You might think I write enough posts on Einstein’s theories of relativity, including the last one, but this one is less esoteric. It arose from a question I answered on Quora. Like a lot of questions on Quora, it’s provocative and you wonder whether the questioner is serious or not.
Before I came up with the title, I rejected 2 others: Relativity theory for dummies (which seemed patronising) and Relativity explained without equations or twins (which is better). But I settled on the one above, because it contains a thought experiment, which does exactly that. It’s a thought experiment I’ve considered numerous times in the past, but never expressed in writing.
I feel that the post also deals with some misconceptions: that SR arose from the failure of the Michelson-Morley experiments to measure the aether, and that GR has no relationship to Newton’s theory of gravity.
If the theories of relativity are so "revolutionary," why are they so incompatible with the 'real' world? In others(sic), why are the theories based on multiple assumptions in mathematics rather than the physical world?
You got one thing right, which is ‘theories’ plural – there is the special theory (SR) and the general theory (GR). As for ‘multiple assumptions in mathematics’, there was really only one fundamental assumption and that determined the mathematical formulation of both theories, but SR in particular (GR followed 10 years later).
The fundamental assumption was that the speed of light, c, is the same for all observers irrespective of their frame of reference, so not dependent on how fast they’re travelling relative to someone else, or, more importantly, the source of the light. This is completely counter-intuitive but is true based on all observations, including from the far reaches of the Universe. Imagine if, as per our common sense view of the world, that light travelled slower from a source receding from us and faster from a source approaching us.
That means that observing a galaxy far far away, the spiral arm travelling away from us would become increasingly out-of-sync with the arm travelling towards us. It’s hard to come up with a more graphic illustration that SR is true. The alternative is that the galaxy arms are travelling through an aether that permeates all of space. This was the accepted view before Einstein’s ‘revolutionary’ idea.
True: Einstein’s idea was premised on mathematics (not observation), but the mathematics of Maxwell’s equations, which ‘predicts’ the constant speed of light and provides a value for it. As someone said (Heinrich Hertz): “we get more out of [these equations] than was originally put into them.”
But SR didn’t take into account gravity, which unlike the fictitious aether, does permeate the whole universe, so Einstein developed GR. This was a mathematical theory, so not based on empirical observations, but it had to satisfy 3 criteria, established by Einstein at the outset.
1) It had to satisfy the conservation laws of energy, momentum and angular momentum
2) It had to allow for the equivalence of gravitational and inertial mass.
3) It had to reduce mathematically to Newton’s formula when relativistic effects were negligible.
Many people overlook the last one, when they claim that Einstein’s theory made Newton’s theory obsolete, when in fact, it extended it into realms it couldn’t compute. Likewise, Einstein’s theory also has limitations, yet to be resolved. Observations that confirmed the theory followed its mathematical formulation, which was probably a first in physics.
Note that the curvature of spacetime is a consequence of Einstein’s theory and not a presupposition, and was one of the earliest observational confirmations of said theory.
Source: The Road to Relativity; The History and Meaning of Einstein’s “The Foundation of General Relativity” (the original title of his paper) by Hanoch Gutfreund and Jurgen Renn.
Addendum: I elaborate on the relationship between Newton's and Einstein's theories on another post, in the context of How does science work?
2 comments:
Just a short note regarding SR (Special Relativity)
Let me bring up length contraction. That is when "objects" shrink in length because of SR. The object has to be going "fast". As I am famous for saying "Here's the trick": When the object moves along the x-axis at a very fast speed, it "shrinks" along the x-axis. BUT -- listen to this (it's good) -- it doesn't shrink along either the y-axis or z-axis. Further... OK, never mind, I'll let you wrap your head about that fact first.
Actually, I discuss this in another post, although I talk about the distance shrinking rather than the object itself. Ian Miller argues that it's the ruler that changes, and I'd concur, because I'd argue that the ruler for measuring distance travelled is the clock.
However, you're talking about the length of the object. I was surprised to learn that one needs to take this into account when comparing 'simultaneity' between different reference frames, which is described in this video.
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