What do they mean when they say space time is curved? I keep hearing a lot of talk about Space Time being the 4th dimension, and no matter how many trampoline examples I see, I just don’t get it.
In: Physics
You actually can’t picture it but not for the reason that it’s 4d – that’s actually not a problem. The issue is that curved spacetime is formulated “intrinsically”, meaning from the perspective of people living on the manifold (us). This is done using something called “the metric” which describes the relationship between distances on the surface with respect to a predefined coordinate system. The metric then describes how distance and time measurements vary as you move through space and time along your coordinate grid.
This is like the walking on the globe examples others have given. Something missed is that you can’t prove whether you’re walking along the inside of the sphere or the outside by taking any measurement of the surface. They have the same metric.
The metric tells us everything it is possible to measure about the distances, angles and curvature but it doesn’t allow you to actually make a picture that you could be certain was the true “shape” of spacetime *no matter how many dimensions you could picture*. You can (kind-of) make pictures of several spacetimes that have the same metric as the ones we measure, but it’s not actually that helpful.
Another reason for this is that the metric is strictly local, it actually doesn’t tell you anything about the space as a whole, it just tells you that when you make a measurement at a point, this is what you can measure – and if you then see someone else measure something, how their measurement will be different to your measurement from your perspective. This is subtly different to describing the surface itself.
Tldr: differential geometry is hard and you can only begin to understand curved spacetime by learning a lot of very very dense and quite abstract math (compared to say high school math)
I want to say the trampoline example is bad but I won’t because that’s as close as it gets to see it in real. The below video breaks that misconception (??).
In short, imagine a 3d mesh instead of a single plane like the trampoline. That’ll help you visualize what space time curvature is. We know how it bendd but I guess we still don’t know why!
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