What is Space and Time in String Theory?

[david findley]

--I understand that the original basis of string theory was as explanation for the ontological origin quanta .

I have a few questions:

1) What is the origin and material make-up of the string? (How can we avoid the metaphysical pit-fall of an infinite regress in regards the ontological origins of fundamental elements?)

2) How is Space and Time defined ?

3) How do strings relate to the Big Bang ?

Thank you =)


(Edit)

It is also important to make a logical analysis of string theory:

An argument is only logically valid and sound if the conclusions follow from true premises. Premises in string theory are indefinitive . Therefore, until string theory can come to definitive conclusions regarding such basic elements as Space and Time, (and even its own ontology,) then all of the conclusions stemming therefrom are both invalid and unsound.

I would like to inquire into the possibility that the plausability of string theory has been grossly exaggerated by inventive mathematics and popular culture. Further, it seems that logically baseless introductions (ie 'gravitons',) have rendered the the general theory absolutely ridiculous--

if that which is strictly illogical may be considered 'ridiculous'.

 

[mitchell porter]

We should distinguish between the mathematics of string theory, the ontologies that physicists use informally in order to make sense of it, and the unknown true ontology of the world.

Physics is still dominated by the picture of reality developed by Kepler and Galileo, according to which we distinguish between "primary properties" like location, shape, and duration, and "secondary properties" like color, taste, and smell. We describe the world of primary properties in a quantitative way, using geometry, calculus, etc., and the secondary properties we just ignore. Physics also employs more concrete concepts like force, energy, etc, but even they are conceptually anchored by their quantitative relations to other physical quantities, and not by a particular metaphysics.

Point masses interacting according to Newton's law of gravitation can serve as a paradigm example of this physical ontology. Such a world can be described by a set of functions showing how the positions of the point masses change over time. You may try to interpret or complete the ontology using some concepts of substance and cause, but the theoretical essence is in the type of mathematics employed - trajectories through an "R^3" space (three-dimensional, with real-number coordinates), which obey a differential equation.

To this abstracted and geometrized description of the world, quantum mechanics adds probability and uncertainty. Instead of exact trajectories, quantum mechanics has wavefunctions which provide probabilities for all the possible particle locations. In general, a quantum theory always has this feature: it has "observables" which are the effective ontology of the theory, but the mathematics of quantum theory only describes the state of the world indirectly, by offering a probability for each possible value of an observable, rather than an exact deterministic description as in the classical theory.

String theory is a quantum theory of "strings" and "branes" in a multi-dimensional space-time. So we have extended objects that are vibrating, splitting, and joining, and this dynamics itself is only being described probabilistically.

I believe most string theorists would think of the theory in this way - strings moving through Einstein's space-time, in a quantum way. There may be a few who implicitly use some other ontological framework to make sense of their work. There may be quite a few who hope that string theory will reveal to them a whole new ontology deeper than Einstein's concept of space-time. But the common reference point among string theorists is a certain mathematics which is used to describe e.g. the probable amount of energy concentrated in a particular vibrational mode of a string.

Now let's consider your questions.

1) What is the origin and material make-up of the string? (How can we avoid the metaphysical pit-fall of an infinite regress in regards the ontological origins of fundamental elements?)

2) How is Space and Time defined ?

3) How do strings relate to the Big Bang ?

The important question is number 2. Until such time as string theory yields a space-time concept of its own, it should be understood in terms of Einstein's concept of space-time, i.e. special and general relativity. You need to understand those first before you can understand string theory.

Question number 1, the "material make-up of the string": Recall that a certain mathematical description is the essence of the theory. In the classical theories, the essence of a point particle is that it is described by a single coordinate point in a continuum space. Analogously, a string is a "curve" in such a space. Existing string theory is effectively agnostic beyond that. You are free to propose any sort of ontology you wish, as being the true ontology of string theory. The minimum requirement is just that your ontology contains entities described by the mathematics actually employed in string theory.

Question number 3, how do strings relate to the Big Bang? The Big Bang is the beginning of time in Einstein's theory of gravity before you add quantum mechanics, a point at which, extrapolating backwards, the energy density of the universe would have been infinite. String theory does not yet adequately describe such spaces, just flat spaces and "anti de Sitter" spaces (though people are certainly working on cosmologically realistic spaces as well). So we don't really know whether a realistic string-theory cosmology, extrapolated backwards, also begins with a moment of infinite density, whether there's a "bounce" from a preceding period of collapse, or whether some other possibility is implied, such as the universe starting from a small loop in time (Gott and Li) rather than from a "first moment".

It is also important to make a logical analysis of string theory:

An argument is only logically valid and sound if the conclusions follow from true premises. Premises in string theory are indefinitive . Therefore, until string theory can come to definitive conclusions regarding such basic elements as Space and Time, (and even its own ontology,) then all of the conclusions stemming therefrom are both invalid and unsound.

I would like to inquire into the possibility that the plausability of string theory has been grossly exaggerated by inventive mathematics and popular culture. Further, it seems that logically baseless introductions (ie 'gravitons',) have rendered the the general theory absolutely ridiculous--

if that which is strictly illogical may be considered 'ridiculous'.

It's a small point, but your definition of logical validity is somewhat backwards. Logical validity is independent of the truth or falsehood of an argument's assumptions. It is logically valid to say "If all horses are purple, then no horses are white", even though the premise is false, because saying that an argument is logically valid is a statement about the internal validity of the chain of reasoning.

This matters for how we assess physical theories. Physics today has not proceeded by determining necessarily true ontological facts, and then deducing their implications. It proceeds by hypothesis, deduction, and experiment. We say: suppose there are a set of fields obeying a certain equation - what would that imply? We figure out what it would imply, and then we test this against observation. - In reality, the back and forth between theory and experiment is not so systematic. Nonetheless, physics today is about experimentally testing hypotheses that can be stated mathematically.

String theory, both as mathematics and as a physical hypothesis, is a work in progress. We know that mathematically, you can describe a zillion possible stringy worlds, distinguished by the shape of their extra dimensions. It is logically possible that one of them would match experiment exactly. We have also discovered (this is "AdS/CFT") that some field theories, resembling the real world in certain respects, are equivalent to string theories - they are two descriptions of the same thing. This makes it even more plausible that the real world has a string-theory model, though we really need to get a proper string-theory answer to the question about the Big Bang, to say that it's fully realistic.

Most of these statements are at the level of the mathematical theory, which as I said is understood informally using an ontology combining quantum uncertainty with Einstein's space-time. Presumably there is a better, deeper ontology. But good luck trying to work it out by pure logic alone.