Space is Relative: A 17 Yr Old's Exploration

[greg_rack]

TL;DR

Since I'm broadly confused :)

Hello everybody, my question may sound stupid, especially speaking of such a mind-blowing and important theory... but here I am!
I'm 17 and I'm reading a fabulous book by Stephen Hawking, "A Brief History of Time", and it introduced me to relativity theories... I literally started looking the world differently, it blew my mind!
But anyway, paradoxically, I think I've understood anything about it, apart from one thing: what do they mean with "relative space"?

 

[PeterDonis]

what do they mean with "relative space"?

That "space" depends on your choice of reference frame, since your choice of reference frame determines how spacetime is split up into "space" and "time". There is no unique way to do this because there is no unique choice of reference frame; all reference frames are equally valid.

 

[greg_rack]

That "space" depends on your choice of reference frame, since your choice of reference frame determines how spacetime is split up into "space" and "time". There is no unique way to do this because there is no unique choice of reference frame; all reference frames are equally valid.

Thank you so much, now it's clear!
And also, since spacetime curvature is affected by gravitational fields, how could it be affected by an osberver's velocity(e.g. the twins paradox)?

 

[PeterDonis]

spacetime curvature is affected by gravitational fields

It's really the other way around. Spacetime curvature causes gravitational fields (more precisely, it causes particular kinds of "gravitational fields"--other kinds can be produced in flat spacetime by being inside an accerating rocket). Spacetime curvature itself is caused by the presence of matter and energy.

how could it be affected by an osberver's velocity(e.g. the twins paradox)?

It isn't. An observer's velocity has nothing to do with spacetime curvature.

 

[Herman Trivilino]

I'm 17 and I'm reading a fabulous book by Stephen Hawking, "A Brief History of Time", and it introduced me to relativity theories... I literally started looking the world differently, it blew my mind!

Pick up a copy of Spacetime Physics by Taylor and Wheeler if you want to begin to understand relativity.

 

[anuttarasammyak]

And also, since spacetime curvature is affected by gravitational fields, how could it be affected by an osberver's velocity(e.g. the twins paradox)?

For the twins to meet again at least one of them have to change his/her course. It could break symmetry between them. Relativity does not always mean equality.

Let her twin get on a merry-go-round and him twin wait at the gate. It takes time T for one around.
On arrival her time is
$$\sqrt{1-\frac{V^2}{c^2}}\ T = \sqrt{1-\frac{R^2 \Omega^2}{c^2}}\ T = \sqrt{1+\frac{2\Phi}{c^2}} \ T$$
where R the radius, $\Omega=\frac{2\pi}{T}$ angular velocity, $\Phi=-\frac{1}{2}R^2\Omega^2$ potential energy per mass of centrifugal force which is zero at the center of merry-go-round. She and he agree with their time difference. He in IFR interprets it is due to time dilation by Lorentz transformation with V. She, not in IFR, interprets it is due to potential $\Phi$ in her FR. In his IFR she rotates and in her FR he rotates relatively. IFR or not makes difference.