General Relativity - The Warping Of Space-time

General Relativity Part 1

Special relativity came about when Einstein saw Maxwell's equations on electromagnetism contradicted Newton's Laws of motion. General relativity came from the next big contradiction in modern physics.

Newton could describe how gravity affected objects, but never knew how it actually worked. He admitted this himself, saying it was up to his readers to decide gravity's mechanism, as he also thought it was absurd to think gravity could act on two objects instantaneously across space.
Special relativity sets the cosmic speed limit at c and so we can see this contradicts what Newton predicted.

Einstein would need a theory where gravity and special relativity were compatible. A theory where gravity's effect was limited by the cosmic speed limit c.

Free-fall

If you fell from the Empire State building to the ground, during your fall you would feel no forces on you despite accelerating. OK, that's not entirely true but if we could remove air resistance then yes, you would not feel any forces. Close your eyes while you fall and you can't distinguish whether you are falling or whether you are in deep space where no forces are acting on you.

This suggests that free-fall is actually inertial motion (inertial motion is when you are moving at a constant velocity)
and if free-fall is inertial motion then gravity can't be a force.
This is because F = ma and if motion is inertial, a = 0 and so F = 0.

Fictitious Forces And Gravity

Consider being on a roller coaster. When the roller coaster starts, you feel the seat pushing on you in the direction of the acceleration. Change the roller coaster to a rocket going up, and you feel the floor of the rocket pushing up on you. If the rocket accelerates at 9.81m/s², you can't tell the difference between the gravity you feel on Earth and if the rocket is accelerating. The force you feel from the rocket would be exactly the same as the force you feel from the Earth's surface.
We call this force a fictitious force as it isn't real and is just the result of you being in a non-inertial reference frame.
Well the fictions force from acceleration feels the same as the force we feel from the Earth keeping us from falling through the ground.
So what if the force we feel from the ground is actually fictitious due to the Earth accelerating us upwards?
This establishes the fact that fictitious forces due to acceleration and gravity can not be distinguished.

Acceleration

Imagine being on a circular ride as shown in the diagram below.

What happens if people on the ride attempt to measure the radius of the circle? They would go to the centre of the circle and use a ruler to measure the distance to an edge. The direction they measure in is perpendicular to the velocity of the ride and so their rulers will not be length contracted. This means we will measure the same radius as them. When the riders try to measure the circumference something interesting will happen however. The direction they are measuring in is parallel to the velocity of the ride and so their rulers will be length contracted. This means they measure a different circumference to us. Geometry told us that pi = circumference/diameter
Well the riders are going to measure different a circumference to us and so they will get a different value for pi! How can special relativity violate basic geometry? Well the reason why is that pi is 3.141... only in Euclidean planes. If we move onto curved surfaces, the circumference of circles for any given radius can change and so the value for pi changes.
From this we can say that acceleration somehow bends space which is why we got weird measurements. It changes geometry from Euclidean (flat space) to Riemannian (curved space).

What about time ?

Remember time dilation? On the ride, people towards the edge move faster than people in the middle. This means people on the edge have slower clocks than people in the middle. The edge is also where acceleration is greater and so we can conclude that
acceleration is somehow warping space and time. 

The Warping Of Space-time

Gravity and acceleration are indistinguishable as seen from our rocket thought experiment. Acceleration warps space and time. Gravity therefore also warps space-time. Gravity is not a force, it is the curvature of space-time. That is what general relativity really boils down to and this is how Einstein explained gravity.

This explanation still probably isn't enough to justify general relativity over Newton's theory on gravity. We have claimed free fall is inertial motion but this doesn't really make sense because we definitely see falling objects accelerate. If we claim this is because it is actually us accelerating upwards and that falling objects are inertial, then why is the Earth not expanding radially?

These kind questions will be answered in part 2 of this mini-series and hopefully at the end you will have some understanding of why general relativity is superior to Newton's theory of gravity.



Thanks for reading. If you enjoyed this post or any of my others, follow and subscribe to my blog. Feel free to discuss anything related to this post or ask questions in the comments below.


Did you see my previous post? Click the link below to check it out

Special Relativity Overview