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I’ve been trying to wrap my head around general relativity, and it seems to me that what Einstein really did was give up the idea of a perfect Euclidean space.

We idealize the fundamentals of physics so much that sometimes it’s difficult to pull back and look at the bigger picture.

What if the universe is just a shotgun blast of gravitational wells? What if the space we live in is locally and globally warped? What would that look like? Would we be able to notice?

How would that affect our measurements?

Thanks.

WTFisChris
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    Is the universe that we live in a Euclidean space? No. That is essentially the point of GR. – G. Smith May 08 '21 at 05:36
  • GR explains gravity as spacetime curvature. If spacetime is Minkowskian (which means space is Euclidean) then there is no curvature and no gravity. You don’t float off the Earth because spacetime in the vicinity if Earth has curvature and your geodesic is trying to take you toward the center of the Earth. This is the GR equivalent of a gravity well. – G. Smith May 08 '21 at 05:41
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    Books for General Relativity – G. Smith May 08 '21 at 05:47
  • You can use the search box on this site to search for questions and answers about General Relativity, black holes, gravitational waves, cosmology, etc. If you have a question, please try to determine if it has already been asked and answered. – G. Smith May 08 '21 at 05:48
  • Hi WTFisChris. Welcome to Phys.SE. To reopen this post (v1) consider to include your definition of 'a perfect Euclidean space'. Do you mean Minkowski spacetime $\mathbb{R}^{3,1}$? – Qmechanic May 08 '21 at 05:55
  • You may enjoy The General Relativity Tutorial by John Baez. – PM 2Ring May 08 '21 at 08:00

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I'm not sure what your question is; Einstein's general relativity is based on non-Euclidean space/time, and the universe really is a scattershot of locally warped space here and there, in the form of gravitational potential wells surrounding every massive object in it: this is exactly what the universe "looks like" and we do indeed notice it, in the form of things like accidentally-formed gravitational lenses on astronomical distance scales and on the paths traced out by our satellite probes within the solar system as those satellites make their way amongst the planets.

If by "global warpage" you mean the cosmological constant and how it affects things like the Hubble expansion rate over the lifetime of the universe, we can measure that too, so it is also part of what our universe "looks like".

niels nielsen
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  • So I think you get the gist of what I’m asking. I’m trying to get a better understanding of three basic things: pure math, quantum physics, and general relativity. My intuition is that these things only differ in how well we can see them.

    A Euclidean space is a space without time. It exists only as a mathematical construct.

    Real space might be different than that. We can see evidence in things like gravitational lensing and gravitational waves.

    The quantum space is really a limit of our ability to measure things.

     – WTFisChris May 08 '21 at 05:57
  • I guess my question is... – WTFisChris May 08 '21 at 05:57
  • Am I being reasonable in my assessment of all of this? – WTFisChris May 08 '21 at 05:58
  • @WTFisChris No. For example, spaces without time are not necessarily Euclidean. Most people have intuition about physics but most of that intuition is wrong. (You can see thousands of examples on this site.) You cannot learn physics through intuition. – G. Smith May 08 '21 at 06:04
  • I think you might be splitting hairs. When I’m referencing Euclidean geometry, I’m thinking of a pure 3D space where there is an XYZ axis, and parallel lines will never intersect. Really, this brings up another question. How finely can the dimension of time be examined? From what I’ve read, that measurement is incredibly sensitive these days. – WTFisChris May 08 '21 at 06:08
  • And I disagree about intuition. Learning is about building intuition. Which is why I’m asking questions. – WTFisChris May 08 '21 at 06:10
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    Comments on an answer (or a question) are not the place to ask completely new questions. – G. Smith May 08 '21 at 06:10
  • If you can’t build intuition, you can’t build anything. – WTFisChris May 08 '21 at 06:10
  • There should be a easy way to avoid that a question about space is answered with space-time. Says, things fall on earth. This means spacetime is curved. Yet, I am pretty sure that we live in a flat space. Am I wrong? Or is this curvature of SPACE just geometrically imperceptible and manifests only via what classically is gravity? Note that this is genuine and not polemic. Thx. – Alchimista May 08 '21 at 11:15
  • @Alchimista Am I wrong? Yes. Or is this curvature of SPACE just geometrically imperceptible? Yes. – G. Smith May 08 '21 at 16:08
  • @G.Smith so a short answer to the question could be that space is curved (although imperceptibly so, and euclidean geometry works for many tasks and uses we are familiar with)? – Alchimista May 08 '21 at 20:31
  • @Alchimista, I think you are right. Euclid is fine, 99.999% of the time. The physicist Richard Feynman once calculated the spacetime curvature due to the mass of the earth as measured at the earth's equator and according to him the curvature produced a 1/4" error in the circumference. – niels nielsen May 08 '21 at 20:45
  • @Alchimista Yes. – G. Smith May 10 '21 at 03:22