Talk:Klein–Gordon equation

message: When did they come up with this mod to Schrodingers equation??. A bit of history would be good here.--Light current 03:56, 2 October 2005 (UTC)
replies: text: From memory, the equation came very shortly after Schrodinger's equation. It was the first attempt to form a relativistic wave equation. I am pretty sure it predated the Dirac equation. I think it was a pretty obvious extension of Schrodinger's equation to the relativistic case, which is why lots of people thought of it at the same time. --DannyWilde 04:15, 2 October 2005 (UTC)
replies: text: Insufficient. Currently the Dirac equation page does a better job than this page, explaining the original physical motivation for its consideration as well as the reasons for the later abandonment of the K-G eq (as per a typical intro to RQM course). This page must furthermore explain how those reasons were nullified in order for the K-G eq to finally be readopted in modern QFT. E.g., potentially negative probability density does seem absurd, why isn't that a problem if describing a scalar field? 150.203.48.127 (talk) 02:52, 17 April 2008 (UTC)
thread_title: Need history

message: It seems inappropriate to say that the equation applies to particles in anyway, since the modern interpretation is that it is the equation satisfied by all quantum fields (not just scalars/pseudoscalars). Threepounds 02:49, 15 November 2005 (UTC)
thread_title:  Particles? 

message: B. Roy Frieden claims to have developed a "universal method" in physics, based upon Fisher information.  He has written a book about this.  Unfortunately, while Frieden's ideas initially appear interesting, his claimed method is conversial:
Frieden's work is highly controversial; see for example
*
* (the reviewer has some positive comments but concludes that Frieden's work is "misguided")
* eprint (highly favorable)
* unauthorized electronic reprint
*Physics from Fisher Information: A Unification (a review) from Cosma Shalizi (Computer Science, University of Michigan) (highly critical)
*Physics from Fisher Information (a review) from R. F. Streater (Mathematics, Kings College, London) (highly critical)
*Physics from Fisher Information thread from sci.physics.research, May 1999 (mostly critical)
*Fisher Information - Frieden unification Of Physics thread from sci.physics.research, October 1999 (mostly critical)
Note that Frieden is Prof. Em. of Optical Sciences at the University of Arizona.  The data.optics.arizona.edu anon has used the following IPs to make a number of questionable edits:
#
##20 May 2005 confesses to being Roy Frieden in real life
##6 June 2006: adds cites of his papers to Extreme physical information
##23 May 2006 adds uncritical description of his own work in Lagrangian and uncritically cites his own controversial book
## 22 October 2004 attributes the uncertainty principle to the Cramer-Rao inequality, which is potentially misleading
##21 October 2004 adds uncritical mention of his controversial claim that the Maxwell-Boltzmann distribution can be obtained via his "method"
## 21 October 2004 adds uncritical mention of his controversial claim that the Klein-Gordon equation can be "derived" via his "method"
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##9 September 2004 adds uncritical description of his work to Fisher information
## 8 September 2004 adds uncritical description of his highly dubious claim that EPI is a general approach to physics to Physical information
##16 August 2004 confesses IRL identity
##13 August 2004 creates uncritical account of his work in new article, Extreme physical information
##11 August 2004 creates his own wikibiostub, B Roy Frieden
These POV-pushing edits should be modified to more accurately describe the status of Frieden's work.---CH 23:54, 16 June 2006 (UTC)
replies: text: I know nothing about Frieden's work, but it can be noted that the Fisher information metric is equivalent to the flat-space metric on an n-sphere, and when complexified is equivalent to the Bures metric of quantum mechanics. Well, the Fubini-Study metric I guess I forget the details. Misha Gromov wrote about this, nicely pointing out that if you take a bunch of ordinary statistical probabilities living on a simplex: \sum_n p_n=1 and take their square root you get quantum probability amplitudes: \sum_n |\psi_n|^2=1 which is the equation for a point on a sphere. Geometrical fun and games ensue, especially with \sum_n p_n \log p_n where p_n is a function of a parameter \lambda and you consider \partial p_n / \partial\lambda and presumably Frieden had fun with those games. I mean, so yes, you probably can derive QM from Fisher information, but so what? What does this tell you that you don't already know? 67.198.37.16 (talk) 17:45, 16 December 2020 (UTC)
replies: text: Oh. Ewwww. I see what the problem is. This review: Studies in History and Philosophy of Modern Physics 33 (2002) 327–343 Essay review Physics fromFisher information D.A. Lavis, R.F. Streater. Indeed, there is cause for concern. 67.198.37.16 (talk) 18:15, 16 December 2020 (UTC)
thread_title: [[B. Roy Frieden]]'s anonymous POV-pushing edits

message: After taking a look at the derivation of the Klein-Gordon equation I think I may have come across an error in the derivation.  In the portion of the equation where the energy operator is plugged in you have -i times hbar times the del operator.  When this quantity is squared you should get hbar squared times the laplacian.  Instead the derivation has -hbar squared times the laplacian.  —Preceding unsigned comment added by 207.230.130.223 (talk) 18:46, 2 October 2008 (UTC)
replies: text: (-i)^2 = -1 \, JRSpriggs (talk) 05:54, 3 October 2008 (UTC)
thread_title:  Error in derivation of the Klein-Gordon equation 

message: Should there not be a lot of m0s instead of ms around? what do you think?CecilWard (talk) 05:22, 2 January 2012 (UTC)
replies: text: Why clutter things up with a lot of unnecessary subscripts? At this level, we are never going to talk about "relativistic mass" rather than "rest mass". Relativistic mass, if one had to refer to it, would be described as energy divided by the speed-of-light squared. JRSpriggs (talk) 12:45, 2 January 2012 (UTC)
thread_title:  Masses without zero subscripts 

message: Is it just me, or is the following juxtaposition in the lede expected to confuse:
:It is the equation of motion of a [...] field whose quanta are spinless particles. [...] Any solution to the Dirac equation is automatically a solution to the Klein–Gordon equation, [...]
Any solution to the Dirac equation has spin 1/2, which is not a spinless particle. My interpretation is that the first statement only true if one (quite unnecessarily) imposes a spinlessness restriction on the field via definition (usually for purposes of simplicity of exposition). The second statement is true if this restriction is dropped, but only then. Is the Klein–Gordon equation considered in this article to apply to spinor fields or not?  Let's clarify this. My own preference is to be encyclopaedic and not pedagogical, thus preferring the general case in which the Klein–Gordon equation is taken to apply to arbitrary particle fields (of any spin), making the second and not the first statement true. —Quondum 09:11, 7 June 2014 (UTC)
replies: text: Perhaps the first sentence should be re-worded. I think you are misinterpreting it. It is not saying that the Klein-Gordon equation is only true for spin-zero particles. Rather it is saying that spin-zero particles merely obey it while particles of higher spin also obey other equations which imply the Klein-Gordon equation. JRSpriggs (talk) 10:02, 8 June 2014 (UTC)
replies: text: I've reworded it to make this interpretation clearer. —Quondum 18:58, 8 June 2014 (UTC)
thread_title:  Curious juxtaposition 

message: I added a section on the derivation of the current conservation for a complex scalar field. Someone whould also add a proof using the U(1) symmetry and Noether theorem (or add a link if this is already proved somewhere else). I'll do it myself when I have the time if no one else does that. Ggf4t (talk) 12:38, 13 January 2015 (UTC)
thread_title:  Current conservation 

message: A section on the retarded, advanced and Feynman propagators would be nice. The momentum-space form is obviously 1/(p^2-m^2) and it's static, non-wave form fourier xform is the Yukawa potential and the non-static generic propagator has explicit forms given here and in several other places, e.g. a Feynman article from the 1950's on the theory of the positron.  A discussion of the Lorentz invariance of the green's functions would be nice. A discussion of what happens in dimensions other than 4D is especially very interesting, since apparently, Huygens principle holds only in 3+1D or more generally, only for odd spatial dimensions.  Google for "huygens hadamard" for more info. Hadamard conjecture.  The results are very surprising and should be covered here. 67.198.37.16 (talk) 22:19, 15 January 2016 (UTC)
thread_title:  Green's function and N≠4 

message: Can we change the metric signature to +--- ? This would make it compatible with standard textbooks and with other WP articles.  Are there any QFT textbooks anywhere that use -+++ ? 67.198.37.16 (talk) 17:21, 16 December 2020 (UTC)
thread_title:  Metric signature 

message: I think the first time derivative of \phi is approximated incorrectly. The term thrown away is a correction of size E'/m relative to the one that is kept. In the second time derivative these corrections of this size are kept, so, if we want to truly expand the second time derivative to order E'/m we should keep all terms of this size.
Another possible mistake is the sign of the overall phase in the definition of  \psi in terms of \phi, which should be reversed in my opinion to give \psi=u(x) \cdot \exp{(-iE'/h)} \cdot \exp{(+i m/h)} consitent with E'=\sqrt{p^2+m^2}-m.
— Preceding unsigned comment added by Foice (talk • contribs) 09:38, 26 June 2021 (UTC)
thread_title:  Non relativistic limit 

message: Some of the symbols are just appearing as squares. I think it's delta squared but wasn't sure. 137.50.173.2 (talk) 11:41, 7 February 2024 (UTC)
thread_title:  Symbols not appearing