Background: The key idea here is that any object is always moving (relative to some other object, I suppose) through space-time at the speed of light. For objects at rest (e.g. me, relative to my chair), all of that motion is going through the time dimension. However, for moving objects, some of that motion is "spent" on spatial dimensions, and so less remains to go through time. Just like if you travel north-east for 100m, you won't get as far north as if you travelled due north for that distance. I find this analogy quite powerful, because it explains (in a reasonably understandable sort of way) why it is that time slows down as objects approach the speed of light, and also why nothing can ever move through space at faster than lightspeed.
But what about light itself? A photon moves through space at the speed of light, so there is no motion leftover for it to move through the time dimension. Greene explicitly says that photons are no "older" now than they were at the birth of the universe. So how did those photons get into the present, if not by passing through time like everything else?
Some musings: I really haven't got much of a clue, so I'm hoping a more knowledgable reader will be able to enlighten me here. But I'll offer some thoughts anyway...
I'm guessing the problem must be due to me having too much of a naive-absolutist conception of space and time. Perhaps the apparent paradox can be solved by expressing space and time in purely relational terms.
I can't yet see how that helps, but to get a feel for it, let's consider the constancy of the speed of light:
If two cars, each travelling at 50 km/h (relative to an observer sitting on the footpath) are travelling in the same direction, then they are stationary relative to each other. If moving in opposite directions (e.g. about to have a head-on collision), then their relative speed is 100 km/h. All nice Newtonian stuff so far. But light is different. No matter how fast you're moving, in whatever direction, photons are always travelling at a constant speed c (the speed of light) relative to you (and everything else for that matter).
To apply the 4-d space-time stuff to the above examples:
- The observer sees all the cars as going at the same speed (50 km/h), so they all move through time at the same rate relative to him (which is very close to full-speed, but not quite).
- The same-direction cars are relatively stationary, so they move through time at full speed (i.e. slightly quicker than from the observer's perspective).
- The head-on cars are going relatively fast, so each moves through time relatively slowly (though the difference at this scale, compared to the speed of light, is so tiny as to be indistinguishable to humans).
So what about photons then? No matter the frame of reference, their speed is always the same: c. So no matter the frame of reference, their movement through time is always the same: zero.
Well, that was no help.
Any ideas... anyone?
Update: see here for the answer.