Are the transformations just observed ones or real ones?

[Dale]

If an object undergoes linear acceleration, its length - as measured in a fixed inertial frame - will change over time.

Not necessarily. For example, consider a modification of Bell's spaceship scenario where the ships are connected by an elastic band. In the launch frame the length of the band does not change over time during the linear acceleration.

 

[Dale]

I just don't understand why you say that. It's BOTH a disagreement between frames AND a change over time.

Can you provide a source which derives length contraction as a change over time? If not, then I contend that it is not a change over time.

If an object is undergoing rigid motion then that fact can be used together with length contraction (between frames) to determine the length of the object in a given inertial frame over time, but that does not mean that the over-time comparison is length contraction.

 

[Samshorn]

[Length contraction is] BOTH a disagreement between frames AND a change over time.

Right, and of course Lorentz's theorem of corresponding states is, in a sense, the whole basis for the physical significance of the systems of coordinates related by Lorentz transformations. The equilibrium configuration of a solid object, originally at rest in one standard system of inertial coordinates, when set into motion and allowed to reach equilibrium in another system of standard inertial coordinates, is found to be spatially contracted in terms of the original coordinates. Of course, in terms of the second system of coordinates the object was spatially contracted in its original state, and after the acceleration (and stablization) it exhibits its rest length in terms of the second system.

Needless to say, the fact that the the spatial contraction of a solid equilibrium configuration after accelerating from one frame to another agrees exactly with the Lorentz transformation between those frames is not merely a coincidence. It is the basis for the physical significance of the Lorentz transformations. If the equilibrium configurations of solid objects didn't physically contract when set in motion, then the Lorentz transformations would not have any physical significance. Note that, if length contraction didn't imply that the spatial extents of solid objects change as their states of motion change, then it obviously couldn't account for the Michelson-Morley experiment. Relative to a single inertial coordinate system, the arms of the interferometer must change their lengths (in different directions) as the apparatus is re-oriented.

Now, I certainly agree with you that there is no easy way to prove what the final length would be without using multiple frames...

Sure there is (well, depending on what you consider "easy"). Lorentz did it in 1904. That is his Theorem of Corresponding States. Given the correct laws of mechanics and electrodynamics expressed in terms of any single system of inertial coordinates, the spatial contraction of any given equilibrium configuration when set in motion can be determined. This leads unavoidably to the conclusion that the equilibrium configuration contracts spatially in the direction of motion by the factor sqrt(1-v^2). Of course, this all assumes no plastic deformation of the object, representing a permanent change in the equilibrium configuration. As Einstein said, "This conclusion is based on the physical assumption that the length of a measuring rod does not undergo any permanent changes if it is set in motion and then brought to rest again".

It's important to be clear about this, because confusion on this point has served as the launching pad for many neo-Lorentzian crackpots. For example, some individuals have made careers out of writing articles for philosophical magazines advocating the Lorentzian interpretation of special relativity. Their basic mis-understanding is the same as the one expressed by some participants in this thread, namely, they mistakenly think if the laws of physics, expressed in terms of one system of coordinates S1, predict that physical phenomena will behave in a way (contracting, slowing, etc) that ensures they will satisfy the same formal laws in terms of a relatively moving system of coordinates S2, then (so they think) this proves that the S1 coordinates are the "true" coordinates and S2 are just mathematical artifacts. The obvious flaw in this reasoning is that it applies equally well to S2 as the true coordinates and S1 as mathematical artifacts. Lorentz himself credited Einstein with pointing out this "remarkable reciprocity", which reveals Lorentz invariance as a fundamental symmetry of nature, and makes it meaningless to argue for the primacy of S1 or S2 - at least in terms of the local physics. Neo-Lorentzians habitually conflate the possibility of a Lorentzian interpretation with its necessity or physical meaningfulness.

The same applies to Euclidean geometry (as a physical description, not an abstract axiomatic system). It would make no sense to claim that the Pythagorean theorem applies only to the coordinates of a single un-moved rod in terms of two relatively tilted coordinate systems, and to deny that it applies to re-oriented rods in a single coordinate system. We can obviously define any families of coordinate systems we choose, and there can be all kinds of funky differences between the descriptions of solid objects depending on which specific coordinate system we select, but that has no physical significance. The physically significant coordinate systems are the ones that correspond to the operationally defined metrical behavior of equilibrium configurations of solid bodies.

 

[A.T.]

If an object undergoes linear acceleration, its length - as measured in a fixed inertial frame - will change over time. That follows immediately from the Lorentz transformations.

No, it doesn't immediately follow from the Lorentz transformations. You have to additionally assume that the proper-length of the object stays constant (or doesn't increase too much) over time.

 

[Dale]

The equilibrium configuration of a solid object, originally at rest in one standard system of inertial coordinates, when set into motion and allowed to reach equilibrium in another system of standard inertial coordinates, is found to be spatially contracted in terms of the original coordinates.

While this is true, that doesn't mean that it is the phenomenon that is referred to by the term "length contraction". As I mentioned before, all of the derivations I have seen specifically refer to the between-frames comparison.

Sure there is (well, depending on what you consider "easy"). Lorentz did it in 1904. That is his Theorem of Corresponding States.

I would be interested in this. Do you have a link? This type of derivation would make it clear that Lorentz referred to the over-time comparison as "length contraction".

 

[Samshorn]

All of the derivations [of length contraction] I have seen specifically refer to the between-frames comparison.

I would say the derivations you've seen actually do cover both aspects of length contraction, provided you keep in mind the physical meaning of "frames", i.e., of standard inertial coordinate systems. Remember, they are the coordinate systems in terms of which the laws of physics take the same simple homogeneous and isotropic form. This means that the equilibrium configurations of a solid object (for example) will be the same, for any state of motion of the object, when expressed in terms of the co-moving system of inertial coordinates. With this understanding, the fact that those systems are related by Lorentz transformations implies length contraction, which entails the equivalence between (1) the contraction of a solid object (at equilibrium in terms of a given reference frame) when the object's state of motion is changed, and (2) the difference in spatial extent of an unaccelerated object in terms of two different frames of reference. The whole point of special relativity - the reason it works and has physical significance - is that these two things are perfectly equivalent, or rather, they are the same thing, looked at in two different ways.

While this is true, that doesn't mean that it is the phenomenon that is referred to by the term "length contraction".

Yes it does. More precisely, it means that the comparative differences in spatial lengths corresponding to processes (1) and (2) are simply two manifestations of the same attribute (Lorentz invariance) of physical phenomena. They are the same thing, and that thing is called length contraction.

I really think it would help if you thought about the corresponding facts of Euclidean geometry. In terms of a Cartesian system of coordinates, the x projection of a rod of length L is Lcos(q) where q is the angle between the rod and the x axis. So if q=0 we have x=L, but if q>0 the x projection is less. This can be called “x contraction”. Your claim is that the term “x contraction” applies only if we hold the rod fixed and compare the x projections of two different coordinate systems, but not if we hold the coordinate system fixed and consider the x projections for two different orientations of the rod. Hopefully you can see that, given that the coordinate systems are ultimately defined in terms of equilibrium configurations of rods, these two situations are equivalent.

I would be interested in this. Do you have a link? This type of derivation would make it clear that Lorentz referred to the over-time comparison as "length contraction".

Do you have access to a copy of "The Principle of Relativity", in the Dover edition? If not, I'd highly recommend it. It contains the original papers of Lorentz, Einstein, and Minkowski on relativity. In particular, Lorentz's 1904 paper contains his theorem of corresponding states, by which he provides a physical justification for the Fitzgerald contraction effect that he had previously just postulated ad hoc. By 1904 he had realized that precisely this contraction was to be expected as a consequence of the form of the physical laws (expressed in terms of a single coordinate system):

"If we suppose each particle of a solid body to be in equilibrium under the action of the attractions and repulsions exerted by its neighbors, and if we take for granted that there is but one configuration of equilibrium, we may draw the conclusion that the system S', if the velocity v is imparted to it, will of itself change into the system S. In other terms, the translation will produce the deformation [by the factor sqrt(1-v^2) in the direction of v]."

But I hope you don't think this is just an antiquarian derivation. Again, every derivation you've ever seen entails essentially the same concepts. Given the laws of physics, expressed in terms of any single coordinate system, if we determine the result of accelerating a measuring rod to some state of motion, we can obviously determine the amount of spatial contraction it undergoes, simply by applying the laws of physics in that single coordinate system. The physical significance of the Lorentz transformations is that they relate the coordinate systems in terms of which the laws of physics take the same simple form, and hence the equilibrium configurations of objects are the same.

 

[Dale]

I would say the derivations you've seen actually do cover both aspects of length contraction, provided you keep in mind the physical meaning of "frames", i.e., of standard inertial coordinate systems.

No, they don't. The derivation of length contraction (between frames) only requires the principle of relativity and the invariance of c. As such, it is always valid, regardless of the scenario and regardless of the specific theory of matter. The over-time interpretation requires a theory of matter with "rigid" objects, and further it is only applicable in scenarios where the objects undergo purely rigid acceleration.

The derivations of length contraction that I have seen have been based on the Lorentz transform without requiring the additional assumptions.

Remember, they are the coordinate systems in terms of which the laws of physics take the same simple homogeneous and isotropic form. This means that the equilibrium configurations of a solid object (for example) will be the same, for any state of motion of the object, when expressed in terms of the co-moving system of inertial coordinates.

You are here assuming solid objects in equilibrium configuration, and also the laws that produce such objects. It is therefore of limited applicability, and none of the derivations I have seen introduce such needless complexity and limitations. As I said, the additional assumptions required for over-time length contraction are NOT implied by the usual derivations of between-frames length contraction.

"If we suppose each particle of a solid body to be in equilibrium under the action of the attractions and repulsions exerted by its neighbors, and if we take for granted that there is but one configuration of equilibrium, we may draw the conclusion that the system S', if the velocity v is imparted to it, will of itself change into the system S. In other terms, the translation will produce the deformation [by the factor sqrt(1-v^2) in the direction of v]."

This seems to be a postulate of Lorentz's theory (which is consistent of my understanding of his theory) rather than a derivation, but since postulates aren't derived it seems completely valid to me. It does make it clear that the over-time interpretation of length contraction was a correct historical usage of the term. I will make sure to modify my comments accordingly in the future.

 

[Samshorn]

The derivation of length contraction (between frames) only requires the principle of relativity and the invariance of c.

Well, relativity along with memorylessness, isotropy, and homogeneity of inertia. And the point is, those are precisely the principles that imply that the two aspects of length contraction are equivalent -as they must be if the Lorentz transformation is to have any physical significance.

As such, it is always valid, regardless of the scenario and regardless of the specific theory of matter. The over-time interpretation requires a theory of matter with "rigid" objects, and further it is only applicable in scenarios where the objects undergo purely rigid acceleration.

No, not at all. As you said, the derivations require the principle of relativity, which asserts that the laws of physics take the same form when expressed in terms of any system of inertial coordinates. This signifies that - by definition - the equilibrium configuration of a solid body (governed by the laws of physics) will be the same, regardless of its state of motion, when described in terms of a co-moving system of inertial coordinates. For example, the arms of Michelson's interferometer, when their orientation changes, undergo changes in their spatial lengths in terms of the single reference frame of the Earth. It doesn't matter what kind of acceleration or process created that object in that state of motion, nor does this require any "theory of matter", it requires only the existence of stable and persistent entities, such as the "measuring rods and clocks" on which Einstein based his theory.

The derivations of length contraction that I have seen have been based on the Lorentz transform without requiring the additional assumptions.

No, you're overlooking the fact that the physical significance of the Lorentz transformations is entirely due to the fact that inertial coordinate systems (i.e., coordinate systems in terms of which the laws of physics take the same simple form) are related by those transformations. You could dream up any weird kind of coordinate transformations you like, and "derive" the "length contraction" implied by those coordinates, but it would have no physical significance. Length contraction is not an algebraic fact derived from an arbitrarily selected transformation, it's a physical fact due to the Lorentz invariance of physical phenomena, as exemplified by Einstein's (ideal) measuring rods and clocks.

Again, the analogy to Euclidean geometry makes this perfectly clear. As explained previously, the x-contraction is purely a function of the angle between the rod and the x axis, regardless of whether we rotated the rod or the coordinates (because ultimately the coordinates are defined in terms of the persistent properties of ideal measuring rods). Granted, a real physical object could be deformed by rotation, just as a real physical clock could be broken by acceleration, but this doesn't invalidate the concept of ideal measuring rods and clocks. It's understood that we don't rotate the arms of Michelson's interferometer fast enough to deform them. This is why Einstein noted that "This conclusion is based on the physical assumption that the length of a measuring rod does not undergo any permanent changes if it is set in motion and then brought to rest again".

This seems to be a postulate of Lorentz's theory (which is consistent of my understanding of his theory) rather than a derivation...

Well, he originally just postulated it, but by 1904 he derived it (more or less) from the laws of electrodynamics (combined with the "molecular force hypothesis" that says whatever forces hold the elementary particles together transform the same way that electromagnetic forces do) in terms of a single reference system. This is called the Theorem of Corresponding States. Note that Heaviside and Searle had already derived in the 1800s the fact that the spheres of equi-potential of an electric charge are contracted into ellipsoids by the factor sqrt(1-v^2) in the direction of motion, so physical length contraction is not a surprising phenomenon.

 

[stevendaryl]

Can you provide a source which derives length contraction as a change over time? If not, then I contend that it is not a change over time.

*IF* a rod has an equilibrium length L when at rest, then Lorentz invariance of the forces within the rod would imply that it would have that length in any inertial reference frame. So, if a rod starts off at rest in frame F, and then is gently accelerated to speed v, and then allowed to return to its equilibrium length, then its length will beL/\gamma in frame F.

Now, not everything has an equilibrium length. A lump of chewing gum doesn't. But if it has an equilibrium length, then its length will necessarily decrease if you set it gently in motion.

 

[stevendaryl]

No, they don't. The derivation of length contraction (between frames) only requires the principle of relativity and the invariance of c. As such, it is always valid, regardless of the scenario and regardless of the specific theory of matter. The over-time interpretation requires a theory of matter with "rigid" objects, and further it is only applicable in scenarios where the objects undergo purely rigid acceleration.

Right. In the cases in which an object has an equilibrium length, then it will undergo physical length contraction if it is accelerated (as measured in its original rest frame). But that really is the normal case when people are talking about rockets and measuring rods and so forth. If rods didn't have equilibrium lengths, then they would be pretty useless for measuring.

When people talk about Rindler coordinates for a rocket undergoing constant proper acceleration, the usual assumption is that the rocket's length remains constant in Rindler coordinates. If that were not the case, then that would be kind of weird.

 

[Dale]

Well, relativity along with memorylessness, isotropy, and homogeneity of inertia. And the point is, those are precisely the principles that imply that the two aspects of length contraction are equivalent

No, they are not equivalent. If they were equivalent then both over-time and between-frames length contraction would necessarily apply in the same situations. Over-time length contraction does not apply when objects undergo non-rigid acceleration whereas between-frames length contraction does. Therefore they cannot be equivalent. It is a proof by contradiction and none of your response changes that simple and obvious fact.

Over-time length contraction is not equivalent to between-frames length contraction because it requires additional assumptions which can be violated in specific scenarios. Please re-read your own explanations to see the clear fact that you are making those additional assumptions.

Please do not post more of the same, they are not equivalent as you should be well aware by now.

 

[Dale]

Right. In the cases in which an object has an equilibrium length, then it will undergo physical length contraction if it is accelerated (as measured in its original rest frame). But that really is the normal case when people are talking about rockets and measuring rods and so forth.

Yes, in the case where you additionally assume a constant equilibrium length then the between-frames length contraction together with those additional assumptions imply the over-time length contraction. While that is the normal case when talking about rockets etc. it is not the case when talking about currents or Bell's spaceship or many other scenarios. This is because the additional assumptions required for the over-time length contraction are not met. Therefore, from a pedagogical standpoint it is not good to confound those two distinct concepts, which is why the modern usage is between-frames as can be clearly seen from the derivations.

 

[DrGreg]

This is, of course, an argument over words and not an argument over physics. The argument can be avoided by just doing the maths and not attempting to describe it with words.

I would say that the primary meaning of length-contraction is the between-frames version. I would say that the over-time version is a consequence of, or corollary to, length-contraction, as it applies only in special cases where objects behave as if they are "rigid", whereas the between-frames version always applies.

I think this matters because people learning the subject can get confused. They think that "acceleration causes contraction", and then get confused in cases such as Bell's spaceship paradox, or electrons moving in an uncharged wire, where things accelerate but don't move closer together.

They can even get confused when A and B start out initially at rest relative to each other, then B accelerates and then coasts at constant velocity relative to A. They understand that B contracts relative to A's frame, because "acceleration causes contraction", but they don't understand that A contracts relative to B's frame. Either they don't accept it at all, or they think A's contraction is an illusion and B's contraction is "real". And all because of a misunderstanding of what "length-contraction" really is.

 

[kaplan]

No, it doesn't immediately follow from the Lorentz transformations. You have to additionally assume that the proper-length of the object stays constant (or doesn't increase too much) over time.

Yes, you're right. But it will stay constant, at least if (a) it's reasonably rigid, or I accelerate it slowly enough, and (b) I measure the length long after the acceleration is over.

All of which is to say that I don't understand what DaleSpam is getting at.

 

[Dale]

Yes, you're right. But it will stay constant, at least if (a) it's reasonably rigid, or I accelerate it slowly enough, and (b) I measure the length long after the acceleration is over.

All of which is to say that I don't understand what DaleSpam is getting at.

What I am getting at is that (a) and (b) are additional assumptions which are not always valid. What is known as length contraction in modern terms does not include those additional assumptions and is therefore more general.

 

[Samshorn]

This is, of course, an argument over words and not an argument over physics.

I agree that some of the disputation is due to inapt wording (on my part), but I think there may be some actual physics lurking in this discussion. What I've been talking about is the physical meaning of the Lorentz transformation in terms of the equilibrium configurations of physical entities, exemplified by ideal measuring rods and clocks. Others here are focused on non-equilibrium configurations of physical entities, and they want to be sure no one confuses these with equilibrium configurations. That's fine, and I applaud their efforts to make that important distinction. But that distinction doesn't contradict what I've been saying - see below.

I would say that the primary meaning of length-contraction is the between-frames version. I would say that the over-time version is a consequence of, or corollary to, length-contraction, as it applies only in special cases where objects behave as if they are "rigid", whereas the between-frames version always applies.

The point I've been laboring (apparently without success!) to convey is that "frames" are ultimately defined in terms of ideal measuring rods and clocks, so when we talk about evaluating length "between frames" we are actually talking about evaluating two different sets of ideal measuring rods (and clocks) in two different states of motion - but of course these two sets of ideal measuring rods and clocks must be 'intrinsically identical'. For example, a one meter rod at rest in S must be 'intrinsically identical' to the one meter rod at rest in S'. But this has meaning only if we know what 'intrinsically identical' means - and therein lies the rub.

One way of establishing the intrinsic identicality of relatively moving rods would be to create two sets of measuring rods in a single reference frame and compare them side-by-side to make sure they are equal, and then accelerate (arbitrarily slowly) one set of rods to some state of motion. But this implies that a "between-frame" comparison is nothing but a disguised over-time comparison of ideal rods. This is unacceptable to anyone who insists that the between-frame comparison is not equivalent to an over-time comparison of ideal rods. That person needs to contend that each ideal measuring rod can serve as a measuring rod only for one specific frame, and can never be put into another frame for comparison with any other rod. But then how do we physically correlate ideal measuring rods in different states of motion?

Conceptually we can define a certain molecular structure, consisting of a certain number of (presumed) elementary particles arranged in a certain way, maintained by the electromagnetic interactions and whatever other interactions (e.g., the strong nuclear force) are involved in maintaining the equilibrium structure, and then we could create a similar arrangement of elementary particles at rest (on average) in a different frame and allow it to reach equilibrium, and declare that these two structures are intrinsically identical. But of course the simplest way of doing this would be by the first method (i.e., by creating them side by side and then accelerating one arbitrarily slowly), and in any case it is obviously equivalent to the first method. So, again, the frame-comparison is equivalent to the over-time comparison of ideal measuring rods in equilibrium.

Note well that this does not imply that an over-time comparison between ideal measuring rods (or any other physical configurations in equilibrium) is equivalent to a comparison of configurations that are not in equilibrium. That should go without saying. By the way, I really think the Euclidean analogy for x-contraction of a rod makes this perfectly clear. No one disputes that Lcos(q) is the same regardless of whether q was due to re-orienting the frame or re-orienting the rod.

 

[stevendaryl]

Yes, in the case where you additionally assume a constant equilibrium length then the between-frames length contraction together with those additional assumptions imply the over-time length contraction. While that is the normal case when talking about rockets etc. it is not the case when talking about currents or Bell's spaceship or many other scenarios. This is because the additional assumptions required for the over-time length contraction are not met. Therefore, from a pedagogical standpoint it is not good to confound those two distinct concepts, which is why the modern usage is between-frames as can be clearly seen from the derivations.

I thought one of Bell's points in his thought experiment is that the intuition that objects undergo physical contraction when they are accelerated gives the correct answer immediately. The normal behavior of a string that is accelerating is for it to be contracted (relative to its initial rest frame). To prevent contraction, you have to apply stress to the string (you have to stretch it relative to its equilibrium length). So with large enough acceleration, the string will break.

I agree that equilibrium length is not always an appropriate concept, but then, neither is the concept of the "rest frame of an object". If the object is not rigid, then the pieces can have nonzero velocity relative to each other, and it doesn't make sense to talk about a single rest frame for the object.

 

[stevendaryl]

I think this matters because people learning the subject can get confused. They think that "acceleration causes contraction", and then get confused in cases such as Bell's spaceship paradox, or electrons moving in an uncharged wire, where things accelerate but don't move closer together.

As I said to Dale, Bell's spaceship thought experiment is a case where the intuition of physical contraction gives you the RIGHT answer. The normal case for an accelerating string is that its length becomes shorter with time. To prevent this, you must exert additional stress on the ends of the string (you must stretch it relative to its equilibrium, velocity-dependent length). Eventually, that stress will cause the string to break.

 

[Samshorn]

As I said to Dale, Bell's spaceship thought experiment is a case where the intuition of physical contraction gives you the RIGHT answer.

Right, that was the whole point of Bell's paper. He used that spaceship example to show that many people who've been taught special relativity in the standard way are unclear about the fact that length contraction implies that coherent physical objects actually do tend to spatially contract when put into motion (just as the x component of a rod's length actually does tend to get smaller when it is re-oriented away from the x axis).

 

[Dale]

This is going nowhere.

The two length-contraction concepts are distinct with the over-time definition requiring additional assumptions than the between-frames definition. The over-time derivation and definition of length contraction does have a legitimate historical basis. The modern usage and derivation is the between-frames definition of length contraction.

 

[TrickyDicky]

Moderator's note: this post was moved from another thread.

This is, of course, an argument over words and not an argument over physics. The argument can be avoided by just doing the maths and not attempting to describe it with words.

I would say that the primary meaning of length-contraction is the between-frames version. I would say that the over-time version is a consequence of, or corollary to, length-contraction, as it applies only in special cases where objects behave as if they are "rigid", whereas the between-frames version always applies.

I think this matters because people learning the subject can get confused. They think that "acceleration causes contraction", and then get confused in cases such as Bell's spaceship paradox, or electrons moving in an uncharged wire, where things accelerate but don't move closer together.

I don't think this is only an argument over words, precisely being intent on addressing the physics of it instead of just the abstract mathematical aspect is what makes both length contractions the same physically and have them separated only in a very abstract sense where even the concept "length contraction" which is a very physical one loses its content.
I mean that if we are talking about a change in length we either implicitly assume there is an "equilibrium length", or rigidity consistent enough to measure a length at all or there is no sense at all physically in talking about "length contraction" consistently. Yes we always have the mathematical definition of the lorentz transformation but that is just an abstract operation wrt to lenghts if we don't give it some physical meaning to the concept length or to its putative contraction as something empirical.

What I am getting at is that (a) and (b) are additional assumptions which are not always valid. What is known as length contraction in modern terms does not include those additional assumptions and is therefore more general.

See above. But in this case I'd say you are more interested in the semantic aspect so it is alright to make the distinction.

I agree that equilibrium length is not always an appropriate concept, but then, neither is the concept of the "rest frame of an object". If the object is not rigid, then the pieces can have nonzero velocity relative to each other, and it doesn't make sense to talk about a single rest frame for the object.

That's it, and as I wrote above it doesn't make sense to talk about "length contraction" either in any physical way. Only in an abstract mathematical sense that will not have a physical consequence unless we add the corresponding obvious assumption about ideal rods and consistent lengths in equilibrium (body rigidity at low speeds wrt c).

Yes, in the case where you additionally assume a constant equilibrium length then the between-frames length contraction together with those additional assumptions imply the over-time length contraction. While that is the normal case when talking about rockets etc. it is not the case when talking about currents...

I would say then that if we agree (wich is maybe debatable) that in the case when talking about currents we cannot make that assumption, one should abstain from using physical length contraction as an explanation for magnetic fields as they do in the video, it causes more confusion than understanding and ultimately it is not physically correct, don't you think?