Monday, January 18, 2010

Lecture 2

Questions from last time:
1. How do particle accelerators create massive particles from small, naturally occurring particles?
Every particle has an associated antiparticle with opposite charge. When particles and antiparticles meet, the charge adds up to zero and the mass can be converted to energy (E = mc^2). Likewise, energy can be converted to mass. In a high-energy particle collider, the accelerated beam of particles collides with an accelerated beam of antiparticles creating a huge amount of energy. In particle colliders, the energy created by these collisions allows new particle-antiparticle pairs to form. This energy is sometimes converted into mass in the form of heavy particles that have not occured naturally since the very beginning of the universe.

2. Why strings?
The idea came out of work by Leonard Susskind:


The two main goals of string theory are to unify the fundamental forces, and to find the most elementary form of matter.
The idea that all of matter could be made up of vibrating strings is elegant because a list of fundamental particles is replaced by a string, and a vibrating string is dynamic enough to allow many possible forms.

By quantum mechanics, every force except gravity is given by a particle:

The next video explains how string theory describes gravity at the quantum level and hence why string theory allows a "theory of everything" and could in fact unify the forces by including a particle corresponding to gravity: the graviton.

Recall: We will never be able to "see" a string. There is currently no way to PROVE string theory, although we may be able to find supporting evidence in the near future (possibly by using the LHC)
There are currently 5 versions of string theory and we don't know which one is right. It's possible that they all are, or that none of them are.

So why the big deal about String theory?
Here are some of the problems string theory addresses/may potentially solve. Some of these we have already discussed.
  • quantum physics & general relativity, two theories accepted by modern physics, are incompatible at small scales and high energies. In particular, they allow no insight into what happened at the time of the big bang.
  • why is gravity so weak compared to the other forces?
  • why is gravity so different than the other forces? As it stands, we can unite all of the forces except for gravity by using quantum physics. It has long been a goal to unite all four of the fundamental forces: gravity, electromagnetic, weak and strong (say what each is, try to describe a little bit of how they're united).
  • what is the smallest unit? Throughout history, scientists have been chipping away at the smallest units of matter- from atoms to electrons to quarks (more detail) String theory provides a smallest unit- the String
  • how did the universe begin?
  • Is it possible that other universes may exist?
We will address all of these questions (or as many as we have time for) in this course.

Goal of physics to move towards simplicity; many people perceive simplicity as beauty.



I- String theory works best in 10 or 11 dimensions

String theory makes the most sense in an extra dimensional setting; i.e. more than the 3+1 that we are aware of. For a long time, string theory was dismissed for exactly this reason. However, even though we cannot perceive more than 3+1 dimensions, there is no reason there couldn't be additional dimensions.

No physical theory (we know of) dictates that there should only three dimensions of space.
Although we only perceive 3-dimensions, extra spatial dimensions are a logical possibility.
Einstein's theory of relativity still holds in 10 and 11 dimensions.

There are currently 5 distinct theories of string theory. Each is similar in that it involves strings vibrating in 10 dimensions, but the mathematics of each theory is somewhat different. In 1995 Ed Witten developed a single theory, M-theory, involving 11 dimensions, to replace the existing 5-theories.
Not shown in class:

So how could it be that there are 10 or even 11 dimensions? And what are extra dimensions?

II-There are multiple ways physicists explain extra dimensions that are "hidden" from view.
A- Small dimensions
B- Small curled up dimensions

C- The possibility that we are trapped on a "brane." An analogy is the way shower droplets are confined to the curtain. Branes make far larger extra dimensions possible.
(We will discuss branes more tomorrow)
D- We may be in a 3-dimensional "pocket" of space.

III- What can extra dimensions add to our current theories?
Extra dimensions could ultimately reveal connections that we miss in 3-dimensional space.
For example, consider viewing your hand in only two dimensions. You would see 2-d dimensional cross sections. Maybe 5 circles corresponding to your fingers, or to your knuckles; in 3-dimensions we see the entire picture and the way that these parts are connected.
Another example is quasicrystals- used on nonstick frying pans. Generally, a crystal is a highly symmetric structure of atoms and molecules with a basic form repeated. Quasicrystals lack the regularity you would see in a regular crystal, however, if we consider the pattern in five dimensions, there is such an ordered structure.

IV- How can we imagine these extra dimensions?
Thinking about extra dimensions isn't too hard, it's trying to imagine them that's hard.
For example, just as we can describe a point in three coodinates (0,0,1), we can describe a point in 5 coordinates (1,0,0,1,1), but it would be substantially more difficult to plot.

A- Flatland
Flatland is a novel narrated by a character named "A. Square" who presents to the reader life in a two dimensional world. The story is designed to provoke thought concerning dimensions other than the ones with which we are familiar, and A. Square himself is forced to do the same. First when he visits a one dimensional world in a dream, and then when he is visited by a three dimensional sphere who appears to him as a circle increasing and then decreasing in size.

Ask the class to break into groups for 10 minutes and discuss:
How would a 4-d sphere appear to us?
How about a 4-dimensional being?
What could a 4-dimensional being do that we couldn't? examples: perform surgery without making an incision
How would a 4-dimensional being see us?

Here is what a 4-dimensional cube looks like:

B- Building up the dimensions
A line segment consists of two points connected by one one-dimensional line (1d)
By connecting two such line segments with two additional line segments, we have a square (2d)
By placing one square above the other and connecting them with four additional squares, we have a cube (3d)
By placing one cube above another and connecting them by adding six additional cubes, we have a hypercube(4d)
and so on...

C- Imagining the Tenth Dimension

V- Can we verify extra dimensions?
The LHC could detect evidence of extra dimensions by finding particles called Kaluza-Klein modes which travel in extra dimensions but would leave traces in our 3-dimensional world.
Evidence for extra dimensions will likely be indirect; we will need to piece it together.

VI- What do extra dimensions imply?
Extra dimensions permit theories of parallel universes, warped geometry, the multiverse...
We will be discussing some of these tomorrow.

Additional Videos:
TED talk by Brian Greene introducing string theory:
Physicist Brian Cox discusses the Large Hardron particle Collider:
Flatland explanation:

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