So what happens to the effective field theories of electroweak, strong, and gravitational interactions at energies of order 10<sup>15</sup>–10<sup>18</sup> GeV? I know of only two plausible alternatives. One possibility is that the theory remains a quantum field theory, but one in which the finite or infinite number of renormalized couplings do not run off to infinity with increasing energy, but hit a fixed point of the renormalizable group equations. ... The other possibility, which I have to admit is a priori more likely, is that at very high energy we will run into really new physics, not describable in terms of a quantum field theory. I think that by far the most likely possibility is that this will be something like a string theory.
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Traditionally, fundamental theories of nature have had a tendency to break down at short distances. This often signals the appearance of new physics that is discovered once one has experimental instruments of high enough resolution (energy) to explore the higher energy regime. Before asymptotic freedom it was expected that any quantum field theory would fail at sufficiently high energy, where the flaws of the renormalization procedure would appear. To deal with this, one would have to invoke some kind of fundamental length. In an asymptotically free theory this is not necessarily the case — the decrease of the effective coupling for large energy means that no new physics need arise at short distances. There are no infinities at all, the bare coupling is finite — indeed it vanishes. The only divergences that arise are an illusion that appears when one tries to compare, in perturbation theory, the finite effective coupling at finite distances with the vanishing effective coupling at infinitely short distances.
Thus the discovery of asymptotic freedom greatly reassured one of the consistency of four-dimensional quantum field theory. One can trust renormalization theory for an asymptotically free theory, independent of the fact that perturbation theory is only an asymptotic expansion, where it gets better and better in the regime of short distances.
If grand unified theories are correct, we ought to be able to derive the relative power of the strong, weak, and electromagnetic interactions at accessible energies from their presumed equality at much higher energies. When this is attempted, a wonderful result emerges. ...in the form first calculated by Howard Georgi, Helen Quinn, and Steven Weinberg ...The couplings of strong-interaction gluons decrease, those of the [weak interaction] W bosons stay roughly constant, and those of the [electromagnetic interaction] photons increase at short distances [or high energies]—so they all tend to converge, as desired.
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... It was (in part) Gross’s excessive enthusiasm for string theory in the mid-80s that drove me (as an impressionable grad student at Princeton) away from theoretical physics (and into astronomy). String theory may have been a beautiful idea, but it made no predictions that could be tested experimentally in the then-foreseeable future. That’s not science. A quarter century later and the theoretical physics community has yet to wake up and realize that there is new physics right under their noses – just not the new physics they’ve been expecting (GUTs, strings, membranes, etc.). Galaxy dynamics are consistent with a single, universal force law, but this unexpected behavior has largely been ignored because it doesn’t fit with particle theorists’ dreams of super symmetric dark matter particles. That we do not understand the observed behavior makes it more interesting than the “expected” (but unobserved) new physics: who ordered this?
Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered.
The chance is high that the truth lies in the fashionable direction. But, on the off-chance that it is in another direction — a direction obvious from an unfashionable view of field theory — who will find it? Only someone who has sacrificed himself by teaching himself quantum electrodynamics from a peculiar and unfashionable point of view; one that he may have to invent for himself.
In the early 1960s there existed a successful quantum theory of the electromagnetic force (QED), which was completed in the late 1940s, but the theories of the weak and strong nuclear forces were not yet known. In UC Berkeley, where I was a graduate student during the period 1962 – 66, the emphasis was on developing a theory of the strong nuclear force. I felt that UC Berkeley was the center of the Universe for high energy theory at the time. Geoffrey Chew (my thesis advisor) and Stanley Mandelstam were highly influential leaders. Also, Steve Weinberg and Shelly Glashow were impressive younger faculty members. David Gross was a contemporaneous Chew student with whom I shared an office.
No other theory known to science [other than superstring theory] uses such powerful mathematics at such a fundamental level. ...because any unified field theory first must absorb the Riemannian geometry of Einstein's theory and the Lie groups coming from quantum field theory... The new mathematics, which is responsible for the merger of these two theories, is topology, and it is responsible for accomplishing the seemingly impossible task of abolishing the infinities of a quantum theory of gravity.
Ten years ago, it was common (and correct) to distinguish the two main approaches to by saying that string theory ... was perturbative, and background dependent while the other approach ... was non-perturbative and background independent. In light of this, it is not surprising that most relativists were not interested in string theory. …
One of the main things that has changed over the past decade is that we now know that string theory does not just involve strings. Higher (and lower) dimensional objects (called s) play an equally fundamental role. Using these branes, convincing evidence has been accumulated that all five of the perturbative string theories are just different limits of the same theory, called . (There is no agreement about what the M stands for.) There is yet another limit in which M theory reduces to eleven dimensional .
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It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory.
Why are the theories of physics so similar in their structure?
There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon, we try to fit it into the framework we already have—until we have made enough experiments, we don't know that it doesn't work. So when some fool physicist gives a lecture at UCLA in 1983 and says, “This is the way it works, and look how wonderfully similar the theories are,” it's not because Nature is really similar; it's because the physicists have only been able to think of the same damn thing, over and over again.
Another possibility is that it is the same damn thing over and over again—that Nature has only one way of doing things, and She repeats her story from time to time.
A third possibility is that things look similar because they are aspects of the same thing—some larger picture underneath, from which things can be broken into parts that look different, like fingers on the same hand. Many physicists are working very hard trying to put together a grand picture that unifies everything into one super-duper model. It's a delightful game, but at present time none of the speculators agree with any of the other speculators as to what the grand picture is.
Why are all the theories of physics so similar in their structure?
There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon we try to fit it into the framework we already have-until we have made enough experiments, we don't know that it doesn't work.
Another possibility is that it is the same damn thing over and over again-that Nature has only one way of doing things, and She repeats her story from time to time.
A third possibility is that things look similar because they are aspects of the same thing- some larger picture underneath, from which things can be broken into parts that look different, like fingers on the same hand. Many physicists are working very hard trying to put together a grand picture that unifies everything into one super-duper model. It's a delightful game, but at the present time none of the speculators agree with any of the other speculators as to what the grand picture is.
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