Suppose there exist particles with zero rest mass ($m_0=0$) which are not photons. Let them have a non-zero finite energy $E$. Do they also, just like photons, travel through space with the speed of light?
Do all particles with zero rest mass and finite energy have to travel with speed of light in vacuum?
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3$\begingroup$ Yes, en.wikipedia.org/wiki/Massless_particle $\endgroup$– AlmostCluelessApr 10, 2020 at 7:43
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$\begingroup$ It's unfortunate that that Wikipedia article uses relativistic mass. (It also has some ungrammatical English and poor typography). $\endgroup$– PM 2RingApr 10, 2020 at 7:59
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1 Answer
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Yes, it can be derived from the energy-momentum-relation of SRT. $$ E^2 - (pc)^2 = (m_0c^2)^2 $$ which for $m_0 = 0$ becomes $$ E^2 - (pc)^2 = 0$$ $$\implies \frac E p = c \quad(*)$$ Since $$ E = \gamma m_0c^2$$ $$ p = \gamma m_0v$$ $$\implies \frac E p =\frac{c^2}{v} \quad(**)$$ $(*) = (**)$ yields $$ v = c$$
answered Apr 10, 2020 at 7:52
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$\begingroup$ That derivation is a little shaky because it involves the indeterminate form $0/0$ in the 2nd last step. $\endgroup$– PM 2RingApr 10, 2020 at 7:56
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$\begingroup$ No, that step is fine. $E$ and $p$ are nonzero. You can take the ratio for finite $m_0,\gamma$ and then the limit as $m_0 \to 0, \gamma \to \infty $ $\endgroup$ Apr 10, 2020 at 8:38
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$\begingroup$ @RogerJBarlow Sure, it's fine if you take limits. That's why I said it's shaky, rather than saying it's definitely wrong. $\endgroup$– PM 2RingApr 10, 2020 at 8:43