# Fitzgerald -Lorentz contraction

Why would the Michelson-Morley experiment be the experiment which proves "length contractions" of measuring rods if everything within the experiment lie on the same frame of reference?
According to Relativity, no contraction should exist at all in this case.

If the mathematical derivative of this constant comes from the "calculated" results of this particular experiment, how can we be certain it isn't flawed?

Andre

## Answers and Replies

Doc Al
Mentor
Why would the Michelson-Morley experiment be the experiment which proves "length contractions" of measuring rods if everything within the experiment lie on the same frame of reference?
It didn't prove "length contraction", but it did provide evidence for the non-existence of an ether. (Lorentz did propose a contraction hypothesis to explain the null results, but that was replaced by special relativity.)
According to Relativity, no contraction should exist at all in this case.
Right. Nothing contracts.
If the mathematical derivative of this constant comes from the "calculated" results of this particular experiment, how can we be certain it isn't flawed?
What constant?

mgb_phys
Homework Helper
I think the OP meant formula not constant.
If you assume the speed of light is constant then you can explain the results of the MM experiment by assuming a contraction in the length in the direction of motion.

Doesn't just a 'classical' picture of the experiment being contracted give you the lorentz contraction formula? I thought that's how lorentz came up with it.

Doc Al
Mentor
I think the OP meant formula not constant.
I'll bet you're right.
If you assume the speed of light is constant then you can explain the results of the MM experiment by assuming a contraction in the length in the direction of motion.
If you assume the speed of light is constant for all observers, as did Einstein, the null results follow immediately. If you assume that light travels with respect to an ether, then you can explain the null results by assuming that motion through the ether produces a length contraction, as Lorentz proposed.

I suggest the OP read Arnold Arons' thorough exposition of this topic in his 1965 textbook Development of Concepts of Physics. It's a model of clarity!

It didn't prove "length contraction", but it did provide evidence for the non-existence of an ether. (Lorentz did propose a contraction hypothesis to explain the null results, but that was replaced by special relativity.)

However, lenght contraction was the proposed solution to the nul result.

Right. Nothing contracts.

What constant?

If I'm not mistaken, the constant "c" of the light's velocity (a little pun on the side) was proposed by Dr.Einstein in order to rid of the ether theory, but also to explain the nul result of the M&M experiment.

The experiment was first proposed in order to detect the ether, which came from Maxwell's equations ; if I'm not mistaken, it seems that the qualities( permeability and permittivity) of free space were properties of the ether itself, which gave a constant velocity for light within the ether.It was because of Maxwell that Michelson believed light to have a constant velocity within the ether, in the first place; this, being needed, in order to afterwards calculate the velocity of the earth through space.

Now, since the theory Relativity implies there to be length contractions between moving frames; it must have been taken from the M&M experiment itself, for where else was this implied before?

But since within the Michelson and Morley experiment, nothing within the experiment moves, that is, observer relative to source, then no time dilations, nor length contractions are to be expected...which begs the question; why does the theory of Relativity imply there to be a contraction of measuring rods in the first place?

Andre

I'll bet you're right.

If you assume the speed of light is constant for all observers, as did Einstein, the null results follow immediately. If you assume that light travels with respect to an ether, then you can explain the null results by assuming that motion through the ether produces a length contraction, as Lorentz proposed.

However, not because of any measuring rod contractions. The particle theory of light could predict the same nul result.

Andre

However, not because of any measuring rod contractions.

Andre

huh? whats that mean?

Doc Al
Mentor
Now, since the theory Relativity implies there to be length contractions between moving frames; it must have been taken from the M&M experiment itself, for where else was this implied before?

But since within the Michelson and Morley experiment, nothing within the experiment moves, that is, observer relative to source, then no time dilations, nor length contractions are to be expected...which begs the question; why does the theory of Relativity imply there to be a contraction of measuring rods in the first place?
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: http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html" [Broken]

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huh? whats that mean?

Simply that even by assuming the speed of light to be invariant, the Michelson and Morley experiment would not involve any measuring rod
contractions nor any time dilation factor. Yet, any book on Relativity will identify the Michelson and Morley experiment as being responsible for the development of theory of Relativity....the Lorentz transform was taken from this.

Now, we know the reason why Michelson suggested a length contraction....it was in order to explain the nul result....but why would Relativity need a length contraction in order to explain it's theory?

Andre

.but why would Relativity need a length contraction in order to explain it's theory?

Andre

this is simple relativity 101 stuff. dont they teach this stuff anymore? if you assume the speed of light is constant (which the Michelson and Morley experiment showed) then a few simple thought experiments are sufficient to prove that length contraction, time dilation, and loss of simultaneity must occur.

look up "light clock"

with a light clock one can measure distances by simply bouncing light off objects and measuring the travel time of the light pulse.

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this is simple relativity 101 stuff. dont they teach this stuff anymore? if you assume the speed of light is constant (which the Michelson and Morley experiment showed) then a few simple thought experiments are sufficient to preve that length contraction, time dilation, and loss of simultaneity must occur.

look up "light clock"

with a light clock one can measure distances by simply bouncing light off objects and measuring the travel time of the light pulse.

The measurements of time will lead me to believe there was a dilation of time experienced on the moving frame....now, tell me why I should believe there was any length contractions involved? What measurements made me assume this?

Andre

imagine a pulse of light bouncing between the front and back of the moving object.

imagine a pulse of light bouncing between the front and back of the moving object.

Good; this is what I'm interested to know; I'm not interested in any thought experiments, but real experiments proving that length contraction exists.
In your though experiment, I can always think of the moving object as remaing the same length even if I assume the velocity of light is constant.

Andre

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: http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html" [Broken]

I will read the link that you gave me and get back to you; My question, I guess, would be, would the theory of Relativity have
developped even without the Michelson and Morley experiement?

Andre

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Good; this is what I'm interested to know; I'm not interested in any thought experiments, but real experiments proving that length contraction exists.
In your though experiment, I can always think of the moving object as remaing the same length even if I assume the velocity of light is constant.

Andre

no, you cant. remember that to a person on-board the moving object the light pulse must move at c. we have already established the time dilation so the only way that light pulse can appear to move at c is for length contraction to take place. you need to do some math to see exactly how long the pulse will take to bounce back and forth from your persective. its not that hard really. its just algebra.

no, you cant. remember that to a person on-board the moving object the light pulse must move at c. we have already established the time dilation so the only way that light pulse can appear to move at c is for length contraction to take place. you need to do some math to see exactly how long the pulse will take to bounce back and forth from your persective. its not that hard really. its just algebra.

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

Doc Al
Mentor
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 $L = L'\sqrt{1 - v^2/c^2}$.

If you are interested in experimental evidence for relativity, read the sticky at the top of this forum: http://75.126.60.30/showthread.php?t=229034" [Broken]

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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 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: http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html" [Broken]

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

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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 $L = L'\sqrt{1 - v^2/c^2}$.

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: http://75.126.60.30/showthread.php?t=229034" [Broken][/QUOTE]

Andre

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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

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
Mentor
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.
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.
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.

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