Having trouble with Einstein's Derivation of E=mc^2

[Andrew Mason]

Not quite sure what you're referring to here. Which kind of arguments?

Non mathematical arguments.

Hmm. I think you're losing me here. If I'm wrong about this, I should revise a couple of paragraphs in my paper. So I guess I'd better figure out if I'm wrong about this.

I'm well aware that light's velocity can't increase, but that's not what I meant by momentum being imparted. How exactly does it end up getting explained WHY the intensity and frequency of light is augmented? I thought this thought experiment showed that light was more like a projectile that we thought, which can be "pushed" by, and can itself "push," other bodies--not by being imparted or imparting more velocity--but because it has energy, and energy has inertia, which is essentially "pushing power" (i.e., a body's resistance to "push" and therefore its equal and opposite "push" back). This makes it more like a projectile because a projectile can hit you harder due to its emitter's movement towards you, OR due to your movement towards the emitter. In fact, the principle of relativity states that these are the same situation.

Light imparts momentum to the emitting body and to a receiving body. But the emitting body does not push back on the emitted light. The receiving body does not push back on the light that it absorbs either. Force (pushing) is a Newtonian concept that requires a rest mass and an inertial reference frame. Light has neither. Newtonian physics cannot explain the mechanics of the interaction between light and matter.

Now, in your language above, it sounds like you're stating it in terms incommensurable with relativity. You say "The light is not "attached" to the reference frame of the emitter," But the you also say "Rather it is the measurement of its energy by another observer in another inertial frame of reference that explains the difference in momentum/energy measurements of the light." 'Another' from what? If light isn't attached to a reference frame, then there's no "other" reference frames.

The "other" reference frames are the interial reference frames other than the inertial reference frame of the emitting body.

I thought that light was attached to reference frames, just not its velocity, but its intensity and frequency. Then, if it was attached to the reference frame of the emitter, then it could exhibit augmented intensity, as explained EITHER by my motion relativity to the emitter, OR the emitter's motion relative to me. Again, it's like a projectile, say, a bullet, that hits you with more energy if the gun is moving towards you, or if you're running towards the gun.

The conventional doppler effect partially explains why observers in reference frames other than the reference frame of the emitter measure photons to have energies and momenta that differ from that in the emitter's reference frame. But this does not account for the full magnitude of the difference. Only SR can explain the complete difference.

Light is not attached to any inertial reference frame. The reference frame of the emitting body equivalent to any other inertial reference frame. If we make some assumptions about the energy of the light as measured in the inertial frame of the emitter, the light tells observers in other reference frames something about the relative speed of the source. But there is no fundamental difference between light viewed in the source frame or in any other inertial reference frame.

AM

 

[jwdink]

Light imparts momentum to the emitting body and to a receiving body. But the emitting body does not push back on the emitted light. The receiving body does not push back on the light that it absorbs either. Force (pushing) is a Newtonian concept that requires a rest mass and an inertial reference frame. Light has neither. Newtonian physics cannot explain the mechanics of the interaction between light and matter.

That's interesting. That sounds like a denial of the law of equal and opposite reaction, no?

Also: would it be fair to say that this thought-experiment points to the fact that we need to rethink "push" as a limiting case of a more general concept of energy-transference?

Light is not attached to any inertial reference frame. The reference frame of the emitting body equivalent to any other inertial reference frame. If we make some assumptions about the energy of the light as measured in the inertial frame of the emitter, the light tells observers in other reference frames something about the relative speed of the source. But there is no fundamental difference between light viewed in the source frame or in any other inertial reference frame.

Hmm, I still think I'm missing something. I'm tempted to say that some redshifted light IS attached to an inertial reference frame, because I can observe that there is relative motion between my measuring devices and the emitter, and therefore discern what that light beam would look like if it were attached to other reference frames. As long as you're saying that "light had frequency=n because of the relative motion between reference frame A and B," then it seems like you're admitting that it was attached to one of those reference frames.

 

[Andrew Mason]

That's interesting. That sounds like a denial of the law of equal and opposite reaction, no?

It is not a violation of the principle of conservation of momentum because light carries momentum. But that is all. The third law says that:

\sum_{i=0}^n F_i = \sum_{i=0}^n m_ia_i = (\sum_{i=0}^n m_i) a_{cm} = F_{ext}

The photon that is emitted is not accelerated. What is experienced by the emitting body in releasing the photon is a slight change in momentum: \Delta p = h\nu/c. The "force" it feels is dp/dt. So if the rate of photon emission per second is n, the force is dp/dt = nh\nu/c.

Also: would it be fair to say that this thought-experiment points to the fact that we need to rethink "push" as a limiting case of a more general concept of energy-transference?

The concept of "force" at this level is not very useful. Change in momentum or energy is much more useful.

Hmm, I still think I'm missing something. I'm tempted to say that some redshifted light IS attached to an inertial reference frame, because I can observe that there is relative motion between my measuring devices and the emitter, and therefore discern what that light beam would look like if it were attached to other reference frames. As long as you're saying that "light had frequency=n because of the relative motion between reference frame A and B," then it seems like you're admitting that it was attached to one of those reference frames.

A hydrogen atom has a particular spectrum when measured in the rest frame of the emitting atom. An observer moving relative to the emitting atom will see those spectral lines shifted to the red or blue due to the relativistic doppler effect. This does not mean that the light is attached to the emitting frame, however. It is attached to no inertial frame of reference. It just carries certain characteristics or information of the emitting body.

AM

 

[jwdink]

The concept of "force" at this level is not very useful. Change in momentum or energy is much more useful.

Yeah, that's what I figured. You must admit that that is a bit weird-- how do you define energy?

It is not a violation of the principle of conservation of momentum because light carries momentum. But that is all. The third law says that:

\sum_{i=0}^n F_i = \sum_{i=0}^n m_ia_i = (\sum_{i=0}^n m_i) a_{cm} = F_{ext}

The photon that is emitted is not accelerated. What is experienced by the emitting body in releasing the photon is a slight change in momentum: \Delta p = h\nu/c. The "force" it feels is dp/dt. So if the rate of photon emission per second is n, the force is dp/dt = nh\nu/c.

But, if I measure the momentum of the photon emitted from an emitter moving relative to me, don't I measure it as having more momentum than if the emitter was stationary? That sounds like the body imparted momentum to the photon.

 

[Andrew Mason]

But, if I measure the momentum of the photon emitted from an emitter moving relative to me, don't I measure it as having more momentum than if the emitter was stationary? That sounds like the body imparted momentum to the photon.

The body does impart energy/momentum to the light photon: E = h\nu ; p = E/c But it does this simply by releasing the photon. One can use different mental images to model what happens to light emitted from a moving source. My only point here is that the emitting mass does not "push" the photon. A push requires mass to push against and causes the emitted mass to accelerate. The effect of a moving source on emitted light is properly explained as a relativistic phenomenon and not a mechanical phenomenon.

The relativistic effects of photons emitted from a body moving at relativistic speeds relative to the observer are seen in a synchrotron. The light is not only very energetic. It is also very highly collimated in the forward beam direction. This is a purely relativistic phenomenon. This is because the light emitted in all directions from a jiggled" electon moves much farther in the forward beam direction than in the direction perpendicular to the beam in a given time in the laboratory frame. This is not because the photons acquire the electon's forward momentum and travel faster in the forward direction than in the perpendicular. Rather it is because time dilation causes the perpendicular speed of a photon to be much slower than the forward speed in our frame of reference. This results in all the light moving at a sharp forward angle.

AM

 

[jwdink]

Okay, that all sounds good. Quick question, just out of curiosity:

Rather it is because time dilation causes the perpendicular speed of a photon to be much slower than the forward speed in our frame of reference.

That can't be correct, right? I thought a photon's speed was the same in all reference frames?
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Anyways, thanks for all your help, I greatly appreciate it. Our discussion really helped me clarify my ideas, fix misunderstandings, and understand a lot of the fallout that is not apparent from just reading the original papers.

 

[Andrew Mason]

Okay, that all sounds good. Quick question, just out of curiosity:
That can't be correct, right? I thought a photon's speed was the same in all reference frames?

Think of a photon in the electron frame emitted by the moving electron (v = .99c) in a direction perpendicular to the direction of motion and a photon emitted at the exact same time in a forward direction. In the electron's reference frame, they both travel at the same speed, c. In the lab frame they travel at the same speed, c.

Lets say that in the lab frame the photons are released when the electron is 10 metres horizontally from a detector (as measured in the lab frame). The detector is situated 10 cm above the electron beam path and is horizontally 10 m from the point at which the photon is released. In the time that it takes for the photon to travel that 10 m (actually 10.005 metres (\sqrt{10^2 + .1^2}) to the detector, in the lab frame the electron has moved horizontally about 9.90 m. So in the electron frame the photons have only traveled about 10 cm.

The result is that in the lab frame the photon that was emitted upward in the electron frame has traveled in a sharp forward angle. In the electron frame, the photons travel 10 cm in the same time that they travel 10 m in the lab frame. The only way this can occur is if there is a difference in measurement of time between the two frames (time dilation).

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Anyways, thanks for all your help, I greatly appreciate it. Our discussion really helped me clarify my ideas, fix misunderstandings, and understand a lot of the fallout that is not apparent from just reading the original papers.

It has been a very interesting and enjoyable discussion. I have to credit you for asking the questions.

AM