Roman Jackiw, “Surprising Successes of Field Theory” - LNS46 Symposium: On the Matter of Particles
PRESENTER: Well, it's time to start the afternoon session. Seems to me Lee is giving me too much work to do today, but I'd like to take a few minutes to talk about the Center for Theoretical Physics, which is the title of this session I see. Since everyone is reminiscing, permit me a few minutes of it.
I came back here after having been a graduate student in 1956, the same year that Francis Lowe came from Illinois. At that time, Sidney Drell had been the assistant professor, and I think he had already left. And Felix Villars was here as maybe assistant professor at that time too, plus Viki and Herman and Frances Friedman may have been around. I don't remember that.
But it was a small group, which was very nice. As I remember it as a young man, we didn't interact that much, but it was still a pleasant place to be. But it was small.
In 1960, I went to Paris for a year and had some time to think about things. And I remembered my experience in Copenhagen, where I had been from '54 to '56, and I came back in '61 with the burning idea that MIT wasn't taking advantage of Viki and Herman. I mean, they were the great men, and they had just a few people around them. And there was an opportunity to create something here, and so I started beating on both of them, if I remember, around '62.
It took a few years, but Peter Demos, who was the director of the lab, agreed that it was a good idea, and we started to build up a nuclear group. And then when Viki came back from CERN, we had some success building up the nuclear group-- got some post-docs and so on. And the idea which we had been thinking about to make it into a bigger thing, including both high energy and nuclear, came to fruition. Viki suggested that we really go to the Institute and do something big.
And thanks to his efforts and Herman's, we got the Center started in 1967. The Institute was very forthcoming. It gave us enough money to build that beautiful area that we've got that people were very jealous about, as I remember, and people still do remark on, because it was a nice job architecturally. And it certainly has given us a beautiful home.
Herman was the first director of the Center for some years, and then he became department head after Viki and Francis came in as director. Francis takes the position. I'm not sure he's here, but he takes the position that you stay in a job only a few years, and then you quit.
And then he did, and I became director, and I lasted a lot longer. I'm not taking that position, I guess. He became provost later and took the same position-- stayed for five years, and he was out.
We now have John Negele as director. He's really pulled it together in a way that I think none of us did before in terms of organization and real attention to detail. I think that the idea and the fact that we did it has really paid off. I mean, the Center has published, I don't know, a couple of thousand publications since we started keeping record. And it really has been a center. People have come from all around the world and really very happy about the way it has turned out, and I hope it continues into the future.
We're hearing from people who have been associated with the center this afternoon and who are in it-- some of them. Our first speaker is Roman Jackiw, who's been here quite a while. I really can't remember the date. But it's been a pleasure having him here, particularly for me, because off and on we have collaborated a bit. And it's always been great to have to pay attention to Roman when he would say, well, where's the beef, in everything we ever did. And it's a pleasure to introduce Roman, so he'll speak.
JACKIW: So thank you. The title I chose is Surprising Successes of Quantum Field Theory. And perhaps the greatest surprise about field theory is that today it continues to provide the only framework for discussing successfully dynamical issues of fundamental physics.
I was looking for a numerology that might render significant the peculiar 46th anniversary that we're celebrating, and the only coincidence I could come up with was a sort of dyslexic calendrical one. In 1864 is when historians date the birth of field theory. This is, of course, Maxwell's electromagnetic field theory, which has survived-- indeed, one can say which has precipitated the two revolutions of 20th century physics, relativity and quantum mechanics.
In its quantum version, electromagnetism has been verified with fantastic precision. And the generalization that electromagnetism suggested the non-Abelian Yang-Mills theory is an ingredient-- together with quark and lepton field theories-- in the standard model of elementary particles. And that field theory-- the standard model of elementary particles-- gives a flawless account of the relevant experimental data up to the present time.
Now, the standard model is the most recent triumph of field theory, and parts of it were put together at MIT at LNS by Steve Weinberg. And he is here, and doubtlessly you will hear from him about that tomorrow, so I need not dwell on it. In fact, the success of the standard model has left very little for quantum field theorists to do in fundamental physics, and some have decamped the subject-- returned to the S-matrix program in its newest incarnation, string theory. Gabrielle Veneziano developed that departure, again, at MIT, LNS, CTP, and he will describe it later.
Other field theorists have turned to unexpected topics. And I want to describe to you here one such unexpected investigation-- an investigation which is unexpected on two counts. First of all, it's unexpected that a particle physicist might work on it. And the second reason it's unexpected is one doesn't even think that a scientist can work on this, but perhaps it's appropriate for this commemorative event.
So to travel into the past-- to observe the past, perhaps to influence it, to correct the mistakes of one's youth-- has been mankind's abiding fantasy for as long as we've been aware of a past. And today, I want to describe to you some modern investigations of this topic, which are being carried out at MIT at LNS.
Now, before the 20th century, time travel was discussed only in works of fiction and among the innumerable authors who are surely familiar-- Mark Twain, H.G. Wells. And in fact, Wells marks a transition. He was a graduate of London's Imperial College of Science and Technology. And because of this 19th century scientific enthusiasm, he couched his novel The Time Machine in a scientific language, and this gave us an early work of science fiction. So Wells marks the transition between fiction and science.
After 1900, it became possible to discuss time machine scientifically. And the reason it became possible to discuss time machine scientifically was because of the development of special relativity. And the question may be posed in this way-- it makes absolutely perfect good sense, and we would all agree that it makes perfect good sense, to speak of traveling and returning to the same point in space.
But since Einstein tells us that space and time are equivalent, a natural question then is, can we, after a journey, return to the same position in time? If we can return to the same position in space and space and time are equivalent, perhaps it should be possible to return to the same position in time. This question was analyzed and answered, in fact, many years ago. And what is established is first of all recognizing that the space with which special relativity deals-- that is to say the ordinary flat Minkowski spacetime-- it is flat and rigid. And time travel, in fact, is possible, but it requires faster than light velocities.
And one can think of this result-- the result which was obtained, the result that you can travel into the past if you can travel at a velocity faster than light-- you can think of that result as a continuation of the familiar time dilation story-- the familiar time dilation story of special relativity. And that story begins with the statement that if you start from rest, the faster you go, the slower flows time. That statement continues with the observation that if you go at the velocity of light, time stands still. And then the next extrapolation which is mathematically correct is that if you could go faster than the velocity of light, you would go backwards in time.
However, there are no known objects that go faster than light, and therefore, time machines can not be constructed with the physics and engineering possibilities provided by special relativity. However, it should be stressed that there is no logical prohibition against exceeding light velocity. And indeed, physical consistency of a hypothetical world in which there are objects traveling faster than light-- these objects are called tachyons-- the physical consistency of such a world was established.
And even tachyons were looked for experimentally. Experiments were performed to see whether one could find any trace of objects traveling faster than light, and none were found. There are no tachyons, as best as we can tell. Time travel based on tachyons is not possible, and the entire subject was summarized by Gary Feinberg almost 20 years ago late of Columbia University. And that sort of ends the discussion of time travel based on special relativity.
But then we come to general relativity-- again, Einstein's work. And now, the spacetime which was rigid and flat in the special relativistic context-- the spacetime is no longer fixed, and it can take on all kinds of unexpected geometrical shapes. And the nature of spacetime is determined by the matter content of the universe.
And in particular, for some special weird forms of matter, there can be geometries which permit time travel into the past with a velocity that is less than the velocity of light. And if you can find a geometry which permits travel into the past-- the technical phrase is that the geometry possesses closed timelike curves. Closed timelike curves are paths in this flexible geometry of general relativity which permits one to travel into the past at velocities less than the velocity of light.
Now, the first solution to Einstein's theory with closed timelike curves was obtained in 1949 by Godel, and it permits construction of time machines. And this solution which Godel obtained caused great puzzlement. And the reason it caused great puzzlement-- because first of all, there is no experimental evidence of people traveling in time. We don't have any visitors from the future visiting us here in their past.
And second of all, our notions of causality-- which to be sure are already challenged by quantum mechanics, but still they're with us long enough and strongly enough. But they prejudice us against considering geometries with closed timelike curves where effects precede causes. So although Godel's solution was certainly a fact, it caused great resistance in the physics and mathematics community. It encountered great resistance in the physics and mathematics community.
But upon further reflection, it's clear that Einstein's equations of general relativity will always permit some kinds of solutions which possess these closed timelike curves. And the reason for that is because the structure of Einstein's equations-- could you lower that a little bit? Just lower it, yeah. The structure of Einstein's equations is that the distribution of matter determines the spacetime geometry.
On the other hand, we don't really have any a priori ideas about what the distribution of matter should be, so what we could do is run the equation in the other direction. Let's just take that geometry for spacetime which permits a time machine, plug the geometry into the Einstein equations, and come up with a formula for the matter which will support that solution. And in that way, one can say one has found a time machine solution. To be sure, one has found it by construction, but still it is a legitimate bona fide solution of Einstein's equations.
There were reactions to Godel's solution and to all these other possible solutions, and here is Einstein's own reaction. He mentions that Kurt Godel's time machine solution raises for him the problem which he thought about already when he thought of the theory 40 years earlier, and without really being able to resolve the problem-- the problem being, how do you prevent the theory from predicting time machines?
And then just a few years ago, Hawking commented on Godel's solution. And once again, he says Godel presents a solution which is the first to be discovered in which it's possible to travel into the past. This leads to paradoxes. What happens if you go back and kill your father when he was a baby? And then he says what people always say-- it is generally agreed that this cannot happen in a solution that represents our universe.
But Godel was the first to show that it was not forbidden by Einstein's equation. And his solution, as I mentioned, generated a lot of discussion of the relation between general relativity and the concepts of causality. So as you see, our defense-- as well as Einstein's and Hawking's-- against these solutions and against the puzzles that they entail is to assert that they are unphysical. They had to be excluded on physical grounds. But they are unphysical in the sense that one asserts that the matter distribution which gives rise to a time machine geometry-- one simply asserts that the matter distribution which gives rise to a time machine geometry is unphysical.
So Godel, when he found his solution, the matter distribution that he used was a uniform energy density in all of space. And we can, of course, see that that is not the situation in our universe. So in that sense, we can say Godel's solution is unphysical.
These days, one hears of time machines being studied at Caltech by Kip Thorne and his colleagues, and these time machines make use of wormholes. Wormholes is another exotic and presumably unphysical form of matter where there is a tiny little channel in spacetime that connects the past and the future. And through this channel, there runs a closed timelike curve. And once again, one could say, well, mathematically that's true. That peculiar form of matter implies time machine geometry. But one could say on physical grounds, perhaps we can exclude that. After all, we don't really see any evidence for such wormholes.
Now, the reason for the current activity in this subject derives from the recent realization that another form of matter called cosmic strings supports closed timelike curves. So first of all, I have to tell you, what are cosmic strings? Now, cosmic strings are hypothetical but entirely physical structures that may have survived from a cosmic phase transition and can be responsible for the present day large scale structure in the universe.
Only completely conventional physical ideas are relied upon in cosmic string speculations, and completely conventional astrophysicists and cosmologists make use of these ideas in building theories. Some astrophysicists occasionally even report sightings of cosmic strings, but thus far, evidence has been inconclusive. Nevertheless, one could not view cosmic strings as unphysical. The fluctuations in the temperature that lead to the Harrison-Zel'dovich spectrum that's so much talked about these days-- cosmic string proponents maintain that cosmic strings can give rise to that, and that can be another example of the physical acceptability of the concept of cosmic strings.
And therefore, if indeed cosmic strings give rise to closed timelike curves, there is something new that we physicists have to confront and explain, because we would not want to say that cosmic strings are an unphysical form of matter. So the first thing I have to do for you is to describe to you in a little bit greater detail the geometry of space and of spacetime that is caused by cosmic strings.
And we'll think of a cosmic string as a kind of defect-- like a vortex line in space, let's say along the z-axis, and this is like a defect. It's like a defect in helium which survived after a cosmic phase transition. But it sits in the universe there, and it has a certain mass density per unit length. And if it has that mass density per unit length, we can then say it's a form of matter. We can stick this form of matter into the Einstein equation and determine the geometry of spacetime that this form of matter creates.
And the geometry of spacetime that it creates is in fact very simple. There is no structure in time, so I didn't even bother drawing the time axis here. Along the axis of the cosmic string, also there is no structure. The only interesting structure is in the plane perpendicular to the cosmic string, and the structure in this perpendicular plane is very interesting indeed. In fact, that plane is flat. It's just like the surface that I'm standing on here.
However, if you go around the cosmic string, you don't go around to 2 pi degrees, but you go around less. There is a certain amount of missing space which this cosmic string causes, and this missing space-- the angular amount of space which is missing-- is proportional to the mass per unit length of the string. So that is the geometry of a cosmic string.
And in a sense, it's analogous to the physics and the presence of a constant magnetic field. You know that charged particles moving in a constant magnetic field along the z-axis have non-trivial motion really only in the plane perpendicular to that z-axis. And one can just focus on the physics in that plane. And that kind of focus is the subject of Landau theory, of the quantum Hall effect, of high-TC superconductivity.
Well, an analogous story can be told gravitationally. And there, the cosmic string plays the role of the magnetic field, and then the interesting physics is confined to the plane perpendicular. And the only interesting thing about that plane is that even though it is flat as if there were no cosmic string, there is some amount of missing space.
Now, in the next transparency, I'm going to draw the spacetime. And now what I've done is I've suppressed the z-axis. I can't draw four axes on a plane, so I've suppressed the z-axis.
Here is the cosmic point now. That's what's left of the cosmic string. Here is time as I promised you. It's sort of structuralist. It just goes up and down. And here is the plane perpendicular with its missing deficit angle, and here is the world line of the cosmic string provided it's stationary-- so it's not moving. It just stands at the same place, and time flows nicely and uniformly.
Now, this is a spinless cosmic string. The only attribute this cosmic string has is mass per unit length. But now we could give the cosmic string another attribute. We could also give it some spin. So we now contemplate about a cosmic string that is not only carrying a mass per unit length, but carries a spin per unit length.
And then we ask, what is the space time that such a spinning cosmic string produces? And that spacetime is a picture very similar to the previous one, except time-- where before was just freely flowing from minus infinity to plus infinity-- now acquires a helical structure. And the pitch of this helix is proportional to the spin per unit length.
Now, this becomes rather technical and mathematical. Here is not the place to give the detailed account. Just let me assure you that this helical structure has the consequence that it is possible to find closed timelike curves, and it is possible to construct time machines. So spinning cosmic strings give rise to time machines, and this is a result which was established actually some years ago.
And a result which one can still escape from, because one can say, well, although cosmologists make use of cosmic strings, they only make use of spinless cosmic strings. And we could say that a spinning cosmic string is unphysical. And consequently, once again, there's no real reason to think about these closed timelike curves that are created if you have a spinning cosmic string.
However, last year, Richard Gott at Princeton asked the following question. Suppose you have two cosmic strings, each one spinless, but each one moving with a velocity relative to the other so that the entire system possesses angular momentum. It is to be understood that what caused the closed timelike curve was the angular momentum. And in the first example, the angular momentum was simply carried on that single string as intrinsic spin, and that maybe is unphysical.
But now, we're going to have spinless strings that all the cosmologists would like to have, and we're going to let them move, which we didn't do before. Certainly, the cosmologists want their strings to move. And once this string is moving, then there's going to be angular momentum in this system. And the question arises, will there be a closed timelike curve, and will this allow the construction of a time machine?
So here is a very schematic drawing. Here is one cosmic string, here's another cosmic string. Here is the missing space of one, here is the missing space of the other. And now, it shouldn't come as a surprise if I tell you that if a light path goes from A to B, this is sort of the direct line. Then another light path which goes from A to B but surrounds the cosmic strings, and consequently doesn't really have to traverse this missing region of space because this space isn't there, then another light ray going on this surrounding path can beat this light ray.
And in fact, this is possible. Detailed analysis of this geometry shows that you can beat a light ray. And having beaten a light ray, you can construct a closed timelike curve. And once you can construct a closed timelike curve, you can build a time machine. And so Mr. Gott correctly pointed out that two cosmic strings moving with a certain velocity will produce a closed timelike curve.
But of course, the velocity has to exceed a certain minimal velocity. Because we know, for example, that if the cosmic strings are standing still and spinless, then nothing will happen. So this there is a critical velocity that has to be exceeded, but this critical velocity that each string has to exceed is less than the velocity of light. And therefore, it appears that one can construct a time machine using completely acceptable physical ideas and constructs.
Now, this discussion by Gott produced great interest, because for the first time, the question of time machines became scientifically physical and only awaited the development of engineering possibilities. And the accounts of this were carried in the popular and semi-popular press. Only this New Scientist and Science are really accurate. The others make it sound as if it's going to be built very soon.
The practical applications and financial possibilities were discussed. However, also a business pitfall in commercial development was noted in the syndicated press. And then we decided that since the subject was so interesting and so provocative, we should look into it further.
Now, there is, of course, a catch, and it's interesting to find where the catch is. What happens is the following-- one needs a pair of moving strings, and each of the pair is non-tachyonic-- is moving with a velocity less than the velocity of light. But you can ask, what is the center of mass energy of the pair? So you have to add up the energies of the individual strings.
Now, the concept of energy is a concept which is a conserved quantity, which arises from the fact that spacetime allows translations. And because it allows translations, you have the concept of energy. But when the spacetime is as chewed up as it is in the presence of cosmic strings, the concept of energy still exists, but the addition laws for combining it are highly non-trivial and highly non-linear.
And consequently, when you add the energies of the individual non-tachyonic strings, you discover that the total energy is that of a tachyon. And therefore, even though the Princeton construction was mathematically correct, it once again belongs into that category of constructions which makes use of a math or distribution which is unphysical. Why is it unphysical? Because even though each individual cosmic string is non-tachyonic, the assembly of two is tachyonic.
And consequently, they could never be produced. You might imagine, for example, producing these cosmic strings by the decay of something else. And of course, they cannot be produced moving at that high velocity, which is required for closed cosmic strings.
So that is the catch. There's the obstacle to Gott's time machine. When the velocity of light exceeds this critical velocity, we can not do it in our non-tachyonic world. This was further investigated by further colleagues at LNS and our frequent collaborator, Gerard 't Hooft, and confirming that-- for the time being at least-- we are still safe from time machines. And the most recent string-inspired attempt at violating causality doesn't survive.
Now, further questions remain and motivate further study. And one can ask, why is one actually studying this kind of subject? And the first answer-- the kind of more highfalutin answer-- is that the concept of time is very poorly understood in fundamental physical theories. We don't know what gives time its observed direction.
Indeed, the whole notion of time is puzzling in the context of general relativity, which tells us that the spacetime is unknown until the matter distribution is known, and the matter distribution determines the spacetime. So one wonders, what is time before one has the matter? One hopes that studying puzzling aspects of the theory-- like these time machines-- will somehow give us some clues about the nature of time in physical theory.
But actually, another reason was the same one I mentioned at the beginning-- that there is, in fact, very little to do that is interesting in fundamental physics owing to the successes of the standard model. And therefore, at the present time, some of us are studying time itself. Thank you.