no experiment has yet to show that photons have no mass.
That's because it's a very hard thing to show. What they have shown experimentally is that the mass has to be smaller than 10^-18 eV/c, which is 1.782662 x 10^-54 kg, which is 1 / 10^-24th the mass of an electron which is by far the lightest particle predicted.
And I'd be interested to hear how E=mc^2, a central component of special relativity, causes it to conflict with general relativity. Do tell!
Basically the sun revolves around the earth - what ever we think now is correct no matter what anyone else says.
We used to think the earth was flat, and we were wrong. Then we thought the earth was a sphere and we were wrong (it's actually an oblate spheroid). But if you think believing the earth is a sphere is just as wrong as thinking the earth is flat, then you're wronger than the both of them. (paraphrased from Asimov). We know Newtonian physics is wrong, relativity significantly improves on the accuracy of Newtons predictions. That doesn't mean I drop an apple and expect it not to fall because Newton was wrong. Similarly, we know that relativity is wrong (the predictions break down in several extreme situations), but that doesn't mean that I expect E=mc^2 to be wrong tomorrow or time dilation to be proven wrong or any of the other well known relativistic effects. They have been shown empirically to be correct to fractions of fractions of a percentage point, that evidence doesn't just go 'poof' when a more refined theory comes along.
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