# Is Lorentz contraction bona fide or only a “perspective”?

Wolfgang Stracke
Hello,

I do not fully understand nature of Lorentz contraction. Is it bona fide effect or not?

https://en.wikipedia.org/wiki/Michelson–Morley_experiment

The article says:

“This allows a more elegant and intuitive explanation of the Michelson-Morley null result. In a comoving frame the null result is self-evident, since the apparatus can be considered as at rest in accordance with the relativity principle, thus the beam travel times are the same.”

Does that mean, that according to relativity Earth does not move?

according to Einstein:

"Here the contraction of moving bodies follows from the two fundamental principles of the theory, without the introduction of particular hypotheses; and as the prime factor involved in this contraction we find, not the motion in itself, to which we cannot attach any meaning, but the motion with respect to the body of reference chosen in the particular case in point. Thus for a co-ordinate system moving with the earth the mirror system of Michelson and Morley is not shortened, but it is shortened for a co-ordinate system which is at rest relatively to the sun."

What does "not shortened" mean?

Does that mean, that there is a contraction of the Michelson Morley interferometer only in a reference frame of the Sun (as if an observer is there) but the interferometer itself is not actually shortened? Or is it actually shortened but since our tools are distorted (clocks run slower and measuring rulers get shorter) we cannot notice it?

I have realized, that if interferometer is actually shortened, then speed of light on the Earth is actually not equal $c$, but appears to be $c$ due to contraction/dilation. It is equal to $c$ only in the frame of Sun.

However, if speed of light in Earth frame is c, then contraction cannot be bona fide, or in simple words, is only "perspective" from the "point of view" of observer "on the Sun"

What is the proper way to explain null result of Michelson - Morley experiment?

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Or is it actually shortened
Science concerns itself with what one can measure. Ever since Galileo, we have realized that there is no way to measure "actual" velocity. All we can ever measure is velocity relative to something.

Einstein showed us that "actual" length and "actual" duration are on similarly shaky footing. We can only measure them individually if we first choose a frame of reference.

Does that mean, that according to relativity Earth does not move?
Relativity, both Einsteinian and Galilean, mean that "does it move?" is an incomplete sentence. You can only ask "does it move relative to some other object?" Whether or not the Earth is moving depends on which object you compare it to. There is no absolute sense of "moving".
What does "not shortened" mean?
Not subject to Lorentz contraction.
Does that mean, that there is a contraction of the Michelson Morley interferometer only in a reference frame of the Sun (as if an observer is there) but the interferometer itself is not actually shortened? Or is it actually shortened but since our tools are distorted (clocks run slower and measuring rulers get shorter) we cannot notice it?
The problem here is the word "actually", which doesn't really have an operational definition.

The simplest way to understand relativity is the block universe. In this interpretation, the L-shaped interferometer you see on the table is a 3d cross-section through a 4d worldtube. So what different frames regard as "the interferometer" are cross-sections through a worldtube taken at different angles, and naturally the sizes are different. The two frames are measuring different things.

Think of a sausage. A slice through it perpendicular to the long axis is circular but a slice at an angle is elliptical. We can argue about who is "actually" measuring the sausage, or we can simply note that we're measuring different things.
I have realized, that if interferometer is actually shortened, then speed of light on the Earth is actually not equal $c$, but appears to be $c$ due to contraction/dilation. It is equal to $c$ only in the frame of Sun.

However, if speed of light in Earth frame is c, then contraction cannot be bona fide, or in simple words, is only "perspective" from the "point of view" of observer "on the Sun"

What is the proper way to explain null result of Michelson - Morley experiment?
I don't think "bona fide" has a useful definition here. Lorentz contraction is a coordinate effect - it turns out that by choosing a definition of simultaneity you are choosing what slices of spacetime you want to call "all of space at the same instant of time". And the natural way to define the slices, for objects in relative motion, turns out to be different. Depending on the (hyperbolic) angle that these slices make with the worldtube of the interferometer, you regard differently-angled slices of that 4d entity as "the interferometer now", and naturally measure different sizes for it.

Lorentz contraction and time dilation are the result of choosing to measure different aspects of an object. The relationship between measurements in two frames is well defined, but they are not measuring the same thing.

Wolfgang Stracke
Yes, but the result of the experiment in simple words can be explained either by contraction of the interferometer (velocity of light is different from ##c##) or by absence of it (velocity of light is ##c##). We don't speak about sophisticated philosophy but about real experiment that had been conducted by Michelson and Morley. The article does not introduce "4d entity" but gives explanation either this way or that way. I believe that existence of "4d entity" came after the experiment and philosophical comprehension of it.
Because if interferometer is contracted indeed, then the Sun should appear a bit longer from our point of view, but, I believe, we cannot measure it since our tools are not precise enough.
On the other hand, if relativity of simultaneity is the truth, the Sun should appear shorter. This way we can tell whether contraction of the interferometer is real or not, even "relatively" real.
But I don't understand how to lean against the relativity of simultaneity here, since the Earth rotates (moves) around the Sun and we cannot say that the Sun moves around the Earth.
Does that mean that the Earth appears to be a bit shorter as seen from the Sun, but the Sun appears to be a bit longer as seen from the Earth?
P.S. Should we also remember that the whole Sun system rotates around the center of our galaxy?

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Using the Earth and the Sun is not a simple example, because we are not comparing global inertial reference frames. We would either need to invoke the full theory of general relativity, or if we use a simplified scenario with a piece of string holding the Earth in orbit we would need to compare a non-inertial reference frame to an inertial one. Non-inertial frames make life more complicated without adding to understanding.

If, instead, we put two interferometers in two spacecraft and have them pass by each other at high relative speed but with engines off, then we can use special relativity. In this case, both ships will measure the other's interferometer to be length contracted and their clocks to be ticking slowly. Both will conclude that the null result of their own experiment is due to them not moving, and that the null result of the other experiment is due to movement cancelling out the contraction and time dilation effects.

The whole point of relativity is that you can explain the result either as "the interferometer is not moving and is not contracted" or "the interferometer is moving and is contracted". Neither explanation is more correct than the other, and both lead to the conclusion that the speed of light is ##c## for each observer. That is easiest to understand in Minkowski's 4d picture, even more so when you get to general relativity, but other models are possible. I don't think any other is in serious use today.

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Does that mean, that according to relativity Earth does not move?
According to Relativity earth does not move relative to earth.

Does that mean, that there is a contraction of the Michelson Morley interferometer only in a reference frame of the Sun (as if an observer is there) but the interferometer itself is not actually shortened? Or is it actually shortened but since our tools are distorted (clocks run slower and measuring rulers get shorter) we cannot notice it?
It means that there is no such thing as an actual length. Lengths are all relative to some specified reference frame. There is the length relative to the sun’s frame and the length relative to the earth’s frame. Those are different values, but they are equally valid.
Because if interferometer is contracted indeed, then the Sun should appear a bit longer from our point of view, but, I believe, we cannot measure it since our tools are not precise enough.
On the other hand, if relativity of simultaneity is the truth, the Sun should appear shorter. This way we can tell whether contraction of the interferometer is real or not, even "relatively" real
No, if you work out all of the numbers the predictions turn out to be the same either way.

Wolfgang Stracke
Using the Earth and the Sun is not a simple example, because we are not comparing global inertial reference frames. We would either need to invoke the full theory of general relativity, or if we use a simplified scenario with a piece of string holding the Earth in orbit we would need to compare a non-inertial reference frame to an inertial one. Non-inertial frames make life more complicated without adding to understanding.

If, instead, we put two interferometers in two spacecraft and have them pass by each other at high relative speed but with engines off, then we can use special relativity. In this case, both ships will measure the other's interferometer to be length contracted and their clocks to be ticking slowly. Both will conclude that the null result of their own experiment is due to them not moving, and that the null result of the other experiment is due to movement cancelling out the contraction and time dilation effects.

The whole point of relativity is that you can explain the result either as "the interferometer is not moving and is not contracted" or "the interferometer is moving and is contracted". Neither explanation is more correct than the other, and both lead to the conclusion that the speed of light is ##c## for each observer. That is easiest to understand in Minkowski's 4d picture, even more so when you get to general relativity, but other models are possible. I don't think any other is in serious use today.
Hmm... but the Earth and the Sun is the real – life example...

Well, as far as I understand, explanation of Michelson Morley experiment cannot be reduced to the simple model of Special Relativity, since there are some non - inertiality. As far as I understand, quite complex for average Joe theory of General Relativity bust be taken into consideration to explain Michelson Morley experiment.

Poor 19th – 20th century physicists! They were looking for too simple explanation!

Sadly, the article in Wikipedia oversimplifies it. I believe you could dramatically improve it.
By the way, what other models do you mean? Are these models are also applicable?

Wolfgang Stracke
According to Relativity earth does not move relative to earth.

It means that there is no such thing as an actual length. Lengths are all relative to some specified reference frame. There is the length relative to the sun’s frame and the length relative to the earth’s frame. Those are different values, but they are equally valid.
No, if you work out all of the numbers the predictions turn out to be the same either way.
That's the straight answer! Thank you!

Dale
Wolfgang Stracke
The whole point of relativity is that you can explain the result either as "the interferometer is not moving and is not contracted" or "the interferometer is moving and is contracted".
Could you please to clarify one little detail in regard of this sentence? Can we say about ourselves that we are relatively at rest (and our interferometer is not contracted and speed of light is c in our frame) or can we say that we on Earth are moving ourselves relatively to someone and speed of light is not c in our frame, but we still measure it as c since the interferometer distorts? If the both explanations are valid, why should we restrict ourselves only with first one?
If we think, that we are moving ourselves, then speed of light in the Sun frame is c, but it is not c in our frame,
It seems even more logical that one is at rest and another is moving. Why should we point our finger at someone else but not at ourselves?

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Can we say about ourselves that we are relatively at rest (and our interferometer is not contracted and speed of light is c in our frame) or can we say that we on Earth are moving ourselves relatively to someone and speed of light is not c in our frame, but we still measure it as c since the interferometer distorts?
Yes, both work

If the both explanations are valid, why should we restrict ourselves only with first one?
Mostly because it is the one that fits better with general relativity later. It will be easier to transition to GR later if you think in the first way. It will be even easier if you think in the 4D way that @Ibix mentioned above
If we think, that we are moving ourselves, then speed of light in the Sun frame is c, but it is not c in our frame,
It can still be c in our frame, even if we are moving relative to the sun.

Ibix
Hmm... but the Earth and the Sun is the real – life example...
Not unless you want to invoke complicated scenarios without understanding simple ones first. The Sun is not involved in the Michelson and Morley experiment. You don't say where the Einstein quotation comes from, but I suspect he was speaking fairly casually (Edit: It's the end of chapter XVI of Relativity: The Special and the General Theory, and is indeed a non-rigorous treatment), using the Sun as a convenient object moving relative to the Earth and simply ignoring the complexities he introduces thereby. I prefer not to ignore them, since they inevitably come back to bite me in a discussion like this.
Well, as far as I understand, explanation of Michelson Morley experiment cannot be reduced to the simple model of Special Relativity
Of course it can! I just laid out a scenario where it can easily be understood with no hint of general relativity. In fact, the Earth's gravitational field is sufficiently weak that you could use SR for the experiment with an observer in a train passing the lab. Or just walking around it. What you can't do, without invoking either general relativity or non-inertial frames, is consider an observer on the Sun - Einstein's comment notwithstanding.
As far as I understand, quite complex for average Joe theory of General Relativity bust be taken into consideration to explain Michelson Morley experiment.
No - you need GR or SR in non-inertial frames if you want to use experiments and/or observers on the Sun. Michelson and Morley did not do that - their entire experiment was contained in a basement.
Poor 19th – 20th century physicists! They were looking for too simple explanation!
...and Einstein found a simple explanation. He did not add complicating factors such as the Sun to do so.
Sadly, the article in Wikipedia oversimplifies it. I believe you could dramatically improve it.
There is at least one Wiki editor among the senior members of this forum.
By the way, what other models do you mean? Are these models are also applicable?
The only other one I'm aware of is Lorentz Ether Theory. This essentially picks one frame and declares it to be real, and measurements made in any other frame are, in some sense, wrong. Which frame is the "real" one is not detectable. This interpretation is disfavoured by Occam's Razor, since it makes exactly the same predictions and requires an additional assumption - which frame it is that is "real" has to be taken on faith.
Can we say about ourselves that we are relatively at rest
Relatively at rest with respect to what?
we on Earth move ourselves relatively to someone and speed of light is not c in our frame,
This is rather confused. We naturally tend to adopt a frame in which we ourselves are at rest. If we do this, we use clocks and rulers at rest with respect to ourselves and we measure the speed of light to be ##c##. We don't have to treat ourselves as at rest, though, and we can pick a frame in which we are moving. If we use clocks and rulers that are at rest in this frame (i.e., moving with respect to us), we measure the speed of light to be ##c##.

I don't know quite where you're getting this idea that the speed of light isn't ##c##. I suspect you're implicitly mixing measurements between frames. Perhaps if you specify precisely what it is you think you are measuring (clocks and rulers at rest in which frame, measuring what), it would become clear.

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Wolfgang Stracke
I don't know quite where you're getting this idea that the speed of light isn't ##c##. I suspect you're implicitly mixing measurements between frames. Perhaps if you specify precisely what it is you think you are measuring (clocks and rulers at rest in which frame, measuring what), it would become clear.
It is clear from the article, that in moving frame propagation times along the legs is the same, because of Lorentz contraction of longitudinal leg. Lorentz contraction makes propagation times the same, it is obvious, that in moving frame speed of light is longitudinal direction is not c. It is clear that speed of light in direction of motion of the interferometer is lower since front mirror recedes and in backward direction it is very high, since after reflection light approaches point of departure much faster.

I still feel a bit confused. If speed of light is c in all frames, but it is not c in moving frame due to contraction of interferometer, how to reconcile these concepts? Only by assuming, that Michelson interferometer was not moving itself, and nobody cannot think about himself as about moving one. If everyone thinks, that he doesn't move, as the article in Wikipedia suggests, then speed of light is c in all frames and that leads to relativity of simultaneity.

But, if at least one of two observers thinks about himself "I move and I cannot detect my motion because of Lorentz - contraction and time dilation" then relativity of simultaneity naturally disappears, only by some sort of mental effort.
Of course, if nobody makes any mental efforts, that leads straight to relativity of simultaneity.

Hence, by means of changing our way of thinking we can affect physics and even laws of nature. That demonstrates our superiority over mother Nature.

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it is obvious, that in moving frame speed of light is longitudinal direction is not c
Hmm, not only is this not obvious, this is not true.

If you do the Lorentz transform you see that ##c^2 t^2 = x^2 + y^2 + z^2## which means the speed of light is c in all directions. This is true in any inertial frame.

then relativity of simultaneity naturally disappears,
You still have relativity of simultaneity. Since you cannot detect your motion through the ether you also cannot detect the aether simultaneity. So all you can do is use Einstein’s synchronization convention.

Hence, by means of changing our way of thinking we can affect physics and even laws of nature. That demonstrates our superiority over mother Nature.
Good luck with that

Pencilvester