View Full Version : Time dilation
Koveras00
Apr15-03, 10:16 AM
Could anybody explain the theory behind time dilation and how exactly time dilation works?
ahrkron
Apr15-03, 11:37 AM
Well... that's a big question (especially due to that "exactly" part).
You should probably give a try to Tom's
Physics Napster (http://www.physicsforums.com/showthread.php?s=&threadid=31).
Post number 13 in the first page of the thread has many good links about relativity.
Loren Booda
Apr15-03, 03:48 PM
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.
Stranger
Apr15-03, 09:59 PM
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.....
If you wanted a simpler explanation (very briefly) the theory behind time dialation is relativity.
It works on the basis of the speed of light being constant and most the other physical equations being re-written around that fact. This (at risk of being too simplistic) includes how fast time seems to pass. Time dialation is time taking longer to pass and compensates mathematically for various other things.
The other thing you should know about it is that it is incredibly complicated, doesn't work anything like the way you would guess and is 100% real.
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
Originally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?
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
Koveras00
Apr17-03, 11:39 PM
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.
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?
for me,
the simpliest way to understand time dilation is, as you travel near the speed of light, time slows down..
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?
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.
re - "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."
There is a footnote in another of Einstein's 1905 paper (same issue of journal that he published what we call "special relativity"). The footnote reads
"The constancy of light is contained in Maxwell's Equations"
That means that if you assume that Maxwell's equations hold true then it follows that the constants in those equations are independant of the frame of referance - otherwise you'd be able to speak of a prefered frames of referance. These constants (permitivity (e) and permiability (u) of free space - I think they're related to each other though) determine the speed of light
c = 1/sqrt(eu)
So you really don't need to invoke the constancy of light as a second postulate if you assume Maxwell's equations are valid as they stand.
Pete
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
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 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.....
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.
When the spaceship is passing by me, the light will first be "blueshifted" as it (spaceship)gets closer, making each ray of light coming towards me as having a shorter path to follow...now this blueshift is not a relavistic shift, but a classical one.Therefore the time of the event for the light hitting the ceiling will be viewed as being shorter than,after the spaceship has passed me, the time of the event for the light travelling back towards the floor,as it will be viewed to be longer, since the light will have been redshifted.
The observed time ought to be equal to both observers, it seems.
mich
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.
Hello Loren:
Would you not agree that if light would travel in a medium,
the observation above would also be detected, but without any dilation of time involved?
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.
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
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
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.
But considering the above postulates, the light must always remain c
nevertheless still leaving the time as being 2L/c.
As for the distance between the emiter and detector changing, I'm not sure why you're saying this.
mich
Originally posted by mich
[B]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), ...
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
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
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
dr-dock
Apr21-03, 05:14 PM
Originally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?
first explain what is time for ya and i'll probably tell you about dilation
Mich, I think we need to face observed facts. There are plenty of ways the universe could work mathematically, but only one way that it actually does.
ps. I think you meant:
2L / 0.5[(c+v)+(c-v)]
not:
2L/(c+v) + (c-v)/2
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
That is what makes Special Relativity so special; there is no difference between the two situations you described!
My analogy contained one fatal flaw. It used an absolute frame of reference; the floor on which both of us stood and by which the cars propelled themselves. In reality, there is no absolute frame of reference. So saying that the light source is moving toward you is exactly the same as saying that you are moving toward it, and will yield exactly the same observed results.
BTW; Brian Green's book The Elegant Universe contains one of the best analogies I have ever seen to describe time dilation. It seems to me that I have already played it out elsewhere in these Forums, so I will see if I can find that thread (just so I don't take up a bunch of space repeating myself).
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
Sorry Pete; I forgot some brakets,as Jackel pointed out.
T= 2L(distance)/[(c+v)+(c-v)/2](average velocity of light)
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
Thank you for replying Pete;
I agree with most of what you wrote, Pete, but,the cause for the shift when the source is moving is due to a change in wavelength while the change of shift which happens when the observer moves, or changes speed is due to a change in the speed of sound relative to the observer. In the case of light, this cannot be the reason.
mich
Eugene Shubert
Apr22-03, 05:37 PM
Originally posted by Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works? 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/relativity
Originally posted by jackle
Mich, I think we need to face observed facts. There are plenty of ways the universe could work mathematically, but only one way that it actually does.
ps. I think you meant:
2L / 0.5[(c+v)+(c-v)]
not:
2L/(c+v) + (c-v)/2
Thanks for replying, Jackel:
I agree, Jackel; and I'm no physicist; but some thing are bothering me, concerning relativity, as there were things bothering me concerning the 1st and 2nd laws of Keppler, until Janus helped me out.
Now I do understand that the observations of Michelson and Morley experiment gave a negative shift change.
But in the 20th century, light was viewed once again as having a particle characterist, and the M&M experiment could simply be explained in terms of particles instead of waves, without the need of
implying a Lorentz length contraction or Relativity time dilation.
p.s. Thanks; yes that's what I meant.
mich
Originally posted by LURCH
That is what makes Special Relativity so special; there is no difference between the two situations you described!
My analogy contained one fatal flaw. It used an absolute frame of reference; the floor on which both of us stood and by which the cars propelled themselves. In reality, there is no absolute frame of reference. So saying that the light source is moving toward you is exactly the same as saying that you are moving toward it, and will yield exactly the same observed results.
BTW; Brian Green's book The Elegant Universe contains one of the best analogies I have ever seen to describe time dilation. It seems to me that I have already played it out elsewhere in these Forums, so I will see if I can find that thread (just so I don't take up a bunch of space repeating myself).
Thanks Lurch, I appreciate you finding the thread, I'd be interested in reading it.
As for the statement that there's no special frames, I have a hard time with this. This is because, if the source changes it's frame of reference, the observer needs to wait L/c time to observe the change of shift while if the observer changes his/her frame of reference, he/she will immediately observe the change.We know the latter example could be explained as a change in light speed, but we are forbidden to claim this; I don't see any other reason for it, since it cannot be due to a change in wavelength...we are speaking of a classical light shift not a relativistic one.
mich
Koveras00
Apr23-03, 08:50 AM
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?
Does this means that not only light, but anything else can cause dilation?
And why do only time slows down for things at speed of light not any other slower speeds?
Time dialation doesn't exist between two things that are at rest. As they speed up, there is a tiny, tiny, tiny dialation that increases very slowly. As the speed approaches speeds which are well beyond our every day experience, the dialation sharply increases and eventually becomes noticable, powerful and ultimately (at light speed) dialation is so strong time starts to sort of freeze.
You will probably have loads of questions about how anything like this could actually be true. Its a normal response, and happens to anyone who studies it. It doesn't work quite the way you might think.
Upon further reflection, I realize that the post in which I had described Brian Green's analogy of time dilation was in PF 2.0, so I beg everyone's patients as I repeat myself:
Imagine a dry lake bed. On this lake bed are parallel lines drawn north-to-south. These lines are exactly one mile part. A car driving exactly 60 mph directly east cross this lake bed will across one line every minute. However, if the car were to travel northeast at a 45o angle, (maintaining a speed of 60 mph) it would take two minutes to get from one line to the next. Although the total speed of the vehicle has remained constant, half of that speed is now be expended to achieve northward progress, leaving only half to achieve eastward progress.
It is Mr. Green's contention that we can think of all objects in the universe as having a total velocity of c. Under normal circumstances, most of this velocity is expended in progress through time. However, any motion in any of the three other directions is subtracted from forward progress through time. This is time dilation.
If the car were to travel straight north, it would never cross the next line eastward on lake bed. All of its total velocity (of 60 mph) would be devoted to traveling northward, leaving none to achieve eastward progress. In the same way, any object that devotes its total velocity of c to progress through any of the three spatial dimensions will cease to make progress through the dimension of time. It will never reach the "next moment" in time, because it will be traveling parallel to it.
Koveras00
Apr24-03, 03:52 AM
Originally posted by pmb
=================
------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
What if the light is swapped with a moving object moving at a much more slower speed? Will there still be time dilation?? And will the speed of the moving object be the same to the two observers?
I think you have misunderstood the equation. v stands for any speed and could be anything up to the speed of light. Dialation increases as v increases getting serious as v -> c . c is a universal constant.
Dialation happens not because of c but because of v. If v goes anywhere near c there is extreme dialation. c being constant regardless of v demonstrates the dialation will occur.
Therefore, the light doesn't cause the dialation. The light is there to demonstrate the dialation. You could replace it with a blue banana or remove it completely. Dialation still happens.
Your next question might be:
"If dialation increases with speed, becomes extreme when speeds get towards light speed and we are surrounded by light everyday, why don't we see any dialation in everyday experience?"
This is why it is called "relativity". Time passes depending on your perspective (inertial reference frame). Light has no power to cause time to dialate between two third parties. If the light were to look at you, then it would see you as if you were frozen, but two third parties at everyday speeds see nothing unusual when they look at each other. Time is passing differently depending on perspective.
Koveras00
Apr24-03, 07:09 AM
sorry...i think i misquote it... i meant to quote without the equation.
So, what if the light was changed into some blue banana?? Will there speed of the blue banana be the same to the both observer?
no, the blue banana will travel rather slowly compared to light at speed b relative to observer 1 and b* relative to observer 2 and will have the classical equation for adding velocities:
b is not equal to b*
classically: b=sqrt(b*^2+v^2) because you are adding velocities which are at right angels
The bananna will seem faster to first observer because when the second observer threw the bananna it had his own speed added to it (speed v).
The second observer who threw the banana will not notice the effect of speed v on the bananna at all because he himself is travelling at speed v.
Unlike light, the bananna will slow down because of air resistance and probably splat against the mirror!
Koveras00
Apr24-03, 09:01 AM
Originally posted by jackle
no, the blue banana will travel rather slowly compared to light at speed b relative to observer 1 and b* relative to observer 2 and will have the classical equation for adding velocities:
b is not equal to b*
classically: b=sqrt(b*^2+v^2) because you are adding velocities which are at right angels
The bananna will seem faster to first observer because when the second observer threw the bananna it had his own speed added to it (speed v).
The second observer who threw the banana will not notice the effect of speed v on the bananna at all because he himself is travelling at speed v.
So what makes light different frm the blue banana?? (The blue banana could use the classical equation but not light)
Light is far too fast to obey classical physics.
Remember light is not allow to get faster than it already is relative to anything else. It has to have a constant speed no matter. The bannana can change speed relative to different people.
Originally posted by Koveras00
What if the light is swapped with a moving object moving at a much more slower speed? Will there still be time dilation?? And will the speed of the moving object be the same to the two observers?
If T is the time recorded on the moving clock and t the time on the stationary clock then
t = T/sqrt[1 - (v/c)^2]
when v << c
t~T
Originally posted by mich
Thank you for replying Pete;
I agree with most of what you wrote, Pete, but,the cause for the shift when the source is moving is due to a change in wavelength while the change of shift which happens when the observer moves, or changes speed is due to a change in the speed of sound relative to the observer. In the case of light, this cannot be the reason.
mich
They're the exact same phenomena. The *reason* whey the wavelength changes is *because* the period decreases. Note that
c = Period/Wavelength = T/L --> L =T/c
Note that Frequency is the reciprocal of period = f = 1/T
L = 1/fc
So you can say that the distance the wave travels from source to observer decreases as the source is approaching and the distance becomes longer when the source is receding. The distance the wave travels happens during the period equal to the reciprocal of the frequency, Therefore the wavelentgh increases when the source is approaching and decreases as the source is receding.
For light its the same thing. Let the light source emit flashes which, in the rest frame of the observer, is equal the the period of the source of light which we wish to observe.
As the distance between source and observer descreases the there is less distance the travel. However the frequency at which you see those pulses is the same as the frequency of the light so the light has a higher frequency as well. And the wavelength is inversely proportional to the frequency.
Pete
I made a new web page for this. See
http://www.geocities.com/physics_world/light_clock.htm
There is a derivation in this page which is pretty easy to follow.
Pete
Originally posted by pmb
[B]They're the exact same phenomena. The *reason* whey the wavelength changes is *because* the period decreases. Note that
c = Period/Wavelength = T/L --> L =T/c
Note that Frequency is the reciprocal of period = f = 1/T
L = 1/fc
So you can say that the distance the wave travels from source to observer decreases as the source is approaching and the distance becomes longer when the source is receding. The distance the wave travels happens during the period equal to the reciprocal of the frequency, Therefore the wavelentgh increases when the source is approaching and decreases as the source is receding.
Thanks for replying, Pete:
I think we need to be careful here,Pete; the wavelength will indeed
change proportional to the light source's change of inertial frame,
but only if there's a medium which carries light at a specific speed relative to it... relativity claims that this medium does not exist.
If the light is made of particles and therefore follow the laws of ballistics, the frequency will change but not because of a change of wavelength, it will be due to the change of the speed of light particles, which, again, relativity forbids.When the observer changes
it's frame of reference, then in both situations, that is, the wave theory as well as the particle theory, it is due to a change of light speed. So relativity is not agreeing with either one.
Now imagine a star one light year away from an observer which explodes and exists no more.
it's light will continue to be seen by the observer for another year.
During that year, the observer decides to speed towards the star (which exists no more). The light will be blue shifted...but what caused the shift? I believe that we are left with only two things to deal with... the observer and the light.Both,the particle theory and the wave theory would claim that the shift will be caused by the change in light speed relative to the observer...but relativity denies this.
What is relativity's explanation?
mich
Thanks for the post Lurch:
I do find the analogy very well thought of; my problem is not in the relavistic shift of light which expresses time dilation as your post represents. If the speed of light is invariant to all observers, then, it is clear that either a time dilation or length contraction or both need to exist.
My problem is in the classical light shift which is observed. I don't understand relativity's explanation of this.
mich
Originally posted by LURCH
Upon further reflection, I realize that the post in which I had described Brian Green's analogy of time dilation was in PF 2.0, so I beg everyone's patients as I repeat myself:
Imagine a dry lake bed. On this lake bed are parallel lines drawn north-to-south. These lines are exactly one mile part. A car driving exactly 60 mph directly east cross this lake bed will across one line every minute. However, if the car were to travel northeast at a 45o angle, (maintaining a speed of 60 mph) it would take two minutes to get from one line to the next. Although the total speed of the vehicle has remained constant, half of that speed is now be expended to achieve northward progress, leaving only half to achieve eastward progress.
It is Mr. Green's contention that we can think of all objects in the universe as having a total velocity of c. Under normal circumstances, most of this velocity is expended in progress through time. However, any motion in any of the three other directions is subtracted from forward progress through time. This is time dilation.
If the car were to travel straight north, it would never cross the next line eastward on lake bed. All of its total velocity (of 60 mph) would be devoted to traveling northward, leaving none to achieve eastward progress. In the same way, any object that devotes its total velocity of c to progress through any of the three spatial dimensions will cease to make progress through the dimension of time. It will never reach the "next moment" in time, because it will be traveling parallel to it.
Hi mich
re - "I think we need to be careful here,Pete; the wavelength will indeed change proportional to the light source's change of inertial frame, but only if there's a medium which carries light at a specific speed relative to it"
No. That is incorrect. The frequency change as well as the wavelength change has nothing to do with the medium. It has to do with the shorter/longer distances the signal has to travel.
re - "If the light is made of particles and therefore follow the laws of ballistics, the frequency will change but not because of a change of wavelength, it will be due to the change of the speed of light particles, which, again, relativity forbids."
That also is not true. Light can be thought of as being composed of particles - photons. These photons do *not* change speed. The speed of the photon is indepenant of the speed of the source. However their energy (does* change with the speed of its source. And the wavelength associated with that energy also changes with the motion of the source.
re - "During that year, the observer decides to speed towards the star (which exists no more). The light will be blue shifted...but what caused the shift?"
The shift is due to the shorted distance the wave has to travel.
Pete
Hi Pete;thanks for replying.
Originally posted by pmb
[B]Hi mich
No. That is incorrect. The frequency change as well as the wavelength change has nothing to do with the medium. It has to do with the shorter/longer distances the signal has to travel.
Maybe I'm wrong,Pete, but I'll try to explain why I said this.
The characteristic of the wavelength is the distance between two crests, or lets say between two photons, although this is not accurate,but will do for now.
When an obect oscillates in a medium, it will produce some waves; the length between two crests is called a wavelength and is dependant to the frequency of the oscillator as well as the speed of the wave within the medium, which, by the way, remains always constant relative to the medium.
Now if the oscillator displaces itself within the medium, it will
produce shorter wavelenths in the direction of motion, and longer ones in the opposite direction...this is due to the speed of that particular wave remaining constant to the medium.
In the case of ballistic, since no medium is involve, the wavelength is dependant to the oscilator's frequency only,so that if the oscillator changes it's speed, overlooking the acceleration, the wavelength will remain the same relative to the oscillator.
Now if we put an observer in the distance. In the former case, where there is a medium involved,and lets say the observer is stationnary to the medium, the observer will see a shift of light, or a frequency change due to the change in wavelength, since the speed remains a constant, whereas in the latter example, we know that the wavelength remains the same relative to the oscillator, and since the oscillator changed it's speed, then, the observer will see a change of frequency due to the change of speed of the wave, or light particle.
If, in both cases, the observer changes it's frame of reference, both changes in frequencies will be due to the change of
speed of the wave, in this case, light, which, I agree, relativity forbids.
."
That also is not true. Light can be thought of as being composed of particles - photons. These photons do *not* change speed. The speed of the photon is indepenant of the speed of the source.
I do understand that this is what relativity is saying, but my question remains how can the observed classical shift be explained?
However their energy (does* change with the speed of its source. And the wavelength associated with that energy also changes with the motion of the source.
However, Pete, this speaks of only the relavistic shift, and I do understand this...
re - "During that year, the observer decides to speed towards the star (which exists no more). The light will be blue shifted...but what caused the shift?"
The shift is due to the shorted distance the wave has to travel.
Pete
To speak of change in frequency due to shorter distances the light needs to travel is to speak of the well known doppler effect;
as I tried to explain above, it does indeed explain a change in frequency but due to a change in wavelength or a change in speed of the wave; and I don't see how it explains the prediction of relativity...in my opinion.
mich
Hi Pete:
I read your web page and I just figured out that this is what you were trying to explain in page 1 of this thread.
I now see that I've misinterpreted your explanation.
Originally posted by pmb
I made a new web page for this. See
http://www.geocities.com/physics_world/light_clock.htm
There is a derivation in this page which is pretty easy to follow.
Pete
Now concerning this explanation, which I have seen before in a physic's book writen for laymen, I have some questions.
My problem is that the sketch is 2 dimentional, and misses the dimention of depth. The observer who views the moving clock can only see the light which comes towards him/her.As the moving clock passes by the observer, the light coming towards him/her, will first be blue shifted, as the light has less and less distance to travel. After the
clock passes the observer, the light will be redshifted making the event of the light returning to the ground as being longer than the event of the light hitting the ceiling, making the triangle to be not an isosceles one.
mich
Hi mich
My problem is that the sketch is 2 dimentional, and misses the dimention of depth. The observer who views the moving clock can only see the light which comes towards him/her.
That page was not intended to explain doppler. Its just a nice easy way to determine what the proper time is compared with the "observer's time"
As the moving clock passes by the observer, the light coming towards him/her, will first be blue shifted, as the light has less and less distance to travel. After the
clock passes the observer, the light will be redshifted making the event of the light returning to the ground as being longer than the event of the light hitting the ceiling, making the triangle to be not an isosceles one=
The frequency of the light does not alter the geometry of th diagram. The triangle is isosceles and I can't see how you concluded that it wasn't based on frequency.
Pete
Hi,Pete, and thanks for replying;
Originally posted by pmb
Hi mich
That page was not intended to explain doppler. Its just a nice easy way to determine what the proper time is compared with the "observer's time".
But it seems that the doppler effect does have something to do with this, since the observer cannot see the proper time due to the light shifts...during red shift the event "seems" slower than proper time, during blueshift the event "seems" faster than proper time.This is the what we could call the observer's time, it seems.
The frequency of the light does not alter the geometry of th diagram. The triangle is isosceles and I can't see how you concluded that it wasn't based on frequency.
Pete
I do agree, in a sense,to what you are saying if you speak of the triangle as simply a geometry of what will "seem" to happen as seen to the observer. my problem is the time, or velocity dimentions
put on the sketch.
As the light source is moving(in a straight line, for we are speaking of S.R.), the light source frame will move closer and closer to the observer until, after it has passed the observer, it will then
move further and further away from the same.We therefore have a blue and red shift, which affects the "observers" timekeeping of the event.
I think our objections lies in the time the light moves from the emitter to the ceiling(mirror), as seen by the observer, to be not the same "observed time" for the light to move from the ceiling(mirror) to the detector, being my opinion, and that you would claim, if I'm not mistaken, the two observed time would be the same in your opinion.
mich
Hi mich
re - "Hi Pete, and thanks for replying" - You're welcome! :-)
But it seems that the doppler effect does have something to do with this, since the observer cannot see the proper time due to the light shifts...during red shift the event "seems" slower than proper time, during blueshift the event "seems" faster than proper time.This is the what we could call the observer's time, it seems.
I see the problem now. You're confusing what is "seen" to what is "measured". They are very different things. It's incorrect to base what you see on what actually is. The rate a which a clock ticks depends only on the speed of the clock. It is not running fast as it approaches us and then runs slow as it moves away. IT may look that way but that is a doppler effect. Doppler is not a time dilation phenomena per se. Even if the moving clock ran at the same rate as the stationary clock there would still be a doppler shift.
re " As the light source is moving(in a straight line, for we are speaking of S.R.),"
Think of it like this. We can put light detectors along the path of the clock. At each detector we have a clock and a recording device. When the light passes it then it notes the time and records the event. All of the clocks are synchronized in the rest frame. We then later gather up all the data and deduce the rate at which the clock ticked. It's kind of a bookkeeping system. From the books we analyze the data and then we'd conclude that the clock ran slower!
Pete
Hi Pete, and thanks again for replying; you're a very patient person.
Originally posted by pmb
I see the problem now. You're confusing what is "seen" to what is "measured". They are very different things. It's incorrect to base what you see on what actually is. The rate a which a clock ticks depends only on the speed of the clock. It is not running fast as it approaches us and then runs slow as it moves away. IT may look that way but that is a doppler effect. Doppler is not a time dilation phenomena per se. Even if the moving clock ran at the same rate as the stationary clock there would still be a doppler shift.
Yes, Pete, I think we are pretty much at the heart of the issue.
For now, my problem is not with time dilation nor with length contractions, but simply how does S.R explain the doppler effect?
When the observer changes it's frame of reference, the light from a far away source(and as I've mentioned before, the source need no longer be there)will shift...but why? How does S.R. explain this shift?
Think of it like this. We can put light detectors along the path of the clock. At each detector we have a clock and a recording device. When the light passes it then it notes the time and records the event. All of the clocks are synchronized in the rest frame. We then later gather up all the data and deduce the rate at which the clock ticked. It's kind of a bookkeeping system. From the books we analyze the data and then we'd conclude that the clock ran slower!
Pete [/B]
I actually find your explanation on the difference between seeing and measuring the light path interesting.
I will chew on what you have written and get back to you on this.
At first sight, you seem to be saying that detector 1 observed the light leaving the source at T1=0, and detector 2 observed the light hitting the ceiling at T2=x, x-0 would be a time period greater than
the time period it took for the light to travel from the source to the ceiling in the apparatus' frame of reference...This is interesting;if this experiment was made I would be interested in reading about it if you have the info.
My first thought on this would be , since we are speaking of incredible velocities,could the observation of identifying the event T=0 take a period of time to observe, meaning that the moment that event is observed the apparatus has already travel a certain unknown distance;leaving us with simply a "probability of time period" where T1=0. The same could be said with the observation of T2, creating possibly what might "seem" to be a dilation of time due to the "area of probability" involved?
mich
Howdy mich!
re - "Hi Pete, and thanks again for replying; you're a very patient person." - I try to be. Besides - I try to have infinite patients with people who are polite. After all, when I was an undergrad my prof would let me pick his brains for a long time and he never got impatient with me. Most, if not all, people here are very polite. I wish it was like that at the newsgroups. People there tend to attack others with whom they disagree at the drop of a hat.
re - "For now, my problem is not with time dilation nor with length contractions, but simply how does S.R explain the doppler effect?"
I think you'll be better off going to this site
http://www.tcm.phy.cam.ac.uk/~nrc25/red/index.html
Downloading the handout called "Special Relativity" and reading the section on doppler. Then come back and we can talk about what you think of it. I've pretty much run out of ideas on how to explain that at this point. But this might be helpful. Let me know.
re - "I actually find your explanation on the difference between seeing and measuring the light path interesting."
I should update the page to relfect that part. Are you familiar with how clocks are synchoronized in SR?
re - "I will chew on what you have written and get back to you on this. At first sight, you seem to be saying that detector 1 observed the light leaving the source at T1=0, and detector 2 observed the light hitting the ceiling at T2=x, x-0 would be a time period greater than the time period it took for the light to travel from the source to the ceiling in the apparatus' frame of reference..."
Yes. You've got it! When relativists use the term "observer" what they are really refering to is a collection of clocks and rods!
Read more about this at
http://www.eftaylor.com/pub/chapter1.pdf
page 18 where it says "The observer is all the recording clocks in one frame"
re - "This is interesting;if this experiment was made I would be interested in reading about it if you have the info."
The principle has been tested many times. In fact one of the more famous experiments has to do with the life times of Muons in the atmosphere. Cosmic rays hit the atmosphere and generate muons. Some of those muons head downwards towards the Earth. The depth they go depends on when they decay. So by measuring how many muons are found at different heights we can observe time dilation happening. Faster particles live longer. And when they decay is probalistic. So basically their lifetime increases with speed as measured in the Earth frame.
re - "My first thought on this would be , since we are speaking of incredible velocities,could the observation of identifying the event T=0 take a period of time to observe, .."
Classically this is not a problem. Just have the light arrive at both places (detector and opposite mirror) at the same time.
Pmb
Originally posted by mich
Yes, Pete, I think we are pretty much at the heart of the issue.
For now, my problem is not with time dilation nor with length contractions, but simply how does S.R explain the doppler effect?
When the observer changes it's frame of reference, the light from a far away source(and as I've mentioned before, the source need no longer be there)will shift...but why? How does S.R. explain this shift?
mich
I don't know if this helps, but earlier in this conversation, a description was given of the blue shift resulting from the light source being in motion. In that scenario, it was easy to see that the speed with which light passes the observer does not have to accelerate in order for that light to be blueshifted. The cause of the blue shift was that, for each lightwave emitted by the light source, the distance between the source and the observer was less than it had been when the previous wave was emitted. Looking at it from that perspective, there was no question about the "medium" through which the light traveled, nor the rate at which it traveled.
Perhaps it would be easiest to apply this same type of view to the situation in which the observer is "in motion", and the light source is "stationary". According to relativity, there is no difference between these two situations. The only important thing is that during the time between two wave peaks (or two photons), the distance between the light source and the observer has decreased. From one frame of reference, the light source is "stationary", and the observer is approaching it. From another, the observer is "stationary" and the light source is approaching him. Of course, from yet another perspective, both could be seen to be approaching one another at equal speeds. But from any perspective, the distance between the two is decreasing.
That do anything for ya?
Yo Pete:
I thank you for the web site address; I looked and found it really interesting; I have saved it as a favorite, and will try to read it all when the time permits.
I nevertheless read the part concerning the doppler effect.
It reads: "Doppler Effect"
Consider a source of EM waves that is moving in the frame S. We wish to determine the time, as measured in S, between the arrival of successive crests in the wave (i.e. the period of the wave).
In the rest frame of the source, S0, the interval between crests (i.e. the period in the rest frame) is T0.
----I gather from here, that, in frame So, it takes T0 time for two wave crests to pass at the same point, which this in turn can be translated in frequency, so that f=1(wavelength)/T0 -----
RELATIVITY AND ELECTRODYNAMICS 9
In the lab frame, S, we want to calculate the time between arrival of crests at a detector. To do this we must take into consideration the time when the crest is emitted, t1, the time interval in S between the crests which will be time dilated,gammaT0, and the time taken for the EM wave to propagate the distance the source will have moved between emission of the two crests of the wave,gammaT0V . The time interval in the lab frame between successive crests must then be given by
delta t = (t1 + gammaT0 + gammaT0V/c)-t1
= gamma(1+v/c)T0 = [1+ beta(v/c)/gamma]T0
The new frequency would then be f'=1/delta t.
--- t1 is self explanatory, gamma T0 represents the relativistic shift,which is always a red shift,or time dilation, and I don't have a problem with this as well. the time taken for the EM wave to propagate the distance the source will have moved between emission of the two crests of the wave,gammaT0V, is where my problem lies.
I have read in a book, to simply think of many sources one in front of the other systematically firing photons(or bullets) sequencially.
The bullets will always have a specific velocity but a frequency shift will exist when compared to one source stationnary emiting photons (or bullets) at a same time interval.
This case is the same as the one found in a moving source through a
medium. What is being changed is the wavelength. While a blue shift appears in one direction, a red shift will exists at the opposite end,if bullets are fired in the opposite direction as well,which in this case, an experiment such as the M&M experiment could
observe this. I "personally" cannot understand how a doppler effect can exist without either the existance of a medium or the change of light velocity.
Originally posted by pmb
Howdy mich!
re - "Hi Pete, and thanks again for replying; you're a very patient person." - I try to be. Besides - I try to have infinite patients with people who are polite. After all, when I was an undergrad my prof would let me pick his brains for a long time and he never got impatient with me. Most, if not all, people here are very polite. I wish it was like that at the newsgroups. People there tend to attack others with whom they disagree at the drop of a hat.
Thanks, I appreciate it. I know that my knowledge in physics is very limited, and I sometimes wonder if I'm being annoying.
Yes. You've got it! When relativists use the term "observer" what they are really refering to is a collection of clocks and rods!
I went throught this in my head....and of course I was stuck in a paradoxial conclusion. The invariance of the speed of light is much "trickier" than I thought it would be.
1st, it seems to me that one observer "can" be enough as long as we
do the correct calculations. For example, when I spoke of blue shift
and red shift, I was not claiming that I believed the blue shift was a true contraction of time and that the red shift was a true dilation of time; but only apparent.All the data coming to that one observer ought to be enough, it seems, to make a proper observation. While collections of rods and clocks need to be used, if the observer is on the same inertial frame as those clocks and rods and takes everything in consideration,every info which comes to him (one point) ought to be enough.
Concerning the experiment; let us say that both observers from the two different frames send a light at the celing and then back, each in their own frames. First, a common point of time (T0) need to exist.
Therefore, from a third frame, a light signal can be sent to the two
other frame,and detect that both frames received the signal simultaniously...relative to the 3rd frame.
Now we know that after the signal is received,a light will be sent from the two observers towards the ceiling within each their own frames. Observer from the 1st frame will calim that "his" light hit the ceiling "before" the light of the second frame hit it's ceiling.
Of course, the observer from the second frame will claim the same thing. This is said to be due to a time dilation factor.
My problem is this: If "both" observers cannot agree to a single event(light hitting the ceiling),"my light hit the ceiling first, not yours!!!Then, they cannot agree with the event of receiving the light signal from the 3rd frame as being a simultaneous event at the same time. In fact the same thing will be argued..."I received the light signal first, not you!!" It seems that relativity would agree as well; just because the observer on the 3rd frame claimed they received the signal simultaniously, does not make it so."
Therefore, if both claimed to receive the signal and also claim that their light hit the ceiling first, the time "period" for the light to travel to the ceiling remains the same.
I will stop here as the post is getting too long.
Thanks for your yime
mich
Pmb [/QUOTE]
Thank you Lurch for responding:
Originally posted by LURCH
I don't know if this helps, but earlier in this conversation, a description was given of the blue shift resulting from the light source being in motion. In that scenario, it was easy to see that the speed with which light passes the observer does not have to accelerate in order for that light to be blueshifted.
At first sight, yes, but then I thought, how is this light shifted
if not due to a change in light speed? The answer must be that it is due to a change in wavelength.I cannot see any other reasons.But a change in wavelength could be detected by an observer on the same inertial frame as the source, by the M&M experiment. Notice that the change in measuring rods and time contraction experienced by the observer could not account for the amount of doppler observed.
The cause of the blue shift was that, for each lightwave emitted by the light source, the distance between the source and the observer was less than it had been when the previous wave was emitted. Looking at it from that perspective, there was no question about the "medium" through which the light traveled, nor the rate at which it traveled.
Except for those two causes, what else can be responsible for a change in frequency?
Perhaps it would be easiest to apply this same type of view to the situation in which the observer is "in motion", and the light source is "stationary". According to relativity, there is no difference between these two situations. The only important thing is that during the time between two wave peaks (or two photons), the distance between the light source and the observer has decreased. From one frame of reference, the light source is "stationary", and the observer is approaching it. From another, the observer is "stationary" and the light source is approaching him. Of course, from yet another perspective, both could be seen to be approaching one another at equal speeds. But from any perspective, the distance between the two is decreasing.
Notice Lurch, that every use of words being used such as "observer in motion", "distance between source and observer changing", "both source and observer moving" involves a velocity or a change thereof.
It's easy to imagine a doppler effect using such words. Butwhat about
"the invariance of the speed of light". At first, I believed it to be a fairly easy concept to grasp....I certainly don't any more.
That do anything for ya?
"every feedback that I have received makes me think a bit harder, so yes; it did do great for me, thanks.
mich
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