Expert: Philip Stahl - 9/7/2004

Question
hello there. i was reading about string theories and came across these few paragraphs....

"Is spacetime fundamental?
   
   Note that there is a complication in the relationship between strings and spacetime. String theory does not predict that the Einstein equations are obeyed exactly. String theory adds an infinite series of corrections to the theory of gravity. Under normal circumstances, if we only look at distance scales much larger than a string, then these corrections are not measurable. But as the distance scale gets smaller, these corrections become larger until the Einstein equation no longer adequately describes the result.
   In fact, when these correction terms become large, there is no spacetime geometry that is guaranteed to describe the result. The equations for determining the spacetime geometry become impossible to solve except under very strict symmetry conditions, such as unbroken supersymmetry, where the large correction terms can be made to vanish or cancel each other out.
    This is a hint that perhaps spacetime geometry is not something fundamental in string theory, but something that emerges in the theory at large distance scales or weak coupling. This is an idea with enormous philosophical implications."

of particular interest to me is the last paragraph. can you perhaps give me a little insight as to what the enormous philosophical implications are that the author is referring to? hope this isn't too taxing a question :) thanks in advance for any help you could offer.

Answer
Hello.

The author you cited is not breaking any really new ground for insight, so far as I can see, only rehashing the warp and woof of a controversy that dates at least as far back as the 1940s-50s.

The debate was perhaps first enunciated by Charles Misner and John Wheeler in their paper (in 'Annals of Physics', Vol. 2, p. 525, 1957) wherein they stated:

"Two views of the nature of physics stand in sharp contrast: a)the space-time continuum serves only as arena for the struggles of fields and particles, b) there is nothing in the world except empty curved space. Matter, charge, electromagnetism and other fields are only manifestations of the bending of space Physics IS geometry".

This is probably the gist of what the author you cited was referring to. In his view then, physics is NOT reducible to geometry, because the string "correction terms" at large distance dilute any unambiguous result. (Though to be sure, much the same complaint may be lodged against quantum 'renormalization' techniques which use similar 'corrections' to dispense with unwanted infinities. But, we use them just the same - because for the time being- they provide reasonable results).


Here's the deal: Einstein's theory of gravitation (General Relativity) is based on a mathematical concept - proper time- which is used to define the invariant separation between two events. Every other physical concept in the theory is derived from it.

To get proper time, one needs a near perfect 'clock' (or something doubling as such, e.g. hyperfine transitions in atoms, frequency of light emitted by a particular atom etc.)

Therein lies the rub, since as (Ernst) Mach has noted, such time itself is an abstraction.

"It is utterly beyond our power to measure the changes of things by time...time is an abstraction....It is an idle metaphysical conception"

cf. 'The Science of Mechanics', p. 273, Dover Publications.

In other words, one ends up using an "idle metaphysical conception" to assess an abstraction. Resulting in such frivolous nonsense as "absolute time" - a concept actually debated by serious people, but in the end no more useful than arguing over the number of angels dancing on the head of a pin.


Let's even forget for the moment that fluctuations in gravity on a quantal scale imply fluctations in curvature of space on immeasurably small scales.

What is the point of all this?

Only to show that, in the end, such questions reside more with the realm of philosophy and philosophy is not science.

The great physicist Richard Feynman was one of many to assert that "the sole test of validity for any theory is experiment."

He also noted that it isn't particularly useful to extrapolate to any *assertions of necessity* unless one has measurements to serve as a guide. Else, everything is open - so far as a theory is concerned- unless refuted outright by experiment or actual observations.

Thus, for now, it isn't particularly useful to say "spacetime geometry is not something fundamental in string theory".

Without the measurements one way or other - as opposed to speculations - it's a moot point. In physics, we don't worry about these things.

For now, at the appropriate scales of interest, string theory "works" about as well as quantum renormalization "works".

Neither is perfect, but we aren't after perfect, only obtaining reasonable results by looking at specific problems - often in limited contexts, and with some answers "indeterminate".


Hope this provides some rough answer to your question.