In addition to the experimental tests of $E=mc^2$ of the previous post, let us consider a bit more the difficulties of such tests. On microscopic scale the required accuracy is hard to reach in a convincing way. This includes both nuclear and chemical reactions measuring mass before and after reaction. It is possible to restrict the science to just consider the binding energy as it is, as a form of energy, without connecting it to any mass defect which is difficult to assess.
In any case, on macroscopic scale the accuracy requirement may be less of a problem and so we may envision the following tests:
- Stretch an elastic spring to give it energy to do work. According to $E=mc^2$ its mass should increase. Compare with an unstretched otherwise identical string using a balance scale and record the difference.
- Similarly, use a balance scale with two weights in balance to record if heating changes the balance.
Would we be able to measure an increase of mass from stretching or heating both increasing energy? That would certainly be most surprising and the measurement accuracy would again not be sufficient to validate anything like that. So such experiments would probably be inconclusive and not serve to validate $E=mc^2$.
Neither does it seem possible to get a validation on cosmic scales, since if increasing the speed of a planetary object would increase its mass, it would not change its reaction to a gravitational potential since all objects independent of mass react the same way.
We conclude that it seems exceedingly difficult to verify the truth of $E=mc^2$ on any scale. What about the possibility of disproving it? First, one would ask for theoetical support and then we enter muddy waters including Einstein's argument from 1905 and so theory is not sufficient. To disprove it experimentally is also hard since it requires even better accuracy than verification.
The net result is that $E=mc^2$ is hard to verify/disprove since it is such a small effect. It is like verifying/disproving the existence of ghosts, which is impossible. Does this mean that we can anyway assume that $E=mc^2$ or that ghosts exist, since it does not change anything? Occam's Razor then tells us that it is better to forget all about it, since it does not seem to serve any purpose. Or maybe it does:
The magic formula $E=mc^2$ then appears as a fetish carried by physicists used to boost their importance by connecting the formula to the undeniable power of nuclear energy and weapons. Is this the true role of $E=mc^2$? Is this the reason that still after 118 years there is no real verification, only countless suggestions that there is. A fetish does not need any verification only an agreement that it brings magic power.
A final reflection: $E=mc^2$ connects mass, which is gravitational mass, with $c$ as the speed of light as a stream of "photons" without mass. This certainly seems contradictory. But the argument goes like this: The momentum of a photon is given $p=\frac{E}{c}$ where $E$ is its energy, and momentum is formally given by $p=mc$ with $m$ the mass of the photon and $c$ its velocity. So we derive $E=pc=mc^2$. Voila!
The only trouble is that the photon is massless with $m=0$, so the argument has no meaning, which is an indication that also $E=mc^2$ is without real meaning: To rely on photons without mass traveling with the speed of light to conclude something for bodies with mass traveling at much smaller speeds, seems to be completely off-the-wall. But it is modern physics at its best.
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