Talk:Lorentz factor

Rather Technical

I'm not going to tag it as such, but, as someone with just a passing knowledge of astrophysics and cosmology, this article is pretty unreadble to the layman. Perhaps a little more background on exactly what the equation means before diving into the details? --JD79 23:13, 19 May 2007 (UTC)

-- I agree. I skimmed through this article and the only thing that hinted at what the damn thing actually was, was from the equation! I had to go to the simple english article for a layman. I think a description of what it represents would be helpful. 89.241.255.57 (talk) 21:26, 17 September 2009 (UTC)

-- 100%. Even the opening line doesn't really tell us what the Lorentz factor is, only where it is found (in special relativity). I found out more about Lorentz factors by taking the definition and plugging numbers in. — Preceding unsigned comment added by 99.251.177.224 (talk) 16:00, 31 March 2012 (UTC)

Incorrect stuff?

According to Einstein, the Lorentz transformation is: t'=t(1-v/c)/√(1-v²/c²) which is not equal to what this page says.

Also, regarding the "proof", if A holds the laser beam parallel to his direction of travel, then following the same logic one would obtain ct'=ct-vt thus t'=t(1-v/c), where is this wrong? --Lucian 20:24, 27 May 2005 (UTC)

It seems that the article has t' and t switched. Perhaps the classic mirror-clock example would be better.

If you have the light going in the same direction that A is, I don't think you can derive the Lorentz factor. You'd have to know about length contraction. - mako 04:42, 3 August 2005 (UTC)

Merge from Lorentz term

These articles are talking about the same thing, so they should be merged. "Factor" gets 196,000 Google hits, while "term" gets 384, so they should be merged here. There is a reason for the terminology; you add terms and you multiply factors.

Finally, let me note that gamma is not ambiguous. Possibly this article should include a discussion of which powers of gamma appear most often, and where; but there is only one gamma. Melchoir 02:55, 9 March 2006 (UTC)

I merged the talk page and the article. I kept in the note about ambiguoity - simply because I don't know about that. Feel free to edit. Fresheneesz 10:03, 26 March 2006 (UTC)

Discussion from Lorentz term

Not Suitable Content for Wikipedia Article

This article is not suitable for Wikipedia. It is just another example of Eric Baird writing his musings about special relativity. "Lorentz term" is not standard usage (and of course, it's a factor, not a term), and there is no need for Wikipedia articles to be making up new terminology. The article contains no actual informative content. It ought to be deleted.130.76.32.15 18:38, 5 October 2005 (UTC)

response

the Wiki page term says:

"A term (mathematics) is a basic component of a mathematical expression."

While term (mathematics) says:

"In elementary mathematics, a term is either a single number or variable, or the product of several numbers and/or variables."

In equations such as the relativistic Doppler equation, the overall equation can be broken down into two compoenents, a propagation component or term, and a Lorentz component or term.

Lorentz terms crop up all over special relativity's mathematics, and also show up in other branches of mathematics, in other contexts.

Where the Lorentz term occurs alone on one side of an equation, it might be more usefully referred to as a factor, a ratio that can be multiplied into a starting value to obtain the desired end result. However, often it's not just the Lorentz component in play, for instance, the "relativistic Doppler" equation can be broken into two parts, an explicit propagation term and a Lorentz term. In this case, "Lorentz term" is a natural form of words, not a neologism.

If we look at the wiki page Lorentz factor, we see that the opening sentence is

"The Lorentz factor is a convenient term to define in special relativity." (emphasis added)

, so if the complainant is really sure that the piece of mathematics is not a term, he or she ought to also be complaining about the "Lorentz factor" page.

Now, distinctions ... the "Lorentz factor" is widely invoked in discussions of special relativity when the physical consequences of special relativity are being discussed. Which is most of the time. A Google search throws up thousands of occurences of the phrase "Lorentz factor". The phrase "Lorentz term" only throws up about 290, and these tend to be more discussions of the mathematics rather than physics. That was the context that this short article was meant to address: most specifically the issue of using gamma as a replacement for the Lorentz term.

What the article was trying to say was that, as a technical issue to do with the way that equations are written, although writing the term as "gamma" is shorter, the fact that "gamma" can mean either a Lorentz increase or a Lorentz decrease means that the use of "gamma" is not a good idea unless part of the article is set aside to explicitly state which version gamma is standing in for.

The use of an undefined "gamma" can cause confusion, as can switching between the two versions of the Lorentz term. I think that there was an article in Am. J. Phys on this topic, but I don't have a reference.

While writing the article on Doppler equations, I could have put this in as a footnote about the usage and appearance of Lorentz terms, but I thought that since the subject of correct usage crops up so frequently it might as well be a separate page, with a listing under the "equations" category, where anyone interested in the more "equationy" issues might find it.

While it might be argued that perhaps "Lorentz term" ought to be merged into "Lorentz factor", I didn't feel like being responsible for making a page about physics get sidetracked into issues of correct equation writing.

While this page might not beconsidered to have any useful physics content, it does make a useful point about the usage of terms ... at least a mainstream journal thought that it was enough of a point to publish a piece on the subject. Dry? Boring? Perhaps, but still worth documenting.

PS: Perhaps requests for page deletions ought to be done from a signed-in account, especially when they make a fuss about the author's identity and complain about that person's actions elsewhere, otherwise it can start looking as if the request masy be motivated by personal dislike rather than about the actual content of the article.

Wikipedia is supposed to be a friendly place, and I think it would be a shame if it looked as if some people were trying to get individual articles deleted based on personal antipathy towards certain authors. The value (or otherwise) of an article should be assessed neutrally according to content and context, not according to who wrote it. Using a consistent signiture in these fraught situations helps avoid suspicions that someone may be deliberately posting delete requests under alternative ID's to settle a personal grudges incurred under their main ID: I understand that sockpuppetting is frowned upon in Wikiland. Sometimes Wiki logs a user out and they end up posting anonymously by accident, but in cases like this, I think its in the complainant's interest to take special care not to give the impression that they may be deliberately using multiple ID's in bad faith. ErkDemon 05:12, 8 October 2005 (UTC)

Another way to calculate the Lorentz factor

I have just discovered that the Lorentz factor can also be calculated as follows:

$\gamma ={\sqrt {\beta \left({\frac {1}{\beta }}+\sum _{n=1}^{\infty }\beta ^{2n-1}\right)}}$

GoldenBoar 12:19, 29 April 2006 (UTC)

${\sqrt {\beta \left({\frac {1}{\beta }}+\sum _{n=1}^{\infty }\beta ^{2n-1}\right)}}={\sqrt {\sum _{n=0}^{\infty }\beta ^{2n}}}$

--Anareth (talk) 17:22, 20 May 2016 (UTC)

Yet another, scientific calculator (and Sci-Fi) friendly, way to calculate the Lorentz factor

I have one, too, and it puzzles me to no end, for its implications (OTOH, admittedly, it significantly shortens calculations when you use a scientific calculator):

$\gamma ={\frac {1}{cos(arcsin(\beta ))}}={\frac {1}{sin(arccos(\beta ))}}={\frac {\mathrm {d} t}{\mathrm {d} \tau }}$

If we rearrange it, reciprocal of gamma is "time rate" of moving object relative to observers time rate, just as v is velocity relative to observer,

${\frac {1}{\gamma }}={\frac {\mathrm {d} \tau }{\mathrm {d} t}}=cos(arcsin(\beta ))=sin(arccos(\beta ))$

In other words, *like* if there was a single, complex velocity vector with constant modulus of exactly c, for each, observer and the observed alike. In other words, not only is c *maximum velocity*, it is also *the only velocity* as well!

Observed speed, relative speed of observed in observer's frame of reference is v and relative time rate of observed in observer's frame of reference is reciprocal of gamma (note that gamma is relative, per observer).

Further implication is that each object without acceleration is actually traveling through spacetime along its own time axis, with complex velocity, modulus of which is always c. An object is at rest from the standpoint of an observer if their c-vectors are parallel, if they are "traveling futurewards together" (they agree on the direction where future lays).

v is observed object's c-vector's "spatial component" (projection of object's c-vector on an straight line laying completely in observer's 3d space, i.e. 3d space perpendicular to observer's c-vector direction) and reciprocal of gamma is its "temporal component" (projection of object's c-vector on observer's c-vector direction).

Further on, acceleration of an object is equivalent to rotation (inclination) of its c-vector from its original direction. Therefore, acceleration is rotation of c-vector and if object is constantly accelerated, not by adding energy from another reference frame (as in particle accelerators), but through use of conservation of momentum (reactive propulsion, as in... rocket ships), then c-vector can be "driven" to be perpendicular to observer's c-vector (rocket ship, theoretically, could reach 1.0 c) or even to point backwards (180 degrees angle) to observer's c-vector - travel backward in (observer's) time. —Preceding unsigned comment added by 147.91.1.45 (talk) 13:59, 25 January 2008 (UTC)

Rapidity

Currently rapidity is redirected to Lorentz factor. The rapidity concept is so integral to the spacetime models that it needs to be set out early in relativity study. Even before the physical models are considered there should be a mathematical foundation, such as split-complex numbers. Attempts to make informed instruction without the rational underpinnings run into problems for understanding. Please, if you can help write so people understand by appropriately staged learning, it could make a difference along the line. Thank you ahead of time.Rgdboer 23:15, 26 August 2006 (UTC)

I think that the point here is that rapidity is a special relativity concept worth of its own page, and doesn't seem to have any particular reason to be tacked on to the Lorentz Factor article. Why it is not mentioned in the special relativity article at all is beyond me. cleverless 4:00, 30 April 2007 (EST)

Rapidity now has its own article. Editors may be interested in the discussion at Talk:Rapidity. Mathematical transparency is the issue.Rgdboer (talk) 01:14, 30 November 2008 (UTC)

Derivation

I'm having trouble understanding the derivation of the Lorentz factor. First, which light are we talking about? I assume we are talking about light that A emits at the starting time, not further light that is emitted as A travels, but I wasn't sure, because I didn't understand the rest. It would seem to me that B would see A and the light L travelling both leaving the starting point P perpendicular to each other, while from the frame of reference of A, the light L would be travelling back at an angle. This is the reverse of what the article says, so I am wondering what I am missing.

Thanks for any help,
vivacissamamente 16:08, 11 February 2007 (UTC)

I think an illustration would be useful here, so that everyone can easily see the Pythagorean Theorem at work. I have not diagrammed it to see if the derivation is correct, but a picture would make it easier for everyone to understand the derivation. I'm new. I hope I am not breaking any talk page guidelines. Thanks.

Vidigod 02:43, 23 March 2007 (UTC)

The claim "This distance is the same distance that A sees the light travel" is preposterous! Why in the hell would I assume that? —Preceding unsigned comment added by 121.73.79.100 (talk) 23:31, 16 February 2008 (UTC)

Not at rest in co-moving frame?

The gamma factor can have various different values. a) If a particle is at rest in the moving frame then there is only one gamma= 1/(1- (v/c)^2)^(1/2). Here v is both the particle speed (in the lab frame ) and the moving frame speed with respect to the Lab.

b)However a particle may have a speed v'in the S' frame , a speed v in S frame (the Lab)and the frame S'move with Vs with respect to S .... the composition of velocity gives

          v'= (v'-Vs)/( 1- v*Vs/c^2)              

no gammas appear. However as written v and v' are not the components of a four vector.

To write four vectors there will be at least three gammas

gamma1 = 1/(1- (v/c)^2)^(1/2). v is the particle velocity in the S frame

gamma2= 1/(1- (v'/c)^2)^(1/2). v' is the particle velocity in the S' frame

gamma3=1/(1- (Vs/c)^2)^(1/2). Vs is the speed of frame S' wr to S gamma 3 would enter in the LorentZ transformation along with (Vs/c)gamma3

www.geocities.com/serienumerica2 reibaretti2004@yahoo.com —Preceding unsigned comment added by 69.89.32.22 (talk • contribs)

wrong identity

In all presentations of SRT that I know of, gamma is a substitute for c/sqrt(c^2-v^2) - thus that's the mathematical identity. According to physics theory, gamma is equal to (but not identical to) dt/dtau.

Harald88 13:59, 22 August 2007 (UTC)

I now correct it Harald88 17:30, 26 August 2007 (UTC)

lorentz factor

i requested you to have an example on how to solve lorentz factor with an explanations

requesting about lorentz factor

i requested you to have an example on how to solve lorentz factor with an explanations —Preceding unsigned comment added by 121.1.53.49 (talk) 09:40, 28 June 2008 (UTC)

\equiv sign

Hello, what does $\equiv$ sign mean in this formula $\gamma \equiv {\frac {c}{\sqrt {c^{2}-u^{2}}}}={\frac {1}{\sqrt {1-\beta ^{2}}}}={\frac {\mathrm {d} t}{\mathrm {d} \tau }}$ ? Wht is it not simply =? Thanks Pamputt (talk) 21:22, 21 July 2010 (UTC)

Here, and often, it means “is thereby defined as equal to.” It was used here to make more explicit the fact that $\gamma$ was being defined. Sometimes, it may mean instead “is equivalent to.”

--Anareth (talk) 17:38, 20 May 2016 (UTC)

velocity addition formula with velocity expressed as gamma

the velocity addition formula with velocity expressed as gamma is:

z = x y + sqrt(x^2 - 1) sqrt(y^2 - 1)

http://www.physicsforums.com/showthread.php?p=3036746#post3036746 — Preceding unsigned comment added by Just granpa (talk • contribs) 17:36, 14 December 2010 (UTC)

Expansion

This article could do with some expansion and organization. I propose adding a coule of new sections

• one for different Representations of it, in terms of velocity v and rapidity φ (already included) and momentum p:

$\gamma ={\sqrt {1+\left({\frac {p}{mc}}\right)^{2}}}\,\!$

Here we could incorperate the power series expansion and approximations can be under a sub-heading in this section.

• one for Applications - in the Lorentz transforms, its ubiquity in length contraction, time dilation, mass defecit (which follow from lorentz transformations anyway but still), and its use in the Maxwell-Juttner distribution. All loose ends of its use hinted in the first few paragraphs can be fully organized under this section. Of course links to all articles (at least the most important/useful ones) that need γ will be included. Also really this type of section should come before approximations (as it will comprise exact formulae) - approxm's are a last-resort endevour, i'm sure anyone will agree.

Also the Derivation section is purley about time dilation - which has its own article. γ arises naturally when deriving Lorentz transformations which are more general. Perhaps this section could be deleted (though I'd rather not since its someone else's work, and is a correct and fair attempt to show how γ arises) and a sentence somewhare (introduction?) should say that γ arises in the Lorentz transformations and link to the derivations there?

What are other opionions?--F=q(E+v^B) (talk) 15:22, 3 December 2011 (UTC)

It seems no one has replied in a week. I'll just do it - it can't be a big deal. Further issues not previously mentioned are:

• There is an inconsistency in the rapidity section: r suddenly becomes y. I'm not sure if r or y is standard for rapidity. Its probably better to use the more standard φ - consistent with the main article.
• There is also some inconsistency when the article says "actual time" and "actual distance" of some object - there is no such thing. "Actual" space and time could imply "absolute" space and time... which is definitley not good...
• The following sentences:

" v is the velocity as observed in the reference frame where time t is measured,"

"An object moving with respect to an observer will be seen to move in slow motion given by multiplying its actual elapsed time by gamma."

"Its length is measured shorter as though its local length were divided by γ."

need (at a minimum) to be re-written to:

" v is the relative velocity between inertial frames,"

"An object moving with respect to an observer will be seen to move in slow motion, an elapsed time measured in the observer's frame t ' is related to elapsed time in the objects frame t, by the factor γ,

$t'=\gamma t\,\!$ "

"The length of an object (along the direction of motion) with respect to an observer appears contracted, the measured length in the observer's frame is related to the length in the object's frame, through the factor of 1/γ,

$x'=x/\gamma \,\!$ "

(embedded in a list of formulae so the reader can see how). Currently these are not clear eneogh. I have tried to keep the explaination of what these effects and formulae are and how γ contributes to them - since they are explained in the linked articles and will detract from this article's meaning.

• It would be better to render all of the formulae as LaTeX rather than inline and buried in the text. Also its not good to have links in a formula such as "tanhr = γ", it appears odd and much less professional.
• Some of the greek letters are italicized and some are not. It should be one or the other, so i'll italic them (matches appearance with formulae).
• Why is this definition of rapidity used in particle physics included?

$y={\frac {1}{2}}\ln \left({\frac {E+p_{L}}{E-p_{L}}}\right)$

It serves no purpose. Really it should be transferred to the main article - but i'll leave that for now.

• Shouldn't this be in the lead paragraph?

"Sometimes (especially in discussion of superluminal motion) γ is written as γ (uppercase-gamma) rather than γ (lowercase-gamma)."

• For good measures:
  • Added more sources,
  • I corrected as many obvious spelling mistakes using the microsoft word processor.

--F=q(E+v^B) (talk) 20:54, 10 December 2011 (UTC)

Wrong Order

This article is written in the wrong order. The Lorentz factor γ is something that comes out of solving the relativistic equations

x = γ(x' + vt' ) and x' = γ(x – vt). To use relativistic equations (from which the Lorentz factor was derived) as an application of the Lorentz factor is ridiculous. I propose a rewrite of the article. — Fly by Night (talk) 00:57, 28 December 2011 (UTC)

Well, lets change "applications" to occurance and "formulae involving the factor". I'll have a quick look at re-writing.-- F = q(E + v × B) 08:30, 27 January 2012 (UTC)

Actually - what is so wrong about the order??? First is the lead, then the definition (which it is a defined factor), then it immediately shows where it is used, so that readers immediately get the idea that its not for the sake of it and where it occurs, then come the alternative forms it takes - but these are less often used and also just contains the series expansion. It would help if you said why you think the article is disordered and what to re-write, instead of just stating it. -- F = q(E + v × B) 08:30, 27 January 2012 (UTC)

Never mind - it has been dealt with.-- F = q(E + v × B) 00:32, 28 January 2012 (UTC)

Removal of content

I removed the derivation, since there are links to the main articles on the Lorentz transforms, time dilation etc where the derivations of the formulae, including how the factor arises, are all there. No use repeating content essentially in other articles.-- F = q(E + v × B) 09:01, 27 January 2012 (UTC)

Large gammas

There are a remarkable number of 9's in a large gamma. Perhaps we should extend the table. Frank Layden (talk) 02:51, 4 December 2013 (UTC)

Approximate gamma

Would like to know how to approximate gamma for very very large values of v. Just granpa (talk) 06:26, 29 June 2016 (UTC)

Something for wp:Reference desk/Science or better, for wp:Reference desk/Mathematics. Good luck. - DVdm (talk) 07:04, 29 June 2016 (UTC)

reciprocal Lorentz factor

I would suggest changing the notation used here for the reciprocal Lorentz factor (γ⁻¹) to τ (tau) and not α (alpha). Using alpha for the reciprocal Lorentz factor is confusing, since in the Bohr model, the speed of an electron in neutral hydrogen is given by β = α (where β = v/c and α is the Sommerfeld constant). Using tau for the reciprocal Lorentz factor is particularly notable from the title of Poul Anderson's novel Tau Zero, which should probably be mentioned in the article as a popular-culture reference for the Lorentz factor (technically the spaceship in Tau Zero is moving at an incommensurably small [effectively infinitesimal] tau, and not at a tau of zero). Nicole Sharp (talk) 18:39, 20 September 2016 (UTC)

If using α causes confusion, using τ will cause even more confusion, as α is nowhere used in the article, whereas τ is used for proper time. Too bad for Anderson. - DVdm (talk) 21:15, 20 September 2016 (UTC)

Special Theory Of Relativity

In what velocity is reached,will be sufficient for showing on the relativistic effects, just like time dilation, length contraction, relativistic mass, relativistic energy, relativistic force, relativistic momentum, relativistic power are starting to appear, because, i.e. E=Mc². If v<<c, then Mc²=M0c²(1–v²/c²)^–1/2 =>Mc²=M0C² {1+1/2(v²/c²)} =>Mc²=M0c²+1/2×M0v² Soumik Mondal (Subhra) (talk) 08:39, 30 October 2020 (UTC)

@Soumik Mondal (Subhra): Please, see Special relativity, Time dilation, Length contraction, Relativistic mass, Relativistic energy and Relativistic momentum (as mentioned avobe). Relativistic power and Force doesn't make sense. regards, — A. Shohag (ping_me or Talk) 10:45, 30 October 2020 (UTC)

@Soumik Mondal (Subhra): Please don't use article talk pages to chat about the subject. Here we discuss the article, not the subject. See wp:Talk page guidelines. Thanks. - DVdm (talk) 11:52, 30 October 2020 (UTC)