Has the formula e=mc² been proven? Or is it based on an observation?

Answer

Hi Benjamin,

That’s actually a very fundamental question about the physics you’re asking there. You can ask the same question about all the laws of physics, such as Newton’s laws (basic laws of classical mechanics), Maxwell’s laws (basic laws of classical electromagnetism), Schrödinger’s equation (which is the basis of quantum mechanics) , etc. Are these laws proven or are they based on observations?

What we are trying to do in physics in general is to write a description of nature, ie of physical phenomena. For this we use mathematical models, usually based on differential equations. The strength of the models is that they start from a small number of “axioms” (such as Newton’s laws, for example) that are applicable to a range of physical phenomena. In particular, and most importantly, they allow us to make predictions about new experiments. For example, Newton’s laws are of great importance in engineering, mechanical engineering, aerospace, etc.

It is not possible to prove these axioms. But on the other hand, these basic laws have been verified through a countless number of experiments (both in the lab and in the field); furthermore, no experiment has ever been found in which these basic laws were found to be wrong (within the approximations of the model, of course; an example of what I mean by this is that, of course, Newton’s laws are only valid as long as an object is moving at a speed that much less than the speed of light). So there is so much experimental data that supports the Basic Laws that there is really no reason to doubt it. But that in itself is not conclusive “proof”.

So there is no single formula in physics that can be formally proven. The formula E = mc^2 is usually derived via Einstein’s thought experiment (the one with that lamp in that closed box; I’m sure it’s in your physics book!) from the basic principles of special relativity, namely that the laws of the physics are the same in every inertial frame and that light propagates in every inertial frame at the same speed of light, and the conservation of energy and quantity of motion.

E = mc^2 can thus be derived from the basic principles of relativity, mechanics and electromagnetism, but these basic laws cannot be “proven” themselves. I repeat again that E = mc^2 has proved correct in countless experiments (for example all nuclear reactions, both in the lab and in nuclear power plants) and no counter-experiment has ever been found.

Conclusion: The laws of physics cannot be “proven” in the strict sense of the word, but are supported by experimental observations. They also allow us to predict new, similar physical phenomena.

Greetings,

Philippe Tassin,
Vrije Universiteit Brussel & Iowa State University