String Theory's Graviton and Spin-2 Particle Controversy

According to the current physics dogma, the graviton is a spin-2 particle. One argument for this involves the fact that Einstein's field equations are rank-2 tensors. Rank-2 tensor corresponds with spin-2 particle? If that's the case, then a 1/2-spin electron should correspond with a 1/2-rank tensor--but there is no such tensor! Just when you've given up hope that the graviton is a spin-2 particle, another argument is thrown against the wall to see if it will stick. In the following video, Leonard Susskind presents that argument:

There is a rule that says that left-moving energy must equal right-moving energy along a closed string. Each point along the string (represented by sigma) could serve as a starting point and the end point (equal zero and 2pi); i.e., the closed string and its points are invariant. Because right-moving and left-moving energy adds to zero, and because the invariant string and its points are equivalent, the closed string must have right-moving energy and left moving energy, and those two energies must be equal. Clear as mud, right? But that's essentially the argument in favor of spin-2 particles. Here is how the graviton is represented:

The a's and b's in parenthesis are the creation operators for the x and y axis, respectively. Complex numbers are used to show angular momentum. Notice there are two angular-momentum creation terms; one for left motion and one for right motion. There are two possible states: the two angular momenta going clockwise or counter-clockwise. Now compare this setup to the photon's:

The photon has only one momentum or one spin. There is no right-left motion business. And why should there be? When angular momentum completes a cycle, the total displacement is zero. If there is a vector moving left, there is an equal, opposite vector moving right. No need for an extra spin. An extra spin is redundant. This is why the left-right-motion argument fails to justify a spin-2 particle. Nature only requires one spin to complete a cycle that adds to zero. Here is the math:

Take the integral of the entire cycle of the spin (360 degrees) and you get the equivalent of the right-left-motion business--which is zero.

Bearing all this in mind, does the graviton (assuming it exists) need to be a spin-2 particle?

Debunking Bosonic String Theory's 26 Dimensions

About one hour into the above video, Leonard Susskind (one of my favorite professors) shows how string theorists mathematically derived 26 dimensions. Are you thinking what I'm thinking? If there are really 26 dimensions, then why do most string theories have fewer dimensions? This question made me watch the video with a CSI-investigator disposition.

The original goal was to get a minus-one ground state, so when a creation operator is applied, the photon will have zero mass. Imagine an x-y plane or system going down the z axis with momentum p. The frequency of the ground-state oscillator is n/2. Here is the desired equation and result:

If the result is infinity plus -1, that's OK, according to Susskind, it's just absorbed into the momentum along z and can be ignored. After some fancy math, including a Taylor expansion, the final result is ...

According to Susskind, if we drop the infinity (that lop-sided 8) we end up with -1/24. We need -1, so multiply by 24--that gives us 24 dimensions. Add the z axis and time, and that brings us to 26 dimensions. Voila!

But here's the rub: What if the result was the desired -1? How many dimensions would there be then? Let's see ... multiply by 1. That gives us one dimension. Add the z-axis and time--that brings us to two space dimensions and one time dimension!

Obviously the math and/or logic is seriously flawed.

Since it is OK to do away with infinities, we could take another approach. If you stop and think about it, we ignore infinities whenever we measure anything. How long is a meter? It's an infinite number of points. How big is a circle? It contains and infinite number of points. Everything we measure would be infinite if we didn't invent arbitrary units of measurement. We can do that here:

So instead of having 1/2 of an infinity, why not have 1/2 of a unit of ground state? And, while we're making changes, why do the frequencies of the ground state oscillators have to be a positive number when the ground state is negative? Why not be consistent? You'll note I made both sides of the above equation negative. The result is -1/2. Multiply by 2, add z and time--and voila! We live in a universe with three space and one time dimension after all!

Update: Here is another way to arrive at four dimensions instead of 26. It's based on the premise that the desired result is infinity plus -1/2. This ensures that within the infinity, there is a negative ground state.