On Saturday 05 March 2016 08:11:46 Oscar Benjamin wrote: > On 5 March 2016 at 02:51, Gregory Ewing <greg.ew...@canterbury.ac.nz> wrote: > > The masslessness of photons comes from an extrapolation > > > >> that leads to a divide by infinity: strictly speaking it's just > >> undefined. > > > > No, it's not. The total energy of a particle is given by > > > > E**2 == c**2 * p**2 + m**2 * c**4 > > > > where p is the particle's momentum and m is its mass. > > For a photon, m == 0. No division by zero involved. > > > > For a massive particle at rest, p == 0 and the above > > reduces to the well-known > > > > E == m * c**2 > > The distinction I'm drawing is between physical fact and mathematical > convenience. For other particles we can say that the 1st formula above > holds with m taken to be the mass of the particle at rest. We can > extend that formula to the case of photons which are never at rest by > saying that in the case of photons m=0. That's nice and it's > mathematically convenient in the calculations. It's analogous to > extending the natural definition of the factorial function by saying > that 0!=1. We can't prove that 0!=1 but it's useful to define it that > way. It wouldn't be a disaster to simply leave 0! undefined: it would > just make some equations a little more complicated. > > Since the generally accepted physical fact is that photons are never > at rest we are free to define their "rest mass" (use any term you > like) to be anything that is mathematically convenient so we define it > as zero because that fits with your equation above. Turning full > circle we can then use the equation above to say that they are > massless since they would hypothetically be massless in some other > situation even though genuinely massless photons are not thought to > exist in physical reality (unless I'm really out of date on this!). > > >> Something I don't know is if there's some theoretical reason why > >> the binding energy could never exceed the sum of the energies of > >> the constituent particles (resulting in an overall negative mass). > > > > Conservation of energy would be one reason. If you > > put two particles together and got more energy out than > > went in, where did the extra energy come from? > > That's the point: the energy balance would be satisfied by the > negative energy of the bound particles. The binding energy can be > defined as the energy required to unbind the particles (other > definitions such as André's are also possible). From this definition > we see that the binding energy depends on the binding interaction > (electromagnetic or whatever) that binds the particles together. > > The only examples I know of where the binding energy is computed > approximately for e.g. a hydrogen atom predict that the binding energy > is proportional to the (rest) mass of the bound particle(s). If it's > guaranteed that the binding energy always somehow comes out > proportional to the mass of the particles with a coefficient > necessarily smaller than 1/c**2 then you could say that the bound > product could never have negative energy. I just can't see off the top > of my head an argument to suggest that this is impossible. > > -- > Oscar
I've never heard of a massless photon, and they do exert a push on the surface they are reflected from, its even been proposed to use it as a space drive. The push is miniscule indeed at normal illumination levels but some have calculated how much laser power it would take to move something like a solar sail. Practically, the cost of the energy and the size of the laser needed are impractical. Cheers, Gene Heskett -- "There are four boxes to be used in defense of liberty: soap, ballot, jury, and ammo. Please use in that order." -Ed Howdershelt (Author) Genes Web page <http://geneslinuxbox.net:6309/gene> -- https://mail.python.org/mailman/listinfo/python-list
