Hi, i am new here. I was reading about general relativity and stumbled on the effect of time dilation where time seems to slow down when you travel close to the speed of light. Can someone explain how does it happen?
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Hi, i am new here. I was reading about general relativity and stumbled on the effect of time dilation where time seems to slow down when you travel close to the speed of light. Can someone explain how does it happen?
Order of Kilopi
Our old friend Wikipedia has a pretty good explanation.... [go there]Originally Posted by sforce21
Everyone is entitled to his own opinion, but not his own facts.
Order of Kilopi
There is a great deal on this here and, of course, on the internet that is far better than anything this amateur can say, but I'll join in anyway...
[If you do Google for it, try Special Relativity, it addresses this on an easier level since gravity and accelerated motion is left out of the equation. Cougar's link is a nice one.]
Einstein showed that space and time are not two separate absolutes. He showed that we have to combine them to obtain an absoute. This is contrary to intuition. But, a lot of things are not intuitive. If you've been to the top floor of a 100 story skyscraper you will experience no difference in how things behave. But, if you had this same skyscaper on a hypothetical planet of only a mile in a diameter that had a faster rotation rate, you would experience a difference in how you and other things moved around [the floor when comparing floor 1 with floor 100]. This principle still is true on existing skyscrapers but it is not easily measured.
Time doesn't slow down for the person watching their watch, it is stationary observers who will notice that a travelers time runs slower. There is a difference in spacetime that becomes noticeable once the relative speeds between the two are significant.
The key to this came about when Einstein discovered that the speed of light had to be measured as a constant regardless of any motion by any thing. This makes things very odd but this oddness has been found to be very true.
The easiest way for me to see a glimpse of what they are talking about is in the famous train analogy. Here it is...
Mr. Square is moving at the same speed of the train so light travels straight down the vertical distance, d, which is equal to the speed of light multiplied by the time it took to get there (ct).
But observers outside train will see Mr. Square go by and will see light move a distance of ct' (t' being simply the time measured by any observer outside the train).
Now we can use math to help solve for the time differences. Fortunately, we can use a simple right triangle equation and solve it. Hopefully, the math makes sense, but let me know if anyone needs help with it (or I have muffed it).
Last edited by George; 2007-Jun-29 at 07:12 PM.
We know time flies, we just can't see its wings.
Order of Kilopi
I remember explaining all this to my wife as we cycled across the Somerset levels next to each other. It is surprisingly easy to explain using a pair of bicycles.
As a librarian, she was not entirely interested, it has to be said.
Established Member
General Relativity?
Einstein first proposed 'time dialation' effect in his Special Theory of Relativity. The General Theory of Relativity extends the special relativistic effects to include Gravitation and non inertial refrence frames.
Relativity on the World Wide Web
Order of Kilopi
That's nicely concise, but is there a language where "X" means addition? I think the graphic should use + in place of X in the formulae. And by the way, sforce21, if the math seems a bit magic there, it's because there's a crucial assumption that is embedded in it: note that the speed of light, c, is assumed to be the same in both frames. If we were shooting bullets instead of light, we'd have to use c and c' for the speed of the bullets in the two frames, and you'd get normally intuitive "Galilean" relativity if you used the way c and c' would relate for bullets. But for light, we get to use the same c, as that's the fundamental postulate of relativity theory-- the speed of light is the same in all frames, as George mentioned. That's what is causing all the violence with space and time, and is the source of the time dilation.Here it is...
A little known fact about relativity that most people are confused about is that they think the speed of light being constant is a fundamental truth about reality, but actually there is some leeway there in terms of how we define things. The reason the speed of light comes out constant in all reference frames has to do with the way we define distance, in a way that is always consistent with sending out a light beam and timing how long it takes to come back. If you define distance in a way that is always consistent with that time measurement, it is completely obvious that you will always infer the speed of light to be the same. So the real question is, why does reality work out in such a way that a definition of distance that is always equivalent to the light timing measurement is a good way to define distance with regard to all other kinds of physics? For example, what if the moving person in the graphic had a stick of length D, and they hold it out and say "look, the length the photon travels corresponds to the length of this stick". Meanwhile, the stationary person holds out a stick of length D' and says, "no, this stick gives the length of the distance that the photon travelled." Those definitions of distance are consistent with light timing experiments in their own particular frame, but each person would clearly see what is "wrong" about the other person's distance measurement. The stationary person says the moving person is using a stick that is rotated with respect to the light path, so just because the light starts and finishes at opposite ends of the stick in no way suggests that this is a proper distance measurement. Meanwhile, the moving person says that the stationary person is the one who has their stick rotated with respect to the direction of the light path.
Note that if you are not constrained to lie the stick along the direction of the path, as you perceive that direction, you can get any length you want for physical displacement, by controlling the direction you move the stick as you connect the two ends of the displacement. Even if you specify the direction you must move the stick, you can still get a range of distances by altering the skew of the stick. Skewing sticks might seem like a weird way to measure distance, but remember there's no agreement as to what "skewed" even means. So the whole business has to do with our convention for measuring distance-- the ruler must lie along the direction of the path. The two observers can't agree what direction that is, so they get a different answer for that length.
In short, I see relativity as emerging not from a requirement that the speed of light be constant in all frames, but rather that we choose a convention for measuring distance that forces the speed of light to be constant in all frames (because it is always consistent with a light timing measurement). The reason we choose that distance convention is that it is quite convenient for obtaining a unique concept of distance for each observer, and works well with the other laws of physics, but it is still just an arbitrary convention. Because that convention cannot be applied in a consistent way for observers in relative motion, we get length contraction. Time dilation then follows from another arbitrary convention-- the meaning of simultaneity for observers that are not in the same place, which is also consistent with light timing measurements. See the pattern? We build our conventions around consistency with light timing measurements, then get all amazed that the speed of light comes out the same in all reference frames! The real question is, why are these the most useful conventions-- what gains and sacrifices do they imply?
In technojargon, this all means that the distance and simultaneity conventions we choose, when confronted with reality, spawn the Lorentz group as the symmetry of spacetime transformations. What other measurement conventions can be chosen and what mathematical objects would they spawn as their key transformation symmetry? Only when one looks at that does one get insight into what reality is doing, rather than what we are imprinting onto reality.
(edited for clarity)
Last edited by Ken G; 2007-Jun-29 at 06:49 PM.
Order of Kilopi
Oops. It is now fixed. [That one equatioin has 11 separate elements and I was rushing. The train's flat car was much easier to produce than the equation.]
I stay confused, so I like to say "measurement of the speed of light" rather than alternative ways of seeing it, though I am interested in learning of them.A little known fact about relativity that most people are confused about is that they think the speed of light being constant is a fundamental truth about reality, but actually there is some leeway there in terms of how we define things.
I'm gonna guess that if they both used the same amount of time of travel for the photon, and they stop the train, the sticks will be the same length. I say this because I expect both time and the photons speed to be the same when measured by each in their own reference frame. This seems logical, so it is probably wrong, especially since length contraction is real. [Also, I don't mind being the sacrificial lamb for pedagogical purposes, especially since you don't use intense flames.For example, what if the moving person in the graphic had a stick of length D, and they hold it out and say "look, the length the photon travels corresponds to the length of this stick". Meanwhile, the stationary person holds out a stick of length D' and says, "no, this stick gives the length of the distance that the photon travelled."]
I don't understand the rotation of the stick issue. Why would an observer claim the other persons's stick appears rotated?The stationary person says the moving person is using a stick that is rotated with respect to the light path, so just because the light starts and finishes at opposite ends of the stick in no way suggests that this is a proper distance measurement.
Kinda. If time is altered, the stick looks changed. If the stick contracts, time looks changed, but the speed of light is seen to be the same. They are one in the same no matter how you say it; tomato, tomahto (or how you spell it). Is this close?Time dilation then follows from another arbitrary convention-- the meaning of simultaneity for observers that are not in the same place, which is also consistent with light timing measurements. See the pattern?
We know time flies, we just can't see its wings.
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