Book recommendation

Tired of reading books about physics?  Want the real McCoy”?  Well written and informal?  Contains stuff whose names you know but don’t understand — Jones Polynomial, Loop Quantum Gravity, Quantum field theory, Gauge groups and transformations —  etc. etc.

Up to date?  Well no, it’s 25 years old but still very much worth a read, so very unlike molecular biology, chemistry, computer science etc. etc.

Probably you should know as much physics and math as a beginning chemistry grad student. If you studied electromagnetism through Maxwell’s equations it would be a plus.  I stopped at Coulomb’s Law, and picked up enough to understand NMR.

This will give you a sample of the way it is written

“Much odder is that we are saying the vector field v is the linear combination of . .  partial derivatives.  What we are doing might be regarded as rather sloppy, since we are identifying two different although related things: the vector  field and the operator v^i * d-/dx^i which takes a directional derivative in the direction of v.”

“Now let us define vector fields on a manifold M. .. . these will be entities whose sole ambition in life is to differentiate functions”

The book is “Gauge FIelds, Knots and Gravity” by John Baez and Javier P. Muniain.

The writing, although clear has a certain humility.  “Unfortunately understanding these new ideas depends on a through mastery of quantum field theory, general relativity, geometry, topology and algebra.  Indeed, it is almost certain that nobody is sufficiently prepared to understand these ideas fully.”

I’m going to take it with me to the amateur chamber music festival.  As usual, at least 2 math full professors will be there to help me out.  Buy it and enjoy

 

 

The weirdness of gravity

We experience gravity every waking moment, so it’s hard to recognize just how strange the gravitational ‘force’ actually is. Push a toy sailboat, a rowboat, and a yacht with the same amount of force (effort). What happens?

The smaller the boat, the faster it moves. Physicists would say the acceleration (change in velocity over time e.g. from the boat not moving at all to moving somewhat) is inversely proportional to the mass of the boat. This is Newton’s famous second law force = mass * acceleration. This isn’t actually what he said which you’ll find at the end.

So in every force except gravity, the bigger the force the more the acceleration. In Galileo’s famous experiment (which Wikipedia says might actually not have occurred), he dropped 2 objects of different masses from the leaning tower of Pisa and found that they hit the ground at the same time, so the acceleration of both due to the ‘force’ of gravity is the for all objects regardless of their different masses.

This implies that gravity is a force that adjusts itself to the mass of the object it is pushing on to produce the same acceleration. Weird, but true.

General relativity says, that the motion must be considered not just in space and time, but in 4 dimensional space-time where space can become our conventional time and vice versa. Here all paths are as straight as possible — because the 4 dimensional space-time we inhabit has an intrinsic curvature, produced by the masses found within it.

What Newton said: “The change of motion is proportional to the motive force impressed and is made in the direction of the straight line in which that force is impressed” By motion Newton means what we call momentum — mass * velocity.

The change in momentum is of course a change in velocity — which is what acceleration actually is. Note that mass is assumed constant regardless of how fast the object is moving. This isn’t even true in special relativity (which doesn’t include gravity — that’s what general relativity is all about).