I have always wondered that how do scientists measure the mass of a fundamental particle.
Obviously they can't weigh it in a conventional machine we use to weigh other things in our daily life.
And do they use the formula:
$$E^2=m^2c^4+p^2c^2$$
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1 Answer
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The mass of particles can be measure in a variety of ways depending on what's the particle is( and How precise measurement you want). For instance, an electron's mass can be measure as follows
The electron rest mass can be calculated from the Rydberg constant $R_∞$ and the fine-structure constant $α$ obtained through spectroscopic measurements. Using the definition of the Rydberg constant:
$$R_\infty=\frac{m_ec\alpha^2}{2h}$$ so $$m_e=\frac{2hR_\infty}{c\alpha^2}$$
There are other methods, I'm just referencing them. Here
How to measure electron mass? Another.
One most famous way for the measurement is what is called: Shell renormalization scheme
In quantum field theory, and especially in quantum electrodynamics, the interacting theory leads to infinite quantities that have to be absorbed in a renormalization procedure, in order to be able to predict measurable quantities. The renormalization scheme can depend on the type of particles that are being considered. For particles that can travel asymptotically large distances, or for low energy processes, the on-shell scheme, also known as the physical scheme, is appropriate. If these conditions are not fulfilled, one can turn to other schemes, like the Minimal subtraction scheme.
Lastly yes! If the particle is moving, You must use $$E^2=(pc)^2+(m_0c^2)^2$$
