Thursday, May 31, 2007

Superposition in Physics ( another jewel or a mystery ?!)

Superposition plays a central role in physics both in classical and quantum mechanics.
In classical mechanics, two force fields (e.g. electric fields or gravitational fields) existing in the same point in space add together and they are equivalent in every since to a single force having the direction and magnitude of the mathematical vector sum.
Any model to describe how do electric forces add together to form a single electric force along the resultant vector?
What is the difference between the addition of two electric forces and the addition of an electric force and a gravitational force?

In quantum mechanics, the same particle can be in a superposition of two completely different states of energy or momentum or position !! This of course leads to the removal of the definiteness of such old classical concepts as energy and position. In my opinion this is the origin of many of the mysteries of quantum mechanics. How can a particle be in a superposition of two different positions ?? Is there any physical model of that ?? Not only the definiteness of position and momentum have been thrown out in quantum theory but also the definiteness of the concept of particle itself. Discarding definite position makes it easy to imagine the particle as a wave. But what is a wave ?? It's a disturbance in the motion of many particles that propagates through space with a finite velocity. The concept of wave was generalized in electromagnetics to include the abstract concept of a field. What is a field ? Originally It was a mathematical concept to describe the effect of a force. But the fact that we can generate electromagnetic waves from a satellite and receive it thousands of miles away suggests that the field (or the EM wave) is a real thing and not just a mathematical artifact.

3 comments:

new hope half mile ahead said...

The notion of superposition is not that strange after all. If you look at fourier series you can expand a function in sine or cosine. I guess you learned it maybe in your freshman year. we dont question this part too much. But when the same notion is used in expanding wave function than superposition is born.
As far as proofs well Schrodinger cats and of course coherence in Josephson Junction
http://prola.aps.org/abstract/PRL/v63/i3/p326_1

Anonymous said...

Superposition is where an object can be in two or more states, places, or realities, at the same time. This occurs at the subatomic level and is an important factor in Quantum mechanics. Superposition does not happen to objects that are at the atomic level or higher. They obey Newtonian physics, and each object can only be in one state, place, or reality at any given time. A scientist by the name of Erwin Schrödinger tried to explain the difference between the two in a story called: Schrödinger's cat. I am a college sophomore with a dual major in Physics and Mathematics @ University of California, Santa Barbara. By the way, i came across these excellent physics flash cards. Its also a great initiative by the FunnelBrain team. Amazing!!

Tareq said...

Jerry,
Effects of superposition can now be seen on objects in the molecular level. See:
http://ion.elte.hu/~akos/orak/atfsz/dualitas/fulleren.pdf

A relevant question is: what is the limit where we can no longer observe interference?