Whats the deal with String Theory?

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  • #51
jeff
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Originally posted by Mentat
Another question: What is the string explanation for the Big Bang? I had always thought that this t-duality was what was used to explain the postulated "bounce" effect, but now I see I was mistaken in that, so it leaves this question open again.
It wasn't the relation between T-duality and the idea of a "bounce" I was addressing. I was correcting the idea that T-duality allows the possibility that the universe may in some sense be both contracting and expanding. I'll get to the relation between T-duality and the pre-big bang or "bounce" scenario below. Also, one can imagine that certain dimensions might expand while others do something else, but again, this has nothing to do with T-duality, and in fact can even be considered independently of SMT (String/M-theory).

Originally posted by Mentat
So, basically, t-duality is just the duality that unifies some of the different string theories, by creating a symmetry between the physics of higher and lower tori...aren't those higher tori what "branes" are, or is that a different concept also?
Firstly, T-duality (which as I've explained relates theories on large and small tori) is just one type of a web of dualities that relate different descriptions of the same physical systems in SMT.

We'll suppose that spacetime has p noncompact spatial dimensions and one compact dimension given as a circle of radius R. D-branes appear in connection with T-duality as it applies to open strings. The T-duality transformation

(1) R → R′ = α′/R

produces a different but physically equivalent description in which open string endpoints can't move in the compact direction, now of radius R′, but only in the spatial hyperplane extended in the p noncompact spatial directions. However the rest of the string can move in all p+1 spatial dimensions.

Such hyperplanes are actually autonomous objects in their own right, D-branes. Their definition is in fact as surfaces upon which open strings end. Their dynamics are described by the compact components of the massless excitations of open strings whose endpoints live on them. Thus these massless excitations of open strings are in the T-dual picture physically equivalent to fluctuations of the D-branes on which they end.

This picture is greatly enriched by charging open string endpoints with U(n) gauge degrees of freedom and introducing a corresponding flat gauge field background for them to interact with. In this case, the spacetime coordinates of D-branes become noncommuting quantities suggesting that spacetime itself is quantized, but it's true meaning is currently a mystery. It's really in the full supersymmetric theory that D-branes have been so important in identifying the different dualities by which the many nonperturbative results have been established.

The space of inequivalent theories under the T-duality transformation (1) are thus given by R ≥ α′½ suggesting that the string scale α′½ represents in string theory a minimum observable length i.e. an ultraviolet cutoff, and there's considerable circumstantial evidence that it is. In particular, space-time singularities are expected to be avoided (or at least reinterpreted) in any geometric model of gravity which is compatible with string theory. In other words, in quantum string theory, relativistic quantum mechanics should solve the singularity problems in much the same way as non-relativistic quantum mechanics solves the singularity problem of the hydrogen atom, by keeping the electron and the proton a finite distance apart.

As a result, string theory allows us to formulate scenarios in which the universe can be sensibly said to "smoothly" pass or "bounce" from a collapsing to an expanding phase. In this way, string theory gives us a rationale for asking what there was before the big bang, and in no other currently available framework can such a question be meaningfully asked.

If you'd like more detail on any of this stuff, don't hesitate to ask.
 
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Thanks alot for that post, jeff. :smile:

I do have another question though. How does this postulate, that requires there to be a minimum possible size of spacetime, cause the "bounce" effect?

IOW, what is it exactly that causes the Universe to begin expanding again, once it reaches the minimum possible size?
 
  • #53
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Mentat,

Per the "bounce." I think of it in part as a "quantum gravitational degeneracy," like the progression from parent star to supernova to white dwarf with nebula.

Picture the mass-energy of collapsing spacetime as it approaches the Planck density [rho]* at horizon radius R-->L* (the Planck length). Its gaining density in real space, according to T-duality, corresponds to an decrease in the virtual energy density [rho]' for R'=(L*)2/R.

When the two densities and radii reach each other in magnitude, it is equivalent to say that the virtual universe either exchanges, or bounces, with the actual universe at the Planck length. The virtual Mentat also sees what seem the same events occuring, and too cannot distinguish between elastic or transitional processes at L*. [zz)]
 
  • #54
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Originally posted by Loren Booda
Mentat,

Per the "bounce." I think of it in part as a "quantum gravitational degeneracy," like the progression from parent star to supernova to white dwarf with nebula.

Picture the mass-energy of collapsing spacetime as it approaches the Planck density [rho]* at horizon radius R-->L* (the Planck length). Its gaining density in real space, according to T-duality, corresponds to an decrease in the virtual energy density [rho]' for R'=(L*)2/R.

When the two densities and radii reach each other in magnitude, it is equivalent to say that the virtual universe either exchanges, or bounces, with the actual universe at the Planck length. The virtual Mentat also sees what seem the same events occuring, and too cannot distinguish between elastic or transitional processes at L*. [zz)]
I think I understand. Could you perhaps elaborate on the concept of "virtual universe"?
 
  • #55
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Mentat,

Imagine the Planck surface to be a mirror - that is, in the sense of the spacetime without being represented by the image "within." This "reflection" is actually the real spacetime being inverted, through a spherical symmetry of T-duality, to the virtual universe geometry below the radius L*. That virtual spacetime, existing at all points of the global spacetime, is defined by the Heisenberg uncertainty principle and the Schwartzschild metric. Their dynamics, relative to the Planck surface, are equivalent.
 
  • #56
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Originally posted by Loren Booda
Mentat,

Imagine the Planck surface to be a mirror - that is, in the sense of the spacetime without being represented by the image "within." This "reflection" is actually the real spacetime being inverted, through a spherical symmetry of T-duality, to the virtual universe geometry below the radius L*. That virtual spacetime, existing at all points of the global spacetime, is defined by the Heisenberg uncertainty principle and the Schwartzschild metric. Their dynamics, relative to the Planck surface, are equivalent.
Ooooooo-tay! That makes perfect sense.

Thank you, Loren. :smile:
 

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