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

[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