Other people have explained this pretty well already, but here’s a non-rigorous heuristic that might help. What follows is not technically precise, but I think it captures an important and helpful intuition.
In relativity, space and time are replaced by a single four-dimensional space-time. Instead of thinking of things moving through space and moving through time separately, think of them as moving through space-time. And it turns out that every single (non-accelerated) object travels through space-time at the exact same rate, call it c.
Now, when you construct a frame of reference, you’re essentially separating out space and time artificially. Consequently, you’re also separating an object’s motion through space-time into motion through space and motion through time. Since every object moves through space-time at the same rate, when we separate out spatial and temporal motion, the faster the object travels through space the slower it will be traveling through time. The total speed, adding up speed through space and speed through time, has to equal the constant c.
So an object at rest in a particular frame of reference has all its motion along the temporal axis, and no motion at all along the spatial axes. It’s traveling through time at speed c and it isn’t traveling through space at all. If this object starts moving, then some of the temporal motion is converted to spatial motion. It’s speed through space increases, and its speed through time decreases correspondingly, so that the motion through space-time as a whole remains constant at c. This is the source of time dilation in relativity (as seen in the twin paradox) - moving objects move through time more slowly than stationary objects, or to put it another way, time flows slower for moving objects.
Of course, the limit of this is when the object’s entire motion through space-time is directed along the spatial axes, and none of it is directed along the temporal axes. In this case, the object will move through space at c, which turns out to be the speed of light, and it won’t move through time at all. Time will stand still for the object. This is what’s going on with photons.
From this point of view, there’s nothing all that weird about a photon’s motion. From the space-time perspective, which after all is the fundamental perspective in relativity, it is moving pretty much exactly like any other object. It’s only our weird habit of treating space and time as extremely different that makes the entirely spatial motion of a photon seem so bizarre.
That is helpful, and interesting, though I think I remain a bit confused about the idea of ‘moving through time’ and especially ‘moving through time quickly/slowly’. Does this imply some sort of meta-time, in which we can measure the speed at which one travels through time?
And I think I still have my original question: if a photon travels through space at c, and therefore doesn’t travel through time at all, is the photon at its starting and its final position at the same moment? If so, in what sense did it travel through space at all?
[Is] the photon at its starting and its final position at the same moment?
At the same moment with respect to whom? That is the question one must always ask in relativity.
The answer is: no, emission and arrival do not occur at the same moment with respect to any actual reference frame. However, as we consider an abstract sequence of reference frames that move faster and faster approaching speed c in the same direction as the photon, we find that the time between the emission and the reception is shorter and shorter.
Does this imply some sort of meta-time, in which we can measure the speed at which one travels through time?
No it doesn’t. Remember, in relativity, time is relative to a frame of reference. So when I talk about a moving object traveling slowly through time, I’m not relativizing its time to some meta-time, I’m relativizing time as measured by that object (say by a clock carried by the object) to time as measured by me (someone who is stationary in the relevant frame of reference). So an object moving slowly through time (relative to my frame of reference) is simply an object whose clock ticks appear to me to be more widely spaced than my clock ticks. In the limit, if a photon could carry a clock, there would appear to me to be an infinite amount of time between its ticks.
I will admit that I was using a bit of expository license when I talked about all objects “moving through space-time” at the constant rate c. While one can make sense of moving through space and moving through time, moving through space-time doesn’t exactly make sense. You can replace it with this slightly less attractive paraphrase, if you like: “If you add up a non-accelerating object’s velocity through space and its (appropriately defined) rate of motion through time, for any inertial frame of reference, you will get a constant.”
And I think I still have my original question: if a photon travels through space at c, and therefore doesn’t travel through time at all, is the photon at its starting and its final position at the same moment? If so, in what sense did it travel through space at all?
Again, it’s important to realize there are many different “time” parameters in relativity, one for each differently moving object. Also, whether two events are simultaneous is relative to a frame of reference.
Relative to my time parameter (the parameter for the frame in which I am at rest), the photon is moving through space, and it takes some amount of (my) time to get from point A to point B. Relative to its own time parameter, though, the photon is at point A and point B (and every other point on its path) simultaneously. Since I’ll never travel as fast as a photon, it’s kind of pointless for me to use its frame of reference. I should use a frame adapted to my state of motion, according to which the photon does indeed travel in non-zero time from place to place.
Again, this is all pretty non-technical and not entirely precise, but I think it’s good enough to get an intuitive sense of what’s going on. If you’re interested in developing a more technical understanding without having to trudge through a mathy textbook, I recommend John Norton’s Einstein for Everyone, especially chapters 10-12. One significant simplification I have been employing is talking about a photon’s frame of reference. There is actually no such thing. One can’t construct an ordinary frame of reference adapted to a photon’s motion (partly because there is no meaningful distinction between space and time for a photon).
Other people have explained this pretty well already, but here’s a non-rigorous heuristic that might help. What follows is not technically precise, but I think it captures an important and helpful intuition.
In relativity, space and time are replaced by a single four-dimensional space-time. Instead of thinking of things moving through space and moving through time separately, think of them as moving through space-time. And it turns out that every single (non-accelerated) object travels through space-time at the exact same rate, call it c.
Now, when you construct a frame of reference, you’re essentially separating out space and time artificially. Consequently, you’re also separating an object’s motion through space-time into motion through space and motion through time. Since every object moves through space-time at the same rate, when we separate out spatial and temporal motion, the faster the object travels through space the slower it will be traveling through time. The total speed, adding up speed through space and speed through time, has to equal the constant c.
So an object at rest in a particular frame of reference has all its motion along the temporal axis, and no motion at all along the spatial axes. It’s traveling through time at speed c and it isn’t traveling through space at all. If this object starts moving, then some of the temporal motion is converted to spatial motion. It’s speed through space increases, and its speed through time decreases correspondingly, so that the motion through space-time as a whole remains constant at c. This is the source of time dilation in relativity (as seen in the twin paradox) - moving objects move through time more slowly than stationary objects, or to put it another way, time flows slower for moving objects.
Of course, the limit of this is when the object’s entire motion through space-time is directed along the spatial axes, and none of it is directed along the temporal axes. In this case, the object will move through space at c, which turns out to be the speed of light, and it won’t move through time at all. Time will stand still for the object. This is what’s going on with photons.
From this point of view, there’s nothing all that weird about a photon’s motion. From the space-time perspective, which after all is the fundamental perspective in relativity, it is moving pretty much exactly like any other object. It’s only our weird habit of treating space and time as extremely different that makes the entirely spatial motion of a photon seem so bizarre.
That is helpful, and interesting, though I think I remain a bit confused about the idea of ‘moving through time’ and especially ‘moving through time quickly/slowly’. Does this imply some sort of meta-time, in which we can measure the speed at which one travels through time?
And I think I still have my original question: if a photon travels through space at c, and therefore doesn’t travel through time at all, is the photon at its starting and its final position at the same moment? If so, in what sense did it travel through space at all?
At the same moment with respect to whom? That is the question one must always ask in relativity.
The answer is: no, emission and arrival do not occur at the same moment with respect to any actual reference frame. However, as we consider an abstract sequence of reference frames that move faster and faster approaching speed c in the same direction as the photon, we find that the time between the emission and the reception is shorter and shorter.
No it doesn’t. Remember, in relativity, time is relative to a frame of reference. So when I talk about a moving object traveling slowly through time, I’m not relativizing its time to some meta-time, I’m relativizing time as measured by that object (say by a clock carried by the object) to time as measured by me (someone who is stationary in the relevant frame of reference). So an object moving slowly through time (relative to my frame of reference) is simply an object whose clock ticks appear to me to be more widely spaced than my clock ticks. In the limit, if a photon could carry a clock, there would appear to me to be an infinite amount of time between its ticks.
I will admit that I was using a bit of expository license when I talked about all objects “moving through space-time” at the constant rate c. While one can make sense of moving through space and moving through time, moving through space-time doesn’t exactly make sense. You can replace it with this slightly less attractive paraphrase, if you like: “If you add up a non-accelerating object’s velocity through space and its (appropriately defined) rate of motion through time, for any inertial frame of reference, you will get a constant.”
Again, it’s important to realize there are many different “time” parameters in relativity, one for each differently moving object. Also, whether two events are simultaneous is relative to a frame of reference.
Relative to my time parameter (the parameter for the frame in which I am at rest), the photon is moving through space, and it takes some amount of (my) time to get from point A to point B. Relative to its own time parameter, though, the photon is at point A and point B (and every other point on its path) simultaneously. Since I’ll never travel as fast as a photon, it’s kind of pointless for me to use its frame of reference. I should use a frame adapted to my state of motion, according to which the photon does indeed travel in non-zero time from place to place.
Again, this is all pretty non-technical and not entirely precise, but I think it’s good enough to get an intuitive sense of what’s going on. If you’re interested in developing a more technical understanding without having to trudge through a mathy textbook, I recommend John Norton’s Einstein for Everyone, especially chapters 10-12. One significant simplification I have been employing is talking about a photon’s frame of reference. There is actually no such thing. One can’t construct an ordinary frame of reference adapted to a photon’s motion (partly because there is no meaningful distinction between space and time for a photon).