Time Dilation Explained: Theory & How It Works

[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