# Time dilation

Koveras00
Could anybody explain the theory behind time dilation and how exactly time dilation works?

## Answers and Replies

Staff Emeritus
Science Advisor
Gold Member
Well... that's a big question (especially due to that "exactly" part).

You should probably give a try to Tom's
Physics Napster.

Post number 13 in the first page of the thread has many good links about relativity.

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.

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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...

jackle
If you wanted a simpler explanation (very briefly) the theory behind time dilation 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 dilation is time taking longer to pass and compensates mathematically for various other things.

jackle
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.

Staff Emeritus
Science Advisor
Gold Member
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
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?

eureka
for me,

the simpliest way to understand time dilation is, as you travel near the speed of light, time slows down..

Science Advisor
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 preferred 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

jackle
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 dilation 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 traveling 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
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

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

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

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Science Advisor
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
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
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?

jackle
Time dilation doesn't exist between two things that are at rest. As they speed up, there is a tiny, tiny, tiny dilation that increases very slowly. As the speed approaches speeds which are well beyond our every day experience, the dilation sharply increases and eventually becomes noticable, powerful and ultimately (at light speed) dilation 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.

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Science Advisor
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

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?

jackle
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 dilation 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.

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jackle
Your next question might be:

"If dilation increases with speed, becomes extreme when speeds get towards light speed and we are surrounded by light everyday, why don't we see any dilation 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
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?

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 traveling at speed v.

Unlike light, the bananna will slow down because of air resistance and probably splat against the mirror!

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