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Could anybody explain the theory behind time dilation and how exactly time dilation works?
Consider the two postulates of relativityOriginally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?
Originally posted by Loren Booda
Consider yourself at a launch pad, wherefrom a rocket is launched vertically at constant speed v. The rocket sends a monochromatic laser signal back to the pad. A counter on the ground collects the number of wavelengths sent out by the craft on its away trip, as it does with the return trip at the same velocity. It is found, with c being the constant velocity of light in all inertial frames, that the wavelength of the light signal for the away trip exceeds the wavelength of the standard laser signal exceeds the wavelength for the return trip. Think of the observed laser wave train (representing a "standard meter") from the spaceship being dilated as it moves out, and contracted as it returns. Time is measured as [del]t=[lamb]/c, where [lamb] is wavelength.
Regarding the second part of your question; I'm afraid I have no idea why the speed of light is constant. I'm not sure anyone knows, we just keep measuring it and it allways comes up the same.Originally posted by Koveras00
Can anyone explain how and why the wavelength wil be different during the away and return trip and any explanation behind that the speed of light is constant?
It does depend on the background you come from I think chroot. When I talk about time dialation to a lot of ordinary people they think I have been watching too much Star Trek.Originally posted by chroot
jackle,
I certainly wouldn't say it's incredibly complicated... in fact, I'd say it's very simple. Basic high-school algebra is the only mathematical tool you'll need to compute things in special relativity.
- Warren
The problem that I have with this, Stranger, is that in order to "see" the light, its rays need to come towards me first; and let the light's speed coming towards me be constant.Originally posted by Stranger
Another easy meathod to visualize time dilation can be this....
Imagine that you are looking out from the porthole of your spaceship into another.....the two ships are passing each other with a uniform velocity close to the speed of light.....as they pass a beam of light on the other ship is sent from its ceiling to its floor...........there it strikes a mirror and is reflected back....you will see the path of light as 'V' while the person in that ship will see it as a straight line.....with some instrument you could clock the time it takes for the beam to traverse teh V shape....by dividing the length and teh path, you obtain the speed of light...
Now while you are doing this....the person in the other ship is doing the same thing.... to his point of view light simply goes up and down along the same line, obviously a shorter distance than along the V path that you observed...when he divides the distance of the straight line path he observes by the time....he gets the speed of light.....because the speed of light is constant for all observors he should get the same answer as yours.....but his light path is shorter...how can the results be the same.....there is only one possible explanation: his clock is slower.... ofcourse the situation is perfectly symmetrical.....
Hello Loren:Originally posted by Loren Booda
Consider yourself at a launch pad, wherefrom a rocket is launched vertically at constant speed v. The rocket sends a monochromatic laser signal back to the pad. A counter on the ground collects the number of wavelengths sent out by the craft on its away trip, as it does with the return trip at the same velocity. It is found, with c being the constant velocity of light in all inertial frames, that the wavelength of the light signal for the away trip exceeds the wavelength of the standard laser signal exceeds the wavelength for the return trip. Think of the observed laser wave train (representing a "standard meter") from the spaceship being dilated as it moves out, and contracted as it returns. Time is measured as [del]t=[lamb]/c, where [lamb] is wavelength.
Other variations of the trip include moving horizontally across the point of observation, or diagonal trajectories. The Pythagorean theorem may be used to help derive these special relativistic transformations of length, time, mass, velocity and energy.
Good explanation, Lurch:Originally posted by LURCH
Regarding the second part of your question; I'm afraid I have no idea why the speed of light is constant. I'm not sure anyone knows, we just keep measuring it and it allways comes up the same.
Taking that as a given, I have an annalogy that might help you understand the change in wavelength/frequency of light from a moving source.
Suppose I have a whole bunch of wind-up toy cars. Each car, when placed on the ground, travels 2 meters per second. I place one car on the ground every second, all pointed toward you. Cars will arrive at your location at a rate of 1 per second, and they will be 2 meters apart.
Now suppoose that I begin walking towards you at a rate of 1 meter per second. As I place a car on the ground, it begins traveling towards you. One second later, the car has traveled two meters in your direction, but I have also traveled one meter, so when I set the next car down, it is only one meter behind the previous car. Now cars are arriving at your location at a rate of one every .5 seconds, and they are only one meter appart. Of course, if I walk backwards away from you at the same pace, you will receive one car every 1.5 seconds, and they will be 3 meters appart. So the frequency and distance between them changes because their speed is constant, and mine is not.
The way I see this, Pete, when considering a medium for light, the time involved when the apparatus is moving at velocity v, would be 2L/(c+v)+(c-v)/2= 2L/c (relative to the frame), as well.Originally posted by pmb
Consider the two postulates of relativity
(1) The laws of physics are the same in all inertial frames of referance
(2) The speed of light is independant of the source
Not take a mirror and a light emitter/detector (ED) and place them as follows
=================
------E-D--------
---------------------------------------------------> X
Its easy to see that the distance "L" between the mirror and ED does not change as the apparatus (mirror and ED) move to the right with a given velocity.
Let O be the frame in which the apparatus is at rest. So if a flash of light is emitted at ED which travels to the mirror and bounces back to ED then the time taken as measued in this frame is given by
T = 2L/c
Now consider the same thing from a frame of referance in which the entire apparatus is moving in the X direction with velocity "v" - Call that frame O'. Then (I can't draw that here - it gets messed up) the time taken as determined in the frame O must be greater since the light has to travel a greater distance. So T' > T
Do this out and use the Pathagorean theorem and you'll see that
T' = T/sqrt[1 - (v/c)^2]
Pete
Originally posted by mich
The way I see this, Pete, when considering a medium for light, the time involved when the apparatus is moving at velocity v, would be 2L/(c+v)+(c-v)/2= 2L/c (relative to the frame), ...
The same thing happens with sound. A train comming towards you will have a higher pitched sound then when moving away from you. The reason being can be seen as follows. Instead of a whistle thing in terms of beeps. If the train is stationary and it beeps then the sound will travel to your ear at equal time intervals, the same time intgerval at when they left the train. Now consider what happens when the train is moving. The train passes a pole and it beeps just when it is at that pole. The sound has to move from that pole to your ear. However the train is at a different, closer, location when it emits the second beep. Now that beep has a shorter distance to travel so you hear it sooner than if the train wasn't moving! So you hear the beeps at shorter time intervals. That is you hear the beeps at a different frequency.Originally posted by mich
Good explanation, Lurch:
My question is this, though; How does one explain the change in wavelengths when the observer, not the source changes speed,remaining the speed of light the same?
mich
first explain what is time for ya and i'll probably tell you about dilationOriginally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?
That is what makes Special Relativity so special; there is no difference between the two situations you described!Originally posted by mich
My question is this, though; How does one explain the change in wavelengths when the observer, not the source changes speed,remaining the speed of light the same?
mich
Sorry Pete; I forgot some brakets,as Jackel pointed out.Originally posted by pmb
I don't understand this equation. Something is wrong with it. Notice that the first term 2L/(c+v) has the dimensions of time yet the qyantity (c-v)/2 has dimensions of distance/time.
Pete
Thank you for replying Pete;Originally posted by pmb
The same thing happens with sound. A train comming towards you will have a higher pitched sound then when moving away from you. The reason being can be seen as follows. Instead of a whistle thing in terms of beeps. If the train is stationary and it beeps then the sound will travel to your ear at equal time intervals, the same time intgerval at when they left the train. Now consider what happens when the train is moving. The train passes a pole and it beeps just when it is at that pole. The sound has to move from that pole to your ear. However the train is at a different, closer, location when it emits the second beep. Now that beep has a shorter distance to travel so you hear it sooner than if the train wasn't moving! So you hear the beeps at shorter time intervals. That is you hear the beeps at a different frequency.
Same thing with light with one difference - the time between the beeps will be decreased because of time dilation. However the police do not need to take that into account when they uyse this effect when they are at speed traps and using radar to clock the speed of your car! If you get caught try telling him he was the one speeding. You were the one at rest. :-)
This is also the same reason why when you look at a plane or a jet flying in the sky it appears ahead of where the sound is coming from - and that does not mean they are moving faster than sound.
Pete
The only valid explanation of time dilation comes from understanding the Lorentz transformation equations. This is the first step. If you’d like to see a derivation of these basic equations, go to this link: http://www.everythingimportant.org/relativityOriginally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?