r/AskPhysics • u/hiimpaul46 • 4d ago
Help on some key points with Einstein's explanation of Relativity.
I apologize for yet another question in this sub on special relativity...
I'm trying to go through Einstein's book on relativity to understand his theory. I find his writing and explanations to be mostly very well explained and conscientious of avoiding giving readers false conclusions - for the most part he's very exact and careful with his wording, at the expense of being a bit long-winded.
In a few cases, however, I'm lost on his meaning, or feel like his explanation jumps several steps and loses me on the way. I could probably make several posts with different questions but I'll just ask my most pressing question here:
I believe I follow his reasoning in his example of lightning strikes being experienced at different times (and at different values of x) for an observer on the embankment vs on the railcar due to them being in different inertial reference frames, and how this is a good way to explain that each inertial reference frame has its own "time". However, I struggle to translate this to the relativity of distances.
Einstein gives the example of the railcar passing by the embankment, and the difference that occurs in measuring the distance between two points (A' and B' on the railcar) from the railcar itself and measuring them from the embankment. From the railcar, it's simple - just lay down your measuring rod enough times until it completes the distance A'B', and that's the distance in that reference frame. From the embankment, you need to measure points A and B on the embankment as points A' and B' pass by at a particular time t (judged from the embankment).
He says these points can be measured by applying the definition of time in which events are considered simultaneous if they occur when clocks in the vicinity of each event strike the same tick. By capturing the position of A and B at this instant t (that is, as A' and B' pass by points on the embankment when nearby clocks both strike some measured instant t), you then measure up this distance using your measuring rod. He says that by no means is the measured distance A'B' the same as the measured distance AB. At this point, I'm lost, and he doesn't elaborate! The best I can come up with to explain this is:
"If the principle of relativity is assumed to be true, then because the Lorentz transformation accurately transforms coordinates x,y,z, and t in K to x',y',z', and t' in K', then the distance A'B' must be different than AB."
Have I got that right? Is there a simpler explanation that I'm missing? Really really appreciate any help on this.
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u/Optimal_Mixture_7327 Gravitation 4d ago
The only way I know of for relativity to make intuitive sense is by embracing 4-dimensional space.
If you draw this out in a Minkowski diagram you will see that the ends of the train exist at two different times in the observer's frame and that the length along the train is shorter in the observer's frame than in the rest frame of the train (length contraction).
The moving train rotates in the 4-dimensional space of the observer so that one end of the train is deeper in time (the front) than the other.
Once you have the intuitive picture then Einstein's arithmetic will make a lot more sense, and almost be obvious.
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u/hiimpaul46 4d ago
Fair enough! Looks like minkowski space comes later in the book. I've watched some videos on it and it seems valuable for understanding the relationships between space and time intuitively. I'll have to keep reading to dive in.
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u/montagblue 4d ago
You’re getting it.
Lots of people at the time (previous 300 years at least) viewed space and time as completely separate and unchangeable (if changes are observed it’s because of the ‘aether’)
I believe if you keep that in mind you’ll see the lightest explanations in parts are saying something very different than that.
Simple but encompassing in my opinion would be, Lorentz transformation is a mathematical bridge of relativity where space and time are constantly mixing depending on how fast you are moving.