How did they prove the special theory of relativity?

Answer 1

Answer #1:

It was proven during an eclipse. During an eclipse, the stars near the sun can be observed and thus calculate by how much the light beam from the stars are deviated due to the mass of the sun. Newtonian physics can calculate this, but is very inaccurate, usually half the actual answer.

Nowadays, highly precise atomic clock can be put onto air crafts and the slight time dilation is exactly the same as special relativity predicted."

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Answer #2: What's wrong with Answer #1:

The eclipse was used to prove General Relativity, not Special Relativity. Gravitational lensing is the domain of the former, not the latter.

Newtonian physics absolutely cannot calculate gravitational lensing. In fact, under Newtonian physics gravitational lensing isn't even possible, since light is massless and so isn't affected by gravity.

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I have a problem with Answer #2.

My understanding is that the photon has no rest mass, but is never at rest, and has plenty of mass at the speed at which it's always moving, namely 'c'.

Seems to me that the energy carried by the photon is its kinetic energy ... 1/2 m v-squared .

We also know that the energy of the photon is (h nu).

So we can say that (h nu) = 1/2 m v-squared.

Massage this for a while, and we arrive at (Mass) = (2h) / (c lambda) . This seems reasonable ... at least it says that the photon mass is inversely proportional to its wavelength, which is exactly what you would expect if the tiny pellet of mass is the energy carrier.

So now tell me where I have gone wrong.

Answer 2

The energy of a photon is strictly expressed as either $h\nu$ or $hc/\lambda$. It can't be expressed as $mv^2/2$ or as $p^2/2m$ because it has no mass of itself. For any particle, 1/2mv^2 doesn't work at large speeds (>0.1c). The correct form for the kinetic energy is (gamma-1)mc^2, but gamma is undefined for the photon.

(This website needs to implement a MathJax engine to allow LaTeX notation for math expressions.)