# What exactly is spacetime?

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

Hootenanny
Staff Emeritus
Gold Member
Space-time is a mathematical model, something which enables us to describe the physical world around us.

robphy
Homework Helper
Gold Member
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.

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

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.

cristo
Staff Emeritus

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.

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

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.

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
Homework Helper
Gold Member
robphy said:
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,gab) 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
Staff Emeritus
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