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other situation even though genuinely massless photons are not thought to exist in physical reality (unless I'm really out of date on this!).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 -- https://mail.python.org/mailman/listinfo/python-list