Time Dilation Explained: Theory & How It Works

[Koveras00]

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 traveling at speed v.

So what makes light different frm the blue banana?? (The blue banana could use the classical equation but not light)

 

[jackle]

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.

 

[pmb]

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

 

[pmb]

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

 

[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

 

[mich]

Originally posted by pmb
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

 

[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 45^o 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.

 

[pmb]

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

 

[mich]

Hi Pete;thanks for replying.

Originally posted by pmb
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 let's 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 let's 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

 

[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 written 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

 

[pmb]

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

 

[mich]

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

 

[pmb]

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

 

[mich]

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

 

[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.


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 referring 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

 

[LURCH]

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?

 

[mich]

Yo Pete:

I thank you for the website 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 existence 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 referring 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]

 

[mich]

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