# Lorentz-FitzGerald Contraction

Hi, I am having a hard time understanding the Lorentz - Fitzgerald contraction hypothesis (LFCH). I understand that it is a pre-relativity explanation of the null result of Michelson-Morley Experiment. My question is how did Lorentz derive the gamma factor, namely 1/sqrt(1-v^2/c^2), my understanding used to be that he used the results of Heaviside for the calculation of the electric field of point charge, which shows that the electric field of the point charge is contracted by gamma in the direction of motion, and therefore if we assume that the electrical forces dominates at the microscopic level then the length of any object is contracted by the gamma factor. This in turn will make the travel times in the two arms of the Michelson-Morley setup equal, thus yielding the null result.
My questions are:

1.The electric field of a moving point charge in the direction of motion will get contracted by (1-v^2/c^2) (Griffiths introduction to electrodynamics pg 439), and not by the gamma factor. So was my understanding of LFCH wrong? Basically how did Lorentz get the gamma factor? I am not asking for a full derivation, just the main results he used.

2.Is the LFCH based on the idea of absolute velocity? Because in the frame where the experiment was conducted the arms were not moving. But I keep reading that the arms get contracted in the direction of the motion. So motion relative to what? is it relative to the fame of the aether?
My questions are about the implications of the LFCH itself and not about what is right. I know that LFCH is wrong and there are experiments such that of Trounton-Rankine disproved it, if im not mistaken.

Thanks

Take heed. This is how Einstein saw the problem:
1. James Maxwell said that light, in a vacuum, has to travel at a constant velocity, or 186K miles per second. He even went so far as to proclaim this as a natural law. And,
2. Einstein said that all natural laws must be the same, regardless of how fast you're going.
Thus, I don't care how fast you go, you will always see light going 186K MPS. That means, of course, that if you're going 185 MPS, any light beam you look at will stiiiill have to go 186 MPS!
Stiiiil!

But how so?!

By dialating the time, that's how. If you dialate or contract space, you always have to dialate and contract time at the same time.
Notice that, although the pole sees the barn as contracting, the pole can still fit into the barn because the observer on the pole also took the time contraction into consideration, in addition to the space contraction of the barn.
According to the guy in the barn, both doors closed at the same time. But since the guy on the pole sees time as well as space as contracted, the guy on the pole sees the farther door opening first and the closer door opening secondly.

Does it help?

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George Jones
Staff Emeritus
Gold Member
Does it help?

What you wrote has nothing to do with what haaj86 asked. haaj86 wants to know what, historically, motivated Lorentz.

thats called relativity of simultaneity. not time contraction.

is lfch based on absolute velocity? yes. but it doesnt contradict relativity. relativity says that you cant detect an absolute velocity. not that it doesnt exist.

I dont know how lorentz determined that the field wouldbe contracted. I wondered that myself.

I think you should double check Griffiths.

even if it does in fact say that it might simply be a typo.

JesseM
1.The electric field of a moving point charge in the direction of motion will get contracted by (1-v^2/c^2) (Griffiths introduction to electrodynamics pg 439), and not by the gamma factor. So was my understanding of LFCH wrong? Basically how did Lorentz get the gamma factor? I am not asking for a full derivation, just the main results he used.
I could be wrong on the history here, but I always thought that he came up with the contraction factor as a way to explain the null result of the Michelson-Morley experiment, which was supposed to show the speed of the Michelson-Morley apparatus relative to the aether. If you assume that all objects will shrink by this factor when they're moving relative to the aether (along their axis of motion relative to the aether, not in other directions) then you can explain the fact that the experiment failed to show light moving at different speeds relative to the apparatus depending on the apparatus' orientation. See my post #51 on this thread for a numerical example.
haaj86 said:
2.Is the LFCH based on the idea of absolute velocity? Because in the frame where the experiment was conducted the arms were not moving. But I keep reading that the arms get contracted in the direction of the motion. So motion relative to what? is it relative to the fame of the aether?
Yeah, as I said above, my understanding is that it was imagined that an object would shrink by an amount that depended on its velocity relative to the aether.

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My question is how did Lorentz derive the gamma factor, namely 1/sqrt(1-v^2/c^2), my understanding used to be that he used the results of Heaviside for the calculation of the electric field of point charge, which shows that the electric field of the point charge is contracted by gamma in the direction of motion, and therefore if we assume that the electrical forces dominates at the microscopic level then the length of any object is contracted by the gamma factor. This in turn will make the travel times in the two arms of the Michelson-Morley setup equal, thus yielding the null result.
I agree with JesseM. It was my understanding that Lorentz used experiments to argue for the contraction factor. However I think people also commented that Heaviside's calculations would support that, if matter was held together by electromagnetic forces.

I believe this is the correct order of things, because at the time, they knew the results of some experiments suggesting this, but did not know for sure what held material together (they already realized maxwell's equations had problems for this, since there are no stable configurations of charges according to those equations). So Heaviside could be used as a supporting idea, but he didn't use that to derive it.

Later Lorentz showed that the contraction along with a change in time coordinates, would provide another coordinate system in wich Maxwell's equations had the same form. He was inches away from special relativity, but he thought (even after Einstein's paper) that this was more of a useful math trick than an indication of real physical significance.

My questions are:

1.The electric field of a moving point charge in the direction of motion will get contracted by (1-v^2/c^2) (Griffiths introduction to electrodynamics pg 439), and not by the gamma factor. So was my understanding of LFCH wrong? Basically how did Lorentz get the gamma factor? I am not asking for a full derivation, just the main results he used.
So how far away do you have to be to get the same electric force? Remember that force goes like 1/r^2.

2.Is the LFCH based on the idea of absolute velocity? Because in the frame where the experiment was conducted the arms were not moving. But I keep reading that the arms get contracted in the direction of the motion. So motion relative to what? is it relative to the fame of the aether?
I'm not sure I am understanding your question, so this may not help.
Lorentz believed there was an immobile pervading aether that was the medium of the electromagnetic fields. So he felt maxwell's equations should be applied in the rest frame of the aether. So yes, the contraction was supposed to be relative to this.

To connect it back to relativity, he was basically just selecting (and arbitrarily so) one inertial frame and calling it the aether. You cannot detect the aether anymore than you can "detect" some arbitrarily chosen other inertial frame. So we couldn't detect the aether. On the other hand though, since Maxwell's equations and the Lorentz force law were already in their relativistic form this meant Lorentz's idea actually agreed experimentally with special relativity when it came to electrodynamics. That is why electrodynamics was the "hint from nature" that led us to special relativity... the forces were strong enough that it's relativistic form was figured out before we even knew relativity.

My questions are about the implications of the LFCH itself and not about what is right. I know that LFCH is wrong and there are experiments such that of Trounton-Rankine disproved it, if im not mistaken.
LFCH is not wrong, for the reasons noted above. I'm not sure about the Trouton-Rankine experiment, but reading on wikipedia, it sounds like they weren't using Lorentz's ideas. So what was wrong was merely their particular interpretation of electrodynamics.
http://en.wikipedia.org/wiki/Trouton–Rankine_experiment

The Lorentz contraction is quite easy to formulate...Einstein gives an example in RELATIVITY, The Special and General Theory. Fitzgerlad did, I think, length contraction, Lorentz extended it to time dilation; Einstein used them both in relativity.