# String theory with points instead of strings, doable?

Gold Member
Could the higher dimensional spaces of string theory be used by point particles? Take the idea of extra dimensions of string theory and use point particles instead of strings.

Point particles need some type of internal degrees of freedom?

Thank you for any help.

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arivero
Gold Member
Indeed a theory of point particles will produce usual SUSY theories and, via Kaluza Klein, some gauge groups very near of the standard model. What you do not obtail are the winding states.

I'm a philosopher and evolutionary psychologist, and certainly not a physicist. Yet, I'm inquiring if the following extremely simple argument I will offer makes any sense to the physics community. It's an attempt to derive the basic idea of Superstring Theory from simple logic:

The argument is based on a simple error of transference of a generic mathmatics concept into physical science. In math, a point on a graph always represents some object of physical reality (ex. a motorcycle driving down the road at x MPH). In the early stages of particle physics, when the physical attributes of the various particles were being discovered, they were labeled "point particles" as a convenient metaphor for, what was, an indescribable entity. Later, the reference became so habitual that the idea that a point must, ultimately, represent some actual physical extension became lost entirely, along with the idea that nondimensional "points" can never really have any place in physical reality.

If it had occurred to someone to consider what would be the "least extension" for any physical entity, the result would have been String Theory. First, since there are many dimensions (from 4 to 26 based on standard and string models), a physical entity of least possible physical extension would, necessarily, be a one dimensional one (and NOT an "unreal" dimensionless point). Second, it must be a one dimensional entity of the least possible length. While laypeople would think there is no such concept, physicists know that "Planck length" is just such a real limit on length. Thus, a "real" entity (beyond a purely mathmatical concept) of "least possible extension" is necessarily a one-dimensional entity of Planck length ----Viola! A superstring!

Another way to state it is that, if there could possibly be something simpler in the universe (with at least some component of real physical extension) than a one dimensional Planck lenght string, then THAT would probably be the basic building block of the universe instead of the Superstring. But, as that is all but impossible, we're left with the Superstring.

Superstring Theory can be seen as a simple corrective of a misplaced understanding of how math concepts can and cannot translate into physical science.

with the idea that nondimensional "points" can never really have any place in physical reality
Why?
It is just a common sense reasoning telling us again - 'something must be made of something, otherwise it would collapse, and it much have some thickness'.

MTd2
Gold Member
Another way to state it is that, if there could possibly be something simpler in the universe (with at least some component of real physical extension) than a one dimensional Planck lenght string, then THAT would probably be the basic building block of the universe instead of the Superstring. But, as that is all but impossible, we're left with the Superstring.
You are a philosopher, right? So, let's see what is that, in my view, of string theory.
Suppose you live in a simulated universe, like in the movie Matrix. You can see the world functioning normally, with its people that looks like made of flesh, blue sky, sun, water, everything perfectly normal. But, ontologically, nothing is like that, in fact, the real world is just electrons propagating in circuits, and nothing more. The experimental realization of the world do not have a geometric ontological part, but an abstract one. Consider here that there is no real world, except for the electrons and circuits.

Strings in the "real world", or base space (as it is called in string theory), are what I would analogically call the circuits with the electrons in the Matrix. They are designed to yield in the simulated universe, the target space, something equal to our daily world, as it is experimentally measured. Well, it happens that they do not yield 4 dimensions, but 10 of them. Note that the strings themselves have a similar string counterpart in the target space, plus other objects with more dimensions called branes. String theorists take advantage of the 6 extra dimensions, these branes and strings, to describe specific particle interactions, specially the non gravitational ones.

You must have heard of 5 string theories. Well, they are the same. But you will find, on papers, several very different classes of physical models, linked to specifically each of them. Don't worry, it is like using 5 different circuits to compute the same thing. It is just that it is almost infinitely easier, optimized to describe a situation with one circuit than with another. Like using graphics card to boost the performance of a game.

arivero
Gold Member
I'm a philosopher
Then I assume that you are able to produce the result of the existence of five and only five platonic solids in 3D.

Or are you the kind of philosopher never interested on Plato? Nor Aristotle? I am pretty sure that the difference between point as a "tag" for the position of an object and point as a geometric entity (example, the intersection of two lines in a plane, or a vertex in a platonic solid) was already discussed by the ancients.

Most probably the right setup for points was understood by Democritus school. You must consider objects with some spatial extension and objects separating them. In the most trivial case, the line, you have "points" separating "segments". And then "the thing and the no/thing equally are": you could also take the dual view that "segments" separate "points".

The concept of atom was very developed by considering the mental experiment of cutting a cone by a plane parallel to the basis, and compare it with the cut, at the same height, of a cylinder. A lot of questions happen there: are the areas in the cut piece and in the piece left in the table equal? What happens if the cut is indefinitely near the table, is the piece of the cylinder equal to the piece of the cone? Are the areas in the cut piece equal or different in this limit? If you do a indefinite number of cuts and then compose again to rebuild the 3D figure, are you still going to get the original figure, or some other? What happens with the volume, is it preserved? What happens with the area of the surface of the figure, is it preserved?

To resume: the concept of atom is very associated to the cutting procedure, and then to extension, but by itself it is independent of the concept of extension. To build real figures you must specify how the atom (point) relates to space (extension, length, volume) but while there are interdependent concepts, they are not the same concept. This point of view of, er, points, is consistent enough to develop modern calculus and particularly to calculate the volumes of figures.

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I am gratified that a few of you found my little excursion into String Theory at least mildly stimulating, despite it coming from a, basically, layperson's perspective. I was afraid I would have made some glaring error due to a lack of more sophisticated knowledge of the theory. All I felt was that the logic seemed coherent from the assumptions and I would just "throw it out there".

I have a question now. If strings are meant to replace particles as the fundamental physical unit, doesn't that mean the the old quantum duality of "particle/wave" should now be replaced with "string/wave"? Am I wrong in assuming that, below the Planck length, the information from which our physical universe is the projection is still stored in wave form? If not, ---again, I have little techical info about String Theory and would love to be enlightened. If so, well then shouldn't we get rid of the term "wavicle" and replace it with something like "strave"? (Hey, you gotta let me have some fun with this.)

Hmmm ---and maybe I should get rid of the term "techical". Sorry abou the typo.

arivero
Gold Member
Now this it a good question. Not a interesting one, from the point of view of research, but it is not easy to work out the details. The scatering of a string against other string is still a quantum mechanical process, guided by a wave which will collapse with some probability at one angle or other, and will interfere even with itself etc... No changes, then, in the fundamental principles of wave/corpuscle. But the wave is a lot more complicated. An observable X(t) in quantum mechanics (0+1 dimensional field theory) becomes now an observable X(r,t) in quantum string mechanics (1+1 dimensional field theory).

A possible comparision is the calculation of the value of an option on a stock, depending on a price P(t), compared with the calculation of the value of an option of interest rate curves, depending on a price P(a,t), the new coordinate being the amortization time. I am not sure if the comparision is exact beacause I am not economist and perhaps the variables "a" and "t" have some relationship, while r and t above are independents. Other issue with this comparison is that P is a single coordinate, while X is a set of 25+1 coordinates in the case of string theory.