General Relativity Part 2: Problems with Newtonian Gravity
"Put your hand on a hot stove for a minute, and it seems like an hour. Sit with a pretty girl for an hour, and it seems like a minute. That’s relativity."
-Albert Einstein-
If only summarising relativity would be so simple.
From Part 1 we have summarised how time dilation, length contraction and mass increase happens at relativistic speeds. By using the Lorentz gamma factor, we can calculate exactly how much of the spatial dimension is ‘converted’ into the temporal dimension in our 4 dimensional space time. In other words, the length of the object in the direction of relativistic travel decreases by the same factor as the increase in the passing of time in the reference frame. Analogically, we can use plasticin (or Play-Doh), when squeezed in a dimension, it automatically increases its quantity in the other 2 spatial dimensions while retaining the same volume of space. In this analogy, the volume of the plasticin is space time, and the squeezed dimension time, and the other 2 dimensions, the 3 dimensions of space.
I would like to point out here that although space and time are relative, space time as a whole is an unvarying quantity. The same applies to momentum and energy and a host of other physical quantities. The compound value (call it momenergy if you want) is the same! This is the reason why Einstein did not really like calling his ideas having the notion of relative attached to it, which is potentially misleading and highlights only the ‘relative’ part of his theory which is only a constituent part of the whole idea. He sympathised with a group of scientists, who lobbied to have the name changed to the ‘theory of invariance’ but failed because the ‘theory of relativity’ already stuck.
Moving on, we have seen how Newton describes gravity is a mysterious force that somehow instantly reaches out across an immutable, unchanging, universal, 3D space to influence distant objects.
Einstein was aware of the contradictions between gravity and relativity in 1907, but he only began to think seriously about the problem in 1911, when he moved to Prague from Bern (where he was working at the patent office). He realised that there is a close relationship between acceleration and a gravitational field.
Now, on to another Gedankenexperiment. Imagine that you are in an elevator at the top of a tall building holding a ball. Yes, your feet stays where they were, on the floor. If you release the ball, if falls to the floor with an acceleration of 9.81m/s^2. Now, if I cut the cable holding the elevator, the elevator, you and the ball enters a state of free float as it falls down the elevator shaft. Yep, apparent weightlessness.
Now, in another situation, I load you, the ball and the same elevator and blast you into outer space, far away from any objects that can exert significant gravitational influence on you. The elevator is ‘upright’, with the floor pointing towards the ‘bottom’ of the spaceship. Once there, the rocket engine turns off. What do you feel? Yes, apparent weightlessness again! Then, I ignite the engine for another burn, this time firing it in a way that it accelerates the spaceship and everything in it at 9.81m/s^2. Oops, sorry to interrupt your zero G party there. You fall back to the floor of the elevator, with the ball.
Ok, thought experimenting is over. Comparing the situations that I just asked you to imagine, could you tell me that there is any way that you can distinguish the exact moment after I ignited the rocket engine to fire with a = 9.81m/s^2 and when you are still connected to the cable on top of the elevator shaft? Besides that, could you distinguish the exact moment after I turned off the rocket engine in outer space, and the moment after I cut the elevator cable back on Earth?
The answer is, in most cases, you will not be able to distinguish any difference. All your experiments, will behave the same way in both elevators when they’re accelerating or held by a cable on Earth, and likewise applies to when you’re in outer space, of falling down on Earth. What about the exceptions? I’ll go there later.
This inability to differentiate the situations leads to the Principle of Equivalence. It states that ‘No observer can determine by experiment whether he or she is accelerating or is rather in a gravitational field’.
To digress a little, this principle helped solve a problem in physics along the way. All this while, inertial mass and gravitational mass is the same. In other words, the m of an object in F=ma and F=GMm/R^2 is the same in two different equations, yet in Coulomb’s Law, you do not use mass but charge instead. So, why does inertial mass and gravitational mass of an object assume identical values but not for ‘electrical mass’? Before this, it is just assumed that inertial mass and gravitational mass are the same although charge is not related to them. As experiments showed that they are identical, physicists just assumed it to be so without any explanation.
As it turns out, acceleration by contact force (rocket engine) and gravity are indistinguishable according to the principle of equivalence. So, this means that inertial mass and gravitational mass are the same, a different way of interpreting the principle of equivalence.
Back to where we left off. Now, the idea behind General Relativity is to extend the Principle of Relativity to all reference frames, inertial or not. But as you can see with the elevator on Earth, gravity is ‘present’ when you’re still hanging on top of the elevator shaft, but suddenly disappears when I cut the cable and you fall down the shaft. As the force of gravity does not appear in all reference frames, Einstein reasoned that it can’t be one of those deep, underlying, objectively real aspects of the world. In general relativity, a phenomenon should be real only if observers in all reference frames agree about it. Therefore, a phenomenon that’s present in one reference frame but not another can’t be objectively real.
So what is gravity?
