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.
The physical fact is that as far as we know the photon mass is zero. That is, the upper limit of the photon mass is so close to zero (at the time of writing, Adelberger et al. place it at < 10⁻²⁶ eV∕c² ≈ 1.783 × 10⁻⁵⁹ g ≈ 1.957 × 10⁻³² m_e; see below) that we can assume it to be zero without introducing significant error in our *physical* calculations. <http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/photon_mass.html>; but also <http://pdg.lbl.gov/2015/listings/rpp2015-list-photon.pdf> pp., and in general <http://pdg.lbl.gov> → “Summary Tables” → “Gauge and Higgs Bosons”. > […] > Since the generally accepted physical fact is that photons are never > at rest ISTM that this is rather a mathematical fact following from that energy– momentum relation and the assumption that the photon (γ) mass m_γ is zero. It follows rather obviously then that E(m = m_γ = 0, p = 0) = 0. But everything that exists has to have some (non-zero) energy. So photons, and in general any objects, that have no mass *and* no momentum relative to a frame of reference cannot exist for an observer at rest relative to that frame. > 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. No. We know that if our present understanding of physics is a sufficiently complete/correct description of reality, m_γ = 0 is a requirement. Several reasons for that can be given; here are some: 1) If m_γ ≠ 0, the speed of light in vacuum could not be c as, according to special relativity, nothing that has mass m ≠ 0 can move at c relative to a frame of reference – infinite energy in terms of that frame would be required for accelerating it to that speed: The kinetic energy of such a body is Eₖ = E_rel − E₀ where E₀ = E(m ≠ 0, p = 0) = mc² by the energy–momentum relation (see above), and lim E_rel(v) = lim mc²∕√(1 − (v∕c)²) = +∞ v→c v→c –, and photons are the particles of *light*. So m = m_γ ≠ 0 would have profound and measurable implications on the propagation of light, that would *at the very least* be inconsistent with our knowledge of optics that precedes special relativity. <https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies> 2) When one looks into E² = (p c)² + (m c²)² further – which is not just an arbitrary equation that happens to fits observations very well, but is derived from the norm of the four-momentum –, one realizes that if, and only if, m_γ = 0, then also E_γ = E(m = m_γ, p) = p c = ℏk c = ℎc/λ = ℎf (ℏ = ℎ∕2π, k = ||k⃗|| = 2π∕λ — wavenumber, k⃗ — wave vector), which has been experimentally confirmed even *before* the postulation of special relativity in observations of the photoelectric effect (the kinetic energy imparted by light to electrons in a metal’s surface is proportional to its wavelength λ/frequency f). So if m_γ ≠ 0, this would also have profound and measurable implications on the energy transported by light of different wavelengths/frequencies/colors that would be inconsistent with our knowledge of electromagnetic radiation that precedes special relativity. <https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation#Norm_of_the_four-momentum> <https://en.wikipedia.org/wiki/Planck_constant> Finally, 3) if m_γ ≠ 0, the range of the electromagnetic interaction would not be infinite, as because of the uncertainty principle the range r of an interaction depends on the mass m of the particle that carries it: r(m) ≈ c∆t ≈ ℏ∕2mc. This would have profound and measurable implications on fundamental interactions that would be inconsistent with our experimentally very well confirmed (and daily applied) knowledge of quantum mechanics. <http://hyperphysics.phy-astr.gsu.edu/hbase/forces/exchg.html> X-Post & F'up2 sci.physics.relativity -- PointedEars Twitter: @PointedEars2 Please do not cc me. / Bitte keine Kopien per E-Mail. -- https://mail.python.org/mailman/listinfo/python-list
