Talk:Lorentz transformation

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Delete irrelevant animation

The momentarily co-moving inertial frames along the world line of a rapidly accelerating observer (center). The vertical direction indicates time, while the horizontal indicates distance, the dashed line is the spacetime trajectory ("world line") of the observer. The small dots are specific events in spacetime. If one imagines these events to be the flashing of a light, then the events that pass the two diagonal lines in the bottom half of the image (the past light cone of the observer in the origin) are the events visible to the observer. The slope of the world line (deviation from being vertical) gives the relative velocity to the observer. Note how the momentarily co-moving inertial frame changes when the observer accelerates.

The File:Lorentz transform of world line.gif (to the right) should be deleted because accelerated observers are not relevant to this article. It does not even say anything specific, or have any emphasis on, Lorentz boosts (constant velocity) in spacetime, and purely spatial rotations. The caption is also enormous and drags on forever on spacetime, world lines, light cones, etc. without saying anything about Lorentz boosts. The animation doesn't actually distract me personally from the text, but it may distract others.

In all these years I thought to keep it since it may help to show how spacetime looks with different rapidities, but not anymore. The rapidity is a constant in a Lorentz boost, so a continuously varying rapidity may be misleading. It could be added to other relativity articles which involve spacetime diagrams (which can be drawn for flat or curved space), but not here.

(Actually, I'm not 100% sure about accelerated observers in special relativity, it's certainly possible to define coordinate- and four-acceleration in SR, how this fits in with accelerating frames I don't know. In any case this article should concentrate on Lorentz boosts, at most mentioning accelerated frames in passing). M∧Ŝc²ħεИ_τlk 00:50, 26 November 2015 (UTC)

Since there are no objections, I'll move it to world line, spacetime, and spacetime diagram, and delete from this article. M∧Ŝc²ħεИ_τlk 19:04, 9 January 2016 (UTC)

Actually not spacetime but Minkowski spacetime, since spacetime is too general. M∧Ŝc²ħεИ_τlk 19:12, 9 January 2016 (UTC)

1904 paper by Lorentz

Why no mention of the 1904 paper by Lorentz is which he clearly presents his transformations? Martin Hogbin (talk) 12:54, 11 December 2015 (UTC)

Many thanks, especially for the link, I have been carried away, but in the time it took to post this section you could have added it yourself. I'll insert it now. M∧Ŝc²ħεИ_τlk 14:07, 11 December 2015 (UTC)

Hyperbolic geometry and addition of two rapidities in different directions

I'm not 100% sure how to add rapidities if the boosts are in different directions, but surely it has something to do with

1. the line element in velocity space (here Velocity-addition formula#Hyperbolic geometry)
2. Translation:On the Non-Euclidean Interpretation of the Theory of Relativity by Vladimir Varićak
3. the paper Relativistic velocity space, Wigner rotation, and Thomas precession (2004) John A. Rhodes and Mark D. Semon (should be available free on google)
4. the PDF The Hyperbolic Theory of Special Relativity (2006) by J.F. Barrett (should be available free on google)
5. Sexl Urbantke mention on p.39 Lobachevsky geometry needs to be introduced into the usual Minkowski spacetime diagrams for non-collinear velocities.

It would be nice to briefly mention the relation between hyperbolic geometry and non-collinear rapidities, with a diagram of non-commuting boost represented by two hyperbolic triangles (fig.3 in second link, and p.39 in the fourth link). Maybe then we could break the article into "physical formulation", "geometric formulation", "mathematical formulation" sections.

The purpose of this proposal is not to describe all of SR with hyperbolic geometry, just to illustrate how spacetime diagrams extend to non-commuting boosts, i.e. how to show non-commuting boosts in spacetime. M∧Ŝc²ħεИ_τlk 12:45, 13 December 2015 (UTC)

Transformation of the electromagnetic field

I think the EM section should be given after the specification of how tensors transform. Actually, deriving the transformation laws using 3 + 1 spacetime (i.e. using E and B) is difficult. It is rather easy (no bag of tricks needed) using the field tensor F. YohanN7 (talk) 15:54, 15 December 2015 (UTC)

Yes it is tedious to derive the transformations of the E and B fields, but current section is the vector statement which simply mentions that they can be derived from the transformations of velocity and the Lorentz force (only the statement they can be derived is needed, not the actual derivation). It fits in well where it is. In the tensor section, we can still mention the angular momentum and EM field tensors, illustrating how these tensors transform. The reader can make up their own mind which formulation (vector or tensor) is easier. M∧Ŝc²ħεИ_τlk 16:29, 15 December 2015 (UTC)

I don't agree. I think this article should rely on special relativity (with manifest covariance) as much as possible. YohanN7 (talk) 11:08, 16 December 2015 (UTC)

I much prefer for this entire article if the vector formulation of the examples are given first, then the tensor formulation as a second treatment. Cartesian components (including on generators and parameters), vectors, and matrices are more accessible than using index notation and tensors for an introductory article like this.

Maybe we could create a new article Covariant formulation of Lorentz transformations (not set on title), which contains everything in this article in tensor form, using 4-vectors at the outset, and manifest covariance throughout. The tensor section in this article would be moved over there. The group theory can be cast in index form also (using the parameter matrix ω and generator matrix M, commutation relations can be given in index form, with a mention of structure constants). Transformations of spinors could also be given in that article. Do you agree with this?

Otherwise, I'm not keen on what you're saying, but on the other hand I don't want to own the article either. Feel free to move and rewrite the section. M∧Ŝc²ħεИ_τlk 12:20, 16 December 2015 (UTC)

Also, to further reduce this article size, maybe another article just on the problem of general compositions of Lorentz transformations in arbitrary directions could be created (not sure on the title, maybe "Compositions of Lorentz transformations" or something). The parts about hyperbolic triangles and spacetime diagrams for non-collinear boosts could be in there also. It is not in elementary textbooks (obviously), but the topic is a research area in its own right, and included in more advanced books, so it's notable. This article could just link to that article for the results. Would you agree with this also? M∧Ŝc²ħεИ_τlk 12:20, 16 December 2015 (UTC)

On the last paragraph: Transformation of velocities could be reduced to

Main article: Velocity addition formula

+ the formula. Most stuff on combining boosts could be (is already) in Thomas precession. It is what those articles are for.

Then, if you'd rather have this article as a reference (can answer what the formula for transformation of EM fields/3-velocity/momentum/angular momentum, spinors), then I'd agree. Just splash up the formulas. If you want to have this as learning material, then the tensor formulation should go first (after coordinate transformations). It provides the rather simple framework in which all explicit formulas on whatever form can be derived with comparative ease. I'll definitely not insist on this, but it is my POV. YohanN7 (talk) 13:05, 16 December 2015 (UTC)

Agreed on the velocity addition formula (statement and link, if the reader cannot take differentials, will not understand the section anyway so the x-boost is redundant).

For the composition of boosts and equality rotations and boosts, the formulation I've written gives systematically all the cases for two boosts and a boost then rotation, and not all of it is in Thomas precession. The material in this article could be merged into that article, or overwrite the redirect that is Thomas rotation. Didn't you mention that Thomas rotation and Thomas precession could be separate articles here?

"I suggest we collect the advanced stuff somewhere, perhaps Thomas precession, perhaps a new article Thomas rotation, which would make sense because Thomas precession really is a physical phenomenon with mathematical root Thomas rotation. Lorentz transformation would make sense too, but I don't know whether people want to allow for that article to swell much more. Meanwhile, Velocity-addition formula should be reduced to the basics as given in textbooks. YohanN7 (talk) 14:50, 5 July 2015 (UTC)"

If you agree, the compositions as given in this article could go in Thomas rotation, and Compositions of Lorentz transformations could redirect to Thomas rotation.

No - I don't want the tensor formulation throughout this article straight after the coordinates in place of vectors, but suggested another article for a completely covariant formulation all the way through. Yes, yes, yes, tensors are more efficient than vectors. So are differential forms. But if a reader doesn't have the background in tensor algebra what's the point in writing the entire article as manifestly covariant as possible, when vector and matrix algebra in Cartesian coordinates suffices? It will obfuscate what could be expressed in a lower-level language, if you know tensor algebra you also know vector and matrix algebra, but the converse is not necessarily true. M∧Ŝc²ħεИ_τlk 14:43, 16 December 2015 (UTC)

Fair enough. But since you ask, a manifestly covariant approach does make for a logically coherent and elegant, comprehensive, and easily understood (whether new to the reader or not) framework. Full-blown knowledge of tensors per se isn't needed, just index gymnastics. That is what is offered anyway in the physics texts. They don't even explain what covariant and contravariant vectors are, just how to manipulate them. There is nothing that says that we must present thing in the exact order that most (far from all, the really good ones don't (L&L and also Jackson's (non-introductory) text)) introductory textbooks do.

As for the actual topic of this thread, I don't know the order in which subjects are usually taught, but my introductory EM course came after introductory mechanics (including SR). The treatment of how the Lorentz transformation affects the EM field most certainly is introduced after SR has been introduced. Misner, Thorne and Wheeler devotes in Gravitation a complete section to demonstrate the superiority of the covariant approach, and use the transformation of the EM field as an example. They outline how it is done in the non-covariant approach (including the use of a dose of magic), but don't present the actual calculations because of their great length. I think we should follow this approach and present the EM formulas after tensors, and then derive them (the 3+1 formulas). It Is a piece of cake. The reader should not be left with the impression that relativity is harder than it really is. At any rate, this is toward the end of the article, and there is no guideline saying that everything towards the end should be accessible to the lay reader. YohanN7 (talk) 12:06, 17 December 2015 (UTC)

For now, let's follow your idea of moving and rewriting the EM field in the tensor section and see how it looks. My original plan of stating the vector transformations then tensor ones will take up too much space anyway.

(As an aside, for now, let's leave the group theory section in matrix form please. I find it much easier to follow this way. Maybe it can be rewritten back in index notation later). M∧Ŝc²ħεИ_τlk 15:12, 17 December 2015 (UTC)

Okay. I'll give it a try in a few days. It is actually the vector version I'll derive from the tensor version. So there is no change except for move and proof. On your last point, I don't really understand what you mean. It is now in index notation, but a display of the matrix version can be arranged for. This is a 6 × 6 matrix multiplying a 6 × 1 column containing E₁, E₂, E₃, B₁, B₂, B₃ in the EM case. This is (to me) highly desirable to display to make connection to the irreducilbe representations of the Lorentz group. (As it stands, the tensor representations are not irreducible, see posts above.) YohanN7 (talk) 12:39, 18 December 2015 (UTC)

About the aside, I meant this section Lorentz transformation#Introduction to the Lorentz group. Everything is in matrices, not indices. It is easier to follow since matrix multiplications can be done immediately. In particular,

$\langle A,B\rangle =A^{T}\eta B$

is more familiar and accessible (and all that is required) than

$\langle A,B\rangle =A_{\mu }\eta ^{\mu \nu }B_{\nu }=A^{\mu }\eta _{\mu \nu }B^{\nu }\,,$

it is trivial to extract

$\eta =\Lambda ^{T}\eta \Lambda$

from

$\langle A,B\rangle =\langle \Lambda A,\Lambda B\rangle =A^{T}\eta B=A^{T}\Lambda ^{T}\eta \Lambda B\,,$

taking the determinant of this

$\eta =\Lambda ^{T}\eta \Lambda$

is immediate and trivial compared to

$\eta _{\mu \nu }{\Lambda ^{\mu }}_{\alpha }{\Lambda ^{\nu }}_{\beta }=\eta _{\alpha \beta }\,,$

and why use the clumsy Λ⁰₀ when a single simple letter Γ (or anything else) suffices?

Don't get me wrong throughout this thread. I do like tensor algebra and find it elegant and powerful, but it is strange and unfamiliar unless you know it, and don't agree it's "comprehensive, and easily understood" to any reader. Anyway, I'll not push this point further. M∧Ŝc²ħεИ_τlk 13:19, 18 December 2015 (UTC)

Concepts such as "easily understood" are relative. I still maintain that the tensor formulation is superior when dealing with tensors. I did put in a derivation of the transformation law of the EM field tensor in all painful detail. This can be understood by more people than any 3+1 proof. YohanN7 (talk) 12:54, 22 January 2016 (UTC)

I put in the whole story (added spinors and general fields). It will need some explanation, but that will have to wait for a few days. YohanN7 (talk) 12:54, 22 January 2016 (UTC)

Nice work adding a spinors section. The EM field section is good too, but the equations could each be put onto at least a extra line (they stretch past the page on my screen), also the EM field section earlier up is no longer relevant. I'll take the liberty of deleting Lorentz transformation#Transformation of the electromagnetic field and moving the current transformations and diagram lower down. M∧Ŝc²ħεИ_τlk 15:45, 22 January 2016 (UTC)

More planned rewriting

I am planning a rewrite of the vector transformations which could be made more general (examples can be tabulated), and lead onto the tensor analysis quickly. M∧Ŝc²ħεИ_τlk 17:22, 17 January 2016 (UTC)

I'll comment only on the "Tensor transformations" section in your link (which may make me sound overly negative, the rest looks good at first sight); I am not a huge fan of this. It pulls thing out of the hat by listing examples and relies entirely on index gymnastics. It may teach people how to grind the wheels but explains little. The present version of tensor formulation is actually not that bad when it comes to actual content. It has much more than usually found any introductory physics text, and explains what lies behind the gymnastics–even if it does so tersely. YohanN7 (talk) 11:02, 18 January 2016 (UTC)

Your'e not being negative, none of the planned rewrite in my sandbox is guaranteed to happen, its only a provisional draft and may be scrapped altogether if it doesn't work (right now it's probably fairly confusing for newbies to SR as is).

I started off my own tensor section to follow from the vector transformations, and expected blend in your section, or maybe my version could be replaced by your version entirely. If it was in the article, then we would have the basic x-boost covered everywhere, followed by a general vector transformation and speedily onto four vectors and tensors would be much sooner (then the group theory would follow after). I would prefer to have some transition from the basics to tensors (or just index notation), at the same time motivating the use of them, rather than diving straight into them. M∧Ŝc²ħεИ_τlk 12:02, 18 January 2016 (UTC)

Thomas rotation and precession

Also, "Thomas precession" is not the place for the composition of two boosts, which leads to a static rotation. That article should be about the coordinate frame rotating with an angular velocity, with physical implications (yes, some of this is included, but most of that article is just about two boosts equaling a rotation and boost, it doesn't even have the formula for the Thomas precession, nor its occurrence in the Bargmann-Michel-Telegdi equation, see Jackson's Electrodynamics).

All the content of combining two or more Lorentz boosts (in this and Thomas precession) should be in its own article. My preference is Compositions of Lorentz transformations with Thomas rotation as a section in the article, and the link redirecting to that section. Or at the very least, the composition stuff should all just be in Thomas rotation (not Thomas precession), whether or not the article is rewritten in tensor language. M∧Ŝc²ħεИ_τlk 17:54, 16 December 2015 (UTC)

I agree, Thomas precession should be split up. But this is another big article with problems, and we can in the meanwhile collect related things there. A better name for a new article is Wigner rotation (now a redirect). It is notable, while Thomas rotation is not. Anything else than combining two boosts is simple, and can be kept in this article. YohanN7 (talk) 12:14, 17 December 2015 (UTC)

OK, let's put it in Wigner rotation and redirect Thomas rotation to there. I am drafting a merge in my sandbox, which is provisional. M∧Ŝc²ħεИ_τlk 15:12, 17 December 2015 (UTC)

The Wigner rotation, b t w, can be found in chapter 2 in Weinberg. and in Wigner's original (massive and worthwhile!) paper, referenced in the rep theory article. YohanN7 (talk) 12:39, 18 December 2015 (UTC)

I am doing the best to preserve what both of us have written, and will soon overwrite Wigner rotation, so this article and Thomas precession can be immediately reduced. M∧Ŝc²ħεИ_τlk 13:19, 18 December 2015 (UTC)

Some deletion of what both of us have written has been necessary, but now it is almost ready to at least overwrite the Wigner rotation redirect. I'm not sure how or why this section you wrote is a clear and efficient way to obtain the composite velocity, and rotation matrix. (I know it's in Goldstein and likely elsewhere, but I don't see what the point of the manipulations are). You can do it just using block matrix multiplication, and find the composite velocities, axis, and angle. M∧Ŝc²ħεИ_τlk 20:48, 18 December 2015 (UTC)

It is a very clear but horribly inefficient way of finding boost + rotation from boost + boost. The point (see the Goldstein quote) is that there is no way to do this easily. People have tried. (Maybe Ungar did succeed (using a computer algebra system, but never published the full proof), his claimed formula is on that talk page somewhere. Never got further with that before Q stepped in and cooled off the action.) Remember that what one is really after is a formal solution in terms of parameters (depending on the original two boost parameters). It is not a matter of taking a 4×4-matrix of numbers and spitting out a new set of numbers. That is easy (by the same process as described). YohanN7 (talk) 15:08, 28 December 2015 (UTC)

OK. Yes, whichever method is used the composition is very tedious. Its just my POV that block matrices make things less tedious than full matrices, and the useful relations constructed from the given relative velocities automatically follow (I'm not denying how tedious this still is). M∧Ŝc²ħεИ_τlk 20:12, 29 December 2015 (UTC)

It is not only "tedious", it is hard. What you are trying to do is to solve

$e^{{\boldsymbol {\zeta _{1}}}\cdot \mathbf {K} }e^{{\boldsymbol {\zeta _{2}}}\cdot \mathbf {K} }=e^{{\boldsymbol {\zeta }}\cdot \mathbf {K} }e^{{\boldsymbol {\theta }}\cdot \mathbf {J} }$

for ς and θ given ς₁ and ς₂. The ς is relatively easy to get to. The θ = θ(ς₁, ς₂) is the Thomas rotation, which is much harder to find. This is what Goldstein alludes to, and also what has been the subject of a bunch of research papers over 80 years. YohanN7 (talk) 11:12, 8 January 2016 (UTC)

I see now that the article contains explicit formulae. (I haven't dealt with this in a long time.) Do these formulae agree with what is found here (the Ungar ones)? If these are correct, then the "Goldstein-passage" has no relevance. YohanN7 (talk) 12:26, 8 January 2016 (UTC)

I understand exactly what the problem was (finding the composite boost, and the axis-angle vector (not sure what its common name is)).

Yes, the formulae here are correct: the cosine of the angle from the trace of M is an established result given in the citations, the cross product of a and b is definitely proportional to the cross product of velocities (WP:CALC).

I'll have to double check how these formulae agree with Ungar's formulae, at one time (unearthed here) I naively substituted the cross products of a×b and u×v in terms of magnitudes and angles to obtain the relation between the angles as Ungar does, and the resultant formula agreed with one of Ungar's formulae. But since u and v apply in different frames, is it meaningful to define the angle between them? Sexl and Urbantke say no, Ungar and Mocanu say yes. However, S&U just reverse one of the velocities to obtain the perceived velocity from one of the frames. For example, in Σ′, the frame Σ moves with velocity -u (not u) and Σ ′′ moves with velocity v so -u×v defines the axis in this frame. In Σ the cross product of u (velocity of Σ′) with u⊕v (velocity of Σ′′) is proportional to -u×v, in Σ′′ the cross product of -v with (-u)⊕(-v) (or whatever) is again proportional to -u×v. So in all frames, the rotation axis is in the same direction (but the sense of rotation may be reversed), the angle between any pair of 3-vectors is only defined if they are perceived from the same frame. This is something else to clear up in Wigner rotation.

By the way you seem to interchange the rapidity vector ζ and the velocity vector v. Landau and Lifshitz's formula for the line element in velocity space uses velocities, not rapidity vectors. M∧Ŝc²ħεИ_τlk 14:38, 8 January 2016 (UTC)

It is not the case that I distrust you. The thing is this: When in a graduate level textbook (and also elsewhere) you find the statement

It can easily be shown that...,

then you and I as experienced students of science should infer that some very good mathematician/physicist active in the area actually can show the statement (perhaps even with, but usually not with, "ease"). Now, if a textbook (and several papers) say

it is damned difficult to show that...,

then at least my immediate reaction is that there is no way in hell it can be shown by me. YohanN7 (talk) 10:44, 14 January 2016 (UTC)

OK. It would be nice, now that Wigner rotation has its own article (hence more room), to summarize the various axis and angle formulae from Ungar, Mocanu, S&U, (others?), and clarify how the perceived relative velocities relate to the axis in each frame. On google books Gourgoulhon gives a variety of sine and cosine formulae for the Thomas angle, as well as "half-(Thomas) angle" formulae. M∧Ŝc²ħεИ_τlk 12:50, 14 January 2016 (UTC)

Done, now see Wigner rotation. M∧Ŝc²ħεИ_τlk 11:25, 25 December 2015 (UTC)

See also Thomas precession. M∧Ŝc²ħεИ_τlk 20:12, 29 December 2015 (UTC)

Derivation

This is copied from my talk page:

Re: your edits to the Lorentz transformation article...

Not only isn't it the case that "From Einstein's second postulate of relativity follows immediately", but it doesn't follow at all! Rather, it follows from simple algebra (as I showed in the edit you deleted). Einstein's second postulate doesn't figure into it until later in the transformation.

Ross Fraser (talk) 03:47, 11 January 2016 (UTC)

You showed the interval is invariant for light signals. From this you cannot infer directly that it holds for all intervals. This is showed in my version of it in the linked article. You simply require (without proof) that it holds for all intervals. This is a standard undergraduate textbook shortcut. It is also revealing that you claim that the second postulate is not required for the invariance of lightlike intervals. YohanN7 (talk) 10:09, 14 January 2016 (UTC)

My take on this is that the "standard recipe" in undergraduate textbooks is endowed with too many gaps. That the interval is invariant for light signals is a trivial consequence of postulate two, while the invariance of every interval takes a derivation. (The present proof has gaps too, but these are less severe. Namely, what guarantees that every LT is found in this way.) YohanN7 (talk) 10:17, 14 January 2016 (UTC)

"absurd physics" – a critique

just found → this on linkedIn. the diagram seems indeed flawed. please inspect things. best, Maximilian (talk) 11:46, 18 August 2016 (UTC)

Seems very reliable. The author also writes

I am busy with a loong manuscript in which I am doing the mathematics in detail and show that QM and relativity flow seamlessly from Newton's laws (when corrected for mass increase) and Maxwell's laws. Physics has been unified since Maxwell, when not believing the absurd nonsense like "time-dilation" and Schroedinger's cat being alive AND dead!

My sentiments exactly. YohanN7 (talk) 12:39, 18 August 2016 (UTC)

Extreme misuse of LinkedIn Stigmatella aurantiaca (talk) 13:24, 18 August 2016 (UTC)

How is the diagram flawed? It just shows what each observer measures in their frame. Let's see Maximilian's explanation for the flaw in this diagram. M∧Ŝc²ħεИ_τlk 15:25, 18 August 2016 (UTC)

The author seems to disagree with SR and emphasizes Galileo-Newtonian mechanics (see for example [1]). I still don't understand the explanation about the Lorentz transformations... M∧Ŝc²ħεИ_τlk 16:02, 18 August 2016 (UTC)

Debunking antirelativists is highly off-topic here. Let's try to confine it to LinkedIn or to Usenet. Or to Speaker's Corner. - DVdm (talk) 16:15, 18 August 2016 (UTC)

@DVdm: Not trying and debunk Johan Prins here. I simply commented on the fact that he is an "antirelativist", and has written a long rambling incomprehensible "critique" on the LTs. (Even trying to make fun of my diagram in the process, and tar it and WP and the literature with $h!t - not that I care). Also, I simply asked if Maximilian had his own explanation to offer, if any.

@Maximilian Schönherr: No worries and thanks for pointing this out. M∧Ŝc²ħεИ_τlk 17:54, 18 August 2016 (UTC)

that's fine with me. i guess, after some inspection, that mr. prins runs conspiracy theories, so let's ignore this. Maximilian (talk) 17:17, 18 August 2016 (UTC)

Quite. I had a good laugh too . - DVdm (talk) 20:05, 18 August 2016 (UTC)

I think it is a very good exercise of one's understanding of relativity to find the flaws in antirelativist arguments. Some are very subltle and instructive. But this is just too long winded to pick apart. Which is not to say he doesn't have a point. One fundamental flaw is the idea that an event occurs in a particular inertial reference frame (IRF). An event is a point, it has no extension in space or time, and cannot specify, or be considered to be "in" one IRF but not another. The equivalent statement in spatial geometry is that a point cannot specify a set of coordinate axes, nor is its nature or existence dependent upon a choice of coordinate axes. PAR (talk) 01:22, 19 August 2016 (UTC)

We all seem to agree. But I object to even posting here that there are conspiracy theories (or whatever it happens to be) floating around on the internet. It invariably costs people time. Quoting DVdm, "debunking antirelativists is highly off-topic here.", right - but it is also near impossible to debunk them. The people behind conspiracy theories are often not psychologically well. They may be intelligent, but they are unable to listen and learn. If they are psychologically well, they do what they do because they like to mess with people. They like the attention. Yet so, it is hard to resist debunking. This is why I strongly recommend posting links to such theories should be refrained from - even as a good joke. YohanN7 (talk) 08:29, 19 August 2016 (UTC)

I agree. And re "but it is also near impossible to debunk them": actually, it is not just near impossible—it is completely impossible. That's why we don't do that here. - DVdm (talk) 09:13, 19 August 2016 (UTC)

Yes. I strayed off subject - This page is not the place to consider antirelativist theories. A link to an antirelativist wikipedia page is all that is needed. Such a page would, in effect, reveal the errors in thinking , which I fully expect, but do not presume apriori, to exist, of more or less intellectually honest antirelativists, and maybe some comment on the whackazoids. This would be constructive to anyone learning relativity. I don't agree with the generalization that all antirelativist theories are generated by nut cases and are uniformly undebunkable. This smacks of an unscientific "belief" in relativity, rather than the scientific attitude of tentative agreement. PAR (talk) 09:25, 19 August 2016 (UTC)

Readibility problem

Was just reading the article today, found it quite easy to follow, well done. About half way down the formulas are printed as formatting instructions and the article becomes unreadable, just thought you should know.

23 October 2016 AbsoluteZero01 AbsoluteZero01 (talk) 20:29, 23 October 2016 (UTC)

@AbsoluteZero01: everything looks ok here. Exactly where does it go wrong? Which OS? Which browser? Which setting do you have in Preferences, Appearance, Math? - DVdm (talk) 20:38, 23 October 2016 (UTC)

Just checked the article again, it seems fine, the formulas from the Tensors section to the end of the article appeared in formatting text only and could not be read, I don't know what the problem was but it seems OK now. I have never had this with any other article, so I doubt it was at my end. I'm using Firefox, Windows 10, English, Times New Roman. Maybe just a temporary glitch. Thanks for replying so quickly. I can read the rest of the article now. Thank you.

23 October 2016 AbsoluteZero01 AbsoluteZero01 (talk) 22:09, 23 October 2016 (UTC)

Temporary glitch, no doubt. - DVdm (talk) 06:40, 24 October 2016 (UTC)

Simple inference of Lorentz Transformations due to Time Dilation

This derivation is intended for lay readers, which is why the math is explicitly spelt out, and the derivation makes no reference to more advanced topics like 'frame', 'light cone' 'boost velocity' and the like. Indeed it uses no words or terms that are not fully defined within the section, apart from 'space', 'time', 'velocity' and gamma which is derived and defined in the Simple Derivation on the time dilation page.

This is by design.

The intent is that a lay reader may fully understand the lorentz transforms with only a passing knowledge of time dilation. I have therefore added it at a similar position to the Simple Derivation on the Time Dilation page.

I am working on adding the simplest possible space time diagram, to accompany this derivation, in the hope that I may be able to make it less verbose. For the meanwhile: you may find my choice of language a little "old school", but I believe it is the minimal set of words for the proof to be both immediately clear to anyone, and formal. Perhaps modifications should be discussed here first.

That being said, please do expand, clarify or correct it wherever you deem appropriate, particularly any typos that may have crept in while marking this up. Improvements on my rudimentary markup skills are also very welcome. I have checked the presentation as well as I am able.

If anyone can also tell me whether they have seen this derivation before, or if indeed it is likely to be novel, I would be most grateful. A question has been asked on Talk:Derivations of the Lorentz transformations (where you can see preceding discussion) as to whether this derivation would then constitute original research, which is against policy (thank you so much User:DVdm), to which I humbly suggest that this is simply a rearrangement of information already present on the Derivation of Lorentz Transforms page, and also this page, and the dozens of references therein, and also this one that I have just found [[2]] rather than original research per se. The search term I used to find that reference was 'minimal derivation of lorentz transformations', in case you are interested in ferreting such references out. If you have better luck finding a more direct reference than I did, then I would very much like to read it, and will happily add the reference note myself. This is my third post on this site, so my apologies for any unwitting breach in etiquette. Respectfully, Kebl0155 (talk) 17:49, 12 January 2017 (UTC)

I have removed ([3]) the addition per elementary policy wp:unsourced and wp:no original research. We can't have this, as I explicitly told you here. - DVdm (talk) 18:24, 12 January 2017 (UTC)

My sincere apologies for any offence caused. I had thought the reference given above would be sufficient. I will see if I can find a better reference for it. It appears I have been overly bold after all. I hope you do not think me a vandal. I will certainly not repost the section unless or until confirmation of a sufficiently strong reference has been obtained. I would be interested to know your thoughts on the derivation itself. Also, if it's sufficiently original to be unpostable here, does that mean it is original enough for the notion of publishing a paper to be considered? It would be my first, and I don't know how to go about doing that. I defer to your judgement on appropriate action. Very respectfully, Kebl0155 (talk) 18:52, 12 January 2017 (UTC)

No problem, no offence at this point. We can't comment on the derivation itself, as that would be against our wp:talk page guidelines. - DVdm (talk) 19:57, 12 January 2017 (UTC)

Thank you for that. I am partially reassured. I have moved from feeling very discouraged to neither discouraged nor encouraged, but still also perhaps overly cautious, and quite uncomfortable. I retract my specific question on your thoughts, of course, and further apologise for having asked it. I remain very new. The etiquette guidelines do say that talk pages are an appropriate place to provide comfort to damaged egos; though perhaps you may choose to move this conversation to my personal user page instead, as that's all a bit personal. I am going to carefully think about what my next questions on this matter might be, and will do my best to confine them to topics you may be able to answer, so this is probably the last post you'll see from me 'til tomorrow. I would like to leave you with my sincere thanks for the time you have spent in conversation with me over the last few days, particularly given my newness. Respectfully, Kebl0155 (talk) 20:53, 12 January 2017 (UTC)

This article is about the LT and its properties. Derivations of the LTs are for the Derivations of the Lorentz transformations article. No derivations of the LTs should be in this article. M∧Ŝc²ħεИ_τlk 08:47, 13 January 2017 (UTC)

I agree. And that article is more or less at the brink of overflowing... - DVdm (talk) 09:24, 13 January 2017 (UTC)

Thank you all for sharing your thoughts. In point of fact, there is a derivation on this page, in the Derivation section. It is incomplete and inpenetrable to the lay reader. Is that really as it should be? Should that section simply be removed? Or should it be replaced with a derivation that is short, complete and easy to follow? I'm not suggesting that the one that I have presented should be that one; I'm simply asking three specific questions as to whether this page is maximally beneficial. I would argue that it is not. Respectfully Kebl0155 (talk) 10:26, 13 January 2017 (UTC)

The section Lorentz transformation#Derivation is obviously not a derivation. Just a section which shows the starting point to derive the LTs. It made no sense at all to put your edit before this section, which is just one of many ways (tens? hundreds?) to derive the LTs. That is the whole point of having a separate article for derivations. M∧Ŝc²ħεИ_τlk 10:34, 13 January 2017 (UTC)

Let's take my edit off the table. This is not about me. It is reasonable to suggest that the words "Finding the solution to the simpler problem is just a matter of look-up in the theory of classical groups that preserve bilinear forms of various signature. The Lorentz transformation is thus an element of the group O(3, 1) or, for those that prefer the other metric signature, O(1, 3)." at the end of the derivation section does constitute a derviation. Its brevity makes it look a little hand-wavy to the untrained eye, but I expect you would have no trouble convincing me that the full form is not at all hand-wavy; it just does not appear here. It also does not appear on the Derivations page, so my expectation is based purely on trust at this point. It may appear on the Lorentz group page; the necessary group theory is quite beyond my competence to comment further.

I can see that the Generalities section that immediately follows does expand upon the notions introduced in the Derivations section. I can't see that much else on the page relies upon it; that may be a failure in my sight.

The question I am asking is: When a lay reader searches for Lorentz Transformations, is this really the first thing they should see? No-one has answered that. Respectfully Kebl0155 (talk) 11:03, 13 January 2017 (UTC)

The alternate contention that the Derivation section does not contain a derivation, as asserted above, is easily resolved; I have applied a simple fix. My question still stands. Kebl0155 (talk) 11:26, 13 January 2017 (UTC)

Please refrain for editing a t m. You have blanked the section. YohanN7 (talk) 11:35, 13 January 2017 (UTC)

The section does contain a derivation of the set of Lorentz transformations. They are by definition the ones preserving the interval. The only argument one can raise is that it is not proved that all transformations preserving the interval are found this way. This is at least dealt with. Partly by exposing the spacetime translations (which do preserve the interval) and partly by (in footnote) exposing the conformal transformations that do preserve the interval, but for lightlike separated events only.

This section is purely neutral because it is mathematical. It relies on no physical experiment of thought. This is a strength, not a weakness, and it should definitely stay. YohanN7 (talk) 11:50, 13 January 2017 (UTC)

I had merged it into the Generalities section (at least I thought I had). I didn't realise you were also making edits at this time. My apologies. If the Derivation section does not contain a derivation, it should be called something else; otherwise it is misleading. I am not alleging any ill intent with that; just pointing it out. Am I out of line to also point out that these sections contain no references? Are they original research? Kebl0155 (talk) 11:57, 13 January 2017 (UTC)