Yes, exactly. Going fast squishes things. (Actually, going any speed relative to something else squishes things, and results in time dilation, but the effects are extremely tiny at everyday speeds, so they might as well be zero.)
Length contraction occurs in the direction of travel. If you observe a rocket sitting on the ground and measure its height, then later observe it traveling away from you, it will appear shorter.
(Actually, figuring out precisely how an observer would measure the length of a rocket traveling away from them is a good thought experiment in itself. See if you can puzzle it out. Measuring the rocket at rest is easy - you just need a really long ruler.)
You’re in a rocket. People on earth observe you moving away at 0.9c and you observe the earth moving away at 0.9c. We’ve already seen how time dilation causes the passage of time in your rocket to be different from that on earth. But since you and earth agree on your relative velocity (0.9c away from each other) and you disagree on the amount of time spent traveling, you must also disagree about the distance traveled. After all, if you were going a certain speed, your distance traveled is simply your speed multiplied by the time spent traveling.
But you on the rocket will experience less time than me on the ground. Ergo you will have experienced less distance as well. That’s length contraction.
This argument is a bit circular since you have to accept time dilation first. In reality, both effects (length contraction and time dilation) are consequences of the same thing: the constancy of the speed of light.
First, give up the notion that you will gain an intuitive understanding on why this is happening, it is beyond the human mind to do so completely and it will talk effort to get a basic intuitive understanding of the concepts. That said the effort is worth it IMHO.
The first half of this video may help, as there is no way to share math on this forum I have learned to not try and explain on here. They use animations which will help you visualize the core concepts although they don’t directly address the twins paradox a basic understanding of what the spacetime interval is and what a spacetime diagram is helping describe is useful.
Just remember that these are crutches to help our minds think about it, and not a direct representation of what is reality.
Typically the hardest initial task for people is giving up the incorrect idea that space and time are necessarily spatial and temporal, or that an intuitive understanding is really that possible.
The nice thing is that you can solve this paradox in special relativity so the math is relatively simple, here is a khan academy course that you can work up to.
I haven’t taken it, but if you want to “understand” what is going on I will be honest and say that will take that amount of effort to start to understand.
Here is the least intimidating page I could find on an overview on boosts, which is really the minimum you need to know how to calculate to understand the traveling twins paradox.
Understanding boosts and how to relate rapidities is well within reach if you had typical High School math, and if you avoid General Relativity that is all you should need.
If you just want a shorter explanation, which will help you understand, while not being really correct this will get you there with less work.
But that video has serious issues, but does semi cover that the fact that the space traveler "accelerates or turns around" is the critical portion. If a spaceship was flying past another spaceship and neither changed course for all of time they both would see the others clock running slower, there is no universal reference frame and there is no universal clock. But as there is a "boost" in the twin paradox the paths are not following geodesics and are not invariant and I really can't go into that without math.
If you have python experience I can point you at tools that will help a lot, but really to understand this you need to understand the math, Sorry.
At this level our intuition fails, so try hard to shed it.
This is a Special Relativity paradox and really isn’t dependent on acceleration, it is a plot device.
Time dilation is due to differences in relative velocity.
As an example lets say the curtain opens to an twin and the Earth traveling the same direction. The Earth traveling at .5c and the space passing by at .8c. After 14.4 of distant observer years, at which time he instantly tops and waits for the Earth to catch up with him.
For the Twin it was 8.66 years of flight, 8.66 years of waiting
For the Earth 20 years passed
And according to the distant observer, the twin traveled for 14.4 years and the total duration was 23.1 years.
I am calling myself out on this one because in my previous post I used the term acceleration, but this paradox is resolvable without it.
In fact Lorentz transformations don’t account for acceleration at all. This is a good example where analogies fall down at this level.
I know that I gave this same advice concerning quantum mechanics just a day or two ago, but special relativity really is a lot easier to understand than quantum mechanics. I’m not saying it’s easy, but it is possible to develop an intuitive understanding of special relativity.
And Lorentz transformations can account for acceleration, if you use calculus. But you can do them just fine for instantaneous velocity changes using only algebra.
In a universe where it’s possible to circumnavigate like this, you will indeed see a discrepancy when the twins re-unite, despite neither of them accelerating. Such a universe is not Lorentz-invariant, on a cosmological scale, contrary to the assumptions of special relativity (in other words, such a universe does have preferred reference frames).
The Twin Paradox has been mentioned a few times. It refers to the idea that the observer on Earth (“Terence”) and the observer on the rocket ship (“Stella”) each see the other’s clock going slower than their own. So when they (hypothetically) meet again, which one will still be young and spry, and which one will be Methuselah?
Here is a more detailed analysis and explanation of the Twin Paradox problem, and the on-going adventures of Terence and Stella!
Ya that is why I was very careful about adding the “completely” term. SR and some GR can be intuitive with lots of practice, but most for GR and it seems all QFT it seems to be a good indication you don’t understand the concepts.
Ya you can boost from the mobile frame to proper frame ever moment but once you add in rotation it becomes problematic. But I admit, to personally setting an un-official boundary between SR/GR based on the math required, and would consider that more of a localized GR task just due to the fun of dealing with math.
One of these days I will know enough javascript to make a webpage to allow the basic concepts of this more accessible. The machine learning craze has produced the required tensor libraries.
Yes, thank you for that analogy and I think it does make things clearer but I guess I just have to accept that this is the way the universe works and stop trying to use intuition because that just messes things up. But I am clearer now. Thanks again.
It all kind of works like clockwork (forgive the pun) doesn’t it! It’s quite amazing really and it makes me admire the mind of Einstein even more. Thank you sir for a very comprehensive explanation.
Einstein really was on a different level than even the other great minds of history, but special relativity doesn’t really demonstrate that. It’s an idea whose time had come, and if Einstein hadn’t come up with it, there are several others who would have, within a few years (and who in fact had a significant hand in polishing up the fine details of the theory).
Now, general relativity, that’s a different story. Some people had already worked on some pieces of what would become GR, but Einstein was the only one who realized what would happen if you put them together.
Funny, I had been cogitating on starting a thread on just this. Recently a few of us were talking about the history of science, and the question of how GR fitted in came up. I felt that GR was an idea way ahead of its time. And we started to think about the question of: if Einstein had not existed, when would GR have become an idea in its time. To some extent this question hinged on what experimental evidence would there have been that demanded a rethink. A hundred years ago there was no Michelson-Morley for GR.
Gravitational bending of light is covered by Newtonian gravity, it just gets the answer wrong by a factor of two. So I suspect even when gravitational lensing was observed (or even shifts in star positions in an eclipse) there would be a long delay before people decided that the difference in results was not just experimental error or a mistake in mass estimates. Our understanding of the history and nature of the cosmos would not have advanced nearly so much, but by itself I don’t see a significant driver for the science of GR here. The nature of black holes would be poorly understood, but I might guess that special relativity might provide enough of an approximation that we might be able to fit the observed data well enough that nobody was too concerned.
GPS satellites might have been the first clear evidence that something was not right, when they failed to work properly, and failed in a very clear and deterministic manner.
Experiments like looking for gravitational waves or frame dragging would simply have never been tried.
That about exhausts my thoughts. So, absent Einstein, when might GR have been an idea in its time, and pretty much guaranteed to have been developed, and why?
In fact, the famous Einstein-Eddington eclipse expedition, the first measurement of deflection of starlight, gave really bad data, with both the Einsteinian and Newtonian results within its error bars. And yet, in the popular mind, it was hailed as a victory for Einstein.
There was at least the 43 arcseconds-per-century anomalous perihelion precession of Mercury, which had already been observed. And one hypothesis for explaining it was in fact that gravity in some subtle way behaved differently from Newton’s model. But I don’t think anyone other than Einstein had provided any details of how it behaved differently.
Yeah, that was why I suggested any measurement may well have not pointed to GR, as the error was too great.
But I as I wrote, I do find it hard to work out any experimental pointer other than those performed explicitly to validate GR’s predictions that would have pointed the way until perhaps GPS. Which really does underline how amazing Einstein’s work was.
I think frame-dragging and gravitational waves would’ve actually have almost certainly been predicted without Einstein as it is not such a huge leap to obtain these predictions from work done by Lorentz, Poincare and Heavside before Einstein’s annus mirabilis papers were published and long before he started work on GR.
