this is a bit tangential, but I once had a physics professor describe light waves as standing still and everything else is just moving around it.
That is the problem with any argument for some new physics - it might exist, but it can't have much effect or we would detect it. Generally I only see people arguing for new physics because they really want faster than light travel (typically also without all the weird time effects, but a small minority would accept it with time effects)
Since photons move at c, they experience zero time between creation and destruction.
Proper time, τ. But your proper time and my proper time are different, and are only coordinate times, monotonic labels on timelike curves. That means τ is an affine time.
There are other affine times available. And we have to choose an affine time other than τ for null geodesics, the curves which photons (in vacuum) travel along. So, instead of proper time, for photons there's the affine parameter.
The same rule applies: there is nothing special about the affine parameter. I don't have to use a photon's affine parameter when describing physics any more than I have to use the proper time of an ultrarelativistic electron. And I can convert physics done in one splitting of spacetime into space+time to a different splitting of the same spacetime into space'+time'. The coincidences in the spacetime are unchanged by the switch of how we split -- splitting is just a change of coordinates.
If we divide up spacetime into space+time where the choice of time axis along which to order spatial volumes is my proper time, the emission of a photon in the photosphere of the sun and its subsequent destruction in my eyeball happen in a definite temporal order: there is a time delay. There is still a temporal order if we divide up space+time using your proper time, or that of an ultrarelativistic electron.
There are some special technical aspects of dividing up spacetime into space+time using a photon's affine parameter as the time axis, but it's certainly doable. A photon shares a different 3d spatial volume with many other things at each affine parameter labelled point on the photon's curve. Phases of orbits, stages of an elastic collision, and so forth are among the things "snapshotted" into each 3-d spatial volume the photon finds itself in. Those evolve from one 3-d spatial volume to the next to the next.
So returning to the previous picture: if we split up space+time according to the affine parameter of a photon, there will be some 3-d volumes at which the solar photon is much closer to the sun than to my eyeball, and some 3-d volumes where it is much closer to my eyeball than to the sun. The same is true for the solar photon itself: some affine parameter values put it closer to the sun than to my eyeball, and at some affine parameter the photon's journey ends.
If a photon's trajectory is through curved spacetime, there will be a difference in momentum between two points on the trajectory (we are not restricted to the photon's creation or its destruction), which we can calculate using the affine parameter. The physical interpretation is that the photon undergoes a redshift or blueshift between two points in spacetime.
Note that I did not take the lim v->c approach you did in your first paragraph because there are geometrical differences in a Lorentzian spacetime between a null geodesic and a timelike one, even if the timelike geodesic is associated with a speed arbitrarily close to c. The photon is almost always on a null geodesic. A non-massless observer will never be on a null geodesic.
> Since photons move at c
Photons can be made to move slower than c, in which case they are not on null geodesics, and therefore proper time might be suitable for them.
Photons moving at c must be on null geodesics.
Proper time -- one particular affine time -- is undefined on null geodesics. However, they experience a different affine time. One can interconvert, so it does not make sense to say that photons "experience zero time".
Lastly, if the totality of the photon's curve through spacetime is on a null geodesic, the photon won't be able to experience much of the universe evolving around it as it flys away from its creation. However, segments of a photon's curve can be other than null geodesic motion as (for example) they cross through wispy gas clouds or strong magnetic fields in space. Temporarily slowed light <https://en.wikipedia.org/wiki/Slow_light> can in principle receive news of the world. This could have happened for a photon emitted billions of years ago from a high-redshift quasar en route to the JWST.
Extra reading:
https://en.wikipedia.org/wiki/Initial_value_formulation_(gen...
Blau, Frank, Weiss 2006 (section 3 "Brinkmann coordinates are Fermi Coordinates:", 4 "Null Fermi coordinates, general construction", 5 "Expansion of the metric in null Fermi coordinates") arxiv version https://arxiv.org/abs/hep-th/0603109 (link to publication in Class.Quant.Grav. is on the abstract page).
"What is the physical meaning of the affine parameter for null geodesic?" https://physics.stackexchange.com/questions/17509/what-is-th...
It reminds me of my silly One Photon Conjecture. That is, there’s only one photon that pops in an out of space as required by coupling events. Since it doesn’t experience time saying it can’t be in two or more places at the same time isn’t meaningful!
they actually arrive slightly later than neutrinos to observers on earth because neutrinos just plow through virtually anything including stars and planets while photons have to travel the path affected by gravity
photons aren't affected by gravity directly because massless but their path, their limit of causality, is affected
An object at full rest is according to its wave/path equation literally everywhere at all times.
However superconductivity has a bunch of truck sized holes for this. Specifically we don't quite understand Bose-Einstein condensate completely. Funky entities like time crystals appear in the mathematics, etc.
why would you think that neutrinos can magically ignore the curvature of spacetime? completely wrong.
What you seem to be trying to remember is that certain types of extragalactic supernovae produce a tremendous number of neutrinos, and those can be detected on Earth before the associated light does. The reason is that both are produced deep within the dying star, and while the star's outer layers are largely transparent to the neutrinos (not completely: it's neutrino pressure that makes the star explode[1]), the deep-in-the-star supernova photons bounce around inside. That's very much not empty space.
https://www.astronomy.com/science/in-a-supernova-why-do-we-d...
We can detect type SN1a supernovae out to about z=4 (redshift of about four in light-years is about twelve billion years of light travel time from the supernova to us). That's not really enough for the delayed pulse of light to catch up to the neutrinos produced also produced in the dying star's interior at the same time. Also, not all of the emitted photons are likely to scatter off gas and dust in any interstellar medium along the way, so the relative delay at Earth of the bright electromagnetic flash is dominated by the dying star's outer layers.
(There are more complicated electromagnetic signals like light echos <https://en.wikipedia.org/wiki/Light_echo> that can follow on much later; there aren't any neutrino equivalents really).
> photons aren't affected by gravity directly because massless but their path, their limit of causality, is affected
Not sure what you are trying to say here, but photons certainly both feel and source spacetime curvature. In empty space, photons always travel along null geodesics. The distribution of all matter, energy and momentum, the expanding background of inter-galaxy-cluster space, and the collapsing background of galaxy clusters (and galaxies, and components of galaxies like their central black holes and stars) picks out what geodesics fill spacetime. Some are null, and massless things can find themselves on ("couple to") them. Some are timelike, and massive things can find themselves on them.
Geodesics are free-fall trajectories, so are inertial as in "things in motion tend to stay in motion", and barring any further accelerations a photon coupled to a null geodesic will stay on that null geodesic and a neutrino coupled to a timelike geodesic will stay on that timelike geodesic.
Some neutrinos and photons start on parallel geodesics within the supernova's exploding core. Each neutrino stays coupled to its timelike geodesic all the way to detection on Earth. The photons are all forced off their initial null geodesic by mostly scattering off nuclear matter near the star's core, find themselves on a second null geodesic, more nuclear scattering, possibly some scattering off ions in outer layers, and each ultimately might end up on a geodesic that it stays on until it reaches Earth.
- --
[1] on neutrinos driving the explosions and how alot of them stick around as they are captured into heavier chemical elements and isotopes https://www.mpg.de/11368641/neutrinos-supernovae
> To explain how this actually works without making a math video, we have to make a lot of physicists grumpy, so please keep in mind that we are simplifying and lying a bit.
And that simplification / lie is that everything moves at the speed of light in spacetime. We are moving at basically 0 in the space coordinates and 1s/s in the time dimension (which is "light speed" in the time dimension). However... (1:45 in the video)
> Photons, light particles, move at the speed of light through space. They don’t experience any time passing because their speed in that time dimension is 0. In the time dimension they are frozen in place. If you see light on earth, from the photon’s perspective it was just on the surface of the sun and then suddenly crashed into your eye with nothing happening in between.
... and this falls into the Lie-to-children domain. https://en.wikipedia.org/wiki/Lie-to-children#Examples_in_ed...