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It is my understanding that objects in the Universe are not just getting farther apart but space itself is expanding and so in some real sense, higher-dimensional geometry is "real" -- if so, on a much smaller scale, can we observe for example, points whose distance is measured using all 4 (or more) dimensions? Can 4D objects like tessaracts actually be constructed? Does this expansion affect atomic-scale objects like protons and could this have an effect on their stability?

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Space is expanding. But it isn't expanding into a magical higher dimensional spatial superspace. It's merely expanding into the future.

Spacetime itself is 4d and each 4d point in 4d spacetime tells you the moment and the location.

You can imagine a 4d spacetime and have the time of a 4d point be how far it is from the origin. Each time coresponds to a 3d surface in 4d, and later times corresponds to a larger 3d surface.

But there isn't a 4d space. The larger surfaces are actually later times, what you expanded into was the future (a later time) not a different space.

This is also why there isn't a "before the big bang". There isn't a point deeper than the center of the earth.

We have to have a 4d spacetime since observers disagree on how to splice the 4d spacetime in time parts and space parts. And this is because clocks and rulers give readings that depend not only on the where-when you start at and the where-when you end up at. But also on the 4d path you take, making it impossible to objectively break it into a time part and a space part.

Which means we described it as a family of surfaces based on clocks and rulers that moved along radial lines. But others will break it down differently. But we will agree on the full 4d spacetime, it's the objective thing.

Notice that all 4d points are on a radial line to the origin so no point is preferred as a center. And there is no "before the big bang" and there is no larger space, just a 4d spacetime.

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  • $\begingroup$ why is 4D space "magical?" $\endgroup$ – Jeff Mar 13 '16 at 23:08
  • $\begingroup$ @Jeff It's magical because it's not related to predictions. We predict what clocks and rulers read by defining a metric tensor on the 4d spacetime and if you choose to embed the 4d spacetime into some larger thing in a way that changes the predictions you get wrong predictions. And if you embed it in a way where the embedding into the larger thing doesn't change the predictions, then the larger thing is pure mysticism. It's an absurd plan anyway since you need time be able to be "curved" too, that's why you need a metric tensor on a 4d spacetime. $\endgroup$ – Timaeus Mar 14 '16 at 0:20
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    $\begingroup$ Is it not somewhat interesting that space expands faster than light in places and this suggests that we are not therefore dealing with "normal" 3-D space? I don't know if you can conclude that there are extra dimensions from this but certainly it is significant. $\endgroup$ – Jeff Mar 15 '16 at 16:35
  • $\begingroup$ This is also why there isn't a "before the big bang". There isn't a point deeper than the center of the earth. This is cute, but I don't think it really works. You're asserting that the big bang singularity is not removable, so that it's impossible to extend the metric past it -- which is true, but requires calculations to demonstrate, not just words. $\endgroup$ – Ben Crowell Jan 28 at 15:19

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