What really is “time”? (part 2 of 2)
(With this, my quest for trying to understand relativity and hence my blogs on this topic should come to a stop. I think I finally get more than 50% of the qualitative aspects of relativity & even though it is hard to wrap my head around every little aspect without the mathematics, I am somewhat at peace.)
So — A generalized theory of relativity.
All the examples about time’s relative nature (described in part 1) only work for frames of observation that are inertial — frames either moving at a constant velocity or those at rest with respect to the observer. What happens to this theory for accelerating frames of observation — Frames on which a force is continually acting? This is where Einstein’s ‘free falling elevator’ thought experiment comes in.
(I may use the terms “force” and “acceleration” interchangeably below. Force acting on a mass is anyway just some scaled measure of acceleration of a mass.)
Einstein’s Free Falling Elevator
Einstein realized that there is no way to differentiate :
(i) what a person inside a freely falling closed elevator in a gravitational field would experience in comparison from
(ii) what a person inside a freely moving closed elevator in deep space — where there is no gravity — would experience.
Why?
A) If you leave both these elevators as is — Both will just have objects / observer inside floating around freely.
B) If the elevator in deep space (where there is no gravity) is suddenly accelerated in a direction away from the person’s feet with 9.8 m/s², the person would feel his feet pressed against the floor of the elevator. (Even though there is no “upward” in space, let me refer to this direction as “upward” to keep it simple to refer to)
C) If the elevator is at rest on earth’s surface, he/she would still feel his pressed against the floor of the elevator.
Can a person inside these elevators differentiate and confirm which elevator he/she is in for cases B and C? No. In both the cases, objects will fall down to the floor of the elevator, if dropped. In both cases, the person inside will be pressed against the floor of the elevator.
So, let’s generalize a bit — a body at rest in a gravitational field is completely analogous to a body accelerating upward in zero gravity. Also, a body freely falling in gravity is completely analogous to a freely floating body, in zero gravity.
Isn’t this making it hard to explain with Newton’s theory? In Newton’s first law, he described an object at rest as an inertial state of the object. In this inertial state, elevators will continue to be unchanged until a force acts on them. However, a freely falling elevator is continuously accelerating. How can an elevator at a state of rest on earth’s surface be indistinguishable from an elevator in a state of continuous acceleration in deep space?
This contradiction and the thought experiment that led to it was the most enlightening thought of his entire life, Einstein says.
The sheer brilliance of Einstein comes out in his bold proposal where he attempted to explain this apparent contradiction — he argued that space itself had to be curved.
What’s the connection? Why should space itself be curved?
Take a torch and shine its beam from outside the elevator in deep space and imagine sending the beam from one wall of this upward accelerating elevator towards the other wall of the elevator. It will hit the other wall at a slightly lower point. This is because the lift has moved upward, relative to the torch source.
However, a body at rest in gravity seems analogous to a body accelerating upward in free space. We just established that.
So, even for the elevator at rest on earth’s surface, light should hit the other wall at a slightly lower point. Light does not know the difference between the two elevators! This makes it look like light is bending downward and hitting the other wall.
Hey, but wait! Did we not know light only travels in straight lines. Why will it just bend downward and hit the wall slightly lower?
… Unless… Space itself is bent in gravity! (The same guts Einstein showed in relaxing the absoluteness of the flow of time when it did not fit with his logical deduction)
A gravitational field must be curving space … and light must just be following that curve.
THE GRAND CONCLUSION:
Einstein explained that the ‘force’ we experience as gravity is not a force at all. It is a bend in space which is the only natural path available for all of us, including light, to move in. We can hence respect the concept of inertia and we can still move in a curved manner, without the need for an acceleration(force) to explain the continuous change in direction, because, (please repeat after me!)… space itself is curved.
So, Einstein proposed that gravity is actually a geometric aspect of space’s deformation because of matter’s presence in it. Continuous acceleration experienced by a body during free fall in gravity is as much a steady state (“inertial state”) as being at rest without any forces acting on the body because in the former case space itself has deformed in the gravitational field.
Also, this bend in space (gravity) is what matter has available to move around (orbits etc. ) and as it does move… it keeps bending space along with it.
And hence the quote by John wheeler — “Matter tells space how to bend. Space in turn tells matter how to move”.
This is really well understood with the brilliant analogy of a ball on a trampoline. A video I have shared with many is here. Even after seeing it so many times I find the 4:40 point — when a sun-earth-moon system is established — really amazing.
