Talk:Special relativity/Archive 16

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GA date?

Does anybody remember when (even roughly) this article became GA? This Talk page archive does not include the header templates, which is probably not good.--71.141.237.87 20:34, 5 February 2007 (UTC)

Newtonian absolute time and space

In this article and in many others I read, that Newton claimed an absolute time and an absolute space. But, I can not find any citation from Newton talking of an absolute time or space. Moreover, Newton's work is based on Galileo's, and the principle of relativity was already used by Galileo, or not? 84.169.205.73 10:16, 27 March 2007 (UTC)

Newton assumed it implicitly. Can you find any instance in his work where he even considers the possibility of: relativity of simultaneity, time dilation, or length contraction? Galileo's "relativity" is not special relativity. JRSpriggs 10:42, 27 March 2007 (UTC)

Relating to Galilean & Lorentz transformations

We have been studying Galilean and Lorentz transformations since a long time and in its derivation, we usually take y- and z-axis as constants, I mean we write y`= y and z`=z. I cant understand that when a particle is moving in 3-d, how can both the axis remain same. We do not take the value of x,y,z of a particle which is moving in 3-d as constants. —The preceding unsigned comment was added by 59.94.209.92 (talk) 19:03, 8 April 2007 (UTC).

A particle can move in the y or z directions as well as in the x direction, or in a combination of these motions. How the y and z coordinates of a particle change over time is not limited by either transformation law. What is meant is — when the transformation is done, the new y coordinate associated with an event (a certain occurrence in the life of a particle, for instance) is the same as the old y coordinate for that event. And similarly, for the z coordinate. Whereas, the x coordinate which varies in the direction of the new reference frame's motion vis-a-vis the old reference frame must be re-calculated depending on the time.

Notice that there is a difference between particle motions (which can vary arbitrarily) and motions of inertial reference frames (which are not allowed to accelerate). JRSpriggs 09:17, 9 April 2007 (UTC)

Enormousdude

The repeated edits by Enormousdude (see, e.g., here) can be reasonably considered vandalism and should be reverted without worrying about WP:3RR. (in my opinion) Gnixon 19:15, 14 April 2007 (UTC)

I don't know if they make criteria for vandalism, but since Enormousdude is famous for his imperious changes and refusal to discuss them with anybody, I think he is in clear violation of WP:DICK, and can indeed be reverted at will by the community of good-faith editors who ARE willing to use citations, make our cases in TALK, and in general, act as part of a working civilized community. SBHarris 01:59, 15 April 2007 (UTC)

My guess is that the point which Enormousdude (talk · contribs) is missing (if he is not just a troll) is that the laws of electromagnetism are not part of special relativity itself, they are a separate theory. JRSpriggs 09:59, 15 April 2007 (UTC)

Special Relativity without the Second Postulate

There are numerous and highly reliable published sources that all agree that special relativity can be derived without Einstein's second postulate. See the short list of 11 references given by Palash B. Pal in the article, Nothing but Relativity for example.

The abstract to the article Lorentz Transformations from the First Postulate by A. R. Lee and T. M. Kalotas, published by the American Journal of Physics -- May 1975 -- Volume 43, Issue 5, pp. 434-437, says it best:

“ We present in this paper a derivation of the Lorentz transformation by invoking the principle of relativity alone, without resorting to the a priori assumption of the existence of a universal limiting velocity. Such a velocity is shown to be a necessary consequence of the first postulate, and the fact that it is not infinite is borne out by experiment. ”

I see no reason why this elementary detail in modern special relativity that is so relevant to other knowledgeable editors can't be incorporated into the Wikipedia article on special relativity. --e.Shubee 10:43, 15 April 2007 (UTC)

Here's one: This detail is (appropriately) covered in the article Postulates of special relativity referenced in the 'Postulates' section of this article. Alfred Centauri 13:02, 15 April 2007 (UTC)

The issue with the second postulate is in what you demand of the "rules of physics" that the first postulate refers to. If one of those rules is the Galiean transformations, then you have classical mechanics. If instead one of those rules is the constancy of c, then you get relativity. It is the second postulate that makes that switch. --EMS | Talk 16:43, 15 April 2007 (UTC)

EMS, I've been wondering something. Isn't there a subtle assumption in these 'one postulate' derivations w.r.t. the synchronization of spatially separated clocks? And if so, is that not equivalent to the (or maybe 'a') 2nd postulate? Alfred Centauri 20:33, 15 April 2007 (UTC)

In the pure "one postulate" derivations, the important thing is the lack of an assumption of synchonization between arbitrary clocks. Hoewever, my understanding of these derivations is that they leave the limiting speed undefined. One of the things that the second postulate does is to define the limitng speed. IMO you really don't have SR until you have set c as the limiting speed. Another variation is to say "the rules of physics including those of electromagnetism ..." in the first/only postulate, but IMO that is really a fusion of the two postulates as the PoR does not state which laws of physics are to be treated as fundamental. --EMS | Talk 06:19, 16 April 2007 (UTC)

EMS, I agree with you that the "one postulate" derivations leave the limiting (invariant?) speed undefined. But Einstein, at the outset of his derivation, specified that clocks are synchronized by light signals such that the one way speed of light is always measured to be c. Now, to my limited understanding, it seems reasonable to believe that the "one postulate" derivations, where the invariant speed is undetermined, must also assume that distant clocks are synchronized by signals traveling at the invariant speed. Otherwise, the results of physical experiments, as measured with these clocks, would depend on relative motion. If this is so, isn't this assumption equivalent to the Einstein's 2nd postulate? Alfred Centauri 13:30, 16 April 2007 (UTC)

Either classical kinematics or the Maxwell's equations had to be false, if the first postulate is true. The second postulate recognizes that Maxwell's equations are true and classical kinematics are not. Also, see section #Suggested addition to Postulates section above. JRSpriggs 07:59, 16 April 2007 (UTC)

I can't speak in such detail about a derivation that I have not carefully studied. What I can tell you is that these derivations must assume that the spacetime is uniform, isotropic and velocity-invariant, meaning that the properties are the same at all places, in all directions, and as perceived by all inertial observers. It would therefore follow that if a fininte speed for synchronization signals exists as a matter of spacetime structure, that speed itself would be uniform and isotropic in all reference frames. At that point, you have the limiting speed due to that consideration alone.

Kindly note that the one-postulate derivations do not get you all the way to SR! Instead they define a class of theories that at one extreme is classical mechanics (where the limiting speed is infinite) and in another case is SR (where the limiting speed is the speed of light or c). So the second postulate becomes the setting of the limiting speed to c in this class of theories. --EMS | Talk 14:43, 16 April 2007 (UTC)

I do understand that the 'one postulate' derivations leave the invariant speed unspecified but I do think that your emphasis of this point is justified given the idea being pushed by other editors here that the 2nd postulate is redundant. Alfred Centauri 20:37, 16 April 2007 (UTC)

In the paper referenced above, from glancing at the first page, it looks like the authors essentially assume a Lorentz spacetime, then substitute experimental evidence for the 2nd postulate in order to rule out the limiting case of Galilean space for c=infinity. That hardly reads to me like any invalidation of Einstein's approach---in fact, it boils down to starting with his revolutionary insight that space and time are related. Since Newtonian mechanics is invariant in Galilean space(-time), invariance alone can't allow you to "derive" relativity. Of course, the whole issue of trying to find postulates for deriving relativity seems a little off-point to me. Einstein's insistence that invariance and constancy of speed of light must be correct led him to realize that we live in a spacetime described by special relativity. Gnixon 20:53, 16 April 2007 (UTC)

I think that the real point for our purposes is that the consensus opinion within the scientific community is that two postulates should be used for the derivation of special relativity. As originally stated by Galileo, the principle of relativity really does apply to both relativity and Newtonian mechanics. It is the second postulate that distinguishes between the two. People can adopt one postulate. but to work as a single postulate it has to explicitly include Maxwell's equations, light speed constancy, or some other related concept in the postulate itself. This makes it much more specific than the true principle of relativity is. --EMS | Talk 21:19, 16 April 2007 (UTC)

The 'Nothing but Relativity' [1] authors use only the homogeneity and isotropy of space along with the principle of relativity to derive a transformation with an invariant speed that is undetermined. As EMS has eloquently said, that's as far as you can go with one postulate unless you read more into the 1st postulate than there is.

There's another paper in the external links [2] that generalizes the POR further such that there is another degree of freedom in the transformation equations w.r.t. clock synchronization convention. That's more or less what I was alluding too earlier when I asked EMS if there isn't a hidden assumption in these 'one postulate' derivations. Alfred Centauri 23:57, 16 April 2007 (UTC)

Indeed, EMS had already eloquently covered my basic points. I apologize for not reading the discussion fully. I would add, though, that Einstein's real insight wasn't limiting the possible spacetime transformations to special relativity (you can get there from his two postulates or other arguments as already discussed), but rather recognizing that there existed a transformation between space and time. The significance of his postulates was that they couldn't both be satisfied without the existence of that transformation. By the way, my original comment was in response to the first post or two of this discussion, which were the only ones I read carefully. Not sure if that addresses your post, AC, but I'm glad to discuss further if you like. Gnixon 00:12, 17 April 2007 (UTC)

I actually don't understand the comment made by EMS and others above that you have to set the limiting speed to c or assume the validity of Maxwell equations to get special relativity. I have two objections to that. First, suppose that the photon turns out to have a mass after all see e.g. here, then special relativity would still be valid, even though Maxwell's equations are not (at least they would not apply to electromagnetism). Also the limiting velocity would not be the same as the speed of light.

Another objection is that the value of the limiting velocity has no operational meaning because we have yet to define our units. You can always choose your units such that c becomes 1 (unless it is infinite in which case we are dealing with classical mechanics). The term c this a mere rescaling parameter that arises from the fact that we measure time and space in different (from natural) units. This point has been made a few times by Michael Duff, see here and here. As Duff explains in the latter article, you could just as well define different (incompatible) units for distances in the x y and z directions.

E.g. imagine that on the surface of a neutron star there are intelligent creatures that are contrained to move along the surfce. To them the vertical direction is invisible, but it does appear indirectly in their equations of physics. When their Einstein discovers the true laws of physics they get the formula for ds^2 with a c^2 in front of the dt^2 but also a c_{z}^2 in front of the dz^2. Both parametrs would then be dimensionful parameters because they would be associated with concepts from old laws of physics in which these quantities are incompatible. Count Iblis 01:30, 17 April 2007 (UTC)

I think the point is that you have to decide that there exists a limiting (finite) speed. If the photon had a mass, relativity would be correct, and c would be the speed limit, but there just wouldn't be any such thing as the speed of light. That is, "speed of light" is just a convenient name for the speed limit because light always goes that speed. Operationally, the speed of light is just the fastest that anything can go---in SI units it's 3E8 m/s, but that speed limit exists and would be physically the same in any units. This discussion seems to be getting away from the article, and further such discussion should probably at least go to user talk pages. Gnixon 01:38, 17 April 2007 (UTC)

All that you can get from the first postulate alone is that the "Lorentz factor" has the form $\gamma ={\frac {1}{\sqrt {1+K\cdot v^{2}}}}$ for some real number K. If K is positive, then you get "Euclidean" space-time. If K is zero, then you get Newtonian space-time. If K is negative, you get Lorentzian space-time. The second postulate tell us that $K={\frac {-1}{c^{2}}}$. JRSpriggs 03:06, 17 April 2007 (UTC)

I will second Gnixon's request. I do not see any need to deal with hypothetical massive photons as that have nothing to do with this article. As for the use of different scaling factors: That is true and so what? In case you were not aware of it our current measurement systems were devised before SR came along. Also, you can describe the structure of spacetime perfectly well even when there is a different scaling factor for each direction: A simple cordinate transformation on the Minkowski metric will do the trick. --EMS | Talk 03:16, 17 April 2007 (UTC)

References for alternate versions of the postulates

A series of references (textbook quotations) were (finally) cited by User:Enormousdude, which appear to show that the redundancy argument is published. User:Sbharris also linked to a reference (lecture slides) when adding a somewhat better-worded version of the redundancy argument when this became clear.

Given that we finally have some citations satisfying WP:RS in play, I'm prepared to endorse the version produced by User:Sbharris. Can we please stop reverting and start discussing things again? Core to the discussion would be whether or not the textbook citations are valid for the point being made, not opinions on anyone's attitude or credentials. --Christopher Thomas 22:47, 17 April 2007 (UTC)

Except that I'm starting to change my mind on the issue, now. After reading [3], already cited, there is a strong argument that one cannot do the entire SR thing from postuate #1 without reading more into it than anybody intended. Afterall, what does it MEAN to say that all laws of physics are the same in all frames? The laws of gas motion correctly predict the speed of sound in air, but that's for a non-moving media, and nobody expects them to predict the same sound speed to be seen by somebody moving into a wind (ie, through the air). The physics is the same, but assumptions have been made about the medium transmitting the vibration. The same happens with Maxwell's derivation of c, which depends on tacit assumption of being at rest with regard to some transmitting medium, which otherwise would set mu and epsilon differently, not as physical law parameters, but as measured properties of the medium, much as you'd measure gas molecule average velocity in air. So the hidden assumption of "all physical laws are the same" is that mu and epsilon are physical constants, independent of motion, and THIS means that there IS no tranmitting medium. Instead, people in different frames have time and length change so that the rato of mu and episilon remains constant. This goes beyond simply saying that the laws of physics are the same, since universal time for all observers (galilean relativity) was assumed as part of physics prior, to all this. So something more is needed as an assertion, to make Maxwell's law's work. That extra thing is the Lorentz transformation which makes Maxwell's laws give "c" for everyone, by jiggering up time and space, in a certain way. Who said it was fair to do that? The guy moving through air and measuring the speed of sound is working with the same laws of physics, but he's not privileged to jigger them up to give a constant speed of sound, no matter how fast he moves. So why are we allowed to jigger up time and space to make only MAXWELL'S laws predictive, dispensing with a medium for light, but not other waves of other kinds? You see the problem. Something more is needed. Some statement warning that Maxwell's equations are sacrosanct and don't have to be adjusted for medium-motion (rather you change their time and space inputs), but OTHER physical laws describing waves in other media at slower speeds (like sound), are to be adjusted differently. SBHarris 23:54, 17 April 2007 (UTC)

<warning! edit conflicted>

(1) There is, IMHO, no need for this article to address the status of the postulates. There is a separate article for this.

(2) There is, to my knowledge, no scientific consensus that the 2nd postulate is redundant.

(3) Whether the 2nd postulate is redundant or not hinges on the content of the POR so, in fact, this argument should probably be taken to the article on the POR. Alfred Centauri 00:04, 18 April 2007 (UTC)

My complaint about the references provided is that all three are general physics texts instead of relativity texts. Here are two refuting references in relativity textbooks:

• Rindler, Wolfgang (1991). Introduction to special relativity. ISBN 0-19-853952-5. - This source lists "two axioms for special relativity". On the second postulate/axiom Dr. Rindler writes "The acceptance of the relativity principle - Einstein's first axiom - seems harmless enough until we come to his second axiom: ..." which is followed by a formal description of the constancy of the speed of light in a vacuum.
• Bowler, M.G. (1976). Gravitation and Relativity. ISBN 0-08-020408-2. - "If we accept that the equations of electromagnetism are true for all observersin inertial frames and Lorentz covariant, the we must either discard the relativity principle or the equations of particle mechanics must also be Lorentz covariant." (Lorentz covariance refers to being subject to the Lorentz transformations, the equations underlying SR.) This indicates that one has a choice of whether to accept that the equations of EM are true in all inertial frames or not. It is only after one has chosen to accept Maxwell's equations as laws of nature that the relativity principle demands SR.

I could go on. I'm sure that other editors can find additional references, but I am quite satisfied that the consensus is that the two postulate approach should be used here and that alternate approaches can be dealt with elsewhere. --EMS | Talk 02:18, 18 April 2007 (UTC)

There are also books in which Maxwell's equations are derived from Coulomb's law by demanding covariance under Lorentz transformatons, see e.g. the book by Ohanian. I think that there is some hidden historical bias in this discussion (Ohanian also mentions this bias in his book). If you think about it, it is very unnatural from a theoretical physics point of view to start with Maxwell equations (which are already covariant under Lorentz transformations) and then try to derive relativity theory. Only because students know about Maxwell equation before they learn relativity do we teach it in this way. And the reason for that is that in high school physics is taught just like history: We start woth Coulombs Law, Biot Savart, Faraday etc. etc. Count Iblis 12:42, 18 April 2007 (UTC)

Enormousdude's references seem pretty weak to me. We should require a reference that states, in so many words, that the second postulate is redundant. His references possibly imply that, by omission, but that's not good enough. If it's so obvious that it's redundant, it shouldn't be hard to find a textbook which says exactly that. Pfalstad 02:14, 19 April 2007 (UTC)

Good pont, but even if he produces such a reference there is a large amount of refuting references out there. IMO, this is not even an area of controversy for most scientists. --EMS | Talk 16:42, 19 April 2007 (UTC)

Light Cone error?

That's a nice-looking graphic for the light cone, but the caption beneath it doesn't sound right. It says:

"The lower quarter of the diagram shows the events that are visible to the observer, and the upper quarter shows the light cone- those that will be able to see the observer."

The light cone consists of both the lower and upper quarters, no? Also, visibility to an observer is along the past light cone's surface. Visibility of an observer is along the future light cone's surface. So, shouldn't the passage say something like this?:

"The lower quarter of the diagram shows the observer's past light cone -- events that can affect the observer -- and the upper quarter shows the observer's future light cone -- events that the observer can affect." The Tetrast 02:32, 25 April 2007 (UTC)

I see your concern, and largely agree with it. My only complaint is that the vertex of the light cones is the location is an event, not an observer. Admitedly that GIF is tracing out a worldine, but at any given moment that vertex lies as a specific event. --EMS | Talk 03:56, 25 April 2007 (UTC)

I'm unsure how to keep it from getting too wordy. The Tetrast 18:59, 25 April 2007 (UTC)

Caveat

I've just added a new section Special relativity #Caveat:_improper_combination_of_the_equations_of_time_dilation_and_length_contraction which has been copied from Introduction to special relativity. There has been a lengthy discussion over whether this is correct at Talk:Introduction_to_special_relativity#Comparison_of_clock_readings_at_different_places_in_a_reference_frame illustrating, to my mind, that the topic is too complex for that introductory article. I have therefore moved the issue here where there might be input into the discussion from a wider range of editors.

Please note, the discussion on the other page has started to descend into insults. Please keep it WP:CIVIL, people! GDallimore (Talk) 09:50, 27 April 2007 (UTC)

I reverted it. It is misleading. The "area" is a constant, that is, dxdt = dx'dt'. The so-called argument against it is based on ignoring the fact that the variations are in two different directions so that the parallelogram has four corners, not just two corners. JRSpriggs 11:38, 27 April 2007 (UTC)

Or, as I am trying to explain, that there cannot be a paralellogram with invariant area, unless of course a trivially vanishing one with dx = dt = dx' = dt' = 0. For one arbitrary pair of events, the invariant is not dx dt = dx' dt' but dt^2 - dx^2 = dt'^2 - dx'^2 (working in units with c = 1)

The argument is entirely correct, and in fact based on taking into account the fact that the variations are in different spacetime directions. That is the whole point.

So I will add the section with some clarification. DVdm 12:32, 27 April 2007 (UTC)

Re-introduced the section, but changed the notation to make it consistent with its supersection. DVdm 12:57, 27 April 2007 (UTC)

(reset indent) The problem with this caveat is that it does not use the definition of a reference frame as a collection of comoving observers each with their own synchronised clock.

In a given frame of reference clocks are synchronised, they dont just give the same intervals, they give the same absolute readings.

In a given frame intervals can be determined within AND between clocks:

If DT(1) = D12 - D11

and DT(2) = D22 - D21

Then DT= D12 - D21

and DT=DT(1)=DT(2)

So why does the Lorentz transformation contain the phase term vx/c^2? If an observer in a relatively moving frame reports that DT=DT(1)=DT(2) why does an observer in another frame disagree?

The reason for this is that the Lorentz Transformation compares the absolute time in one frame with that in another for a single observer. The use of synchronised clocks at different positions in the moving frame will be perplexing to the stationary observer because it will appear to him as if they have all been artificially set out of sync by the amount of the phase term. Only the two clocks that are coincident with the origin at t=0 will be initially synchronised between frames. All the other clocks that are in the frame that is moving relatively to the frame where the length measurement is being made will be conveniently out of phase by the amount of the phase term for the separation of the clocks.

So, taking two clocks separated by L metres, the clocks will appear out of sync due to the LT by g vL /c^2 but will have been conveniently synchronised at the outset to have an absolute time difference of minus gvL/c^2.

Given this, how can we measure the length of a rod? Suppose we place a mirror at one end and time how long light takes to go to the end and back:

DX = cDT (where T is half the overall time interval)

This works because the rod, the timing device and the mirror are in the same frame of reference. Only the light moves, v is 0 so g is 1 and vx/c^2 is 0.

We can do the same thing for a moving rod in its comoving reference frame:

Dx= cDt

But can we do it BETWEEN frames? Can we measure the length of a rod that is stationary in one frame from another, moving frame?

The definition of a reference frame is a collection of comoving observers each with their own synchronised clock. All we need to do is observe the reading on the clock that is adjacent to front end of the rod when the light is emitted and then read the clock that is adjacent to the front end of the rod when the reflected light returns.

We can then use Dx=cDt to determine the length of the rod as measured from the moving frame.

Clearly then x/t = X/T can be used to compare the two lengths and t and T can be related by the time dilation formula, contrary to the caveat.

The caveat, based on the LT for a single observer, does not take into account the synchronisation procedure between clocks in an inertial frame of reference. Incidently, the derivation of length contraction from time dilation is the standard method:

http://www.cosmo.nyu.edu/hogg/sr/sr.ps

http://physics.ucr.edu/~wudka/Physics7/Notes_www/node79.html

http://www.pa.msu.edu/courses/2000spring/PHY232/lectures/relativity/contraction.html

http://www.drphysics.com/syllabus/time/time.html

etc.... Geometer 14:25, 27 April 2007 (UTC)

I repeat: You don't understand the most basic aspects of this, and I'm really sorry that I don't have the patience to explain them to you. I tried 4 times. That is enough for me. DVdm 14:48, 27 April 2007 (UTC)

GDallimore, here is A Full Mathematical Derivation of the point of the Caveat again (with appropriate notation):

Lorentz transformation valid for any pair of events with coordinate differences Dx and Dt in (x,t)-frame, corresponding to Dx' and Dt' in (x',t')-frame:

Dt' = g ( Dt - v Dx ) [eq1]

Dx' = g ( Dx - v Dt ) [eq2]

Dt = g ( Dt' + v Dx' ) [eq3]

Dx = g ( Dx' + v Dt' ) [eq4]

where g = 1/sqrt(1-v^2) and we use units with c=1 (and obviously v <> 0).

Time dilation equation for clock at rest in (x,t)-frame (showing proper time Dt between the tick events):

Dt' = g Dt [eq5]

Length contraction equation for rod at rest in (x,t)-frame (showing proper distance Dx between the endpoint measurement events):

Dx' = 1/g Dx [eq6]

Lower highschool algebra (fully consistent with what is preceding the subsection):

[eq1] and [eq5] ==> Dx = 0 [eq7]

[eq4] and [eq6] ==> Dt' = 0 [eq8]

[eq5] and [eq8] ==> Dt = 0

[eq6] and [eq7] ==> Dx' = 0

So, taking equations [eq5] and [eq6] together for one pair of events ==> Dx' = Dt' = Dx = Dt = 0.

This shows that both equations [eq5] and [eq6] cannot be taken together to demonstrate a so-called 'invariant area' Dx Dt = Dx' Dt' - unless this area happens to be trivially 0.

That is the point of the caveat. Isn't this obvious? If not, what kind of transformation do you suggest to replace the Lorentz transformation? DVdm 17:35, 27 April 2007 (UTC)

DVdm 17:35, 27 April 2007 (UTC)

No-one denies that two observers in relative motion measure two different sections of the world tube of a rod as its "length". Of course the two observers measure different sets of events as the "rod".

==> No, they don't. Two single events on the end points of a rod are sufficient for two different inertial observers to measure its length, provided the events are simultaneous for the observer for whom the rod is moving. DVdm 17:59, 27 April 2007 (UTC)

The issue at stake here is different, it is whether the time dilation equation can be used to derive length contraction.

==> No, that is not the issue here. That is your agenda, and it has nothing to do with the point I am trying to make. DVdm 17:59, 27 April 2007 (UTC)

The answer is that for a light path they can indeed, validly do this. Both observers are entitled to assume that c is constant and if a frame of reference is a grid of observers then both sets of observers in both frames can measure the time taken for light to bounce around and come back again to the same place where observers in the grids are coincident. Geometer 17:48, 27 April 2007 (UTC)

==> Entirely irrelevant. You obviously still don't get the point. DVdm 17:59, 27 April 2007 (UTC)

(unindent) I have a couple of question here: Is there are reliable source which states that this issue is a concern for relativity theory? Without it, I must conclude that this is a well-meaning bit of original research, and should be removed. Even with a source, is this matter a source of significant concern for relativity theory? If it is not, then I would question whether it needs to be covered at all. Indeed, the best thing to do with a minor but contentious statement in a Wikipedia article is often to remove it. --EMS | Talk 19:44, 27 April 2007 (UTC)

EMS, I have seen many instances on Usenet and on the web where someone comes up with this notion of an 'invariant spacetime area'. This topic has been sitting in the article 'introduction to special relativity' for quite a long time without any problem, until Geometer (by entirely failing to understand the rather simple and evident point) sort of messed it up. I wouldn't say that this is original research. It's just a warning against one of the most simple pitfalls one can meet when seeing the standard equations for time dilation and length contraction: don't just combine those equations, for they talk about different sets of events. So I think it deserves a place in this article, and perhaps even more so, in the introduction article. DVdm 20:27, 27 April 2007 (UTC)

Ouch! DVdm, you began this topic by suggesting that your derivation showed that time dilation could not be used to derive length contraction.

==> No. I did not suggest that in any way. Try reading what I write. DVdm 10:50, 28 April 2007 (UTC)

Indeed, you insisted that the time dilation route to length contraction should be purged from the article Introduction to special relativity.

==> No. I did not insist doing that. I insisted that your agenda has nothing to do with my point which you miserable fail to understand. There's no need to try to dodge this. DVdm 10:50, 28 April 2007 (UTC)

You have since shifted the emphasis but now we have a section that, although interesting to aficionados of relativity is a bit rarefied for Wikipedia and is really a bit of original research or a warning about a type of velocity transformation that I have not seen applied by students. Geometer 10:34, 28 April 2007 (UTC)

==> Everything you have raised was entirely irrelevant to the point I am making, and maintaining that you can have the time dilation equation Dt' = g Dt for a pair of events that does not satisfy Dx = 0, is just trivially plain wrong.

I am not interested in your agenda, and it has nothing to do with any of this. DVdm 10:50, 28 April 2007 (UTC)

I have seen this silliness on USENET too, but USENET is not a reliable source. So I am not impressed by that argument and am disturbed by your wanting to mention this issue in the inrotduction. Wikipedia is not a soapbox, nor is it a place to respond to the foolishness on USENET. Please keep in mind that people skim articles like this, and a mention of something which is invalid sometimes gets mistaken for something valid because it is present in the article. So its being present here could actually do more to put that idea into people's minds than to keep in from being considered.

This also would not be the first time that something of questionable usefulness sat in an article for a while before being reconsidered by a new crop of editors. Wikipedia will always be a work in progress, and it is not unreasonable that statements which were or appeared to be acceptable at one time could later be found to be unacceptable as policies, available information, and other circumstances change. This may well be one of those times. --EMS | Talk 21:14, 27 April 2007 (UTC)

Yes, you make a very good point about people possibly skimming the article and erroneously picking up an invalid concept. The way the caveat is formulated now has become much too explicit. If you (unlike others) at least agree that the point I make is a perfectly valid one, I propose to edit it in a way that is much more concise and less prone to superficial misinterpretation. This really being a caveat for 'beginners' and therefore i.m.o. belonging in the introduction, I am not tempted to put it in there anymore, since I don't think that the introduction article is an article for beginners anyway.

So I propose to remove the subsection, and just insert a much shorter sentence immediately behind the phrase This phenomenon is called length contraction or Lorentz contraction:

Caveat: One might be tempted to combine the above two equations into something like $\Delta x'\Delta t'=\Delta x\Delta t$ or $\Delta x'/\Delta t'=\Delta x/\Delta t/\gamma ^{2}$, but as can be seen from the conditions imposed on the events by the equations, namely $\Delta x=0$ for time dilation, and $\Delta t'=0$ for length contraction, combining the equations for one pair of events can only be valid in the trivial case where all the deltas trivially reduce to zero: $\Delta x=\Delta t=\Delta x'=\Delta t'=0$, in other words for two identical events.

Come to think of it... up to that sentence the section Time dilation and length contraction was written by myself :-)

DVdm 22:31, 27 April 2007 (UTC)

That will work much, much better if this business is to be kept at all. I do like it BTW - It is short and sweet and gets to the point long before one's mind starts to wander. Also the bolding of "caveat" gives it the proper red flag treatment. So I won't remove it, but do see it as another piece of clutter in an already cluttered article. --EMS | Talk 03:13, 28 April 2007 (UTC)

Actually, the argument in the caveat against the definition of an invariant area is incorrect. the area is really an invariant. And if you multiply this area bt Dy and Dz you get an invariant volume Dt*Dx*Dy*Dz=Dt`*Dx`*Dy`*Dz`. The way to show that is not to chose specific cases where Dt=0 or Dx=0. You would have to multiply the volume Dt*Dx*Dy*Dz by the determinat of the Jacobian matrix (simply called the Jacobian) of the coordinate transformatio. Since this transformation is linear, the Jacobian matrix is the transformation matrix itself, which has unit determinant. QED Dauto 04:38, 28 April 2007 (UTC).

I removed the offending section Dauto 04:48, 28 April 2007 (UTC).

We are talking about one single pair of events with coordinate differences Dx, Dt, Dx', Dt' and that therefore satisfy the Lorentz transformation. If you calculate the products Dx Dt and Dx' Dt', you will see that you get different results (unless of course everything happens to be zero - which is exactly the point I am making). Only the quantities Dt^2 - Dx^2 and Dt'^2 - Dx'^2 (where we take c=1) have the same value and form the invariant spacetime interval. I restored the subsection, but casted in the format agreed upon by EMS. DVdm 06:13, 28 April 2007 (UTC)

(reset indent)

EMS, that leaves us with the page Introduction to special relativity that has been almost completely rewritten by someone who thinks that the time dilation equation Dt' = g Dt can be valid for a pair of events that do not satisfy Dx = 0, in other words for a clock at rest in the (x,t)-frame that produces ticks at different places. How do you feel about that? DVdm 06:13, 28 April 2007 (UTC)

It would be very easy to show that the area is the same, if I could show you a diagram. Unfortunately, that is impossible in this medium. But the key thing to realize is that the same argument for area being unaffected by a rotation in plane Euclidean geometry works here. Some of those who have been doing these edits are trolls, but there are others who are acting in good faith, but do not realize that they cannot polish a turd, they must just revert. JRSpriggs 09:02, 28 April 2007 (UTC)

See page 147 of Gravitation (book) for the formula for calculating hyper-volume in space-time. JRSpriggs 09:23, 28 April 2007 (UTC)

I see a hypervolume spanned by 8 events here. I am talking about the interval between 2 events. It seems that you have an entirely different situation in mind. I understand your confusion now. No big deal. DVdm 09:39, 28 April 2007 (UTC)

JRSpriggs, last time when I replied to your objection on the talk page of the introduction article you didn't respond to my reply. Thanks for joining the talk this time.

Please show me how for two arbitrary events with coordinate differences Dx, Dt, Dx', Dt' that satisfy the standard Lorentz Transformation

Dt' = g ( Dt - v Dx ) [eq1]

Dx' = g ( Dx - v Dt ) [eq2]

Dt = g ( Dt' + v Dx' ) [eq3]

Dx = g ( Dx' + v Dt' ) [eq4],

you arrive at an invariant Dx Dt = Dx' Dt'. I get Dt^2 - Dx^2 = Dt'^2 - Dx'^2.

Then show me which two distinct events could possibly both satisfy the time dilation equation for a clock at rest in the (x,t)-frame (showing proper time Dt between the tick events), and the standard length contraction equation for a rod at rest in the (x,t)-frame (showing proper distance Dx between the endpoint measurement events):

Dt' = g Dt [eq5]

Dx' = 1/g Dx [eq6]

And please, for now, stop using the names shit, bull-shit, troll and turd for a trivially simple point you (amazingly) don't seem to get. Even you can make a simple mistake, you know.

DVdm 09:31, 28 April 2007 (UTC)

You are using the LT to compare two point observers

==> No. that is not what I am doing. Please read some introduction to special relativity. DVdm 10:57, 28 April 2007 (UTC)

and asking whether these single observers could make the appropriate observations. In SR we deal with grids of observers whose time measurements can be freely compared within each reference frame. What are the transformation equations for observers who are coincident with the two events in both reference frames? The starting point is to consider that the two observation points in the moving frame are observed by the observer in the stationary frame of the rod to have clocks set to t and t minus phase between clocks from the outset. Geometer 10:51, 28 April 2007 (UTC)

Right now I am seeing apples and oranges flying all over the place, and over what to me is a trivial issue out of the USENET. DVdm - You can create invariant surface and volumes in SR given that you identify all of the vertices for the manifold being defined. Your exercise shows that you cannot generate an invariant area from the two coordinates for a line. So what? The rectilinear boundaries for a line are a function of its orientation even in the geometry of Newtonian physics.

IMO, you are fighting a straw man set up by anti-relativists for their own silly purposes, and by fighting it are implying a lack of invariant areas, volumes and hyper-volumes in SR which simply is not true (and admitedly is not what you are trying to say). I don't see that the collateral damage is worth the bother.

BTW - I don't yet see that I should be removing the caveat, but if I get a sense of there being an active consensus against it I will start doing so. For now, I would prefer that you "see the light" --EMS | Talk 22:21, 28 April 2007 (UTC)

Caveats like this belong to the "Introduction to Special Relativity article". Perhaps an artile like "Relativity for Dummies" is needed  :) Count Iblis 02:07, 29 April 2007 (UTC)

Introduction to special relativity is where is this caveat came from! It was taken out of there on the ground that it is too technical by an editor who suggested that it be placed here. So DVdm did just that. IMO, the issue is whether this item belongs in an extant special relativity article at all. Perhaps an article on misconceptions about special relativity can be created, but without a good sense of what such an article is to accomplish it will end up being AfD bait. --EMS | Talk 04:24, 29 April 2007 (UTC)

(reset indent)

EMS: "...trivial issue out of the USENET...": => Not only USENET. Perhaps even more so on the Web, and Wikipedia is part of the Web as well, isn't it? ;-)

EMS: "...fighting strawman by anti-relativists...": => I don't really see this as a fight with anti-relativists. Just a warning that might help beginners to avoid becoming anti-relativists by failing to understand the, to beginners, de-facto most well known equations of special relativity. I notice that failing to understand them in their proper context is extremely, almost frighteningly widespread, both among beginning amateurs as among, yes, professional physicists. That is the reason why I carefully worded the section Time dilation and length contraction in its current form. I really think the caveat belongs in there.

EMS: "...an editor who suggested that it be placed here. So DVdm did just that...": => Correction: it was moved here by that editor, who, simply failing to understand it, decided that it is too complex for an introduction to special relativity :-)

Good grief, what a fuzz over such a trivial issue. Such a simple statement, but apparently some of the contributors here are even simpler. Yet for some of the more sophisticated contributors, the statement seems to be too sophisticated. A paradox.

Well, since I stand by it, I really think it should be inserted again. To those who find themselves somewhere between the extremes of simplicity and over-sophistication, feel free to contribute. DVdm 09:39, 29 April 2007 (UTC)

Let me try explaining that again. I removed the caveat from that article because it was factually incorrect. It stated that it is not possible to define an invariant area in the space-time diagram. As a pointed out through a simple jacobian argument, an area in these diagrams is indeed an invariant. As an answer, I was told that we are supposed to be talking about only two points in the space-time diagrams, and that in such case, either Dt or Dx would be zero giving an zero area.

To that I say "Duuhh..." Of course that`s the area you should get, because that`s the area contained inside a closed polynonal lin with only to vrtices. With 3 (or more) points in the space-time diagram, though, it is possible to define a polygon that encloses a non-vanishing area. That area will indeed be an invariant. That`s why I think this caveat should be kept out of the article Dauto 16:58, 29 April 2007 (UTC).

No, you were told that both Dt or Dx are zero, when you apply the two equations of time dilation and length contraction to one pair of events.

Please show me how for two arbitrary events with coordinate differences Dx, Dt, Dx', Dt' that satisfy the standard Lorentz Transformation

Dt' = g ( Dt - v Dx ) [eq1]

Dx' = g ( Dx - v Dt ) [eq2]

Dt = g ( Dt' + v Dx' ) [eq3]

Dx = g ( Dx' + v Dt' ) [eq4],

you arrive at an invariant Dx Dt = Dx' Dt'. I get Dt^2 - Dx^2 = Dt'^2 - Dx'^2.

Then show me which two distinct events could possibly both satisfy the time dilation equation for a clock at rest in the (x,t)-frame (showing proper time Dt between the tick events), and the standard length contraction equation for a rod at rest in the (x,t)-frame (showing proper distance Dx between the endpoint measurement events):

Dt' = g Dt [eq5]

Dx' = 1/g Dx [eq6]

Can you do that? DVdm 18:01, 29 April 2007 (UTC)

I don`t know what does both ... or means. I suppose you meant both ... and, except that that doesn`t make sense. You keep asking me how to define an invariant area for two arbitrary events. I think I made it clear that the two events restriction is unreasonable because a polygon with two vertices will always have vanishing area. If you really feel the need to include this silly caveat, it should be about the need to add a third event in order to properly define an invariant area. It shouldn`t say that it is not possible to define an invariant are, though, because that would be factually incorrect. One more question: why did you add your comment in the middle of my paragraph, instead of undr it? You mangled the point I was making by cutting it in half... Dauto 18:41, 29 April 2007 (UTC).

I added my comment at the place where it belonged. If you start making a point with a false premise ("either Dt or Dx would be zero"), it doesn't make sense to continue reading. Of course I meant "both Dt and Dx". The fact that you hadn't noticed that, although it was explicitly stated with the set of equations Dx = Dt = Dx' = Dt' = 0, shows that you hadn't really carefully looked at the statement, so I cut it short at that particular point. I notice that you don't like that, so I will put everyting below your lines now. Sorry.

So, again, can you give me two events that satisfy both Dt' = g Dt and Dx' = 1/g Dx without Dx = Dt' = 0 ? A simple question. DVdm 19:31, 29 April 2007 (UTC)

DVdm - We are supposed to be discussing the article, not the theory. Above you noted that this locig is present on the web, and Wikipedia is part of the web in stating why it should be covered. Wikipedia is not a bulliten board. Wikipedia is not a USENET newsgroup. Wikipedia is an encyclopedia. I asked you above for a reliable source that documents this as a pitfall to be avoided. You have failed to provide one. Without it, I must assume that this is totally non-notable, and should not be present. With one, you may convinvce us all that this caveat belongs here. --EMS | Talk 20:23, 29 April 2007 (UTC)

EMS, you seemed to agree that this is a pitfall to be avoided when you wrote:

"I do like it BTW - It is short and sweet and gets to the point long before one's mind starts to wander. Also the bolding of "caveat" gives it the proper red flag treatment."

But okay, yes, I notice that some of the other contributors here still don't get the point, and, although they obviously won't be able to produce that pair of events I asked them to produce, and therefore might be tempted to silently leave the discussion and watch from the sideline, it amazingly but surely looks like they will need a "reliable source" for this trivial little statement. Well, I don't think I will find one. Actually I don't think I should or will even look for one :-)

By the way, I'm sure you will agree that discussing the reason(s) why the article is modified and/or why the modification should be kept or reverted, is well within the realm of "talking about the article". DVdm 21:21, 29 April 2007 (UTC)

Thanks much. BTW: Please do recall that my approval was of the text an not the caveat itself. As for what is "within the realm of 'talking about the article'": That is always a somewhat blurry line as the facts about the theory need to be understood before they can be presented. My reason for bringing that up was that you were focussing on the technical details of this issue to the exclusion of the practical Wikipedia concerns of notability and attribution, and the issue of whether this point is easily grasped and an aid to understanding the theory. My concern has always been that this is a "trivial little statement", and that has consistently raised a red flag with me as to whether it belongs in Wikipedia at all. --EMS | Talk 01:45, 30 April 2007 (UTC)

Dvdm, Of course I cannot produce the pair of events you`ve been talking about, because it doesn`t exist. And I understand that this is the point you are trying to make, and that you believe that this pitfall is common enough to warant som king of warning in this articl. The point I`m making is that, in making your point, you`ve given the reader the impression that it is not possible to define an invariant area. That would be an even bigger pitfall. It appears to me that it would be preferable to show the reader the correct way to build that invariant. In other words, show them what to do instead of what not to do Dauto 02:13, 30 April 2007 (UTC).

EMS, Dauto, fair enough.

What I will do, in the spirit of showing them what to do instead of what not to do (good point!), is to put a little more emphasis on the conditions under which time dilation and length contraction are applicable. It is now in the text in small print, but I will put these conditions on the same lines as the equations. This way, the skimming reader is less likely to take the equations and just multiply, or even worse, divide them side by side. DVdm 06:45, 30 April 2007 (UTC)

This caveat must be removed, it is entirely inappropriate in this special relativity article. I believe it has been removed at the moment, it should stay that way. Geometer 19:30, 30 April 2007 (UTC)

Yes, the statement is gone, rest assured. Had you actually read the few lines to which you were responding here, you would have noticed that, and there would have been no need for you to write that error prone paragraph with gems like "point observers" and "Dx Dt = Dx' Dt' when two observers time a common light path" and "restatement of the postulate that the speed of light is constant", whereas most of us learned that for light path events we have Dx/Dt = Dx'/Dt'. Apparently YMV quite a bit. But you did write it, and then went for the article to go and remove the caveat... to find that it was actually no longer there, so you quickly returned here to remove that remark. Ouch, just in time! Or was it?

Anyway, since the source of your frustration is no longer there, technically we can't discuss it anymore either, and we won't have to worry being hit by one of your apples and oranges anymore.

Great! Nice! ;-) DVdm 08:11, 1 May 2007 (UTC)

I dont understand why you are so unpleasant. Oh well... Geometer 12:10, 1 May 2007 (UTC)

Apparently your discussion about the caveat has petered out to a stalemate. Undoubtedly because you're discussing at least three unrelated "areas" of dubious definition in your discussion. Is not (scalar) area in relativity too the (magnitude of the) vector product of two four-vectors (ΔR, R, or dR sort) in Minkowski space? —The preceding unsigned comment was added by 4.90.205.48 (talk) 15:34, 14 May 2007 (UTC).

This did not end as a stalemate. DVdm chose to accept the basis of our complaint on April 30 and the resulting edit has been deemed acceptable by all sides. So the final result was compromise and consensus. --EMS | Talk 19:12, 14 May 2007 (UTC)

Great! Nice!, wrote DVdm.

Logic/analysis does not allow for consensus and compromise = stalemate. Logic is correct or incorrect. What precisely then is the consensus and compromise reached on whether each party's "area" is a Lorentz invariant? Is/was the caveat not (ultimately) about the Lorentz invariance or noninvariance of area, or a party's "area"? 4.239.75.246 08:21, 16 May 2007 (UTC) DZTyme

I wrote "Great! Nice!" (see The Fast Show) because we finally could stop worrying about getting hit by one of Geometer's apples and oranges.

The caveat was about the trivial invariance of zero, but since it is no longer in the article, this is not the place to discuss it anymore :-) DVdm 08:46, 16 May 2007 (UTC)

Time Dilation and Length Contraction

Edit concerning the Special relativity page: The dilation and contraction formulas are incorrect. If moving clocks run slower (which they do), then an observer in the chosen rest frame will read a time t on his watch, and the slower time t* on the watch in the moving system. So t* < t as observed in the rest frame. Certainly gamma is greater than 1, so it must be that γt* = t, in order to correct for the time discrepancy.

Similarly, moving objects appear shorter. So if the observer in the rest frame observes a length L for a rod in the moving frame, then L* > L, if L* is the length of the rod in the moving frame. So it must be that L* = γL to correct for the length discrepancy.

I don't know how this error came to light, my guess is that the argument used is incorrect. Please correct me with a logically sound argument if I'm wrong. I also have a text by my side by physicist David J. Griffiths confirming my stand on the issue. If I am correct, then please change it.
P.S. Sorry for all the edits, I just kept thinking of clearer ways to phrase my argument. Woojamon 00:49, 29 April 2007 (UTC)

Please re-read the description in this section again. The clock is at rest in the unprimed system. The observer is in the primed system which is in relative motion w.r.t the unprimed system. The change in time (delta t) in the unprimed system, as observed from the primed system, must be smaller that than the change in time (delta t') in the primed system as observed from the primed system. Thus, the equation is correct. Alfred Centauri 01:00, 29 April 2007 (UTC)

Ah! Well now that it is clear where the observer is located... My apologies, this seems to have been a matter of convention; I was always taught to place the observer in the frame which was chosen as the rest frame. I hope you don't mind if I clarify that in the article like you clarified it here (Especially for the time dilation argument, no reference (that I could tell) was made to where the observer was located).

By the way, sorry about the tag, I'm a newbie on Wikipedia. Can you direct me to a page describing all the tags? Thanks.

Woojamon 01:09, 29 April 2007 (UTC)

Nevermind, did you do more editing than deleting my edit? I could have sworn I didn't read anything about measuring from the moving frame. I've been studying for too long apparently.. Woojamon 01:16, 29 April 2007 (UTC)

I simply used the undo feature. Click on the 'history' tab at the top of the article and then click on the 'diff' link of you choice.

The observer is, by definition, at rest in his frame. As the observer is at rest in the primed frame, the primed time is the time of the observer. To say that the observer is moving w.r.t. the unprimed frame does not imply that the observer's clock runs slower than the unprimed frame. It only implies that there is relative motion between the frames. To the observer in the primed frame, it is the other clock that's moving!

If you feel the text isn't clear on this, then perhaps it isn't clear to others too. Be bold and make your edits. But, don't get to attached to them. As the note says: "If you don't want your writing to be edited mercilessly... do not submit it". Happy editing! Alfred Centauri 01:49, 29 April 2007 (UTC)