The Curvature of Spacetime: Exploring the Relationship Between Mass and Gravity

[anantchowdhary]

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

 

[Hootenanny]

Space-time is a mathematical model, something which enables us to describe the physical world around us.

 

[robphy]

The simplest example of a spacetime [although hardly anyone appears to recognize it as such] is a position-vs-time graph that you will find in any introductory physics textbook.

 

[anantchowdhary]

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

 

[anantchowdhary]

The simplest example of a spacetime [although hardly anyone appears to recognize it as such] is a position-vs-time graph that you will find in any introductory physics textbook.

Could you please explain how?

 

[cristo]

Could you please explain how?

Spacetime is simply a mathematical construct. The spacetime that most people talk about is the 3+1 dimensional spacetime consisting of 3 spatial dimensions, and one temporal dimension.

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

 

[Crosson]

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

Einstein realized that an observer in freefall does not feel his/her own weight.

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.

 

[bernhard.rothenstein]

space-time

The simplest example of a spacetime [although hardly anyone appears to recognize it as such] is a position-vs-time graph that you will find in any introductory physics textbook.

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?

 

[robphy]

The simplest example of a spacetime [although hardly anyone appears to recognize it as such] is a position-vs-time graph that you will find in any introductory physics textbook.

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?

I would say that space-time coordinates locate or label an event... not define it. A point in space-time represents an event, just as a causal curve represents a worldline. (Of course, to define "causal", one needs at least a [conformal] metric structure.)

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_ab) in modern definitions.

My comment [and the bracketed subcomment] is to dispel 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.

 

[pervect]

My comment [and the bracketed subcomment] is to dispel 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.

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.

"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]

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

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.

 

[Chris Hillman]

Elaboration and clarification

Observation supports the claim that spacetime is curved by the oresence of mass, but no explanation as to "how" or "why" has been found.

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.

Do not misunderstand: one can seek a certain kind of answer in mathematics to questions like "why not an inverse cube law?", and this insight is also due to Newton, who showed that only an inverse square force law allows for closed orbits. (See Landau and Lifschitz, Mechanics.) But proving this kind of theorem should be understood as a kind of theoretical argument that a given theory is not theoretically objectionable on certain grounds; a theory can be theoretically unobjectionable in some sense but still disagree violently with experiment.