I think you mean "free-falling in a gravitational field," rather than "moving at constant velocity."
High quality pedantry.

I'll rephrase it into language I like... in motion along a geodesic.

They all mean the same thing though. If something is not moving along a geodesic, it is accelerating, ie not moving at constant velocity.

I can settle on an answer that is both good and bad.
If the photon's existence in the plane bears some angular momentum (nevermind that without time, momentum cannot be defined, take it as an intrinsic value of photons)
then we can describe that angular momentum with a vector, a 2D object.
When that photon is viewed in 4D spacetime, it is still described by a 2D vector - it's Poynting vector (which is pointing where the photon is headed, conveniently enough).
So I can find a way to visualize some aspect of this conundrum.


The big problem is that not all photons have rotational polarization. Some have planar polarization.
Not gonna lie, I don't understand this. What makes some photons different to others though?

It comes down to phase lag and interference. The accelerated electrons (and other charged particles to a lesser extent) are accelerated by the photon, not moved by the photon. The phase lag between the acceleration and velocity of the charged particles results in new wave, with equal magnitude and direction, but a new phase.


As the phase is continually being shifted, the photon's location is moved "backward" a little bit... in a continuous manner.


It's important to note that phase velocity and group velocity are different. The phase change isn't changing the phase velocity, but it's changing the group velocity. So the E-M fields are still propagating at c, but the group velocity of the wave packet appears to move at less than c due to the interference.


(This one is difficult to explain, so don't count these answers as an expert opinion, but a good metaphor.)

It's really difficult to grasp this, I'll probably have to research it a little to see if it's something I can get my head around. I'm happy with the word "interference", that does make me think I can get it, but it's not immediately clear to me.

We have an easy time thinking of something with mass moving faster and faster, but a hard time accepting that no matter how fast it gets, it's still effectively infinitely slower than c, as no amount of acceleration could ever get an object with mass up to c. We have a hard time understanding that no matter how fast you're moving, you still measure c as much faster than you.

I'm actually ok with this, at least I think I am. If the guy going to the sun decides to shine a torch towards the sun, both he and the observer at home (with the help of an amazing telescope) see the light moving at the same speed. What the two observers don't agree on is the distance the light has traveled, and in how much time. Observer A will say it moved x distance in x time, while observer B will say it moved y distance in y time. The ratios of these two figures will always be the same... c. Space and time changes, but velocity does not.

The guy moving at 0.9c doesn't think he's going that fast. He didn't take 20 seconds to travel 150 million km, he took 20 seconds to move 1 million km (these numbers are clearly arbitrary and incorrect). He doesn't think "woah I'm going fast", he thinks "woah the sun is closer than I thought".

I'm still not close to understanding this from the pov of something actually moving at c though. No space, no time, the universe is a singularity. But clearly it isn't. There is time and space. I'm struggling here.

It's not a problem for GR. It's a consequence of SR.

This might be a dumb thing to say, but isn't SR basically GR in flat spacetime (no gravity)? My understanding of SR is that it's a special case of GR where gravity is negligible.