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I've taken SR and GR courses. My impression of this article is that it is a mess. Here's three examples: 1) the vectors u and v are used in a formula, but not defined!! 2) A ball dropping (vx=0) on a ship (vx=k) is used as the example of the addition of velocities! 3) A "fly" is mentioned and yet no example scenario using a fly is given. ... I suggest that first velocity (speed) in one dimension be handled (two parallel vectors), followed by the general case of three objects with different x,y&z motions. If three objects, A, B, & C are used in an example, why not determine the velocities of each of the other two relative to the third? (B,C) relative to A, (A,C) relative to B and (A,B) relative to C? I'd also suggest that both the case where B & C both have positive velocity relative to A, and the case where B's velocity is of opposite sign compared to C's for both the 1-D case and the 3-D case. 71.29.173.173 ( talk) 17:36, 12 July 2016 (UTC)
In the section 'Standard configuration', I was confused by gamma sub v. Took me a while to realize it was not gamma times v. 73.220.235.20 ( talk) 02:46, 2 August 2016 (UTC)
It looks like the following unsourced part (added here, here and here) was removed for the third time now ( [3], [4], [5]):
In classical mechanics vectors : may be referred (using equipollence) to .the same origin and usually are. But by definition they are relative velocities starting from different origins. This point is important in the generalization to Special Relativity where equipollence does not apply in general.
Rightly so—see edit summaries of removals. It is not just unsourced. It also suffers from typographical, grammatical and semantic errors. It reads like gibberish indeed. - DVdm ( talk) 09:15, 16 September 2016 (UTC)
SOURCE ADDED:
Silberstein: The Theory of Relativity 1914 p.179 He says 'In connexion with this we have only the triangle rule and not the parallelogram rule as in Newtonian mechanics. There are no parallelograms in hyperbolic space... etc'
So now please stop your insulting 'gibberish' talk and learn more about what you saying. JFB80 ( talk) 07:33, 19 January 2017 (UTC)
Normally (and consistently on Wikipedia everywhere else Special Relativity is discussed - see for example /info/en/?search=Special_relativity ), one starts in an unprimed reference frame S, in which the velocity of a body is known, and one wishes to find the transformed velocity in a moving reference frame S' that is moving with velocity relative to (and as measured from) the original reference frame. In the Standard Configuration, the co-ordinates are further selected so that the velocity is along the x direction in S, and v is treated as a scalar speed, but in the general case is a vector pointing anywhere.
That is always the Standard Notation convention; one starts in S and moves to S'. The symbols and alwaysrefer to "a body moving in S" and "the motion of S' relative to S" within the Standard Notation, respectively.
However, this page inexplicably moves away from this standard notation in the Standard Configuration section, using V for what is normally v, and even more confusingly, , and for what are the components of in the standard notation.
This then ends up with the Translation of velocity (Cartesian components) section being very confusing and non-standard, as it gives what would normally be the inverse translation (prime -> unprimed), without giving the normal (unprimed -> primed) transformation.
To conform with the standard notation used on this site and elsewhere, it should therefore look like this instead:
This is how it appears in A.P. French's book on Special Relativity, for example, which also uses the standard convention for the meaning of the symbols described above, and used everywhere else on Wikipedia.
This also then makes the formulae consistent with the one-dimensional special case formula shown in the master /info/en/?search=Special_relativity#Composition_of_velocities by which most people will find this page. — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:26, 8 January 2017 (UTC)
We get into further difficulty with the General Configuration section, again because of non-standard notation. The result at the end should look like:
This is the backward transform. It should definitely be accompanied by the more useful forward transform:
The page then suggests: "In order to facilitate generalization and to avoid proliferation of primes, change notation of V to u, and v′ to v"
No! That's a disaster! Now we have and meaning the EXACT OPPOSITE of the conventional uses of and everywhere else. In the current live version, now means what is meant by in the standard notation, actually means in the standard notation, and actually means in the standard notation.
Ouch! Very ouch! No no no! DANGER DANGER DANGER!
The phrase starting with "In order to facilitate generalization..." needs to completely go, apart from the notes. It's WORSE than useless - it's positively harmful. There needs to be NO change of variables here, having used standard notation FROM THE START, and what should then be written in the equation box is:
The above could be further simplified by just writting instead of , as this is the standard meaning of .
and all-important equations for for added speeds become:
and the more useful
This is the ONLY WAY that the equations on this page can be used interoperably with the equations that appear on all the other Special Relativity pages.
This then gives the same equations as are shown on the main page for Lorentz transformations, which links to this page in the hope that it will derive them - which it currently doesn't! See /info/en/?search=Lorentz_transformation — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:30, 8 January 2017 (UTC)
These results are important: it is difficult to develope special-relativistic conservation of momentum in a general way, beyond the specific cases of elastic and inelastic collisions between two particles that are usually offered in text books, without them.
The formulae for also don't appear to be listed on Wikipedia anywhere else; I think we should therefore make the effort to keep the notation consistent with the standard that is used elsewhere on this site, as well as many reference books and other sites.
The Notational Conventions section should probably also be deleted, once the Standard Notation has been adopted - though perhaps a warning might be appropriate here instead?
Using Standard Notation is also the only way to get the formulae on this page to be consistent with the formulae given on the master Special Relativity page, which links to this one as a See Also in the Composition of Velocities section. For this reason, this page really should use the same Standard Notation as the main Special Relativity page; the formulae we currently show on this page are not the same as the ones shown on the master Special Relativity page.
Would you like me to have a go at revamping this section to use standard notation throughout?
Kebl0155 ( talk) 19:57, 8 January 2017 (UTC)
References
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My two cents on the whole issue: If you have the time an ability to improve articles on relativity, then it is a total waste of it to steer up a storm. You can find plenty of talk pages where highly qualified people have spent hours, even days, arguing over such things as units and conventions. Some people even believe that there is a right convention and a wrong convention (choice of units, etc), and that all choices but theirs actually are inconsistent and plainly wrong. They argue furiously time and time again that they are so OBVIOUSLY RIGHT. Such people are called crackpots. You have not gone that far, and it is perfectly okay to have a personally preferred set of units, conventions, etc. But, reading through your posts, you are dangerously close.
In the particular case at hand, yes, I do have a preferred presentation. Namely, the one in the article. It answers the, to me, primary question. In a frame moving with V, an object has velocity v′, which velocity v do we see?
The complementary question is, if we have an object moving with velocity v, which velocity v′ does an observer moving with V see, is to me the secondary question. Apparently, some distinguished authors feel the same way.
But I am not religious about it. Frankly, I don't care. The two presentations are mathematically dual in the usual prescription (reverse sign of velocity, swap primes) for relativistic formulas of this sort. It is just my two cents on which presentation is, by a nose, slightly preferable over the other. But you seem to be upset even over the choice of capital V to denote the velocity of the primed frame.
You are also implicitly suggesting that
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help) (graduate level)should perhaps be tossed. This is something I could actually consider worth spending time arguing over, and is the reason I spend time on writing this post. Make no mistake, there is a reason that an 80 years old textbook is still selling. It is not because it is bad. It is because it is good. Such books just don't come about every decade. As you might note, it is in its forth updated edition, and it has been revised thoroughly over the decades. The same goes for every title in Course of Theoretical Physics. If you ever venture to learn general relativity (perhaps you know it already), then this particular book will give the most bang for the time spent. Without comparison. I don't think I am (in fact I know I am not) the only fan of this book. YohanN7 ( talk) 11:39, 10 January 2017 (UTC)
OK it's done. It took all day. I was very careful. The only bit I couldn't do was the hidden section on 4-velocities; there are actual problems with this section, which is not internally self-consistent, and I cannot resymbolise it until they are fixed. I'm about to start a separate heading for this subsection. Interestingly, while checking the references, I noticed that in may cases the notation had already been resymbolised in some way, including Landau and Lifschitz, even before I started editing this page. I was not able to check two of the alternate notations presented as the references are missing. Kebl0155 ( talk) 18:38, 10 January 2017 (UTC)
I'm clicking on the links for the References in the Notational Conventions section, but apart from Ungar they're not actually going anywhere. I don't know how to fix this. I don't think it's my browser. I can't find places to link to, or even the original books, with Google, so I'm a bit at a loss. Can you help? I very much like the changes you have made since I did the massive resymbolisation by the way - thank you so much. Also having had my attention brought to an etiquette guide by another user, I thought I might apologise if I've been a bit brusque with all this. Sorry about that. The page is looking magnificent. Thank you. Kebl0155 ( talk) 20:03, 11 January 2017 (UTC)
The applications section still uses the old notation. YohanN7 ( talk) 11:10, 12 January 2017 (UTC)
I was unable to resymbolise this section because it was not sufficiently well defined for me to penetrate its meaning, and I sensed either an internal contradiction or sign error, possibly both. Without the proper definition of terms it's hard to tell. Possibly impossible to tell.
Because there are no references or citations for this subsection, I was also unable to check it against any original source. All quotations from this subsection that I tried searching for online turned out to be quotes from this page.
Specifically, the page starts by asserting in the second paragraph that V is a fly's four velocity as seen by a ship, and that V is roughly in the same direction as the x axis. The wording with planes and axes is setting us up for a transform of velocity of some body in the ship's frame into the fly's frame. So far so good.
Next a Lorentz Transformation matrix is given in which the V1 components have opposite sign to the ones in the example matrix in the Proper Transformations section of the Lorenz transformation page. I can just about cope with that, but it would be non-obvious to a lay reader: that indicates it's going to be a reverse transform (either that or a sign error). So we're transforming the velocity of something moving in the fly's frame to that which would be measured in the ship's frame. OK that's confusing, but OK. The section asserts that this 'boosts the rest frame', however it is impossible to boost a frame, as in Special Relativity all frames are inertial, meaning having constant velocity. That's the Special bit. So, I don't know what that actually means. One could legitimately talk about boosting velocities measured within a particular frame; perhaps that is what is meant. Perhaps.
Usually it's best to entirely avoid talking about rest frames (and particularly one should avoid asserting the existence of 'the rest frame') when discussing Special Relativity, as no frame is privileged to be at rest; that's kind of the point, but perhaps that's just my opinion.
The main problem with the terminology/notation at this point is that 'the rest frame' is not actually defined anywhere in this subsection. I can say for sure that if you were to actually use the matrix to multiply a velocity - any velocity - it would transform a velocity having this value measured in the fly's frame to the ship's frame, though.
Personally, I couldn't evaluate the next sentence about 'this matrix rotates the a pure time-axis vector' as either true or false, but again perhaps that's just me.
Here's where things get really tricky. The next bit starts 'If a fly is moving with four-velocity U in the rest frame'. Well now. What are we to do with this. We already have the velocity of the fly as V within the ship's frame. So now we're either changing letters to represent the fly's velocity (Bad), or we're about to attempt to do a Lorentz transformation on this fly with its own velocity (also Bad), or we're talking about a new, second fly (please make it stop).
If this new velocity U (whatever thing that is referring to. The first fly? Some other fly? Some other thing?) in the rest frame (whatever that is) is 'boosted by multiplying by the matrix' (yes it's OK to use the word boost this time because we're talking about a velocity), the new four velocity S will be a velocity that has been transformed from the original fly's frame into the ship's frame (definitely because of the signs of V1 in the matrix).
I just don't know the velocity of what. It certainly can't be the original fly.
So then we have three equations which, from the distribution of pluses and minus signs, have the same form as a transform from a primed frame (right hand side) to an unprimed frame (left hand side). Unprimed normally means rest frame, and would be consistent with the use of an unprimed S on the left hand side. But that then contradicts the assertion that U is in the rest frame. Doesn't it?
The honest answer is that the terms in this subsection are so poorly defined that I cannot tell you for sure what velocity is actually being transformed, from which frame it is being transformed and to what frame, to what the transformed velocity refers, or to what this 'rest frame' refers, or even how many flies there are.
I also tried to start from the end and work backwards, to see if I could get it to make sense that way, but ended up writing 'If a fly is moving with four velocity U′ in the rest frame', and could go no further. I've never seen anyone use primes to describe a velocity in a rest frame before.
Until someone can explain what this subsection actually means, or even what it is trying to say, or even how it is trying to say it, I cannot understand it, let alone find the error with certainty (assuming there is one), let alone resymbolise it for consistency. My apologies if I am being in any way foolish with this; I frequently am. At the moment I couldn't even tell you for sure that this subsection is actually saying anything at all.
I really can't see how anyone with less than a doctorate would be able to follow this subsection as it stands, apart perhaps from the original author, whoever that is, to whom I am sincerely appealing for help, and apologising for any foolishness on my part. I almost certainly have been stupid somewhere.
The subsection has been restored to its original state; it has NOT been resymbolised as part of today's work for this reason.
I'm now going to lie down in a darkened room and try not to think of relativity for a little while. — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:38, 10 January 2017 (UTC)
The patroller probably removed it for reasons other that that the content is problem free. Suggestion: Put that whole hidden section in the dumpster and write a new fresh 4-vector section. I put that old one in a hide box because I weren't able to parse it in reasonable time. Thus I suggest this:
Then one might add in that new section the most general case with , where is the vector of boost generators and are boost parameters (related to ), and perhaps also how the matrix appears in all generality (think it is given in Jackson's EM book) for pure boosts. YohanN7 ( talk) 07:50, 12 January 2017 (UTC)
Actually, the formula is in Lorentz transformation#Proper transformations. YohanN7 ( talk) 09:18, 12 January 2017 (UTC)
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help) (introductory level),I am trying to verify the statement
referenced to
Landau, L.D.;
Lifshitz, E.M. (2002) [1939]. The Classical Theory of Fields. Course of Theoretical Physics. Vol. 2 (4th ed.).
Butterworth–Heinemann. p. 36.
ISBN
0 7506 2768 9. {{
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For full reference, this is stated in a problem as such:
I cannot verify the first formula. The first equality is no problem. It follows from the expression for relativistic relative velocity (which is (12.6) in ref). But then I have to make a couple of intentional errors to get to the right hand side.
I take and and use
Note in place of Note , etc in place of more cumbersome , etc.
I'd highly appreciate if someone could attack this. I have starred myself blind on my calculation. YohanN7 ( talk) 12:37, 17 January 2017 (UTC)
Maybe we should take this to the reference desk... YohanN7 ( talk) 12:20, 18 January 2017 (UTC)
In the section "History", it says:
But we are talking from light traveling in a fluid, so c should be replaced with c/n and "aether" should be replaced with "fluid".
I will wait a day before posting an edit, to give chance for a justification of the current version. — Preceding unsigned comment added by George Albert Lee ( talk • contribs) 20:15, 10 March 2021 (UTC)
JFB80 ( talk) 19:34, 17 March 2022 (UTC)== Velocity composition not linear ==
Regarding my undo of user Randallbsmith's , I think the original formulation with two constants was OK, so I restored it, but do we have a proper inline textbook source to settle it? - DVdm ( talk) 10:16, 11 February 2022 (UTC)
As a quick reference, readers need a definition of u' right below the velocity addition formula. The formula is good, but hunting around for u' did not give me an unambiguous definition. Right below the equation, add "where u' is the relative velocity of the systems." 97.73.100.22 ( talk) 21:53, 31 August 2023 (UTC)quemadojournal.org
This section starts with the sentence "It was observed by Galileo that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward". As a native English speaker (and incidentally a physicist), this sentence is either broken or written in a way that suggests prior context about a heavy body, why it might falling, etc. It should be edited accordingly, although I will refrain since I am not sure if the original author had other intentions. — Preceding unsigned comment added by Mrkinzie ( talk • contribs) 13:37, 27 January 2024 (UTC)
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I've taken SR and GR courses. My impression of this article is that it is a mess. Here's three examples: 1) the vectors u and v are used in a formula, but not defined!! 2) A ball dropping (vx=0) on a ship (vx=k) is used as the example of the addition of velocities! 3) A "fly" is mentioned and yet no example scenario using a fly is given. ... I suggest that first velocity (speed) in one dimension be handled (two parallel vectors), followed by the general case of three objects with different x,y&z motions. If three objects, A, B, & C are used in an example, why not determine the velocities of each of the other two relative to the third? (B,C) relative to A, (A,C) relative to B and (A,B) relative to C? I'd also suggest that both the case where B & C both have positive velocity relative to A, and the case where B's velocity is of opposite sign compared to C's for both the 1-D case and the 3-D case. 71.29.173.173 ( talk) 17:36, 12 July 2016 (UTC)
In the section 'Standard configuration', I was confused by gamma sub v. Took me a while to realize it was not gamma times v. 73.220.235.20 ( talk) 02:46, 2 August 2016 (UTC)
It looks like the following unsourced part (added here, here and here) was removed for the third time now ( [3], [4], [5]):
In classical mechanics vectors : may be referred (using equipollence) to .the same origin and usually are. But by definition they are relative velocities starting from different origins. This point is important in the generalization to Special Relativity where equipollence does not apply in general.
Rightly so—see edit summaries of removals. It is not just unsourced. It also suffers from typographical, grammatical and semantic errors. It reads like gibberish indeed. - DVdm ( talk) 09:15, 16 September 2016 (UTC)
SOURCE ADDED:
Silberstein: The Theory of Relativity 1914 p.179 He says 'In connexion with this we have only the triangle rule and not the parallelogram rule as in Newtonian mechanics. There are no parallelograms in hyperbolic space... etc'
So now please stop your insulting 'gibberish' talk and learn more about what you saying. JFB80 ( talk) 07:33, 19 January 2017 (UTC)
Normally (and consistently on Wikipedia everywhere else Special Relativity is discussed - see for example /info/en/?search=Special_relativity ), one starts in an unprimed reference frame S, in which the velocity of a body is known, and one wishes to find the transformed velocity in a moving reference frame S' that is moving with velocity relative to (and as measured from) the original reference frame. In the Standard Configuration, the co-ordinates are further selected so that the velocity is along the x direction in S, and v is treated as a scalar speed, but in the general case is a vector pointing anywhere.
That is always the Standard Notation convention; one starts in S and moves to S'. The symbols and alwaysrefer to "a body moving in S" and "the motion of S' relative to S" within the Standard Notation, respectively.
However, this page inexplicably moves away from this standard notation in the Standard Configuration section, using V for what is normally v, and even more confusingly, , and for what are the components of in the standard notation.
This then ends up with the Translation of velocity (Cartesian components) section being very confusing and non-standard, as it gives what would normally be the inverse translation (prime -> unprimed), without giving the normal (unprimed -> primed) transformation.
To conform with the standard notation used on this site and elsewhere, it should therefore look like this instead:
This is how it appears in A.P. French's book on Special Relativity, for example, which also uses the standard convention for the meaning of the symbols described above, and used everywhere else on Wikipedia.
This also then makes the formulae consistent with the one-dimensional special case formula shown in the master /info/en/?search=Special_relativity#Composition_of_velocities by which most people will find this page. — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:26, 8 January 2017 (UTC)
We get into further difficulty with the General Configuration section, again because of non-standard notation. The result at the end should look like:
This is the backward transform. It should definitely be accompanied by the more useful forward transform:
The page then suggests: "In order to facilitate generalization and to avoid proliferation of primes, change notation of V to u, and v′ to v"
No! That's a disaster! Now we have and meaning the EXACT OPPOSITE of the conventional uses of and everywhere else. In the current live version, now means what is meant by in the standard notation, actually means in the standard notation, and actually means in the standard notation.
Ouch! Very ouch! No no no! DANGER DANGER DANGER!
The phrase starting with "In order to facilitate generalization..." needs to completely go, apart from the notes. It's WORSE than useless - it's positively harmful. There needs to be NO change of variables here, having used standard notation FROM THE START, and what should then be written in the equation box is:
The above could be further simplified by just writting instead of , as this is the standard meaning of .
and all-important equations for for added speeds become:
and the more useful
This is the ONLY WAY that the equations on this page can be used interoperably with the equations that appear on all the other Special Relativity pages.
This then gives the same equations as are shown on the main page for Lorentz transformations, which links to this page in the hope that it will derive them - which it currently doesn't! See /info/en/?search=Lorentz_transformation — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:30, 8 January 2017 (UTC)
These results are important: it is difficult to develope special-relativistic conservation of momentum in a general way, beyond the specific cases of elastic and inelastic collisions between two particles that are usually offered in text books, without them.
The formulae for also don't appear to be listed on Wikipedia anywhere else; I think we should therefore make the effort to keep the notation consistent with the standard that is used elsewhere on this site, as well as many reference books and other sites.
The Notational Conventions section should probably also be deleted, once the Standard Notation has been adopted - though perhaps a warning might be appropriate here instead?
Using Standard Notation is also the only way to get the formulae on this page to be consistent with the formulae given on the master Special Relativity page, which links to this one as a See Also in the Composition of Velocities section. For this reason, this page really should use the same Standard Notation as the main Special Relativity page; the formulae we currently show on this page are not the same as the ones shown on the master Special Relativity page.
Would you like me to have a go at revamping this section to use standard notation throughout?
Kebl0155 ( talk) 19:57, 8 January 2017 (UTC)
References
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cite book}}
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help)
My two cents on the whole issue: If you have the time an ability to improve articles on relativity, then it is a total waste of it to steer up a storm. You can find plenty of talk pages where highly qualified people have spent hours, even days, arguing over such things as units and conventions. Some people even believe that there is a right convention and a wrong convention (choice of units, etc), and that all choices but theirs actually are inconsistent and plainly wrong. They argue furiously time and time again that they are so OBVIOUSLY RIGHT. Such people are called crackpots. You have not gone that far, and it is perfectly okay to have a personally preferred set of units, conventions, etc. But, reading through your posts, you are dangerously close.
In the particular case at hand, yes, I do have a preferred presentation. Namely, the one in the article. It answers the, to me, primary question. In a frame moving with V, an object has velocity v′, which velocity v do we see?
The complementary question is, if we have an object moving with velocity v, which velocity v′ does an observer moving with V see, is to me the secondary question. Apparently, some distinguished authors feel the same way.
But I am not religious about it. Frankly, I don't care. The two presentations are mathematically dual in the usual prescription (reverse sign of velocity, swap primes) for relativistic formulas of this sort. It is just my two cents on which presentation is, by a nose, slightly preferable over the other. But you seem to be upset even over the choice of capital V to denote the velocity of the primed frame.
You are also implicitly suggesting that
{{
cite book}}
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help) (graduate level)should perhaps be tossed. This is something I could actually consider worth spending time arguing over, and is the reason I spend time on writing this post. Make no mistake, there is a reason that an 80 years old textbook is still selling. It is not because it is bad. It is because it is good. Such books just don't come about every decade. As you might note, it is in its forth updated edition, and it has been revised thoroughly over the decades. The same goes for every title in Course of Theoretical Physics. If you ever venture to learn general relativity (perhaps you know it already), then this particular book will give the most bang for the time spent. Without comparison. I don't think I am (in fact I know I am not) the only fan of this book. YohanN7 ( talk) 11:39, 10 January 2017 (UTC)
OK it's done. It took all day. I was very careful. The only bit I couldn't do was the hidden section on 4-velocities; there are actual problems with this section, which is not internally self-consistent, and I cannot resymbolise it until they are fixed. I'm about to start a separate heading for this subsection. Interestingly, while checking the references, I noticed that in may cases the notation had already been resymbolised in some way, including Landau and Lifschitz, even before I started editing this page. I was not able to check two of the alternate notations presented as the references are missing. Kebl0155 ( talk) 18:38, 10 January 2017 (UTC)
I'm clicking on the links for the References in the Notational Conventions section, but apart from Ungar they're not actually going anywhere. I don't know how to fix this. I don't think it's my browser. I can't find places to link to, or even the original books, with Google, so I'm a bit at a loss. Can you help? I very much like the changes you have made since I did the massive resymbolisation by the way - thank you so much. Also having had my attention brought to an etiquette guide by another user, I thought I might apologise if I've been a bit brusque with all this. Sorry about that. The page is looking magnificent. Thank you. Kebl0155 ( talk) 20:03, 11 January 2017 (UTC)
The applications section still uses the old notation. YohanN7 ( talk) 11:10, 12 January 2017 (UTC)
I was unable to resymbolise this section because it was not sufficiently well defined for me to penetrate its meaning, and I sensed either an internal contradiction or sign error, possibly both. Without the proper definition of terms it's hard to tell. Possibly impossible to tell.
Because there are no references or citations for this subsection, I was also unable to check it against any original source. All quotations from this subsection that I tried searching for online turned out to be quotes from this page.
Specifically, the page starts by asserting in the second paragraph that V is a fly's four velocity as seen by a ship, and that V is roughly in the same direction as the x axis. The wording with planes and axes is setting us up for a transform of velocity of some body in the ship's frame into the fly's frame. So far so good.
Next a Lorentz Transformation matrix is given in which the V1 components have opposite sign to the ones in the example matrix in the Proper Transformations section of the Lorenz transformation page. I can just about cope with that, but it would be non-obvious to a lay reader: that indicates it's going to be a reverse transform (either that or a sign error). So we're transforming the velocity of something moving in the fly's frame to that which would be measured in the ship's frame. OK that's confusing, but OK. The section asserts that this 'boosts the rest frame', however it is impossible to boost a frame, as in Special Relativity all frames are inertial, meaning having constant velocity. That's the Special bit. So, I don't know what that actually means. One could legitimately talk about boosting velocities measured within a particular frame; perhaps that is what is meant. Perhaps.
Usually it's best to entirely avoid talking about rest frames (and particularly one should avoid asserting the existence of 'the rest frame') when discussing Special Relativity, as no frame is privileged to be at rest; that's kind of the point, but perhaps that's just my opinion.
The main problem with the terminology/notation at this point is that 'the rest frame' is not actually defined anywhere in this subsection. I can say for sure that if you were to actually use the matrix to multiply a velocity - any velocity - it would transform a velocity having this value measured in the fly's frame to the ship's frame, though.
Personally, I couldn't evaluate the next sentence about 'this matrix rotates the a pure time-axis vector' as either true or false, but again perhaps that's just me.
Here's where things get really tricky. The next bit starts 'If a fly is moving with four-velocity U in the rest frame'. Well now. What are we to do with this. We already have the velocity of the fly as V within the ship's frame. So now we're either changing letters to represent the fly's velocity (Bad), or we're about to attempt to do a Lorentz transformation on this fly with its own velocity (also Bad), or we're talking about a new, second fly (please make it stop).
If this new velocity U (whatever thing that is referring to. The first fly? Some other fly? Some other thing?) in the rest frame (whatever that is) is 'boosted by multiplying by the matrix' (yes it's OK to use the word boost this time because we're talking about a velocity), the new four velocity S will be a velocity that has been transformed from the original fly's frame into the ship's frame (definitely because of the signs of V1 in the matrix).
I just don't know the velocity of what. It certainly can't be the original fly.
So then we have three equations which, from the distribution of pluses and minus signs, have the same form as a transform from a primed frame (right hand side) to an unprimed frame (left hand side). Unprimed normally means rest frame, and would be consistent with the use of an unprimed S on the left hand side. But that then contradicts the assertion that U is in the rest frame. Doesn't it?
The honest answer is that the terms in this subsection are so poorly defined that I cannot tell you for sure what velocity is actually being transformed, from which frame it is being transformed and to what frame, to what the transformed velocity refers, or to what this 'rest frame' refers, or even how many flies there are.
I also tried to start from the end and work backwards, to see if I could get it to make sense that way, but ended up writing 'If a fly is moving with four velocity U′ in the rest frame', and could go no further. I've never seen anyone use primes to describe a velocity in a rest frame before.
Until someone can explain what this subsection actually means, or even what it is trying to say, or even how it is trying to say it, I cannot understand it, let alone find the error with certainty (assuming there is one), let alone resymbolise it for consistency. My apologies if I am being in any way foolish with this; I frequently am. At the moment I couldn't even tell you for sure that this subsection is actually saying anything at all.
I really can't see how anyone with less than a doctorate would be able to follow this subsection as it stands, apart perhaps from the original author, whoever that is, to whom I am sincerely appealing for help, and apologising for any foolishness on my part. I almost certainly have been stupid somewhere.
The subsection has been restored to its original state; it has NOT been resymbolised as part of today's work for this reason.
I'm now going to lie down in a darkened room and try not to think of relativity for a little while. — Preceding unsigned comment added by Kebl0155 ( talk • contribs) 20:38, 10 January 2017 (UTC)
The patroller probably removed it for reasons other that that the content is problem free. Suggestion: Put that whole hidden section in the dumpster and write a new fresh 4-vector section. I put that old one in a hide box because I weren't able to parse it in reasonable time. Thus I suggest this:
Then one might add in that new section the most general case with , where is the vector of boost generators and are boost parameters (related to ), and perhaps also how the matrix appears in all generality (think it is given in Jackson's EM book) for pure boosts. YohanN7 ( talk) 07:50, 12 January 2017 (UTC)
Actually, the formula is in Lorentz transformation#Proper transformations. YohanN7 ( talk) 09:18, 12 January 2017 (UTC)
{{
cite book}}
: Invalid |ref=harv
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help) (introductory level),I am trying to verify the statement
referenced to
Landau, L.D.;
Lifshitz, E.M. (2002) [1939]. The Classical Theory of Fields. Course of Theoretical Physics. Vol. 2 (4th ed.).
Butterworth–Heinemann. p. 36.
ISBN
0 7506 2768 9. {{
cite book}}
: Invalid |ref=harv
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help)
For full reference, this is stated in a problem as such:
I cannot verify the first formula. The first equality is no problem. It follows from the expression for relativistic relative velocity (which is (12.6) in ref). But then I have to make a couple of intentional errors to get to the right hand side.
I take and and use
Note in place of Note , etc in place of more cumbersome , etc.
I'd highly appreciate if someone could attack this. I have starred myself blind on my calculation. YohanN7 ( talk) 12:37, 17 January 2017 (UTC)
Maybe we should take this to the reference desk... YohanN7 ( talk) 12:20, 18 January 2017 (UTC)
In the section "History", it says:
But we are talking from light traveling in a fluid, so c should be replaced with c/n and "aether" should be replaced with "fluid".
I will wait a day before posting an edit, to give chance for a justification of the current version. — Preceding unsigned comment added by George Albert Lee ( talk • contribs) 20:15, 10 March 2021 (UTC)
JFB80 ( talk) 19:34, 17 March 2022 (UTC)== Velocity composition not linear ==
Regarding my undo of user Randallbsmith's , I think the original formulation with two constants was OK, so I restored it, but do we have a proper inline textbook source to settle it? - DVdm ( talk) 10:16, 11 February 2022 (UTC)
As a quick reference, readers need a definition of u' right below the velocity addition formula. The formula is good, but hunting around for u' did not give me an unambiguous definition. Right below the equation, add "where u' is the relative velocity of the systems." 97.73.100.22 ( talk) 21:53, 31 August 2023 (UTC)quemadojournal.org
This section starts with the sentence "It was observed by Galileo that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward". As a native English speaker (and incidentally a physicist), this sentence is either broken or written in a way that suggests prior context about a heavy body, why it might falling, etc. It should be edited accordingly, although I will refrain since I am not sure if the original author had other intentions. — Preceding unsigned comment added by Mrkinzie ( talk • contribs) 13:37, 27 January 2024 (UTC)