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In "An Introduction to Modern Astrophysics" Carroll and Ostlie describe the curvature of space by mass as:

curving in a fourth spatial dimension perpendicular to the usual three of "flat space."

They then add in a footnote:

that this fourth spatial dimension has nothing at all to do with the role played by time as a fourth nonspatial coordinate [their emphasis, but it still doesn't clarify things for me] in the theory of relativity.

However in the spacetime wikipedia it says:

Hermann Minkowski presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. ...Minkowski spacetime is flat, takes no account of gravity... The presence of gravity greatly complicates the description of spacetime. In general relativity... spacetime curves in the presence of matter.

And it also mentions the curvature of time and not space:

Experiments such as the Pound–Rebka experiment have firmly established curvature of the time component of spacetime... [and] says nothing about curvature of the space component of spacetime.

My confusion seems to be about:

  • Popular explanations separate the four dimensions of spacetime into 3 space and 1 time, so how does curvature in a fourth spatial dimension not lead to understanding spacetime as being 4 spatial dimensions and 1 time dimension?
  • How is a curvature of 3D space interpreted as curving in a fourth spatial dimension while having "nothing at all to do with the role played by time as a fourth nonspatial coordinate"?
Qmechanic
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Glycoversi
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1 Answers1

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In that paragraph in the book, Carroll & Ostlie use the well known bowling ball in a trampoline model of spacetime. This model has A LOT of problems and is usually only considered only as a way to explain to absolute beginners. Not the least of the problems in their book is that they seem to be saying that the 2D sheet is stretched into 3D, and this implies that normal 3D space is stretched into spatial 4D, and that time is another dimension (perhaps the 5th Dimension Age of Aquarius?)

I find that a much better model is to think that near a planet, space itself is dilated and because of this, time is also dilated. It takes a certain amount of time for light to cross a given amount of space. So if that space is dilated then it takes a longer time to cross it. You have to keep in mind that both measurements are intimately connected. 1 second is the time it takes light to travel 300,000,000 meters. So if space has dilated, then a second must also dilate. Thus we have the warping of spacetime near a planet as used in general relativity.

I prefer to use the term "dilated" rather than "stretched" because it implies stretching in one direction (like the bowling ball example) and in reality space is dilated in all directions and so is time.

foolishmuse
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