4 ms·

@fferen Thank you for sharing your work. This is an excellent resource. If you don’t mind, I have a question. If I drive in a straight line on the Earth’s sur

@fferen Thank you for sharing your work. This is an excellent resource. If you don’t mind, I have a question. If I drive in a straight line on the Earth’s surface without stopping and I ignore mountains and oceans and other obstacles, then after 16 days, I will arrive at my starting point. Why is this? It’s because the Earth is a sphere. This is a nice satisfying answer, whereas x^2+y^2+z^2=r^2, while perfectly accurate, is arguably less satisfying. Given this context, my question is, for special relativity, why do time dilation and length contraction happen? Ideally, I’m looking for an answer that has the same satisfying intuitive flavor as “Because the Earth is a sphere”, or at least is suggestive of that kind of answer.

fferen 5y ago
Thanks! I don't believe these two concepts are related. You get back to the same point because the earth is _globally_ a sphere. However, time dilation and length contraction are _local_ concepts: they happen even for very small motions. I guess a global object in spacetime analogous to a sphere in space is the hyperboloid t^2 - x^2 = r^2. Moving on this hyperboloid corresponds to changing boost velocity. But unlike a sphere, it is not closed, so moving in one direction does not get you back to the same point. May add to this answer later.
- drewolbrich 5y ago
  Apologies, I didn't mean to suggest that the two concepts are related. For SR, I'm looking for an answer to "why?" that only has same satisfying flavor as the sphere question. I want the same "aha!" feeling. For example, if I stand up from the sofa and walk across the room and come back and sit down next to my friend, I want a deep intuitive sense that of course it must be the case that less time has passed for me than the amount of time that my friend has experienced. Why does this happen? An answer like "t'=t/sqrt(1-v^2/c^2) describes what happens", while correct, is not satisfying. Similarly, if I wave my hand in front of my face, I want it to seem obvious to me that less time must have passed for my hand than for the rest of my body. Given your experience writing the book, you must have developed an intuitive sense for the behavior of the effects of relativity and why they happen, so I am wondering how you would translate that into words for a general audience. Imagine the context where a random person with a minimal math background at a party was to ask you why less time passes in the sofa scenario, using an actual sofa to demonstrate it. They stand up and walk away from you and return and sit back down next to you and they want you to explain to them why less time has passed for them. They want you to explain why the room around them got shorter in the direction that they were walking. These are effects that, while undetectably small, really happened. They want to know why. How would you answer their question?
  - fferen 5y ago
    I see. I don't know of a great answer, but it comes down to the constant speed of light. The simplest clock is two parallel mirrors with light bouncing back and forth. If someone is moving, then the light seems to take longer to bounce between them, so their clock appears slower. Wiki has a a good explanation: https://en.wikipedia.org/wiki/Time_dilation#Simple_inference https://en.wikipedia.org/wiki/Time_dilation#Simple_inference In the hypothetical party scenario, you could demonstrate with your hands or some objects as mirrors. Not the most satisfying answer, but if relativity was super intuitive, I probably wouldn't have written this book :)
mhh__ 5y ago
I'm not sure a satisfactory answer necessarily exists here. The earth is a sphere, but you are asking a question about a mechanical action whereas time dilation and friends are fundamental statements about the nature of measurement itself.
- Koshkin 5y ago
  That’s exactly what often troubles students of special relativity - why should a physical quantity be defined by the way you are trying to measure it. (The mass is the mass, for example, no matter what device you construct to measure it. In special relativity, on the other hand, the very notion of time interval seems to be tied to observing how light travels between mirrors.)
richardw 5y ago
Not the expert you’re looking for but here’s my intuitive reasoning: Because light will always be moving at the speed of light for you. You move at 0C. As you speed up, time slows down to preserve that.
random314 5y ago
While this might not be the answer you are looking for, but I can present an argument about why time dilation must be true to explain electromagnetism. The experiment produces apparently paradoxical equations that simply happen to work out fine. Trying to explain this experiment forces us to accept special relativity. https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_problem https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_...
cygx 5y ago
Given this context, my question is, for special relativity, why do time dilation and length contraction happen? Place two rulers right next to each other, and their length scales will agree. Now, place them at an angle, and have one ruler measure the other by orthogonal projection. Each of the observers represented by the rulers will conclude that the other one has 'contracted' by a factor given by the cosine of the angle. Now, add a third ruler to complete the triangle. To go from one vertex to the opposite one, you can either follow along a single ruler, or via a bent path along two rulers. The symmetry has been broken, and the bent path will be objectively longer - that's the twin 'paradox'. Things are more complicated than that because Minkowski space is non-Euclidean (for example, less time will pass for the travelling twin, ie the bent path will be the 'shorter' one), but if you want a simple analogy, I think that's a pretty decent one...
random314 5y ago
I found a much better explanation today on hacker news. Linking it here https://gravityandlevity.wordpress.com/2009/04/08/why-cant-i-go-faster-than-the-speed-of-light-hints-from-electrodynamics/ https://gravityandlevity.wordpress.com/2009/04/08/why-cant-i...

fferen 5y ago

Thanks! I don't believe these two concepts are related. You get back to the same point because the earth is _globally_ a sphere. However, time dilation and length contraction are _local_ concepts: they happen even for very small motions. I guess a global object in spacetime analogous to a sphere in space is the hyperboloid t^2 - x^2 = r^2. Moving on this hyperboloid corresponds to changing boost velocity. But unlike a sphere, it is not closed, so moving in one direction does not get you back to the same point. May add to this answer later.

drewolbrich 5y ago
Apologies, I didn't mean to suggest that the two concepts are related. For SR, I'm looking for an answer to "why?" that only has same satisfying flavor as the sphere question. I want the same "aha!" feeling. For example, if I stand up from the sofa and walk across the room and come back and sit down next to my friend, I want a deep intuitive sense that of course it must be the case that less time has passed for me than the amount of time that my friend has experienced. Why does this happen? An answer like "t'=t/sqrt(1-v^2/c^2) describes what happens", while correct, is not satisfying. Similarly, if I wave my hand in front of my face, I want it to seem obvious to me that less time must have passed for my hand than for the rest of my body. Given your experience writing the book, you must have developed an intuitive sense for the behavior of the effects of relativity and why they happen, so I am wondering how you would translate that into words for a general audience. Imagine the context where a random person with a minimal math background at a party was to ask you why less time passes in the sofa scenario, using an actual sofa to demonstrate it. They stand up and walk away from you and return and sit back down next to you and they want you to explain to them why less time has passed for them. They want you to explain why the room around them got shorter in the direction that they were walking. These are effects that, while undetectably small, really happened. They want to know why. How would you answer their question?
- fferen 5y ago
  I see. I don't know of a great answer, but it comes down to the constant speed of light. The simplest clock is two parallel mirrors with light bouncing back and forth. If someone is moving, then the light seems to take longer to bounce between them, so their clock appears slower. Wiki has a a good explanation: https://en.wikipedia.org/wiki/Time_dilation#Simple_inference https://en.wikipedia.org/wiki/Time_dilation#Simple_inference In the hypothetical party scenario, you could demonstrate with your hands or some objects as mirrors. Not the most satisfying answer, but if relativity was super intuitive, I probably wouldn't have written this book :)

mhh__ 5y ago

I'm not sure a satisfactory answer necessarily exists here. The earth is a sphere, but you are asking a question about a mechanical action whereas time dilation and friends are fundamental statements about the nature of measurement itself.

Koshkin 5y ago
That’s exactly what often troubles students of special relativity - why should a physical quantity be defined by the way you are trying to measure it. (The mass is the mass, for example, no matter what device you construct to measure it. In special relativity, on the other hand, the very notion of time interval seems to be tied to observing how light travels between mirrors.)

richardw 5y ago

Not the expert you’re looking for but here’s my intuitive reasoning: Because light will always be moving at the speed of light for you. You move at 0C. As you speed up, time slows down to preserve that.

random314 5y ago

While this might not be the answer you are looking for, but I can present an argument about why time dilation must be true to explain electromagnetism. The experiment produces apparently paradoxical equations that simply happen to work out fine. Trying to explain this experiment forces us to accept special relativity. https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_problem https://en.m.wikipedia.org/wiki/Moving_magnet_and_conductor_...

cygx 5y ago

Given this context, my question is, for special relativity, why do time dilation and length contraction happen? Place two rulers right next to each other, and their length scales will agree. Now, place them at an angle, and have one ruler measure the other by orthogonal projection. Each of the observers represented by the rulers will conclude that the other one has 'contracted' by a factor given by the cosine of the angle. Now, add a third ruler to complete the triangle. To go from one vertex to the opposite one, you can either follow along a single ruler, or via a bent path along two rulers. The symmetry has been broken, and the bent path will be objectively longer - that's the twin 'paradox'. Things are more complicated than that because Minkowski space is non-Euclidean (for example, less time will pass for the travelling twin, ie the bent path will be the 'shorter' one), but if you want a simple analogy, I think that's a pretty decent one...

random314 5y ago

I found a much better explanation today on hacker news. Linking it here https://gravityandlevity.wordpress.com/2009/04/08/why-cant-i-go-faster-than-the-speed-of-light-hints-from-electrodynamics/ https://gravityandlevity.wordpress.com/2009/04/08/why-cant-i...