1. Superstring Theory Topics Motivation
String theory: science or philosophy?
Superstring theory history
String theory fundamentals
- vibrating rings
- size blurring
- more dimensions
- reality check
Branes and cosmology
Motivation
To get a nice, general exposure to this most bizarre of topics. 1 1

2. String theory: philosophy or science, or both?
A scientific hypothesis or theory must make predictions that can be tested.
A framework that attempts to describe the Universe, but which is not falsifiable, is not science. It may be mathematics, it may be religion, but it is not predictive science.
String Theory is a mathematical framework that as yet cannot be tested. Its few predictions are vastly beyond our current technologies to test.
At the very least, the name “string theory” is arguably inappropriate—“string framework” or “string paradigm” might be more suitable. 2

3. String theory: philosophy or science, or both?
“In lieu of the traditional confrontation between theory and experiment, superstring theorists pursue an inner harmony, where elegance, uniqueness and beauty define truth….Are these properties reasons to accept the reality of superstrings? Do mathematics and aesthetics supplant and transcend mere experiment?
—Sheldon Glashow, Paul Ginsparg, 1986
We non-string theorists have not made any progress whatsoever in the last decade. So the argument that string theory is the only game in town is a very strong and powerful one. There are questions that will not be answered in the framework of conventional quantum field theory. That much is clear. They may be answered by something else, and the only something else I know of is string theory.
—Sheldon Glashow, 1997
...you may call it [string theory] a tumor, if you will.
— Sheldon Glashow, 2003 3

4. String theory: philosophy or science, or both?
“I think 100 years from now, this particular period, when most of the brightest young theoretical physicists worked on string theory will be remembered as a heroic age when theorists tried and succeeded in developing a unified theory for phenomena in nature.
On the other hand it may be remembered as a tragic failure!
—Steven Weinberg, 2003
String theory is either a red herring, or it is partially/completely correct.
If the latter, string theory has not produced a single prediction that can be tested with current (or even foreseeable) technology. Until string theory collapses, or generates a testable prediction, it is in a scientific limbo of philosophy.
But let’s look at it! 4

5. The history of string theory
After producing the general theory of relativity in 1915, Einstein devoted the rest of his life to seeking a way to unify electromagnetism with gravity.
Meanwhile, the majority of physicists had abandoned unification efforts, and instead developed quantum mechanics. Quantum, despite its counter-intuitiveness, has made some of the most accurate predictions in science.
Einstein died in 1955, without having unified electromagnetism and gravity.
Within the context of quantum, electroweak unification was achieved around 1973.
In the intervening years, all attempts to reconcile quantum mechanics and general relativity have been failures.
Quantum physics and gravity have never been combined successfully! 5

6. The history of string theory
In 1968, Gabriele Veneziano was researching the strong force interaction at CERN (Switzerland).
He discovered that his mathematical models incorporated a set of equations developed by Leonhard Euler ~200 years earlier.
His use of Euler β-functions was immediately adopted by particle physicists around the world.
In 1970, Yoichiro Nambu, Holger Nielsen, and Leonard Susskind found that if one modeled elementary particles as little vibrating strings—instead of point particles—the mathematics that resulted were Euler β-functions.
While initially interesting, this early version of string theory did not hold up well against the newly developing theory of quantum chromodynamics (i.e., colors in quarks).
String theory, for the most part, went away. 6

7. The history of string theory
In 1974, John Schwarz and Joel Scherk continued work on the theory, and discovered that it inherently included a tiny, zero mass vibrational state that corresponded to gravitons.
String theory was a quantum theory that included gravity!
In 1984 Michael Green and John Schwarz published an improved version of string theory which corrected the problems that had ailed it in the 1970s.
They also showed in addition to modeling matter, the theory might be able to model all four forces.
This started the “first superstring revolution.” 7

8. The history of string theory
During , physicists around the world focused on string theory.
It was discovered that much of physics could be derived from this framework.
Unfortunately, the mathematics is so complex, the equations cannot be solved exactly, or even approximately.
It is only possible to solve approximate versions of approximate, simplified versions of the string theory equations.
The extreme difficulty of string theory mathematics is one often cited criticism of the theory. 8

9. The history of string theory
Another criticism of string theory…
At this point, five separate versions of string theory had developed:
Type 1 string theory
Type IIA string theory
Type IIB string theory
Heterotic-0 string theory
Heterotic-E string theory
You can’t have five theories of everything! There’s only one everything! 9

10. The second superstring revolution
During a conference in 1995, Edward Witten—a leading string mathematician and physicist, presented a critical insight.
With the correct mathematical formulation, he showed that the five separate string theories were really each describing five parts of a single, larger theory.
But…this unification comes at the cost of requiring some ideas that are, perhaps, hard to swallow. 10

11. The second superstring revolution
Modern string theory thus erupted from this second revolution, and it is called “M-theory.”
Oddly, no one seems to know what the “M” stands for, not even Witten—its originator!
Mystery Theory? Maxwell Theory?
Mother (of all) Theories? Matrix Theory?
Membrane Theory? Magic Theory?
Monstrous Theory? Murky Theory? 11

12. String theory fundamentals I: vibrating rings
At the most microscopic level, all fundamental particles are not tiny spheres, points, or even spherical probability distributions.
Fundamental particles are actually tiny strings in fragments, rings, or blobby shapes.
Even the carriers of force, such as gravitons and photons, are strings.
String sizes
A typical atom is m.
The diameter of a proton is approximately m
A string is about one Planck length: 1.6×10-35 m.
IF you scaled a hydrogen atom to the size of the Milky Way Galaxy (100 kpc diameter), a string would be 0.5 mm.
Strings are….small. 12

13. String theory fundamentals I: vibrating rings
All strings are made out of the same stuff—whatever that is… There is no electron stuff, no neutron stuff, etc. There is only string stuff.
This simplification is one reason that string theory could be a “Theory of Everything.”
The only thing that distinguishes one kind of string from another is how it is vibrating.
Vibrational modes determine mass, charge, spin, etc. Strings that are more energetic have more mass. 13

14. String theory fundamentals I: vibrating rings
Since there is an infinite number of vibrational modes, you might think that string theory predicts there should be an infinite number of fundamental particle types.
String theory sidesteps this by “string tension.”
Calculations indicate that the tension in the strings must be extremely high: string tensions are about 1043N.
This corresponds to about 4.5×1011M (i.e., the Milky Way), in 1g!
String tension is related to string theory’s predictions about the particles in the universe…. 14

15. String theory fundamentals I: vibrating rings
Tension is a way of storing energy.
Since the string tension is so high, the energy stored in strings would be very high.
Except for just a few of the simplest vibrational modes, all the predicted particles would have an extremely high energy.
Since energy is equivalent to mass, these higher-vibrational modes would correspond to particles with higher mass.
High mass particles are typically:
Unstable;
Hard to create in accelerators.
This is why we do not see these high-vibrational-mode strings. 15

16. String theory fundamentals II: size blurring
Recall that the wavelength of a photon decreases with increasing energy:
E = hν = hc/λ →
λ = hc/E
Recall also that the de Broglie wavelength of an electron decreases with increasing energy:
λ = h/p
Strings also get smaller as they become more energetic. However, they have a minimum size, about equal to the Planck length (10-35m).
After they reach this minimum size, they get LARGER with increasing energy.
There is a minimum size to strings! 16

17. String theory fundamentals II: size blurring
This minimum size is of supreme importance.
We have learned that at a quantum scale, the exact location of particles cannot be determined.
In other words, their positions cannot be precisely located, nor can their sizes.
Strings are subject to this same quantum effect. But they are also subject to the minimum size issue (unlike a point particle).
If the tiniest strings in the Universe cannot be smaller than the Planck length, they cannot probe sub-Planck-scale distances, and therefore there is a limit to the fine detail of the Universe. 17

18. String theory fundamentals II: size blurring
This tiny amount of smearing to the Universe is crucial because it means that the tiny quantum fluctuations in the Universe are not arbitrarily small.
This minimum size quiets the bubbling fury of microscopic spacetime just enough so that general relativity (gravity) can be reconciled with quantum mechanics.
In other words, the incompatibility between general relativity and quantum has all been an artifact resulting from treating matter as being made of point particles! 18

19. String theory fundamentals II: size blurring
Another way to look at this blurring…
Consider the particle perspective of an interaction, where two particles collide and stick.
This is a definite event—there there is no uncertainty about when and where it happens, other than those from quantum mechanical blur.
It happened here!
But with strings, the interaction is smeared—you can’t specify exactly where the collision occurred. 19

20. String theory fundamentals II: size blurring
When we consider the history of collision as being traced by an intersecting pair of tubes, we have what is called a world sheet. 20

21. String theory fundamentals II: size blurring
Recall that relativity tells us that when you discuss events happening to spatially extended objects, simultaneity is not universally defined.
Depending upon your frame of reference, you will disagree on the timing of the spatially extended impacts of the string parts. 21

22. String theory fundamentals II: size blurring
In contrast with collisions between particles, collisions between rings is smeared….
…and since simultaneity-ambiguities also smear the timing of the events…
…the nature of space, on a fine level, is blurred. Ultrafine detail (on the order of the Planck length) simply cannot exist, since the fundamental interactions do not have fine structure.
The fury of the cosmic foam has been tamed… 22

23. String theory fundamentals III: dimensions
We are accustomed to 3+1 dimensional spacetime.
Let us imagine a simplified spacetime:
This spacetime has 1+1 dimensionality.
Suppose on very close inspection, we discover a second spatial dimension that is curled in upon itself:
Only tiny things—as small as the second curled dimension itself—could explore or even experience the tiny dimension!
A larger structure cannot enter the tiny dimension, and so would be unable to detect it. 23

24. String theory fundamentals III: dimensions
Extend this notion to a geometry with 2+1 conventional (extended) dimensions, and a third dimension that is curled and tiny.
Only tiny structures could enter tiny dimensions. Can you imagine this in 3+1-D?
Weird. 24

25. String theory fundamentals III: dimensions
In order to account for the details of superstring theory, it turns out that not only do we need one additional tiny curled dimension….
…we need seven additional tiny curled dimensions at each point of the more conventional, three dimensional space.
This weird theory of geometry is named after the two mathematicians who pioneered it: Kaluza-Klein theory.
Try to imagine that every spatial point in our Universe (of three extended spatial dimensions and one time dimension) is also home for seven more little spatial dimensions curled in upon themselves.
Can you? 25

26. String theory fundamentals III: dimensions
Why does string theory need the extra dimensions from Kaluza-Klein geometrical theory?
Look closer at the Calabi-Yau dimensions (aka Calabi-Yau spaces). 26

27. String theory fundamentals III: dimensions
Different geometric dimensions give the strings a place to probe, to explore.
Specifically, they give the strings additional “degrees of freedom” so their vibrations can have more specific types of energy. 27

28. String theory fundamentals IV: a reality check
Is there any reason we should believe any of this?
While string theory does predict a great deal that is consistent with physics… …and while it does not predict anything that is measurably wrong… …and while it offers the possibility of unifying the forces of physics… …it does not make any predictions that we have the current technology to test.
Is this a flaw with the theory, or our technology?
A “prediction”
Recall that there are three families of fundamental particles? Why three? Why not two or eight???
Some theories of string theory say that the number of “holes” in Calabi-Yau spaces may result in the number of particle families. 28

29. Brane theory
It has been proposed that strings can expand in dimensionality, from loops or strings to membranes. This is the underlying notion of “brane theory.”
Branes can be 1-, 2-, 3-, n-dimensional, and so are called (in general) p-branes. 29

30. Brane theory
In this theory, other strings living on this brane’s dimensions have their loops stuck into the membrane, but can otherwise slide around on the membrane.
This, it is proposed, is our reality. 30

31. Brane theory: the bulk, and gravitons
There’s more….
It is possible that branes may lie next to each other, like slices of sliced salami.
There could be other dimensions, very close to our own.
This multiverse of stacked branes is called the bulk.
The strings that make up gravitons are unique, in that their ends are not stuck in the brane. In essence, gravitons can leak from our brane to another brane.
This leakage may result in a kind of dilution, and would explain why gravity is so weak—the gravitons are leaking out of our brane. 31

32. String theory and cosmology
What would happen if two branes in the bulk drifted together and touched?
It is possible that a huge amount of energy would be released into the branes. Could this have been the source of energy to start the Big Bang? 32

33. String theory and cosmology
Recall the minimum size for strings? This might also imply that there is a minimum size scale for all things.
The Universe might never have emerged from a single point—instead the Universe might have emerged from a Planck-sized region.
Indeed, a collapsing Universe would reach the Planck-size, and then bounce back. Is this what happened to us, pre-Big Bang?
Many questions…many wild speculations…no data… 33