Relativity, Quantum Mechanics, and M-Theory
After our recent forays into cosmology, particle physics, string-theory and the like, we are left feeling, well, confused. There is just so much to know. Turns out the Theroies of Special and General Relativity are the easy part. But to even begin to grasp the implications of General Relativity, you must first be conversant with classical mechanics, optics, and electromagnetism. These provide the foundation for an understanding of Special Relativity, which in turn (finally) provides a foundation for General Relativity.
Then we find out that GR doesnt work all the time. So now we have quantum physics to explain the stuff GR cant. Now we're getting into some really serious stuff, most of it based on abstract mathematical models. (Someone once said that Einstein was the last person to really build an explanation based on observation -- everything since has been the other way around.) But the two -- GR and QM -- are incompatible. It's as though each is only capable of explaining half of the way things work.
Now some of the best minds in science are racing to build a new model that incorporates both GR and QM. This field -- string theory, or M-thoery -- is even more abstract, built as it is upon the already abstract quantum model. Frankly, to us it seems to require a great leap of faith to have any confidence at all in these theories. At times it seems like pure rationalization, sleight of hand, smoke and mirrors. One of the primary tenets of the new theories is the acceptance, even the reliance upon, the Uncertainty Principle, which basically states that you pretty much can never know anything for certain at the subatomic level. Instead, everything relies upon probability. You must simply believe in the math. But if you dont understand the math -- well, it's enough to make anyone a skeptic.
Therefore, we are pleased to announce a new Palace Flophouse initiative -- to
understand the math. We are going to study it, we are going to ruminate on it, and we are
going to present it in terms that even we can understand.
When we botch it, please set us straight via the Feedback page.
Exercise No. 1: The Lorentz Transformation.
For a coordinate system K.
The distance traveled by a light particle = x.
Distance = velocity x time. So x = speed of light x time (c x t). x = ct.
Since x = ct, x - ct = 0.
Now, the same goes for coordinate system K' since (as we will discuss later) natural laws are the same for any two coordinate systems.
Thus (x - ct = q(x' - c't')) where q is a constant describing the relative orientation of the coordinate systems. Einstein actually wrote it the other way around, with the K' coordinate system at the first part of the equation, but I dont think it matters if you switch them. The thing I'm having trouble with is q as a constant (perhaps more aptly named a modifier?).
More to come.