Talk:S-matrix theory

Used to Redirect
S-matrix theory was a field for more than a decade--- it should not redirect to S-matrix, which is a textbook discussion of the S-matrix in field theory.Likebox (talk) 23:15, 25 March 2008 (UTC)

Unsourceable folklore
I put stuff here that's easy to source. But there's some folklore associated with this idea too.

The S-matrix theory is a position which is ultra-ultra-positivist. Normal positivism says a theory should only involve directly observable elements, and should leave out things which are unobservable in principle. Ok, no problem. But we aren't asymptotic beings, we live in space and time. S-matrix theory leaves out every single aspect of our experience as unobservable! To make this proposal, you have to reject everything around you, all the testimony of your senses. You can't talk about thermal green's functions, you can't talk about off-shell anything, you can't talk about your grocery store, you can't talk about your feet! Everything around us, in the S-matrix point of view, is only an uncalculable, indescribable, not-really-existing intermediate state between free cold particles in the infinite past and free cold particles in the infinite future.

How could sane people believe this? There's this folklore argument (Coleman version):

Suppose you have some quantity which is not S-matrix, which you can measure. Consider an experiment which measures and records this quantity. Assemble a robot, a laboratory, and hydrogen bombs from the collision of some free stable particles. Let the robot perform the experiment, and encode all the results in a stream of radio-waves going out to infinity. Then the robot detonates the hydrogen bombs, blowing itself and the laboratory into smithereens. The S-matrix elements which include this collision process must therefore contain all the information about the experimental results in the electromagnetic part, so the S-matrix in fact encodes the result of any conceivable experiment, in principle, and can serve as the fundamental quantity in your theory.

There is no flaw in this argument, but it's completely mad! The conclusion denies the existence of the whole world. I don't know how to say this with enough feeling: the world absolutely must be more than as an intermediate between two asymptotic states. This isn't fuddy-duddy Ludditism, like "I believe in absolute time, relativity must be wrong". If you actually believe S-matrix theory gives a complete description of the world, you belong in an asylum.

The modern rehabilitation of this position is to understand S-matrix theory gravitationally, as holography. Then it is just saying that the local quantities have holographic counterparts at spatial infinity, or on some Busso surface, which are sufficient to reconstruct the local physics. In AdS space you even still have space/time on the boundary, which goes a long way to settling the stomach. This version is more or less mathematically identical, and yet seems radical, but totally sensible. It also explains with the benefit of hindsight why S-matrix theory was at all successful in the first place, especially in describing quantum gravity, which was not the original goal.

But the ultra-radical positivist position, the positivist to the point of nihilist philosophy, was the original thinking in the 1960s. This is obviously, hands down, no contest, the most radical philosophical position ever proposed by anyone, ever, period. But I have never seen any discussions about the philosophy in the literature, except for one tepid quote by Mandelstam, where he says: "It is not completely obvious to me that the S-matrix is everything".

Where's the outrage? The New York Times headline "Physicists call whole world 'intermediate state', all reality is just illusion". The only evidence that there was some outrage is the silent-treatment in the late seventies and early eighties, and the co-opting of string theory without any mention of where it came from. But if the philosophical insanity is the reason for the silence, I don't see any evidence in the literature. A few people just make technical points about how hard the N/D equations were, or how annoying it was not to be allowed to use current commutators.

But this story should be told, somehow. It is possible that there will be sources at one point, considering that nearly everyone involved is still alive, and the conflicts are now entirely historical.Likebox (talk) 06:17, 25 April 2009 (UTC)


 * The silence on this matter may be political, not scientific. The basic message of S-matrix theory is probably popular with religious fanatics -- that nothing is real except how you prepare yourself for eternity. It would make a great motto for a suicide bomber. Perhaps this has been debated by ontologists, such as Atheists in the Center for Scientific Inquiry, Christians in the Templeton Foundation, Jews in the Weissman Wave, etc. 198.228.228.160 (talk) 07:59, 23 April 2013 (UTC) Collin237

How can a single matrix be a representation of a ten-dimensional group?
Basic_principles begins with the statement


 * 1) Relativity: The S-matrix is a representation of the Poincaré group;

Most probably this is some sort of physicists' slang but mathematically I believe this does not make sense: to have a representation of the Poincaré group requires several matrices to represent translations and Lorentz transformations.

Unfortunately I am not a person to correct this - I do not know enough physics for that.

Could anyone please make this more understandable for a non-insider?