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fckm · 11-30-2004, 07:13 PM

Moment and Energy are the two of the most fundamental concepts in all of physics. For classical objects, the momentum of the object is equal to it's mass times it's velocity:

p=m*v

During the early 1900's, a bunch of physicists came up with some wacky ideas, now refered to as quantum mechanics. One of these guys named deBroglie had a wacky idea that the momentum of an object is inversly poportional to the object's "wavelength":

p=h_bar * k
h_bar = angular planck's constant
k=2*pi/lambda = wavevector

Thus, even though light doesn't have any mass, by deBroglie's theory, it still has momentum. (This has been verified experimentally).

For a classical particle, the Force acting on that particle has the effect of changing that particle's momentum.:

F=dP/dt , Force is the derivative of momentum with respect to time.

Thus, if you have a particle who's mass is constant with time, the force acting on the particle will change it's velocity:

F= m*dv/dt = m*a.

Since a photon carries momentum, any classical particle which absorbs the photon will have it's momentum changed by an amount equal to the photon momentum. If there's a stream of N photons, of wavevector K, in an amount of time T, then the momentum imparted per unit time is:

N*h_bar*K/T

then this acts as a Force on the classical particle, such that the particle is accelerated:

m*a=N*h_bar*K/T

The problem is a simple momentum conservation problem, as long as you realize that photons do indeed have momentum, despite not having any mass. Because of these two things, 1) photons have no mass but do have moment 2) momentum is conserved, physicists usually say that momentum is a fundamental quantity, like energy. There are ways of measuring or calculating momentum and energy, but no answer to the question "what _is_ momemtum/energy?".

Now, one of the issues with modern society is that everyone is so quick to point out all the "cool" predictions of quantum mechanics without giving a good explanation of the classical background to it all. When talking about light, a lot of people are quick to point out the particle nature of light, and completely forget about the fact that light is nothing more than changes in the electromagnetic field.

Looking at Maxwell's equations (the equations which describe the behavior of electric and magnetic fields), we can see two fundamental constants. Epsilon0 and Mu0. These two constants can be measured experimentally and are properties of the free space of the universe. (I'm sure there are more fundamental explanations, but I don't know them).
Maxwell's equations are a set of Differential Equations, and when combined in a certain way, form Wave Equations. Solutions to the wave equation are usually sines and cosines. That's why you usually see "waves" graphed as sinusiods. Since the wave equations govern the evolution of waves, they also govern how fast waves can propogate through a medium. The so call "speed of light" is determined by the two constants, epsilon0 and mu0 in the wave equation. The "speed of light in a vaccum" is simply calculated using the above constants. Since light is a wave in the electromagnetic field, it travels at the speed governed by the constants epsilon0 and mu0.

When light is traveling inside a different medium, such as water, the constants epsilon and mu are no longer equal to the free-space constants epsilon0 and mu0. Consequently, light traveling in water actually travels slower than light traveling in a vaccum. Thus, when people talk about The Speed Of Light, they're talking about the c (speed) as defined by the free-space epsilon0 and mu0 (free-space permiability and permiability).

Before Einstein came on the scene, people had already measured the two constants, and had determined The Speed Of Light. However, they didn't understand it's full importance, or it's fundamental nature until the theory of special relativity came out. The Speed Of Light isn't just the speed at which EM fields propogate, but coincidentally, it was also some sort of cosmic speed limit.

In almost all cases, if a person has never taken quantum mechanics, there is NO need to think of light as a particle. It is too confusing and not very illuminating. I suggest that in the future, think of light as ocsillations of the EM field, just like waves on a string.

11-30-2004, 07:13 PM	#25 (permalink)
fckm Insane Location: Ithaca, New York	Moment and Energy are the two of the most fundamental concepts in all of physics. For classical objects, the momentum of the object is equal to it's mass times it's velocity: p=mv During the early 1900's, a bunch of physicists came up with some wacky ideas, now refered to as quantum mechanics. One of these guys named deBroglie had a wacky idea that the momentum of an object is inversly poportional to the object's "wavelength": p=h_bar k h_bar = angular planck's constant k=2pi/lambda = wavevector Thus, even though light doesn't have any mass, by deBroglie's theory, it still has momentum. (This has been verified experimentally). For a classical particle, the Force acting on that particle has the effect of changing that particle's momentum.: F=dP/dt , Force is the derivative of momentum with respect to time. Thus, if you have a particle who's mass is constant with time, the force acting on the particle will change it's velocity: F= mdv/dt = ma. Since a photon carries momentum, any classical particle which absorbs the photon will have it's momentum changed by an amount equal to the photon momentum. If there's a stream of N photons, of wavevector K, in an amount of time T, then the momentum imparted per unit time is: Nh_barK/T then this acts as a Force on the classical particle, such that the particle is accelerated: ma=Nh_barK/T The problem is a simple momentum conservation problem, as long as you realize that photons do indeed have momentum, despite not having any mass. Because of these two things, 1) photons have no mass but do have moment 2) momentum is conserved, physicists usually say that momentum is a fundamental quantity, like energy. There are ways of measuring or calculating momentum and energy, but no answer to the question "what _is_ momemtum/energy?". Now, one of the issues with modern society is that everyone is so quick to point out all the "cool" predictions of quantum mechanics without giving a good explanation of the classical background to it all. When talking about light, a lot of people are quick to point out the particle nature of light, and completely forget about the fact that light is nothing more than changes in the electromagnetic field. Looking at Maxwell's equations (the equations which describe the behavior of electric and magnetic fields), we can see two fundamental constants. Epsilon0 and Mu0. These two constants can be measured experimentally and are properties of the free space of the universe. (I'm sure there are more fundamental explanations, but I don't know them). Maxwell's equations are a set of Differential Equations, and when combined in a certain way, form Wave Equations. Solutions to the wave equation are usually sines and cosines. That's why you usually see "waves" graphed as sinusiods. Since the wave equations govern the evolution of waves, they also govern how fast waves can propogate through a medium. The so call "speed of light" is determined by the two constants, epsilon0 and mu0 in the wave equation. The "speed of light in a vaccum" is simply calculated using the above constants. Since light is a wave in the electromagnetic field, it travels at the speed governed by the constants epsilon0 and mu0. When light is traveling inside a different medium, such as water, the constants epsilon and mu are no longer equal to the free-space constants epsilon0 and mu0. Consequently, light traveling in water actually travels slower than light traveling in a vaccum. Thus, when people talk about The Speed Of Light, they're talking about the c (speed) as defined by the free-space epsilon0 and mu0 (free-space permiability and permiability). Before Einstein came on the scene, people had already measured the two constants, and had determined The Speed Of Light. However, they didn't understand it's full importance, or it's fundamental nature until the theory of special relativity came out. The Speed Of Light isn't just the speed at which EM fields propogate, but coincidentally, it was also some sort of cosmic speed limit. In almost all cases, if a person has never taken quantum mechanics, there is NO need to think of light as a particle. It is too confusing and not very illuminating. I suggest that in the future, think of light as ocsillations of the EM field, just like waves on a string. __________________ And if you say to me tomorrow, oh what fun it all would be. Then what's to stop us, pretty baby. But What Is And What Should Never Be.