Expanding photons.

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I'm interested in this statement being fleshed out more. Are you meaning because time would not seem to pass and so there is no motion, or that its behavior is "wormhole" like?

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I'll take a crack at this.You are right that time would not pass from a photons POV, but I think the more relevant reason is that from its point of view, it is the rest of the universe that is moving a the speed of light.In this case, all distances in the direction in which it would move are contracted to zero. Once it orients itself where it wants to go, there's no where to go!It violates no law to say that matter is moving at c because all relativity says is that no matter can be accelerated to c(or accelerated down to c is you were somehow traveling at plus c).

The big bang model implies that the universe is expanding. At least, that's what I think it implies, though if the universe is meant to mean the entire 4D spacetime structure, i'm not sure.My question is, then: is time itself expanding the same way in which space is expanding? Are two points in the time direction moving further apart and would this have any observational effects?It would seem this would have to be the case since according to Special and General relativity space and time are equivalent. I'm especially thinking about the Lorentz transformations, where one man's space is another man's time and vice versa.Ah the trouble one gets into when they ponder these subjects without a formal education in modern physics.I assume this has something to do with projecting a 4D geometry into a 3D+1 picture, but I still can't figure it out. Depending on how you project the 4D geometry, do you get different "pictures" of the expansion?

would this be a fair way to think of it.From each persons perspective, they are travelling along the time dimension, and the other three dimensions can change in various ways, depending on the geometry of the 4D structure.Now, if the observer changes his frame of reference, he gets a new perspective on this 4D structure. Some of what he considered to be space is now his time, and vice versa. They are just seeing the same shape from different perspectives, and they can theoretically get very different answers for how "space" is evolving through time.For instance, imagine a sphere that is stretched out, an oblong. You can travel straight up the object's long axis, and you find that the rate of expansion of the latitude lines (space) is a certain amount.But, if you had a different perspective and were travelling along the short axis, you'd find that the "latitude" lines were expanding at a much faster rate.Now, i'm not sure such a radical shift in perspective is possible with the 4D structure, but is this an apt analogy?

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However, if one of the dimensions in the 4D space is a time dimension, rotations act in a completely different manner and have subtle new properties.

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A change in velocity is actually a rotation in the 4D space with 1 time dimension that we live in. (Spacetime)
It's the fact that one of the dimensions is a temporal one that accounts for such a radical shift in perspective, because it wouldn't be all that different from 3D space if all the dimensions were spatial ones.

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Hope that helps a bit.

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This is what I struggle with. What is the relationship between time and space?I get confused because distance is in Minkowski space is:ds^2=dx^2+dy^2+dz^2-cdt^2So, as you said, this is 4D space with 3 spatial and 1 temporal dimension. The temporal term is distinct from the spatial ones. This seems to tell me there is a fundamental difference between space and time.But then I see the Lorentz transformation, which show that space and time are equivalent (I think). Since one persons time is another persons space, and vice vera, the difference doesn't seem to be fundamental, but merely dependent on the observer.Basically, one tells me the difference is fundamental, the other tells me its not. Where am I going wrong?