Talk:Special relativity/Archive 23

Prokaryotic Caspase Homolog (talk) 08:44, 13 November 2018 (UTC)

Only because you asked for it explicitly:

Omitting the (hint, hint) is fine if hinting was already done (note the "are" in the text now); Euclidean metric (= Pythagoras = SUM of squares) is well known, but I would avoid mentioning Pythagoras, when the spacetime metric (= DIFF of squares) is addressed nearby. How about renaming the first occurrence of ${\displaystyle \Delta x}$ to ${\displaystyle \Delta r}$? I simply like the ultimately terse definition of the spacetime metric, in contrast to the Euclidean metric, as the difference of ${\displaystyle c^{2}\Delta t^{2}}$ and ${\displaystyle \Delta r^{2}}$ much better than the one with a boring list of components (x,y,z). Orthogonal decomposition of a strictly 1-dim property into three components is no rocket science. Stripped by all refs, and cramming in some wild beasts to put into footnotes or to annihilate totally, this would look like:

In pre-relativistic physics, measured distances (${\displaystyle \Delta r}$) and time lapses (${\displaystyle \Delta t}$) between events are independent invariants. In special relativity, the intrinsic interweaving of spatial and temporal coordinates radically destroys these separate invariances, supported by everyday life experience; just the difference of the squared time lapse and the squared spatial distance, denoted as ${\displaystyle \Delta s^{2}}$, remains as the invariant spacetime interval, demonstrating a fundamental discrepancy between Euclidean and spacetime distances.

${\displaystyle \Delta s^{2}\;{\overset {def}{=}}\;c^{2}\Delta t^{2}-\Delta r^{2}.}$

In three spatial dimensions ${\displaystyle \Delta r^{2}}$ can be expanded, according to Pythagoras' theorem, to

${\displaystyle \Delta s^{2}=c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}),}$

but in simplified 1-dimensional scenarios, as in the analysis of spacetime diagrams, the reduced-dimensionality form from above is often employed.

The invariance of the quantity ${\displaystyle \Delta s^{2}}$ is a property of the general Lorentz transform (also

Lorentz boosts) in x-direction, all other translations and reflections in space and in time, and also all transformations that keep the origin fixed (rotations

).

Demonstrating ...

Objective measures of readability rank the various revised versions of the section, both yours and mine, about three grade levels more difficult to read than what is currently in place. Now, I believe that the first paragraph in any section needs to be maximally accessible, and the difference in difficulty level between the suggestions offered here and what is in place is quite dramatic. As I've stated before, a successful compromise leaves neither person completely happy. I will push as much as I can of your suggestions into main article space to achieve the additional precision of expression that you desire, but I insist on the readability of the first paragraph. Neither of us will get entirely what we want, but that's the nature of compromise... Prokaryotic Caspase Homolog (talk) 23:18, 13 November 2018 (UTC)

Who were I, if I dared to discuss the readability of my English babbling? There is just a faint doubt about the feasibility of "deep learned" programs significantly judging roughly five(!) sentences for their readability. I myself wrote about me cramming in topics I consider interesting for a reader passing by (sometimes with the intent to trivialize high brow lingo). I really feel honored by any small phrase of mine that makes it into an accepted version. I see my cramming in as just offering on topic window shopping for things I find didactically valuable and generally interesting.

Besides being quite satisfied as it stands, there is just this

${\displaystyle \Delta s^{2}=c^{2}\Delta t^{2}-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2}),}$

or worse in its original form

${\displaystyle \Delta s^{2}=c^{2}\Delta t^{2}-\Delta x^{2}-\Delta y^{2}-\Delta z^{2},}$

being preferred to

${\displaystyle \Delta s^{2}=c^{2}\Delta t^{2}-\Delta r^{2}}$

that I do not understand. The latter version easily focuses on the important NEW temporo-spatial metric (with its minus), emphasizes the one-dimensionality of distance and is way shorter and therefore way more clearly laid out. I am convinced that the embedding of one-dimensional spatial distances in 3-dimensional Euclidean spaces via Pythagoras as

${\displaystyle -\Delta r^{2}=-(\Delta x^{2}+\Delta y^{2}+\Delta z^{2})}$

convinces even the faintest hearted. I admit that I am not a fan of this "standard configuration", with its dragging along of two parasitic spatial dimensions, adding nothing to substantial understanding at this level.

Please, do not bother to proselytize me to opinions in reliable sources, I really accept the versions that you find fit for WP. Purgy (talk) 10:10, 14 November 2018 (UTC)

Re recent edits:

• Time dilation: To me it was important to hint to the "lifetime" of muons as an "expectation value", to contrast "high"- and "low"-speed muons, to emphasize "equality" in the respective rest frames, and, maybe not so important, to introduce "proper time". All four items negligible?
• Composition of velocities: I protest. It's about "transformations" of velocities to other frames: u to u'. The LT primarily transform coordinates, their "differential form" is unexplained jargon, the ubiquitous use of the word "addition of velocities" for this situation is abuse of language, be it widespread as it might. "Adding" velocities, as measured in different frames, is a categorical flaw, and each velocity measured in one frame, necessarily introduces another frame: the rest frame of the measured body. This is a delicate topic.
• Standard configuration: This, imho, had no encyclopedic value at all, if it were not for its necessity in introducing Minkowski diagrams, so I do not really understand the perceived emphasis put on it. My personal preference is to start with showing the boost-equations in (1+1) dimensions, generalize to (1+3) dimensions in matrix notation, and reduce the matrix again to "standard configuration". Maybe this would pay the rent in presenting the Thomas rotation, the transversal Doppler effect, ... Summing it up, I think from an encyclopedic POV it is more seminal to introduce the (3+1)-LT with β and γ, and stuff its matrix with 0s, than to put a priori importance on a "standard configuration", simply gained and well defined by these 0s.
• Two postulates: I do not understand the emphasis on this, too. It would be my first concern to derive from clunky postulates some most handy equations to proceed with the development of a closed theory. So why should any researcher resort to the postulates, if it were not for writing a bestseller (... any single formula in a book reduces the paid circulation by ... (unknown source)). Isn't this unencyclopedic, a la textbook? ;)
• Apologies for my off topic curiosity: I know about the constructs of gerunds and infinitives, and I learned back then that "allow" could be used with both constructs (in contrast to "allow for", which is only to be used with the gerund). Was this wrong all the time, has it changed some time in between, or is it a matter of taste? Ignore, if bothering. Thanks.

As usual, something to wholeheartedly disagree to. :) Purgy (talk) 20:19, 23 November 2018 (UTC)

Time Dilation

Before

Time dilation explains a number of physical phenomena; for example, the (expected) lifetime of a muon that starts to exist with a collision of a cosmic ray with a particle of the Earth's atmosphere, then moves at very high speed towards the surface, and decays near there, is measured as greater than the lifetimes of slowly moving muons, generated and decaying in a laboratory. Both muons would, of course, measure identical lifetimes, when looking at their respective wrist watches, and both observe the other as moving, and the moving watch as ticking slower than their own, which is said to show the proper time, as measured by an observer (at rest in its frame).

After

Time dilation explains a number of physical phenomena; for example, the lifetime of high speed muons created by the collision of cosmic rays with particles in the Earth's outer atmosphere and moving towards the surface is greater than the lifetime of slowly moving muons, created and decaying in a laboratory.

Commentary

Both JRSpriggs and I worked on this one. We halved the number of words and simplified sentence structure. Measuring "(expected) lifetime of a muon" is easily misread from what you apparently intended.

Dragging effects

Rindler states, on page 54 of his textbook, "From the point of view of special relativity, however, the result (3.1) is nothing but the relativistic velocity addition formula!" He doesn't even use the word "composition." All of the "delicate" nuances that you insist on should already be implied and understood from previous explication of the relativistic composition of velocities, and should not clutter discussion of dragging effects.

Standard configuration

Shorthand expression "standard configuration" reduces a lot of verbiage. The expression is repeatedly used not just in my writing, but in the legacy "Technical discussion of spacetime" section containing material that I judged to be beyond freshman-sophomore mathematics level. If you wish to start with showing the boost-equations in (1+1) dimensions, generalize to (1+3) dimensions in matrix notation, and reduce the matrix again to "standard configuration" etc. etc. , then you should draft a section for the technical section. It's there for a reason. It sounds to me like your proposal could be a great addition.

Two postulates

You appear to misunderstand my rewording of the section titles. Historically, this article appears to have been written by two camps of editors, a group of "two-postulates" advocates, and a group of "single postulate of Lorentz invariance" advocates. When I started my series of edits, the article was a mishmash of contributions by the two groups, and was very confusing to me, until I understood the historical development of this article. I am a "packrat" and do not like throwing out material. Rather than delete legacy "two-postulates" material, what I am trying to say with my rewording of the section titles is: Traditionally, special relativity has been presented in terms of Einstein's two postulates. This article does not follow this old tradition, but instead presents special relativity using the single postulate of Lorentz invariance.

Use of "allow"

You are referring, I presume, to this edit. "Allow to deal with" is wrong, and this wrongness is not a matter of taste. You can write, "allow one to deal with" or "allow dealing with".

General comment

Please use diffs to pinpoint problematical edits. Otherwise you force me to do a lot of research to pinpoint the exact phrase that you have having issues with. Prokaryotic Caspase Homolog (talk) 12:28, 24 November 2018 (UTC)

Purgy's reply

Thanks for the grammar, apologies for missing links, Roma locuta, ... We are the faithful. Nevertheless, a few remarks:

- no high speed muons, no equal lifetime in specific frames?

- I did not refer at all to "Dragging effects", I experience the content of this section as delicate. I seriously protest against calling the "transformation" of a velocity from one frame to another frame an "addition", not even a composition, just because the transformation in the Galilean transform is represented by an addition. Velocities are never added, the are transformed in a Galilean setting by simply adding a quantity, which is characteristic for the transformation, and necessarily must be of equal dimension ${\displaystyle Ls^{-1},}$ and in a more complex way in STR spacetime. Of course, the transformation, as all LT do, involves a velocity, but I would avoid calling this even a composition. As usual: just to let you know.

- I would prefer not to. Bartleby's English is not firm enough to compose a full section.

- Obviously I am not sufficiently sensitive to experience the nuances of the two sources, or I was trained to ignore all postulate driven derivations after having seen the derivation of the full blown LT from first principles, presented by a real Grandmaster of the Chalk (sort of a W. Lewin, if this is allowed to state wrt lecture quality).

I am around, hopefully not disturbing. Purgy (talk) 18:40, 24 November 2018 (UTC)

Never would I simply revert this edit, but ...

- Given two frames in standard configuration (unprimed, primed),

- and having derived that the parameters ${\displaystyle v}$ and ${\displaystyle v'}$ of the respective Lorentz transformations of coordinates between these frames, both parameters representing measurements in the respective frames, satisfy the equation ${\displaystyle v'=-v}$ in this configuration,

- and having also derived how a velocity ${\displaystyle a}$ transforms under Lorentz transform with parameter ${\displaystyle w}$ (denoted ${\displaystyle {\mathcal {L}}_{w}}$) to ${\displaystyle b={\mathcal {L}}_{w}(a),}$ specifically ${\displaystyle u'={\mathcal {L}}_{v}(u)={\frac {u-v}{1-uv/c^{2}}}}$ and ${\displaystyle u={\mathcal {L}}_{v'}(u')={\frac {u'-v'}{1-u'v'/c^{2}}},}$

- then -using the equation of the premise- ${\displaystyle \qquad u={\frac {u'+v}{1+u'v/c^{2}}}={\text{“}}{\mathcal {L}}_{v}^{-1}(u'){\text{”}}.}$

To me the above conclusion in the last step is immediate/obvious/..., but I see no reasoning that to achieve an inverse of a Lorentz transform

- primed and unprimed symbols are interchanged and a parameter is replaced by its negative,

(both recipes only motivated by the structure of two formulae?), but rather this is coherently done by

- performing an appropriate Lorentz transform (from all primed to unprimed), and then

- substituting the derived parameter identity.

BTW, my editorializing term of velocities being incoherent, if they belong to different frames, is based on the fact that in the inverse Lorentz transformation the parameter velocity and the transformed velocity are derivatives with respect to a different time. This reservation also holds for transforming simple coordinates. Validity of any replacements must be justified for each installment. Purgy (talk) 10:32, 4 January 2019 (UTC)

Remember, I consider the primary target audience for the first half of this article to be lower division college science students and senior high school students. Many of your contributions tend to be detailed to the point of being incoherent to the target audience, although entirely appropriate for the second, "technical" half of the article.

If a lower division college science student asks me what a good book for self-study would be, I would recommend Morin or French. I desire the first half of the article to be at the level of those textbooks.

You can be as detailed and precise as you want in the "technical" half of the article.

Prokaryotic Caspase Homolog (talk) 12:25, 4 January 2019 (UTC)

The normal introductory dialog on relativity says "No aether could be found so there must be constant speed of light", and then we change basic constructs of time and space to fit. But the much more obvious explanation is the Emission theory. It occurred to me as a student, and to Newton long before that. And the binary star refutation was not produced until long after relativity, and Fox's refutation of that much later.

I believe this warrant some solid introductory text. Otherwise it simply does not make sense to anyone that does not already understand it. And it encourages the worst type of thinking in the sciences, merely repeating what authoritative people say without thinking about it.Tuntable (talk) 00:51, 4 April 2019 (UTC)

New sections under consideration

After adding the section on Graphical representation of the Lorentz transformation, it became possible for me to move Causality and prohibition of motion faster than light from where it had been stuck to a more rational location in the article, and then to fence off the old legacy sections behind a "Warning! There be lions and tigers and bears (oh my) beyond this point!" sign.

There is obviously a lot left to be done. Optical effects ought to include relativistic aberration and maybe the Fizeau experiment??? Dynamics, of course, covers force, energy and momentum, collisions, and relativistic mass (and why the majority of physicists consider it to be a deprecated concept). Relativistic mass is a concept that most lay persons have heard about, and I'm sure that many visitors to this article page have been disappointed not seeing any mention of it.

I'm hoping that my reorganization should make it easier to add these additional topics. Prokaryotic Caspase Homolog (talk) 09:33, 11 November 2018 (UTC)

Hmmm... it looks like I need to cover the magnet and conductor thought experiment as a preparatory step before covering relativistic aberration. Prokaryotic Caspase Homolog (talk) 06:48, 18 November 2018 (UTC)

Should experimental results be blended with the main narrative or kept separate?

Currently, almost all discussion of the experimental justification for SR is sequestered in the Status section, not that there is very much of it.

Is this a desirable organization? Prokaryotic Caspase Homolog (talk) 20:49, 14 November 2018 (UTC)

Suggestion to extend the section on relativity and quantum mechanics

I would recommend to add to that section a mentioning of the Thomas precession. An extremely clear, though still elementary, introduction to this effect is provided in the excellent textbook by Stepanov.Efroimsk (talk) 04:43, 10 September 2019 (UTC)