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## Main Question or Discussion Point

What exactly is spacetime?And how can u curve nothing if ur curving space?

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What exactly is spacetime?And how can u curve nothing if ur curving space?

Hootenanny

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Hmmm.How do we come to space-time to curve.I mean what makes space time curve due to mass?

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Could you please explain how?

cristo

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Spacetime is simply a mathematical construct. The spacetime that most people talk about is the 3+1 dimensional spacetime consisting of 3 spacial dimensions, and one temporal dimension.Could you please explain how?

A position-time graph is an example of 1+1 dimensional spacetime, consisting of one spacial and one temporal dimension.

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Einstein realized that an observer in freefall does not feel his/her own weight.How do we come to space-time to curve.I mean what makes space time curve due to mass?

This means that free fall observers see the space-time in their imediate area as flat, and they move through it in straight space-time lines.

Then Einstein uses differential geometry to transform coordinates from the freefalling reference frame to one which is stationary with respect to the freefaller.

The coordinates in this reference frame do not describe flat geometry, so we say space-time is curved.

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I would say that space-time coordinatesrobphy said:Space-time coordinates define an event. A space-time diagram presents two perpendicular axes on which we measure one space coordinate whereas on the other we measure the product between c and the time coordinate. A point on such a diagram defines an event whereas a curve on this diagram represent a world line. Space-time by itself says nothing. Is there more to say?

Modern definitions of "space-time" include not just the manifold (of events) but the additional structure of [say] a pseudoRiemannian metric. Hence the appearance of [say] (M,g

My comment [and the bracketed subcomment] is to

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I have to agree. A space-time diagram is nothing more mysterious, ultimately, than a graph of position vs time, just like one sees in elementary physics.My comment [and the bracketed subcomment] is todispel the public [mis]conception of the mysteriousness of spacetime (and spacetime diagrams)by pointing out that the simplest example is right there in the introductory textbooks. Certainly the emphasis of spacetime [with its then newly uncovered light cone structure] (by Minkowski) and spacetime curvature (later, by Einstein) adds complications to the position-vs-time graph [with its flat, degenerate Galilean metric]. Nevertheless, the basic ideas are already there in the intro textbooks.

"Curved" space-time can be envisioned, with some success, as drawing your space-time diagrams on a curved surface.

Yet it seems that many people just don't seem to "get" the idea of space-time diagrams, in particular regarding to the relativity of simultaneity. I'm not sure what the difficulty is, or if there is a way around it - so far I haven't found any workarounds, the space-time diagram is as simple as it gets (IMO).

LURCH

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That is not known. Observation supports the claim that spacetime is curved by the oresence of mass, but no explanation as to "how" or "why" has been found.Hmmm.How do we come to space-time to curve.I mean what makes space time curve due to mass?

Chris Hillman

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I think it is important to put this more strongly: "why" questions like "why does the presence of mass curve spacetime?" or "why not an inverse cube law in Newton's theory of gravitation?" have in a sense not been part of the physical discourse since Newton's insight that what really matters in studying a given physical phenomenon is obtaining a theory which is self-consistent and which provides models which allows us to mathematically describe the phenomenon in a manner which yields testable predictions. If the predictions of the theory, upon testing, agree with experimental evidence, then, following Popper, we say it has not yet been falsified. Or less dramatically, if a theory passes many such tests, we say it is successful.Observation supports the claim that spacetime is curved by the oresence of mass, but no explanation as to "how" or "why" has been found.

Do not misunderstand: one

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