Fitzgerald -Lorentz contraction

Doc Al

Quote by mich

It seems to me, granpa, that it's easily done. Suppose that a frame (train) is passing by me at "v", and as it passes by, it sends a light signal from the back of the train towards the front (at the time when the back of the train passes by me).Let the legth of the train be "x". The observers on the train measure the speed of light as being "c", while I also measure the same speed, instead of (c+v). Therefore, the distance the light will travel (in my frame of reference) would be x+ vt (t = the time for the light to travel from the back of the train to the front).

In this case t= [x+(c+v)] / c

on the moving frame, the distance "could still be x" while t' would have been dilated.

t'= x/c

No need for length contractions at all. However, if there are indeed length contractions, and certainly it's possible, then there ought to be some experiments which can prove this to be true.

Andre

You can't just pick and choose the parts of relativity that you like and ignore the others. Length contraction, time dilation, and the relativity of simultaneity all work together to give a consistent picture. Your calculations don't match those of special relativity, which has been amply confirmed by experiment.

If you call the rest length of the train (in its own frame) to be L', the time for the light to travel from one end to the other--according to train observers--will be t' = L'/c.

In the track frame, the light travels a distance L + vt, where L is the length of the train as measured by the track observers. Thus the time for the light to travel from one end to the other--according to track observers--must satisfy: ct = L + vt, thus t = L/(c-v). Of course, relativity tells us that the train is contracted, thus [itex]L = L'\sqrt{1 - v^2/c^2}[/itex].

If you are interested in experimental evidence for relativity, read the sticky at the top of this forum: FAQ: Experimental Basis of Special Relativity

*granpa*

yes that would work but you didnt look up light clock like I suggested. time dilation is the only way to explain the different travel times of the light in the light clock (perpendicular to the motion of the object). only length contraction is left to explain the difference in travel time parallel to the objects motion.

mich

Quote by Doc Al

I am puzzled by your reasoning. Is "length contraction" between moving frames a consequence of special relativity? Sure, along with time dilation and the relativity of simultaneity (as described by Einstein in 1905). But that doesn't mean that "length contraction" has anything directly to do with the Michelson-Morley experiment.

For a nice discussion of the Michelson-Morley experiment, followed by lectures on the basic principles and consequences of special relativity, you might try this: The Michelson-Morley Experiment

Ok; I've read through the document; I am not saying it was quite that easy.
I had some misunderstandings on some of Michelson's points of view. For the image of the river,he speaks of currents (being a resistance to flow) which is not found in the M&M experiment. The first swimmer remains beside the bank and swims to and fro with and against the current...ok this I can take. But instead of having the second swimmer aiming 90 degrees from the bank, he writes:

"It won't do simply to aim directly for the opposite bank-the flow will carry the swimmer downstream. To succeed in going directly across, the swimmer must actually aim upstream at the correct angle (of course, a real swimmer would do this automatically)."

But within the experiment, the sources of light are indeed separated by 90 degrees.

He goes on to write :

"Thus, the swimmer is going at 5 feet per second, at an angle, relative to the river, and being carried downstream at a rate of 3 feet per second".

However, if the swimmer points 90 degrees to the other bank (which is what the experiment denotes) then, he crosses the bank in
20 seconds or the distance (100 feet) / velocity (5 feet/sec).However, due to the influence ofthe second velocity, that of the river, he will arrive further away along the bank.

Andre

mich

Quote by Doc Al

You can't just pick and choose the parts of relativity that you like and ignore the others. Length contraction, time dilation, and the relativity of simultaneity all work together to give a consistent picture. Your calculations don't match those of special relativity, which has been amply confirmed by experiment.

I agree, Doc. But I am not picking and choosing; I am trying to understand for what reason Einstein thought about implementing a measuring rod contraction...What was measured in order for him to come up with such a notion?

If you call the rest length of the train (in its own frame) to be L', the time for the light to travel from one end to the other--according to train observers--will be t' = L'/c.

ok.

In the track frame, the light travels a distance L + vt, where L is the length of the train as measured by the track observers. Thus the time for the light to travel from one end to the other--according to track observers--must satisfy: ct = L + vt, thus t = L/(c-v).

ok.

Of course, relativity tells us that the train is contracted, thus [itex]L = L'\sqrt{1 - v^2/c^2}[/itex].

What argument is there for the train to be indeed contracted?What experiment was done to prove this assumption?

[/QUOTE]
If you are interested in experimental evidence for relativity, read the sticky at the top of this forum: FAQ: Experimental Basis of Special Relativity [/QUOTE]

Andre

mich

Quote by granpa

yes that would work but you didnt look up light clock like I suggested. time dilation is the only way to explain the different travel times of the light in the light clock (perpendicular to the motion of the object). only length contraction is left to explain the difference in travel time parallel to the objects motion.

I'm sorry granpa; was there a thread in particular you wanted me to look at for light clocks?Or just the internet?

Andre

*granpa*

a light clock is simply 2 mirrors with a pulse of light bouncing between them. each time it bounces off the mirror the clock ticks. the light path is perpendicular to the motion of the object (in the frame of the object). an observer at rest sees the light take a much longer path. time dilation is the ONLY way to explain it.

time dilation alone cant explain both the light path perpendicular and parallel to the motion of the object.

Doc Al

Quote by mich

Ok; I've read through the document; I am not saying it was quite that easy.
I had some misunderstandings on some of Michelson's points of view. For the image of the river,he speaks of currents (being a resistance to flow) which is not found in the M&M experiment. The first swimmer remains beside the bank and swims to and fro with and against the current...ok this I can take. But instead of having the second swimmer aiming 90 degrees from the bank, he writes:

"It won't do simply to aim directly for the opposite bank-the flow will carry the swimmer downstream. To succeed in going directly across, the swimmer must actually aim upstream at the correct angle (of course, a real swimmer would do this automatically)."

But within the experiment, the sources of light are indeed separated by 90 degrees.

He goes on to write :

"Thus, the swimmer is going at 5 feet per second, at an angle, relative to the river, and being carried downstream at a rate of 3 feet per second".

However, if the swimmer points 90 degrees to the other bank (which is what the experiment denotes) then, he crosses the bank in
20 seconds or the distance (100 feet) / velocity (5 feet/sec).However, due to the influence ofthe second velocity, that of the river, he will arrive further away along the bank.

The path of the light (in the lab frame) in one arm is at 90 degrees to the other. That means that the light must be aimed slightly into the ether wind (if there were an ether wind), exactly like the analogy with the swimmer.

Quote by mich

I agree, Doc. But I am not picking and choosing; I am trying to understand for what reason Einstein thought about implementing a measuring rod contraction...What was measured in order for him to come up with such a notion?

Length contraction is a consequence of the basic assumptions of special relativity, one of which is the fact that the speed of light is the same for all observers.

What argument is there for the train to be indeed contracted?What experiment was done to prove this assumption?

The argument for length contraction (and time dilation, etc.) is given in detail in the follow on lectures on the page I linked in post #9. Read it.

As far as I know, there is currently no direct experimental confirmation of length contraction (it's just too small to detect), but the experimental evidence for relativity as a whole (which requires length contraction) is overwhelming.

Quote by mich

I'm sorry granpa; was there a thread in particular you wanted me to look at for light clocks?Or just the internet?

Once again, if you want to learn about time dilation and light clocks, follow that link in post #9.

mich

Quote by granpa

a light clock is simply 2 mirrors with a pulse of light bouncing between them. each time it bounces off the mirror the clock ticks. the light path is perpendicular to the motion of the object (in the frame of the object). an observer at rest sees the light take a much longer path. time dilation is the ONLY way to explain it.

time dilation alone cant explain both the light path perpendicular and parallel to the motion of the object.

Ok; so, since, according to the observer on the rest frame, measures the path of light horizontal to the moving frame, as experiencing a length contraction, while the path going perpendicular does not, then the observer will measure a difference in time between the arrival of the two light signals...which is simply the M&M experiment done in reverse (the observer being on a different frame from the experiment). This is what I'm asking...was this done? What experiment are we talking about in this case?

Andre

*granpa*

Quote by mich

Ok; so, since, according to the observer on the rest frame, measures the path of light horizontal to the moving frame, as experiencing a length contraction, while the path going perpendicular does not, then the observer will measure a difference in time between the arrival of the two light signals...which is simply the M&M experiment done in reverse (the observer being on a different frame from the experiment). This is what I'm asking...was this done? What experiment are we talking about in this case?

Andre

length contraction is irrelevant. the 2 paths are not the same length yet each measures the speed of light to be the same. hence they measure different amounts of time.
the M&M experiment showed that the speed of light is independent of the observer. simple thought experiments suffice to show that time dilation, length contraction, and loss of simultaneity must follow

mich

Quote by Doc Al

The path of the light (in the lab frame) in one arm is at 90 degrees to the other. That means that the light must be aimed slightly into the ether wind (if there were an ether wind), exactly like the analogy with the swimmer.

But how is the source of light "aimed" ahead the ether wind if the experiment starts first with the light signal going through a half silvered mirror,splitting two rays at a 90 degree angle? From what I see, the light source is aimed at 90 degrees from the second light source and assumes the path of light to be longer instead.

Length contraction is a consequence of the basic assumptions of special relativity, one of which is the fact that the speed of light is the same for all observers.

Why does the constancy of light need to imply this?

The argument for length contraction (and time dilation, etc.) is given in detail in the follow on lectures on the page I linked in post #9. Read it.

ok; thanks; I will.

As far as I know, there is currently no direct experimental confirmation of length contraction (it's just too small to detect), but the experimental evidence for relativity as a whole (which requires length contraction) is overwhelming.

What about the M&M experiment produced by a sensor (observer) on a moving frame?

Once again, if you want to learn about time dilation and light clocks, follow that link in post #9.

ok; thanks.

Andre

mich

Quote by granpa

length contraction is irrelevant. the 2 paths are not the same length yet each measures the speed of light to be the same. hence they measure different amounts of time.

Actually, according to your "thought experiment" the observer stationnary, relative to the experiment will not see any light shifts ( difference of time the pulses arrive at the eye). This agrees with Relativity as well as with the Newtonian particle theory of light would have predicted. However, Relativity would predict the light signals must arrive out of sink when viewed from an observer on a moving frame, whereas the particle theory would not.

Was this experiment performed? If yes, where could I find such an experiment?

the M&M experiment showed that the speed of light is independent of the observer. simple thought experiments suffice to show that time dilation, length contraction, and loss of simultaneity must follow

I respectfully disagree with you on this one, granpa.Within the M&M experiment, the observer (eye, photographic plate) is always within the same frame as the source of light. Because of this, we cannot claim that the velocity of light is the same for all other inertial frames.

Andre

*granpa*

Quote by mich

Actually, according to your "thought experiment" the observer stationnary, relative to the experiment will not see any light shifts ( difference of time the pulses arrive at the eye). This agrees with Relativity as well as with the Newtonian particle theory of light would have predicted. However, Relativity would predict the light signals must arrive out of sink when viewed from an observer on a moving frame, whereas the particle theory would not.

Was this experiment performed? If yes, where could I find such an experiment?

I respectfully disagree with you on this one, granpa.Within the M&M experiment, the observer (eye, photographic plate) is always within the same frame as the source of light. Because of this, we cannot claim that the velocity of light is the same for all other inertial frames.

Andre

wthayta?

the important thing about the M&M experiment is that the earth is moving around the sun and therefore changes speed constantly. if by some miracle the apparatus had been stationary at one point it certainly wasnt later on. also as I understand it the apparatus was rotated 90 degrees without producing any result. thats impossible unless the speed of light is constant for all observers.

what do you mean 'light shifts' and 'arrive at the eye'? there as only one pulse and there as no eye.

mich

Quote by granpa

wthayta?

What does that mean?:)

the important thing about the M&M experiment is that the earth is moving around the sun and therefore changes speed constantly. if by some miracle the apparatus had been stationary at one point it certainly wasnt later on. also as I understand it the apparatus was rotated 90 degrees without producing any result. thats impossible unless the speed of light is constant for all observers.

True; but the experiment was based on the wave theory of light.
Newton's particle theory of light would have predicted the same nul results as Relativity did...except in the case where "changes in speed"or accelerations are implied, something that even Relativity would not have predicted as well.

what do you mean 'light shifts' and 'arrive at the eye'? there as only one pulse and there as no eye.

If I understood you correctly, there was two paths of light; one horizontal to the moving frame, and the other perpendicular.

You wrote:

time dilation alone cant explain both the light path perpendicular and parallel to the motion of the object.

I was centrering on this particular view....sorry if I am not clear.
The idea was that the two light signals would arrive at the same time according to the observer within the frame of the experiment, because both light paths are equal, according to this observer. However, the observer on the moving frame would observe the light signals as arriving at different time since, in his frame of reference, one path is longer than the other.

Andre

*granpa*

Quote by mich

If I understood you correctly, there was two paths of light; one horizontal to the moving frame, and the other perpendicular.

I was centrering on this particular view....sorry if I am not clear.
The idea was that the two light signals would arrive at the same time according to the observer within the frame of the experiment, because both light paths are equal, according to this observer. However, the observer on the moving frame would observe the light signals as arriving at different time since, in his frame of reference, one path is longer than the other.

Andre

thats actually even better than what I was talking about. now I finally see what the trouble is. 2 events that occur at the same place at the same time do so for all observers regardless of velocity. all observers see the light pulses arrive at the same time. thats the WHOLE POINT.

mich

Quote by granpa

thats actually even better than what I was talking about. now I finally see what the trouble is. 2 events that occur at the same place at the same time do so for all observers regardless of velocity. all observers see the light pulses arrive at the same time. thats the WHOLE POINT.

Actually, not really, granpa. Here, again, I apologize for my lack of skills in explaining things.
On the frame of reference of the experiment, the observers will measure both lengths of the light's paths (horizontal and vertical)
as being the same. If two light signals are sent at the same time from a source, one taking the horizontal path, the other taking the vertical path, the two light signals would return at the same time due to the invariant speed of light.
Now, for an observer on a moving frame, the horizontal path has been contracted, according to the theory of Relativity, while the vertical path is not contracted. Therefore, Relativity would predict the two light signals would not return at the same time; this could be detected by observing a shift in the light spectrum.
However, If the horizontal path in not affected by any contractions, then even the observer on the moving frame will agree that both light pulses arrived at the same time.

Andre

*granpa*

you've forgotten to take the objects motion into account.it is contracted but it is moving. you have to do a little algebra to determine the amount of time required for a round trap. it works out. trust me.

mich

Quote by granpa

you've forgotten to take the objects motion into account.it is contracted but it is moving. you have to do a little algebra to determine the amount of time required for a round trap. it works out. trust me.

From my point of view, if the light speed remains constant , the time will be t = distance (contracted) / c for the horizontal path, and
t= distance (non contracted) / c. So I cannot see it other than the observer as measuring a time difference between the two light signals arriving.

Andre

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granpa	yes that would work but you didnt look up light clock like I suggested. time dilation is the only way to explain the different travel times of the light in the light clock (perpendicular to the motion of the object). only length contraction is left to explain the difference in travel time parallel to the objects motion.