3 ms·

It's one of a bunch of mathematical conclusions of Special Relativity (the most famous one being that objects at rest have a "kinetic" energy of mc^2). I'll try

by euyyn 10y ago

It's one of a bunch of mathematical conclusions of Special Relativity (the most famous one being that objects at rest have a "kinetic" energy of mc^2). I'll try to explain it simply, without the math: Imagine a friend and you, moving very fast with respect to each other. You measure your friend's clock as advancing slowly (due to time dilation), on account of the fact that he's moving with respect to you. But your friend measures _your_ clock as advancing more slowly than _his_, because motion is relative. The way to reconcile this mathematically is to give up on absolute simultaneity of distant events. In other words, when two things happen in different places, at the same time according to your clock, they happened at different times according to your friend's clock. This is analogous to how you measure your friend to be in different places in different times (because he's moving with respect to you), but he measures himself to be stationary, always in the same place. To recap: If comparing things at different moments, "being in the same position or not" is relative to the observer. If comparing things at different places, "happening at the same time or not" is relative to the observer. That's how causality comes in. If your friend tosses a very fast ball at you, and the moment you receive the ball you start towards him faster-than-c, you'll arrive where he is before he tossed it (if you went fast enough). That's what the equations say. Now the breaking of absolute simultaneity allows naturally for disagreements on what of two things happened first, assuming they happened far enough from each other that light couldn't cover the distance in time. But by putting faster-than-c velocities in the equations, we have your friend and you disagreeing on what happened first (him tossing the ball, or you arriving where he is?) in what (to him) is the same place. And it's not just a confusion of the mind: all your measuring and recording artifacts will agree with you, and all of his will agree with him. The mathematical conclusion is that if you can send information faster-than-c, you can send it back in time and break causality.

mariodiana 10y ago
I want to make sure I understand "time dilation," as you describe it. I have no formal background in science or math. So, please bear with me. For the sake of making the math easy, I'm going to talk about traveling faster than the speed of light, but only for the sake of argument. You'll see why. I understand it this way. Assume I were traveling away from my friend at twice the speed of light. My time of departure is 12:00:00. After 1 second (my clock) I have traveled 2 light-seconds. Light reflected off the face of my clock now travels towards my friend, reading 12:00:01. We'll call this view of my clock a "snapshot." From my friend's point of view, that snapshot reaches him at 12:00:03. Yes? Now, we allow for 1 additional second, my time. I have traveled in total 4 light-seconds. My 12:00:02 snapshot now travels towards my friend. It reaches him at 12:00:06, his time. Yes? So, from my friend's point of view, my time has seemed to slow down. Is that what you mean by time dilation?
- zo1 10y ago
  Try not to think of time-dilation in relation to "light travelling". Time dilation just means that time passes more slowly for you due to your speed relative to an observer. So imagine you have an identical twin, and you leave on a Journey to a nearby solar system at say 0.9x the speed of light. Your twin stays on earth and for arguments sake you can say he is "stationary" in comparison to you. When you come back, he'll be much more "aged" than you. You had a clock on-board your craft, and it measured your trip as say "2 years". Likewise, your twin also had a clock and it measured your trip as having lasted "20 years". The clocks are not wrong. And trust me, this isn't some science-fiction type thing we're discussing. GPS satellites orbiting the Earth carry very accurate atomic-clocks, and they need to take time-dilation into account in order to compensate for the drift in values, simply due to the accuracy necessary for GPS. Just had a look on the wiki page, and the drift is approximately 38 microseconds per day. When I first encountered this concept in high-school randomly, I was quite shocked at how "non-complicated" the equation for it is. https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity https://en.wikipedia.org/wiki/Time_dilation#Simple_inference... https://en.wikipedia.org/wiki/Global_Positioning_System https://en.wikipedia.org/wiki/Global_Positioning_System
  - mariodiana 10y ago
    In that first link, where it says (referring to the diagram at the bottom right), "Observer moving parallel relative to setup [...]," I don't understand. Parallel to what? Parallel to the mirrors? Parallel to the beam of light? I don't find it to be clear. Can you tell me which it is? Thanks. ------ P.S. Never mind. I follow the diagram now. I'm trying to follow the rest of it.
- euyyn 10y ago
  Ah, good observation! But what you're describing isn't relativistic time dilation. It is called "the (non-Relativistic) Doppler effect", and can be commonly experienced when a race car, an ambulance, or a train passes you: When it's approaching, the noise will have a higher pitch than when it's passed. This is because the frequency of things that move towards us appear higher than they are, and that of things that move away from us appear lower. It's also why stars that move away from us appear more red than they are (they are said to be "red-shifted"). Imagine the same scenario you described (there's actually no need to use faster-than-c speeds for it), but your friend has planted clocks all along the path that you're traveling. Once he's back at his starting position, he synchronizes them all (there are techniques to achieve this - Einstein famously proposed one). Now when you pass him and keep moving away from him, every second you take a picture of your own clock next to the clock planted on the path. In a non-relativistic world, the pictures will show that your clock is always synchronized with all of your friend's clocks. Making the observation this way rids us of the Doppler effect. But a non-relativistic world isn't the real world! In reality, if you go fast enough (close enough to c), the pictures will show e.g. your clock marking 12:00:01 when the clock in the path marks 12:00:02. And your clock marking 12:00:02 when you encountered the next clock in the path marking 12:00:04. In other words, your friend (and everything that's stationary with respect to him) will measure your time passing more slowly. Using these example numbers, in what for them is the pass of 2 seconds, you (and everything moving at your same speed - like your clock) have only aged 1 second. This is relativistic time dilation. It's shocking, but it's a fact that's been established for 110 years (and its mathematical consequences help explain even the microelectronics you and me are using). Now this happens no matter what speed you move with respect to your friend. But for everyday speeds it's so small as to be imperceptible - it only becomes noticeable at speeds like that of GPS satellites. An immediate question is: > Wait, if I move away from my friend, from my point of view my friend is moving away from me. So I should measure his clocks advancing more slowly than mine. And that is correct, and is exactly what would happen! > But the pictures I took show the opposite? No! They show your clock compared to different clocks. And these clocks on the path, that your friend synchronized, by your measurements they all started at different times. I.e. for you, none of these clocks are synchronized. For your friend, they all marked 12:00:00 simultaneously. For you, they all marked 12:00:00 at different moments. In non-relativistic physics, simultaneity was an absolute concept: If two things happened at the same time, they happened at the same time for everybody. In reality, if I'm moving with respect to you, what happens at the same time in different locations for me, doesn't happen at the same time for you.

by euyyn 10y ago

mariodiana 10y ago

I want to make sure I understand "time dilation," as you describe it. I have no formal background in science or math. So, please bear with me. For the sake of making the math easy, I'm going to talk about traveling faster than the speed of light, but only for the sake of argument. You'll see why. I understand it this way. Assume I were traveling away from my friend at twice the speed of light. My time of departure is 12:00:00. After 1 second (my clock) I have traveled 2 light-seconds. Light reflected off the face of my clock now travels towards my friend, reading 12:00:01. We'll call this view of my clock a "snapshot." From my friend's point of view, that snapshot reaches him at 12:00:03. Yes? Now, we allow for 1 additional second, my time. I have traveled in total 4 light-seconds. My 12:00:02 snapshot now travels towards my friend. It reaches him at 12:00:06, his time. Yes? So, from my friend's point of view, my time has seemed to slow down. Is that what you mean by time dilation?

zo1 10y ago
Try not to think of time-dilation in relation to "light travelling". Time dilation just means that time passes more slowly for you due to your speed relative to an observer. So imagine you have an identical twin, and you leave on a Journey to a nearby solar system at say 0.9x the speed of light. Your twin stays on earth and for arguments sake you can say he is "stationary" in comparison to you. When you come back, he'll be much more "aged" than you. You had a clock on-board your craft, and it measured your trip as say "2 years". Likewise, your twin also had a clock and it measured your trip as having lasted "20 years". The clocks are not wrong. And trust me, this isn't some science-fiction type thing we're discussing. GPS satellites orbiting the Earth carry very accurate atomic-clocks, and they need to take time-dilation into account in order to compensate for the drift in values, simply due to the accuracy necessary for GPS. Just had a look on the wiki page, and the drift is approximately 38 microseconds per day. When I first encountered this concept in high-school randomly, I was quite shocked at how "non-complicated" the equation for it is. https://en.wikipedia.org/wiki/Time_dilation#Simple_inference_of_time_dilation_due_to_relative_velocity https://en.wikipedia.org/wiki/Time_dilation#Simple_inference... https://en.wikipedia.org/wiki/Global_Positioning_System https://en.wikipedia.org/wiki/Global_Positioning_System
- mariodiana 10y ago
  In that first link, where it says (referring to the diagram at the bottom right), "Observer moving parallel relative to setup [...]," I don't understand. Parallel to what? Parallel to the mirrors? Parallel to the beam of light? I don't find it to be clear. Can you tell me which it is? Thanks. ------ P.S. Never mind. I follow the diagram now. I'm trying to follow the rest of it.
euyyn 10y ago
Ah, good observation! But what you're describing isn't relativistic time dilation. It is called "the (non-Relativistic) Doppler effect", and can be commonly experienced when a race car, an ambulance, or a train passes you: When it's approaching, the noise will have a higher pitch than when it's passed. This is because the frequency of things that move towards us appear higher than they are, and that of things that move away from us appear lower. It's also why stars that move away from us appear more red than they are (they are said to be "red-shifted"). Imagine the same scenario you described (there's actually no need to use faster-than-c speeds for it), but your friend has planted clocks all along the path that you're traveling. Once he's back at his starting position, he synchronizes them all (there are techniques to achieve this - Einstein famously proposed one). Now when you pass him and keep moving away from him, every second you take a picture of your own clock next to the clock planted on the path. In a non-relativistic world, the pictures will show that your clock is always synchronized with all of your friend's clocks. Making the observation this way rids us of the Doppler effect. But a non-relativistic world isn't the real world! In reality, if you go fast enough (close enough to c), the pictures will show e.g. your clock marking 12:00:01 when the clock in the path marks 12:00:02. And your clock marking 12:00:02 when you encountered the next clock in the path marking 12:00:04. In other words, your friend (and everything that's stationary with respect to him) will measure your time passing more slowly. Using these example numbers, in what for them is the pass of 2 seconds, you (and everything moving at your same speed - like your clock) have only aged 1 second. This is relativistic time dilation. It's shocking, but it's a fact that's been established for 110 years (and its mathematical consequences help explain even the microelectronics you and me are using). Now this happens no matter what speed you move with respect to your friend. But for everyday speeds it's so small as to be imperceptible - it only becomes noticeable at speeds like that of GPS satellites. An immediate question is: > Wait, if I move away from my friend, from my point of view my friend is moving away from me. So I should measure his clocks advancing more slowly than mine. And that is correct, and is exactly what would happen! > But the pictures I took show the opposite? No! They show your clock compared to different clocks. And these clocks on the path, that your friend synchronized, by your measurements they all started at different times. I.e. for you, none of these clocks are synchronized. For your friend, they all marked 12:00:00 simultaneously. For you, they all marked 12:00:00 at different moments. In non-relativistic physics, simultaneity was an absolute concept: If two things happened at the same time, they happened at the same time for everybody. In reality, if I'm moving with respect to you, what happens at the same time in different locations for me, doesn't happen at the same time for you.