# Fitzgerald -Lorentz contraction

1. ### mich

38
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

### Staff: Mentor

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.)
Right. Nothing contracts.
What constant?

3. ### mgb_phys

8,952
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.

### Staff: Mentor

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.

5. ### heafnerj

48
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!

6. ### mich

38
However, lenght contraction was the proposed solution to the nul result.

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

7. ### mich

38

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

Andre

8. ### granpa

huh? whats that mean?

### Staff: Mentor

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

10. ### mich

38
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

11. ### granpa

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.

Last edited: Sep 2, 2008
12. ### mich

38
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

13. ### granpa

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

14. ### mich

38
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

15. ### mich

38
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

16. ### granpa

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.

17. ### mich

38
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

### Staff: Mentor

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: FAQ: Experimental Basis of Special Relativity

19. ### 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.

20. ### mich

38
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