How can time be curved?

Time isn't a physical object, but according to Einstein's theory of gravity, mass bends spacetime towards things with mass and makes them fall. How does a physical object affect something intangible?

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Joshua Noriega Aguilar is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

To be precise, time is not curved, it is the spacetime manifold that has curvature. Such a manifold can be given a coordinate chart - an arbitrary one - that assignes to different points (spacetime events) some labels.

It turns out that we need one time coordinate to label the time slices and three spatial coordinate to distinguish the events within that slice.

What you might satisfactorily say is that the rate of flow of the proper time - the time that your own clock shows - depends on how much spacetime curvature is in your vicinity. This is a quantity independent of any coordinates, a true physical property if you will. This proper time is a measure of your aging, biological processes in your organism, the oscillatory frequencies in atomic transition in the atomic clock you might have etc.

Imagine you and your friend orbiting a static black hole. You get the same clocks and synchronize them. They show the same time and tick at the same rate.

Then your friend stays at his orbit (at a distance $$r_{friend}$$) and you go much closer to the black hole (at a distance $$r_{you}$$). You spend some time there and upon returning, you make a discovery that your clocks show different readings!

In fact, using the Schwarzschild solution you could predict that your clocks will exhibit a ratio of proper times that have passed equal to

$$\frac{\tau_{you}}{\tau_{friend}} = \frac{1-2M/r_{you}}{1-2M/r_{friend}}$$

In the above, I omit the problem of determining when you start and stop the readings and how you account for the travel back and forth. It does not change the fact that your clock will exhibit fewer ticks-and-tocks when you compare it with the one of your friend.

If you think about it, "space" is no more tangible a concept than "time" is. If one can curve, so can the other.

Spacetime is curved in the same sense that the surface of the Earth is curved. Two ships sailing on initially parallel paths may nevertheless converge and meet.

An similar example of time curvature is, if someone on a high altitude point, like the Red Bull guy, flashed a laser pulse down at the ground, and then flashed one again 1 second later (by his clock), the pulses would arrive on a detector on the ground less than 1 second apart by our clock. Less by roughly 10^-12 sec. So the time interval between the two pulse events decreases as we approach the center of the Earth, just as the space interval between the ships decreases as they approach the North Pole.

If it were a black hole instead of the Earth, the pulses could go a lot deeper into the gravity well, and the time between them would approach zero.

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RC_23 is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.

In a general sense, time is just a dimension. We could draw a diagram where we say an object curves in space over time. But we could also flip the diagram and say the object curves in time over space. It's just a matter of perspective.

I think a better way to think of the "curvature" of spacetime is to think of its density changing. Spatial density pushes objects from high density to low density (gravity). Time density tells us things tick at a different rate relative to the "universal clock". Lower temporal density means fewer ticks update an object in the same span of "real" time than an area with higher density.

Of course, "real time" is a hard thing to pin down, and some would argue it's meaningless. But I've always found it easier to acknowledge that there's some relativity to reference frames than to try completely removing them from conversation.

• "Real" (proper) time is what a clock measures. Other notions of time are arbitrary constructions. Sep 16 at 17:16