I've read a number of the helpful Q&As on photons that mention the mass/mass-less issue. Do I understand correctly that the idea of mass-less (a rest mass of 0) may be just a convention to make the equations work?
From a layperson's view, it's difficult to understand how a particle of light (photon) can be mass-less. A physical object (everyday world-large or quantum-small) must have a mass. Yet, if my understanding is correct, the mass of a moving object/particle increases in proportion to its speed/velocity…so that at the speed of light, its mass would be infinite. A photon travels at the speed of light, but it obviously doesn't have infinite mass, right? Can someone formulate a practical explanation that can be understood by middle-school to high school kids? Much thanks for the help.
Wow–your answers to my original Q below clear up much of my confusion. I now have the daunting task of going over these nuggets and working up an equation-less (hopefully) explanation of the mass-less photon for non-physicist types.
Yes, from a layperson's view, it does seem remarkable that an existing piece of matter—
which has to be made of physical substance–could have zero mass at rest (though a photon is never at rest). It would be almost understandable if a piece of matter made of nothing had zero mass, but that seems to be an oxymoron, and "nothing" would equate to nonexistent, right?
In case you might find it interesting: I'm working on a writing project that posits we inhabit a universe that consists of matter (physical stuff) only, and that the NON-physical (aka supernatural) does not (and cannot) exist. For instance, if a purported supernatural phenomenon is found to actually exist, then by definition, its existence is proof that it is mundane/natural. All it would take to disprove this premise is reliable proof that ONE supernatural event has occurred. Despite thousands of such claims, that's never yet happened.
Who else better than physicists to confirm my premise? However, I do wish the TV physicists would explain the terms they throw about, some of which mislead/confuse their lay viewers. Case in point: "The universe is made up of matter and energy" (without properly defining the term "energy" as a property of matter).
The result is that laypersons are left with the impression that energy must therefore be something apart from or independent of matter (ie, nonphysical). Their use of the term "pure energy" without specifying exactly what that means adds to the confusion. (Thanks to your replies on this forum, I now understand that "pure energy" refers to photon particles.) However, "psychics" and other charlatans take advantage of such confusion by hijacking terms like energy (as in "psychic energy"), frequencies, vibrations, etc to give perceived scientific legitimacy to their claims that a supernatural spirit world, etc., exists. As you may realize, the majority of people in the US (per 2009 Harris Poll) and around the world believe in the existence of nonphysical/supernatural stuff such as ghosts and spirits.
My purpose is to give laypersons the information they need to distinguish what's real from what's not.
Thanks so much for help…And, PLEASE, add any further comments you think might be helpful/insightful to better inform laypersons.
Best Answer
There is absolutely nothing conventional about the mass of different particle species. For any particle moving in the vacuum, you may measure the total energy $E$ (including the latent energy) and the momentum $p$. It turns out experimentally - and Einstein's special theory of relativity guarantees - that the combination $$E^2 - p^2 c^2$$ doesn't depend on the velocity but only on the type of the particle. It is a quantity describing the particle type and we call it $$E^2 - p^2 c^2 = m_0^2 c^4$$ This determines the rest mass $m_0$ of the particle. The formula above works for any particle in the vacuum, any speed, and is always non-singular. Photons have $E=pc$ which implies that $m_0=0$. The rest mass of a photon is equal to zero.
Indeed, that's also the reason why one can't really have a photon at rest, $v=0$. If a speed of something is $c$ in one reference frame, it will stay $c$ in any (non-singular) reference frame - that's another postulate of the special theory of relativity. So one can't ever make the speed of the photon zero by switching to another (non-singular) reference frame.
But if you want to see some values for all quantities, you may imagine that a photon at rest could exist and its total mass would be zero. At speed $v$, the mass is increased to $$m_{total} = \frac{m_{0}}{\sqrt{1-v^2/c^2}}$$ For $m_0=0$ and $v=c$, the expression above is clearly a $0/0$ indeterminate form and its proper result may be anything. In particular, the correct value is any finite number. At the right speed, $v=c$, the massless photons can have any finite energy.