I’ve been reading some of the Greene books, and he several time notes that Einstein concluded that it isn’t just light that is moving at c from any frame of reference, it’s everything.
It’s just that different things have their vectors directed into different dimensions. Photons happen to be a special case in that, in any reference frame, all of their “motion” through spacetime is via the space portion (they are thus truly ageless, at least in a vacuum). Hopefully I’ve understood this correctly: this means that something at rest in respect to me has all of its speed in the time dimension, while something in motion in respect to me has some of its speed in space dimensions, which is why its local time appears to move slower from my perspective. Of course, what an objects’ path is through spacetime (what portion is in motion through space vs. motion through time) is relative to ones frame of reference.
Now, I’m of course asking if I have all that right. But I’m also wondering if I can gain a little more insight into this by wondering WHY everything moves through spacetime at c, and whether or why it can’t be slowed down in all 4 “obvious” dimensions at once. This is probably a huge can of worms, but let me also raise a couple of ancilarily questions:
Leaving aside the question of why can’t or whether something can be slowed down in all 4 dimensions, is the FACT that it can’t largely the reason that string theorists would need to argue that all the other spatial dimensions are “rolled up?” Because if they weren’t, then some of the “speed of travel through spacetime at c” could then be transferred into these other spatial dimensions that we can’t observe, thus making the object appear to both slow down in speed relative to us AND time relative to us (which we generally don’t see happening to any degree we can measure)?
Is this part of why GR/SR aren’t compatible with QM? Because the non-specific-locality of QM particles plays havoc with the careful balance of smooth motion through spacetime? If particles have no definate position or velocity through space relative to myself, do they also not have a definate path through time?
I don’t think everything is moving through spacetime at c.
The light cone of the universe and therefore presumably spacetime itself are expanding at c in all directions, but the matter in the universe is only moving at a fraction of c.
Spacetime itself is expanding, but only at the rate defined by the hubble constant Hubble Cite .
There is also the matter of dark energy or quintessence accelerating the expansion of the universe, but at the present time we are in no danger of a “big rip”
Dunno; sounds like we’re not specifically talking about the expansion of the universe, but rather, the properties of the objects in it.
Makes sense, if you think about it, for everything to be travelling at the same speed; light is travelling at c in the regular 3 spatial dimensions, that means it is stationary in the temporal dimension (which would explain why photons don’t experience time) - matter is moving at c in the temporal dimension; by accelerating to motion in the spatial dimensions, you’re diverting part of the motion vector away from the temporal dimension and it experiences time dilation.
Quite elegant.
Historically, no. The postulation of extra dimensions in string theory is due to requiring the theory be Lorentz-invariant, which basically means that things like energy, momentum, and angular momentum are conserved. I’m not familiar with the idea of “motion through extra dimensions” that you describe, but it probably came along long after the original postulation of extra dimensions — making a virtue out of necessity, if you will.
Careful there. Special relativity is compatible with Quantum Mechanics; when you combine the two, you get Quantum Field Theory. You can even do Quantum Field Theory describing particles (other than gravitons) moving in a curved background spacetime; the best-known example of something that uses this formalism is Hawking radiation. The only problem is when you try to apply quantum mechanics to gravity itself; then things tend to go haywire.
But how can a theory that talks about smooth constant motion through spacetime be compatible with a theory that stands in direct opposition to any particle having any sort of predictable, single path anywhere?
I was given to understand that it wasn’t just gravity that was the hangup, but the very nature of the sort of chaotic foaminess of the micro-level itself.
MikeS got it right on question (2), but not on (1). The existence of extra dimensions in string theory comes from requiring the consistency of the quantum theory, but the idea that they are rolled up comes from the fact that if not, matter/energy would be able to move off in those extra directions, thereby disappearing from our universe. This is essentially what Apos suggested.
I think you may be confusing Quantum Mechanics with Quantum Gravity. In QM, particles don’t have definite paths, but the probabilities that you calculate are perfectly consistent with SR: any particle has zero probability of moving faster than the speed of light. (I’m talking here about relativistic QM, more properly called “relativistic quantum field theory”.) In QG, spacetime is supposedly foamy at the smallest scales, but since there is no such thing as QG, I won’t say anything more about it. But anyway, you don’t need spacetime foam in order to have Quantum Mechanics.
I have recently read that bit in Greene’s book as well and what you just wrote about sums it up. Essentially think of it all like vectors. Say you have an object that moves at 100 mph in the East-West direction. Then say it moves in the Northwest-Southeast direction. It is still going 100 mph but takes longer to traverse the same straight East-West distance becuase some of it speed has now been redirected in the North-South direction. Assume we cannot “see” the North South direction (we only notice the East-West part) our assumption is the object is going slower than 100 mph but if we managed to add all its vector components we would actually see everything is going 100 mph.
It is pretty cool…the implications of which are way beyond me though.
To answer the OP, it helps to realize that c = 1. That is to say, since space and time are two aspects of the same thing, it makes sense to measure them both in the same units (say, seconds). Now, how fast is something “at rest” moving into the future? At one second per second, of course. Or to put it another way, at a speed of 1. Or to put it yet another way, c.
Wait: disappearing from our universe? But I thought the extra dimensions WERE in our universe? Don’t they have to be, if the whole point of them is that they are necessary for the physical explanation of “stuff” in our universe?
What I was suggesting is that we can only measure three spatial dimensions and one time dimension. Einstein, according to Greene, says that from our reference point, all things travel at the speed of light through spaceTIME (light in particular just happens to travel only through the spatial dimensions). I was suggesting that if there are other spatial dimensions, then it makes sense that they would be very very small (or, “rolled up”) because if not, an object could appear to slow or stop it’s motion through conventional spacetime from our reference point by transferring some of its motion into these other dimensions. They wouldn’t disappear, as I understand it. They would instead appear to manage the odd feat of not moving relative to us and yet ALSO appear to be moving more slowly in time (because their speed through the larger spacetime would be transferred to the other dimensions).
I think FriendRob is referring to the consequences of what would happen if the extra dimensions were NOT rolled up. We can’t perceive them, so any physical manifestations that take place in those dimensions would be invisible to us, and would appear as if they disappeared from our universe.
This requires that the extra dimensions be so small that they do not affect our perception of our familiar four dimensions - although the weakness of gravity may in fact be a result of its permeating all ten or eleven.
This is somewhat similar to what you, Apos, are saying except that I’ve never come across any speculation that “an object could appear to slow or stop it’s motion through conventional spacetime from our reference point by transferring some of its motion into these other dimensions.” I don’t believe that this could happen in any way.
Is this an original speculation of yours? If not, could you point us to the source for a fuller explanation?
Their being rolled up means that we can’t detect that they exist, but that doesn’t mean that things that happen in them are always hidden from us. Just like something can move through 3d space and not vanish from a 2d plane. It WOULD act very weird as it moved through the third dimension (growing and shrinking, for instance, if a sphere passed through, and vanishing entirely sometimes), but since the dimensions of string theory are rolled up, we don’t see them changing in a measurable way or vanishing/appearing. In Whack-a-Mole’s example, someone watching the strangely too long journey of the second spaceship from point A to point B (even though both of the spaceship’s spedometers say 100mph) might be able to tell what was going on if they noticed that the second, seemingly slower spaceship also appeared to be smaller than it should be towards the end of its journey, thus giving a hint about what this crazy “second” dimension was like.
I don’t know that I’ve read it anywhere else, but it seemed to make sense given what Einstein (apparently!) thought about motion through spacetime. Just as we can make a 100mph journey longer by diverting some of that journey off along a different dimension of travel, further spatial dimensions would seem to be able to offer the same possibility. Unless they were “rolled up”: which would explain why that’s not something that we see in any measurable way.
Of course, without someone that really understands the math, my speculation could be complete goobldeygook and no one would know, certainly not myself!