There is a lot of confusion in this thread. One is the topic of photons vs proper time. tl;dr use affine time for things that move at c, and proper time for things that move at less than c, and remember that nobody's coordinate time is in any sense the time in relativity.

Some quotes from this thread:

> photons [have] no concept of time

and earlier

> Nothing that travels at light speed experiences time. For a photon, emission and absorption is a single event.

and other commenters in the same thread

> Photons ... "subjective" time is zero. In Einstein's theory of special relativity, the faster you go the slower your proper time appears to an external observer

> time within the photon's own reference frame is not advancing at all

and even Don Lincoln in a linked video in this thread: "we have to be careful since the equations of relativity don't apply for travelling at the speed of light, but hopefully you see that this limit trick allows us to get arbitrarily close. So I think we can see that a photon experiences no time ..." Thus everyone above is in good company with these slogans. However, Don Lincoln almost certainly knows he needs to correct s/the/these/ (in the context of the lim v->c analysis in the video), and that his conclusion needs to be understood as "no proper time" in that context. But we also all know that it's a youtube pop sci outreach video, not a university lecture or crucial vital factual no-fake-news hackernews thread.

So, let me make the counter-propostion: photons evolve on their worldlines, so must experience some time.

Additionally, elastic Rayleigh scattering supports the idea that there may be one or more point-coincidences along the worldline of a photon. There can also be non-scattering point-coincidences where the photon's momentum energy is some fraction less than 1/1 of the energy-density (the stress-energy) at some point in spacetime along its worldline even if the photon does not interact non-gravitationally with the rest of the stress-energy there (e.g. at that point there could be one or more of a neutrino, free neutron, dark matter particle, or another photon). We should be able to describe such a point-concidence in coordinates adapted to our photon's worldline, just as we could adapt them to e.g. the free neutron's worldline.

Relativity gives us (for all practical purposes, fapp) total coordinate freedom. Point-coincidence physics are invariant under changes of coordinates.

So we can label any curve any way we like, without changing the physics of anything touching that curve.

Proper time \tau solves the timelike geodesic equation, which makes \tau handy for labelling points along a timelike geodesic, but \Delta\tau = 0 on null geodesics, so is not suitable for them.

There is a unique labelling of points along a null geodesic that does solve the geodesic equation, and that is the affine parameter. See https://physics.stackexchange.com/questions/17509/what-is-th... to save me a bunch of typing. Note that as the third answer says one can use the affine parameter to calculate and explain the gravitational or cosmological redshift as a consequence of the null geodesics picked out by the Einstein Field Equations.

That (and the equivalence principle) is also a satisfying way of understanding the relation E = hf (see the first equation at <https://en.wikipedia.org/wiki/Photon_energy#Formulas>) in a lab-scale patch of flat spacetime.

Otherwise, how do you explain any \Delta f if photons "have no concept of time"? You and others in this thread appear to have been arguing that in Special Relativity the standard inertial frame for massive particles is inappropriate for showing the time-evolution of massless particles. That's true. But the point of relativity is that we can deploy (fapp) any system of coordinates and if we are doing covariant physics (i.e. using tensors; one might start with chapter 11 of J.D. Jackson's textbook which is freely available online (and 2nd ed is on the Internet Archive) and is very widely used in teaching) then it almost doesn't matter what system of coordinates we use.

Almost: we can choose practically useless coordinates, like labelling a curve in a non-monotonic way, or labelling points non-uniquely. In fact, any f(\tau) does both of those on a null geodesic: every point gets labelled with a 0. That's not the photon's fault, that's the fault of trying to use an inappropriate system of coordinates. To be fair, such coordinates seem like obvious choices by a person familiar with their use in inertial frames for massive objects, but who then may be misled into thinking the inappropriateness of the coordinates for objects on null geodesics determines the physics of those objects.

Unfortunately, this mistake is very common, and has led to poor slogans which have been repeated many times by several people in this discussion.

If one wants to sloganize, "proper time is inappropriate for photons because they are massless" (cf. §1.2 on the inverse square law and photon mass in Jackson) "but just as nobody's proper time is preferred in relativity, neither is any proper time; and for photons affine time is a useful substitute".

> Massless particles being required to travel at the speed of light is perhaps a lens to think about it.

Indeed, and I just did that for you, although Jackson and I would flip that around to say that c is the speed of massless particles and experimentally (and for theoretical reasons) photons are massless.

FWIW (I'm probably the only one ever likely to read this), in Ch. 7.0 Lightman, Press, Price, and Teukolsky's Problem Book in Relativity and Gravitation puts the previous comment in reverse (which I love and will steal). The entire brief section quoted below is glorious in its economy of English, too.

Forgive the lazy \latex anyone who actually sees this, including future me.

"If u is the tangent vector to a curve, a tensor Q is said to be parallel propagated along the curve if \nabla_u Q = 0. If the tangent vector is itself parallel propagated, \nabla_u u = 0 (tangent vector "covariantly constant") the curve is a geodesic, the generalization of a straight line in flat space. If x^\alpha(\lambda) is the geodesic (with u^\alpha = dx^\alpha / d\lambda) then the components of the geodesic equation are

0 = (\nabla_u u)^\mu = \frac{du^\mu}{d\lambda} + u^\alpha u^\beta \Gamma^\mu_{\alpha\beta}.

"Here \lambda must be an affine parameter along the curve; for non-null curves this means \lambda must be proportional to the proper length.

"If a curve is timelike, u is its tangent vector, and a := \nabla_u u = Du/d\tau, then a vector V is said to be Fermi-Walker transported along u if \nabla_u V = (u \otimes a - a \otimes u) \cdot V."

See also problem 7.11 and its solution.

Also of interest is Matthias Blau et al. 2006, "Fermi coordinates and Penrose limits". doi:10.1088/0264-9381/23/11/020 hep-th/0603109 which adapts Fermi coordinates to null geodesics. (abs. "(Fermi coordinates are direct measures of geodesic distance in space-time)... We describe in some detail the construction of Fermi coordinates" §4, "We now come to the general construction of Fermi coordinates associated to a null geodesic \gamma in a space-time with Lorentzian metric g_munu. Along \gamma we introduce a parallel transported pseudo-orthonormal frame ... Fermi coordinate are uniquely determined by a choice of pseudo-orthonormal frame along the null geodesic \gamma" "For many (in particular more advanced) purposes it is useful to rephrase the above construction of Fermi coordinates in terms of the Synge world function").