittsburgh's contribution to this new literature. The idea of the workshop is to bring together people working on the topic. Bryan and Tom, along with Giovanni Valente, formed the program committee for the conference.
It is a strict rule of the dissertation defense that the examining committee must be present physically. The occasion of the conference was just the occasion to assemble the committee.
At midday, as the start of the conference neared, I cruised round the Center, noticing that everything was prepared and in order. I scanned the name tags to remind myself who had registered. I noticed one unexpected name.
The first speaker, Valia Allori, had the difficult task of setting up the problems of time in quantum theory. She must speak to a room presumed to hold novices, while at the same time, she can see leading experts on precisely the topic of her talk.
Valia reminded us of the awkwardness of the uncertainty relations. There is a reciprocal indefiniteness in position and momentum in elementary quantum theory. A mechanical translation of it should lead to a corresponding reciprocal indefiniteness in time and energy. But a precise expression of such a relation had proven elusive.
Perhaps the strongest statement of the problem of time in quantum theory came in the form of three propositions, each individually innocent in appearance, but jointly inconsistent.
First is the identification of physical quantities with selfadjoint operators in quantum mechanics. This identification has been quite standard since the 1930s and one of the first things a new quantum mechanic learns.
Second is the difficulty that there is no such operator for time.
Third is the fact that times are routinely measured, and with astonishing precision, at least if one has an atomic clock at hand.
Take all three together and we have a problem.
While Valia laid out this conundrum, I was watching Tom. This conundrum is precisely the one addressed in his dissertation. I could see him listen for a while and then take a few notes on his computer and then listen some more. I needed no telepathy to know what he was thinking. This sets up his talk the next day perfectly. He has answers, and lots of them!
The conference proceeded with a rich array of material. The technical level of the expositions was quite high and a novice philosopher, meandering into the event, would be lost (as was I in many places).
So one would expect these to be serious proceedings. Of course there will be lighter side remarks, injected only to aerate the weighty dough of technical physics. Things didn't quite go that way. Some of the results presented were striking, surprising and unexpected. Humor and the unexpected go hand in hand. That we didn't see it coming is precisely what makes the joke's punch line funny.
We had technical results whose unexpected character had that form. Laura Ruetsche promised to recover the real time of our experience through the "thermal time hypothesis." It was all tied up with a one parameter family of automorophisms and the restriction of the quantum vacuum state to the Rindler wedge of spacetime, picked out by uniformly accelerating observers. That is weighty dough for anyone.
It issued in an airy theorem that one could not have expected:
"An omniscient deity is timeless."
And the best part is that it made perfect sense.
Perhaps the most striking example of the unexpected was Louis Kauffman's talk. He began by pointing to a finite sequence of states in discrete time, X, X', X'', ... With some quick and innocent manipulations, the formulae at the heart of quantum theory appeared on the blackboard. It was startling.
That was just the beginning. We began to drift and soon we were looking at knot theory and nonstandard set theory. He showed us a loop that doubles over itself. This is a set that is a member of itself, Louis told us. And here, pointing to two interlocked rings, are two sets that are each members of each other.
As this performance proceeded, we found ourselves smiling and then smirking; and, from time to time, we turned to each other to see if we were the only ones.
Finally it was time for Tom's talk. I had been looking forward to this. I knew that Tom had a wellworked out account that answered the worries Valia had so carefully expressed.
Tom began by describing the curious blind spot in our physics. When we shoot particles through slits at screens, we worry endlessly about how their arrival is distributed in space. But we give little thought to the timing, even though it is just as important and just as accessible experimentally. We have to find a way that treats these times well.
Tom proceeded to show how it can be done and, given certain theorems, how it might even have to be done. The key idea is to replace the assured localization of systems to intervals of space and time, by a slightly weakened one that allows them to leak out into tails. Do that and the contradiction Valia described can be avoided. (Technically speaking, we replace PVMs, projection valued measures, with POVMs, positive operator valued measures.) This, Tom then showed, could be effected if we replace our normal three dimensionalspace picture of the quantum state by a picture of the state extended into four dimensional spacetime.
It was easy listening for me. I'd just finished reading a dissertation that laid it all out in great detail and I'd just been at the defense. Question time revealed that not everyone had found it quite so easy. There was a protracted discussion of just how a POVM can do what Tom said it could do.
Conference exhaustion was now setting in for me. However there was one major event to come. Abhay Ashtekar, a noted physicist from Penn State, had agreed to keynote the conference. He would have been entirely within his superstar rights if he had decided just to breeze in and make a celebrity appearance. He did not do that. Abhay came to the first talk and to all of them. He sat listening intently and repeatedly offered penetrating questions and remarks. I soon found myself asking "Yesthat sounds fine, but what does Abhay think?" And soon enough I found out!
When the time for Abhay's own presentation arrived, so did some of his more notable colleagues.
Abhay's presentation was a tour de force. The plan was to survey some topics in cosmology, making contact with as many as he could of the ideas concerning time in quantum mechanics that he'd seen in the conference. By the end of his talk, he'd done that. He had also given us a survey of loop quantum cosmology and covered both the blackboard and whiteboard with detailed formulae and diagrams.
We passed through question time and then on to the general discussion promised at the close of the conference. There were many questions in the general discussion. They all went to Abhay
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John D. Norton
