Talk:Introduction to special relativity/Archive 1

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Mixing Time Dilation and Length Contraction
An anonymous user very properly deleted this approach (Could this user get an ID?). This is supposed to be a simple introduction so it would be good to get a conceptually simple approach to length contraction. To my shame I went 'too simple' but there must be a simple approach somewhere.

I took out some of the emphatic text added by the anonymous user, I think it may have been directed at me. I also shifted the warnings into the Caveats section, renaming this Caveats and Warnings. Loxley 19:15, 9 May 2005 (UTC)

Sorry for the anonimity. I didn't know one could get a free ID. I have taken an ID now (DVdm)

Good idea to move the warning. I'd like to re-insert the comment about the combination of the two equations. I have seen it happen quite often on the Web, specially by enthusiastic beginners, either to define some sort of invariant "spacetime area" X*T = X'*T', or to derive some sort of "velocity transformation" by comparing X/T with X'/T'. In each case the dilation and contraction equations are combined without realizing that they can only be valid together in the trivial case where all the quantities are zero: x = X = t = T = 0. Okay with you? Yes, its probably a good idea. Loxley 07:58, 10 May 2005 (UTC)


 * The comment in the text of the article that "It can be tempting to combine the equations for time dilation and length contraction to xt = XT or x/t = X/T (1-v^2/c^2), but taking into account the above, the equations can only be valid together in the trivial case when all the quantities are zero: x = t = X = T = 0; in other words, for a rod with zero length that is also a clock that does not tick" is mistaken.


 * Measurements need not be made at x = t = X = T = 0. The observers can have a lattice of synchronised clocks in their own reference frames and can make estimations of length intervals on the basis of X=cT or x=ct. In fact the length contraction equation must be implied by the time dilation equation or otherwise the speed of light will not be constant! Geometer 11:28, 17 October 2006 (UTC)


 * It seems that you missed the point I was trying to make. I have seen many 'casual readers' on the web and on Usenet combine the standard equations $$x = X \sqrt{1 - v^2/c^2}$$ (length contraction) and $$t = T / \sqrt{1 - v^2/c^2}$$ (time dilation) to arrive at what they call an 'invariant spacetime area' xt = XT, or at a 'velocity that transforms like x/t = X/T (1-v^2/c^2).
 * If you combine the two equations for length contraction and time dilation like they are stated here with the Lorentz transformation, you trivially get x = X = t = T = 0 (or of course v = 0).
 * So I restored the paragraph in the article and added a few words for clarification. DVdm 13:15, 17 October 2006 (UTC)


 * So, you do not disagree that x=ct and X=cT can be used to derive the length contraction from the time dilation equation in the case of a flash of light traversing a region of spacetime? If this is the case I will put this into the text instead of the reference to hyperphysics. Geometer 15:56, 17 October 2006 (UTC)


 * I am not sure what you are aiming at.
 * Write the Lorentz transformation and the time dilation and length contraction equations in terms of coordinate differences, i.o.w, t -> dt, x -> dx, T -> dT, X -> dX.
 * The time dilation equation says something about the time differences between two events that are colocal in one frame (e.g. a moving clock as seen in the 'rest frame'): dt = gamma ( dT + v dX/c^2 ) with dX = 0, giving dt = gamma dT.
 * The length contraction equation says something about two events that are simultaneous in one frame (e.g. two ends of a moving rod, as simultaneously measured in the 'rest-frame'): dX = gamma ( dx - v dt ) with dt = 0, giving dx = 1/gamma dX.
 * For two events, these equations are not compatible unless the two events coincide, i.o.w. unless dx = dX = dt = dT = 0 (or the trivial v = 0). That was my point.
 * This is entirely consistent with the current links to Hyperphysics where you can translate my (x,t,X,T) or (dx,dt,dX,dT) into their (L,T,L0,T0).
 * Can you translate and explain what you have in mind in terms of events?
 * DVdm 17:32, 17 October 2006 (UTC)


 * There is a problem with this article because $$\Delta X$$ and $$X$$ are being used interchangeably. What I am saying is that the formula for length contraction can be derived from:


 * $$\Delta t = \Delta T / \sqrt{1 - v^2/c^2}$$


 * in the case of the distance travelled by a flash of photons and because $$\Delta t, \Delta T, \Delta x, \Delta X $$ all apply to the same event It is valid to substitute for T and t from:


 * $$\Delta x = c \Delta t$$ and $$\Delta X = c \Delta T$$


 * so that:


 * $$\Delta x = \Delta X / \sqrt{1 - v^2/c^2}$$


 * To summarise, what I am saying is that for the distance traversed by a flash of photons it is valid to derive the formula for length contraction from the formula for time dilation. I agree that it is not valid to do so in the case of a measuring rod - indeed, the rods observed by two observers in relative motion are not even the same rod, being diffrent slices of the rod's worldtube.Geometer 19:55, 17 October 2006 (UTC)


 * The deltas do not apply to the same event, like you express it. The deltas are differences between coordinates of two events.
 * ( As an iside, when for simplicity the equations are witten without the deltas, the two events in question are (1) the event with variable coordinates like (x,t), and (2) the 'origin event' (0,0). Switching between the two forms is trivial. But this is irrelevant in this context. )
 * So again, what is your point and what are the physical circumstances in terms of events? You talk about time dilation and length contraction and you show some equations. Which time interval between which events is dilated, and which length between which events is contracted? DVdm 20:49, 17 October 2006 (UTC)


 * What I am showing is that the formula for length contraction can indeed be derived from the formula for time dilation.


 * The two events are the emission and reception of a light pulse. Delta t, or t, for short is the time interval between emission and reception observed by one observer, T is the time interval for the same two events, observed by the other observer. The two intervals are related by:


 * $$t = T / \sqrt{1 - v^2/c^2}$$


 * the distance between the events is x for one observer and X for the other. It is valid to insert T=X/c and t=x/c in the equation above in this case. It is not valid in the case of a rod but it is valid in the case of two events involving a light ray. The substitution gives:


 * $$x = X / \sqrt{1 - v^2/c^2}$$




 * QED.


 * You made the point that "if you combine the two equations for length contraction and time dilation like they are stated here with the Lorentz transformation, you trivially get x = X = t = T = 0 (or of course v = 0)". This does NOT apply to the path of a light ray, it applies to the length of rods where the two ends are measured simultaneously. A photon path involves two events, emission and absorbtion. Rod length in our case involves FOUR events ie: simultaneous contact with each end of the rods for both observers. We can get two of these events to coincide for the two observers by arranging the start of the rod to be at a coincident origin but we cannot get the other end of the rod to coincide for the observers. The best we can do is 3 separate events and this is why, for the rod, "you trivially get x = X = t = T = 0 (or of course v = 0)". Of course, with a light ray there are only 2 events and we can indeed use time dilation to derive the formula for length contraction. Geometer 22:57, 17 October 2006 (UTC)


 * Treating x,t,X,T as intervals (i.o.w. omittigng the deltas), the equation $$t = T / \sqrt{1 - v^2/c^2}$$ is only valid if the events of emission and reception are colocal in the (X,T)-frame, i.o.w. if X = 0. If the events of emission and absorption are not colocal, then the time interval in the (x,t) frame is given by $$t = ( T + v X /c^2 ) / \sqrt{1 - v^2/c^2}$$. This is basic. Just check the Lorentz transformation to convince yourself. This already invalidates your 'proof'.
 * But to continue anyway with your next part, you talk about the case of two events involving a light ray, whereas to be able to talk about emission and absorption, and be allowed to use that specific equation, you need two light rays, one with velocity c and another with velocity -c.
 * Again, try to express yourself in terms of well-defined and unambiguous events and their coordinates in both frames. DVdm 18:59, 18 October 2006 (UTC)

(reset indent) Someone introduced this section with "there must be a simple approach somewhere." and I am trying to show that there is indeed a simple approach.

You have, quite reasonably, pointed out that simple approaches are risky and can lead to errors of reasoning. Most importantly you have highlighted the role of phase because in the Lorentz transformation the term:


 * $$\frac{v X}{c^2}$$ varies with location.

Lets investigate how the phase comes into length contraction. If one observer thinks they have measured a length of a thing by placing a measuring rod simultaneously at the two ends of it the other observer sees this operation to be non-simultaneous by the amount of the phase. Using the Minkowski metric:

For observer 1:


 * $$s^2 = X^2 - \Delta T^2$$

but $$\Delta T = 0$$ because the measurement is made simultaneously so $$s^2 = X^2$$

For observer 2:


 * $$s^2 = x^2 - (c \Delta t)^2$$

where delta t :


 * $$\Delta t = \frac{v x}{c^2}$$, the phase difference between clocks at x.

Therefore, because the spacetime interval is invariant ($$s^2 = s^2$$):


 * $$X^2 = x^2 - (c\frac{v x}{c^2})^2$$

so:


 * $$x = \frac {X}{\sqrt{1-v^2/c^2}}$$

Which is the classic formula for length contraction. Notice that length contraction is actually the result of phase. Indeed, in the case of a rod the two observers are measuring two different entities, each rod being a different set of events! All of this supports what you have said and the phase was brought in from the Lorentz transformation so the derivation is not "simple". But can we produce a simple derivation?

The key to the simple derivation is to use the path of a light ray rather than the length of a material object. Consider two observers in relative motion who are coincident at the moment that a light ray is emitted from their joint position. Each observer has a lattice of synchronised clocks in their own frame of reference. The light ray hits a distant point where it is received by appropriate sets of apparatus in both frames.

This setup is a straightforward way of using a light ray to measure distance. Each observer would independently consider that the distance between emission and reception was given by:


 * $$x = ct$$

for observer 1 and, for observer 2


 * $$X = cT$$

The times are read off from the lattice of clocks and the distances apply to the same two separated events (the reception points are coincident). The constant 'c' is the same for both observers so the distances can be compared if $$t$$ and $$T$$ can be compared.

You pointed out that this comparison might be problematic because of the phase term in the Lorentz transformation. This is not a problem for two reasons:

1. Both observers use lattices of synchronised clocks so the time interval recorded by each observer at the reception point is also the time interval recorded by each observer at the respective origins.

2. Phase results in the clocks at the reception point for observer 1 appearing to observer 2 as if they read a time EARLIER than those at the origin when the two observers coincide. In other words, the effects of phase are precisely cancelled out by the conditions at the start of the experiment where the clock at x metres from observer 1 appears to read $$vx/c^2$$ earlier than the clocks for both observers at the origin. This means that the time interval at the reception point is given by:


 * $$t = \frac {T-vX/c^2}{\sqrt{1-v^2/c^2}} - (-\frac {vX/c^2}{\sqrt{1-v^2/c^2}})$$

which gives:


 * $$t = \frac {T}{\sqrt{1-v^2/c^2}}$$

In other words the formula for time dilation applies despite phase. Put in more mathematical language, if X=x=0:


 * $$t = \frac {T}{\sqrt{1-v^2/c^2}} $$

If X>0:


 * $$t_1 = \frac {T_1-vX/c^2}{\sqrt{1-v^2/c^2}} $$


 * $$t_2 = \frac {T_2-vX/c^2}{\sqrt{1-v^2/c^2}} $$


 * $$t_2 - t_1 = \frac {T_2-vX/c^2}{\sqrt{1-v^2/c^2}} - \frac {T_1-vX/c^2}{\sqrt{1-v^2/c^2}}$$

hence:


 * $$t_2 - t_1 = \frac {T_2-T_1}{\sqrt{1-v^2/c^2}}$$

Given that phase is cancelled out because of the circumstances of our particular experiment $$x = ct$$ and $$X = cT$$ can be used to substitute for t and T in the simple time dilation formula to get the length contraction. Geometer 19:37, 19 October 2006 (UTC)


 * However, reading this through again the reader should really understand that the cancellation of the phase term occurs if they are to understand the LT. Hmmmm... Geometer 19:50, 19 October 2006 (UTC)


 * I will only repeat your setup: "Each observer would independently consider that the distance between emission and reception was given by $$x = ct$$ for observer 1 and, for observer 2 by $$X = cT$$. The times are read off from the lattice of clocks and the distances apply to the same two separated events (the reception points are coincident). The constant 'c' is the same for both observers so the distances can be compared if $$t$$ and $$T$$ can be compared."
 * Since you didn't do it, let's see together how your setup translates to events and coordinates. You have two events: an emission event at (0,0) for both observers, and an absorption event labeled (x,t) for observer 1 but labeled (X,T) for observer 2. Both events happen on the light ray with equation $$x = ct$$ for observer 1 and $$X = cT$$ for observer 2. If you understand the LT it should take you less than a minute to verify that the relationships between t and T, resp x and X are then given by the equations
 * $$t = T \frac {\sqrt{1+v/c}}{\sqrt{1-v/c}}$$ resp. $$x = X \frac {\sqrt{1+v/c}}{\sqrt{1-v/c}}$$,
 * which clearly are not the equations for time dilation resp. length contraction.
 * I repeat: in order to have the equation $$t = T / \sqrt{1 - v^2/c^2}$$, you need two events that satisfy X = 0 (and therefore obviously x = v t), and in order to have the equation $$x = X \sqrt{1 - v^2/c^2}$$, you need two events that satisfy t = 0.
 * I don't think one can get simpler, or clearer, or more correct derivations than this.
 * DVdm 13:08, 20 October 2006 (UTC)


 * Well, you seem to have derived the formula for the doppler effect, see doppler effect. See Hyperphysics - page down for time dilation where there is a nice graph showing a clock ticking away at a location remote from the origin that has the formula that I gave above. Notice that the ticking clock is NOT at x=0 yet the time dilation equation still applies because the phase terms cancel. Another, intuitive way of conceptualising the time dilation is to consider lattices of synchronised clocks. The clocks move on parallel paths in each reference frame and allow the time at the reception event to be referred back to the worldlines of the observers. You would agree that the time dilation equation describes the relationship between time intervals on the observer's worldlines. You would need to demonstrate that the times on the synchronised clocks at the reception event and hence the corresponding times on the worldines of the observers are not related by the time dilation formula to prove your point. Geometer 16:26, 20 October 2006 (UTC)


 * Well, you seem to have provided the setup to derive the formula for the doppler effect, see doppler effect. See Hyperphysics - page down for time dilation where there is a nice graph showing a clock ticking away at a location remote from the origin that has the formula that I gave above. Notice that the ticking clock is NOT at x=0 yet the time dilation equation still applies regardless whether the phase terms cancel, whatever that might mean. Also notice that the ticking clock is at X = 0. Translation legend: (x,t,X,T) or (dx,dt,dX,dT) into their (L,T,L0,T0). DVdm 16:48, 20 October 2006 (UTC)


 * Whether the clock is at X=0 or not, it is definitely not at x=0 so your argument that "in order to have the equation $$t = T / \sqrt{1 - v^2/c^2}$$, you need two events that satisfy X = 0 (and therefore obviously x = v t)" is not true; x does not equal vt in the hyperphysics example (or mine).Geometer 17:05, 20 October 2006 (UTC)


 * The clock is at rest in the (x',t') system, so it is moving at velocity v, so the two events have x' = x1' = x2', so it has dx' = 0. This translates to X = 0 in my variables. For your benefit, I will repeat again, but for the last time: In order to have the equation $$t = T / \sqrt{1 - v^2/c^2}$$, you need two events that satisfy X = 0 (and therefore obviously x = v t). DVdm 17:31, 20 October 2006 (UTC)


 * The two events are the synchronising of clocks when x=X=0 for the observers,


 * ==> That is one event. DVdm 14:33, 25 October 2006 (UTC)


 * however, the distant clocks located where the light is received, do not need to be at x=0 or X=0.


 * ==> Of course they don't. DVdm 14:33, 25 October 2006 (UTC)


 * I am not repeating this for your benefit but for the benefit of the article. The article needs a simple presentation of length contraction.


 * ==> I hope you don't think your 'derivation' was simple. I also hope you don't think it was right. DVdm 14:33, 25 October 2006 (UTC)


 * You are opposing this but for the wrong reasons. Reviewing the derivation given above I believe the the best approach would involve an independent derivation of the phase term. Geometer 10:40, 25 October 2006 (UTC)


 * ==> Well, it's now clear to me that you have no idea what you are talking about. That is why I am opposing this. Sorry for having wasted your time. DVdm 14:33, 25 October 2006 (UTC)

Doesn't this belong in Wikibooks? Oberiko 15:32, 18 Mar 2005 (UTC)

 * I had the same misgiving. (I notice you didn't say "this text belongs in Wikibooks!".) I agree with you, this article is on the edge. There are two questions here however firstly, how far should an encyclopedia explain its topics and secondly what is the minimum coverage required to provide any sort of explanation at all? I think this article is a minimal rendition of special relativity in such a way that the theory is explained. The difficulty here is that the theory is conceptually challenging for most people. Loxley 17:30, 18 Mar 2005 (UTC)


 * I think this material is excellent for Wikipedia but I'm not keen on the equations. Surely a text-only version would suit beginners better. However, all-in-all, I think this is a good article - Adrian Pingstone 19:48, 18 Mar 2005 (UTC)


 * This is a great article. Although I do agree that it would be a pretty weird article to find in a real (print) encyclopedia, I think it's great. -Haon 12:32, 13 October 2005 (UTC)


 * I agree that it belongs in Wikibooks. --Doradus 14:27, 14 February 2006 (UTC)

'c' as a conversion constant
The beauty of Minkowski's four dimensionalism is that it explains why there is a constant velocity for all observers. If a thing travels at a velocity such that its space-time interval is zero then all observers, no matter how fast they are travelling, will observe the thing to be travelling at c metres per second. This is why Minkowski's and the modern approach, is more fundamental than Einstein's original 1905 approach which relied on an assumption (based on the Lorentz invariance of Maxwell's equations)that the speed of the propagation of light in a vacuum is constant. Although Einstein's postulate that the speed of light is constant is correct it confuses students utterly. They go off and ponder how such a thing could occur and, being no Einsteins, and being equipped with no more than school physics, reject the whole of relativity theory. The modern approach overcomes this problem because it predicts that there is a universal constant velocity. In advanced texts 'c' is often not used at all because lengths are specified in light seconds rather than metres. Loxley 10:46, 24 Mar 2005 (UTC)

Thanks
I'm generally very critical of the Wikipedia project. But really, Thanks for this article, it's really good.


 * I also think this is an excellent article. I'm fluent in mathematics but not physics. After reading this article I realize now that I never understood special relativity before, and think I do now. Wow, we don't live in Euclidean space-time, we live in Minkowski space-time - mind blowing stuff! There was however one point in the article that I found confusing.


 * So: $$-(cT)^2 = (vt)^2 - (ct)^2$$


 * I couldn't work out why this is so. If I understand correctly it might be clearer to write


 * So because length is invariant in space time: $$-(cT)^2 = (vt)^2 - (ct)^2$$


 * (e.g. length is invariant under a change of frame of reference, so the length of Bill's space-time interval should be equal from both Bill's and John's point of view). BTW I loved the math.

Why i ?
I think this article needs more information about why there is a i in $$s^2 = x^2 + y^2 + z^2 + (ict)^2$$ There is at least one person (me) that doesn't get it.
 * Minkowski included the 'i' because Euclidean geometry applies on the surface of a sphere of imaginary radius. He reasoned that given that Euclidean geometry seems to apply in our local space then this was due to events being projected so that the observer is at the centre of a sphere of radius $$ict$$. In the first year or two after Minkowski's proposal it was probably believed that the observer at the centre of the sphere was no distance from the surface ie: $$0 = x^2 + y^2 + z^2 + (ict)^2$$ (if we put $$r^2 = x^2 + y^2 + z^2$$ it becomes obvious that $$0 = r^2 - (ct)^2$$).  However, mathematicians had long known about non-Euclidean geometry and realised that you can get an almost identical result using real rather than imaginary time and proposing that the universe is entirely non-Euclidean. See the reference about the non-Euclidean form of relativity at the end of the main article. loxley 16:11, 2 August 2005 (UTC)

Too technical?
"Special relativity for beginners" is an introduction to special relativity for those who are just embarking on the subject. The article as it stands assumes a knowledge of Pythagoras's Theorem and the language, apart from the technical terms, is probably about reading age 18. Someone with a less accomplished mathematical and conceptual background could indeed understand that Special Relativity is an important theory that is complicated but could they really understand Special Relativity at all? If you think they could then perhaps we need a "non-technical relativity" article loxley 09:50, 5 August 2005 (UTC)

I think this is a very good article. However it could use in my opinion an extreamly basic introduction or section giveing a general idea of the theory for younger people, not prepaired for the math end.

This is a good article. I think it's sufficient; I'm 15 and can understand this easily. However, I'm nominating this for articles for deletion in order to drive home the point that this should be merged - the special relativity article should contain this material - forks are bad for the project. Furthermore, all articles should be approachable by anyone, even if it's about a complex subject - we approach increasingly complex subjects by having daughter articles. -- Natalinasmpf 16:44, 17 November 2005 (UTC)


 * Please see Don't disrupt Wikipedia to make a point. AFD shouldn't be used to propose mergers.  It's also possible this will actually result in the article being deleted; if you like the article's content, this is presumably not what you want to happen.  &#8227; &#5339;&#5505;  [[Image:Venus symbol (blue).gif|&#9792;]] [ &#5200; ] 23:30, 17 November 2005 (UTC)

I think that the article is too technical to be called an "introduction". We need something that is extremely simplified, just so that people who dont have the necessary background knowledge can understand special relativity.


 * Yes, I think this article is too technical; it presumes a current fluency in higher mathematics. Nonetheless, a more detailed treatment of this and related subjects than that provided for by certain PBS programs that treat these concepts in a manner that is just too conclusory and glib-even trendy, blithely asserting certain notions as received dogma.  Thus that you are not pandering to the gullible and credulous is appreciated.  It shows that you take your subject matter and potential readers with some seriousness.  However, someone whose primary background is in the social sciences and humanities and whose last math course was college pre-calculus decades ago should be able to apprehend this topic to a greater degree and would be a more effective pedagogical strategy.  Thanks so much.Tom Cod 02:06, 4 November 2006 (UTC)

Are intervals in space-time imaginary quantities?
The example given in the beginning (i.e. a body travelling at velocity v) is applied in the very special case of v=c, from which it is shown that for a body travelling with velocity c any interval is zero. But if we look at the trivial case v < c, then S = sq.rt ( t**2 ( v**2 - c**2 )) = t sq.rt ( v**2 - c**2 ) which is an imaginary quantity! Does it mean that all simple movements in our world are imaginary? Demaag


 * Even if time were imaginary the determination of a complex length is problematical - we must not forget that the length is a vector - See complex number. However, the current wisdom is that time in GR is real and that displacements are bilinear forms governed by a metric tensor. This gives very similar results to imaginary time but involves a curious arrangement of two coordinate systems. Unfortunately most articles on differential geometry miss out a detailed discussion of the derivation of the metric tensor (cf: the work of Carl Friedrich Gauss) and hence fail to explain things properly - probably because the tutors do not want students rushing off at tangents. loxley 08:53, 30 August 2005 (UTC)

This is for beginners???
This is for beginners??? Beginners what? Beginners 2nd year honours physics degree? I seem to have a different idea of "for beginners". I would mean to be for a layman and a general reader.

We need more non-technical, layman's guides in science here. I really feel we are writing for ourselves and our peers too much, not for the real audience.

And, FWIW, I am a physicist!

Paulc1001 08:08, 6 October 2005 (UTC)


 * I largely agree with you; it may however be a useful introduction for beginners with a mathematics background. Thus, I'd rename it: "Special relativity for mathematicians".
 * Harald88 18:40, 17 November 2005 (UTC)

The problem is that the intellectual spectrum between school physics and tensor math is huge. This article is half way along the spectrum. Why don't you mock up a "Special Relativity for Absolute Beginners" here? loxley 14:38, 6 October 2005 (UTC)

Loxley, you're right and that's a problem alright. But it can't be a harder problem than the Physics itself I guess! Even Hawking wrote a book with just a single equation in it. Actually, I was thinking of those without even high school physics, that's quite a lot of people! :-)

Writing such a simplified article is exactly what I intend to do, that's how I came here in the first place. I'm already doing this elsewhere and I plan to extend it to as many technical articles as possible (not just in Physics, I'm an ex-physicist now and have very broad interests) eventually when I can get the time.


 * I agree. It should be written on a level not too much higher than that which would allow it to be printed in the back pages of the science section of the New York Times or the Wall St. Journal; that is an educated "general reader" without a current background in math or technology should be able to credibly struggle with this "introductory" treatment.Tom Cod 02:15, 4 November 2006 (UTC)

Wanna help??:-) Paulc1001 17:45, 6 October 2005 (UTC)

Hi, just thought I'd make sure everyone here knows about WikiProject:General Audience. &#8227; &#5339;&#5505;  [ &#5200; ] 23:18, 17 November 2005 (UTC)

Title alternatives
It's been suggested "for beginners" may not be the best title. If the consensus feels the article should be renamed, what should the new title be? &#8227; &#5339;&#5505;  [ &#5200; ] 23:11, 17 November 2005 (UTC)

Suggestions:
 * special relativity (nontechnical), possibly accompanied by special relativity (simple)
 * special relativity (simplified)
 * special relativity (general audience)
 * special relativity for mathematicians
 * I hope no-one will mind me repeating a couple of suggestions from the AfD:
 * Space-time invariance and four dimensional manifolds in the early evolution of Relativity Theory
 * or, to my mind the more snappy:
 * Space-time invariance
 * Minkowskian relativity
 * My preference is for "Space-time invariance" because, whilst not all the truth in the article, it does capture its essence. Sliggy 00:07, 19 November 2005 (UTC)


 * Indtroduction to Special Relativity - a beginner has no idea what invariance is - this title is much more succinct--Ewok Slayer 22:44, 20 November 2005 (UTC)


 * I'll second this suggestion. It keeps the gist of the current title, but is more respectful of the reader and of the topic. --EMS | Talk 18:37, 21 November 2005 (UTC)


 * I think "space-time invariance" is not really accurate anyway. The invariant being considered is not spacetime, but "invariant length" or "proper time" (depending on whether you're looking at a spacelike or timelike path). But invariance of invariant length just sounds silly, and invariance of proper time sounds like a poem written in the 1970s.
 * Introduction to special relativity might not be bad (please, no extraneous capital letters, though). --Trovatore 18:50, 21 November 2005 (UTC)
 * Minkowskian relativity or The Minkowskian interpretation of special relativity is most accurate. What about a redirect from Special relativity for beginners to The Minkowskian interpretation of special relativity with a link from this (on the second line) to a plain english description (yet to be written)?.loxley 19:29, 21 November 2005 (UTC)


 * To me the word "Minkowskian" carries other baggage, such as the "block universe" idea in which the entire history and future of the universe exists all at once, with determinism as a consequence. I don't think that notion has much relevance to this article. (But maybe that connection is just an error on my part?) --Trovatore 19:37, 21 November 2005 (UTC)
 * Geometrical foundations of special relativity? loxley 10:31, 23 November 2005 (UTC)


 * or maybe Geometrical explanation of special relativity? Harald88 12:03, 23 November 2005 (UTC)
 * Geometrical explanation of special relativity or Geometrical interpretation of special relativity? I could go with either, with a redirect from Relativity for beginners. It should really be prefixed with the indefinite article "A geometrical..." to show that other interpretations are possible but this has been covered briefly in the "caveats" section in the article. loxley 20:05, 24 November 2005 (UTC)

What happened to the illustrations?
At various points the article talks about illustrations, but there are none! What happened to them? Loom91 09:48, 16 March 2006 (UTC)

This article title needs to go
This article has already been transwikied to Wikibooks:Transwiki:Special relativity for beginners, although some months ago and no doubt not the latest version. The title is not encylopedic, and there is no reason to have both this article and Special relativity. The question is, do you all want to merge this, just make this a redirect, or what? An AfD vote will, in my opinion, almost certainly result in merger with special relativity. --Xyzzyplugh 15:06, 22 March 2006 (UTC)
 * Ok, in looking around some more, it turns out there was an AfD done, although for some odd reason it is not mentioned in this talk page as it should be. And it seems that the content of this article might be different enough from the Special relativity article that this one could simply be renamed.  If that's the case, it should be done, as this article title is not encylopedic.  --Xyzzyplugh 17:06, 22 March 2006 (UTC)

The light clock example
A simple explanation of time dilation using the Light clock example.--Zachblume 20:36, 6 July 2006 (UTC)

Please something simple - not like this
Read the first version of the article on the special relativity - I can understand it pretty easily. I don't understand this "intro" at all. I'd suggest to use one of the first versions of the special relativity article, before it became that unreadable mix of equations, as the intro.


 * I thought a lot of this article made sense (and no, I'm not an expert on special relativity). Mo-Al 18:10, 10 August 2006 (UTC)


 * You would do well to provide a link to the specific version you consider to be a baseline. For example, the this link is for the initial version of special relativity.  I will admit this version is simpler and easier to understand, but it is more an essay about SR then a coherent description of it.  It glosses over many features of the theory, and fails to present the postulates of SR at all.  For all of its faults, the current special relativity page is much, much better than this.


 * I will admit that much can be done with these pages. The SR page is serious need of a rewrite to create an organized, coherent, and unified presentation of the theory; while this page needs to do more to bridge that gap between Newtonian physics and SR itself.  (However, it does do a good job of presenting SR as a geometrical theory.)  --EMS | Talk 18:23, 10 August 2006 (UTC)


 * I think, that there should be some really easy explanation of the theory. There are people just asking "What's the SR all about?". They are not interested in Lorentz transformations and all this stuff. I can tell it from my point of view: I knew, there was something about the time and length shortening and systems in relative motion. I wanted to know, what's going on in more detail. I started with the current version of SR and it was a pain. Then I opened the first version of the SR article - and I finally started to understand it in 5 minutes. Is it really necessary to have equations to tell that time and dimension isn't absolute?


 * The "introduction" looks like this:
 * Michelson-Morley experiment - why?
 * Minkowski space, equations, diagrams, invariant, euclidean space... - WTF?
 * John and Bill: $$s^2 = (vt)^2 - (ct)^2$$ - I'm lost


 * --Herr.Schultze 08:00, 11 August 2006 (UTC)


 * Herr.Schultze does not like this article because it seems too technical. As far as I can see all it does is to introduce relativity as a modification of Pythagoras' theorem. This is not technical unless it is considered that the "square on the hypoteneuse equals the sum of the squares on the other two sides" is technical. To my mind the article has the minimum amount of technical detail consistent with explaining relativity, any less and there is no explanation, just waffle. Geometer 08:52, 27 September 2006 (UTC)

Replace this article
I suggest to replace this article, which I believe isn't a non-technical introduction at all, with this one: special relativity - simple explanation. I created it as a working version from the very first special relativity article which is excellent in explaining the topic, simply and quickly. I think that the article should be readable by all people, and that special relativity can be explained that way.--Herr.Schultze 18:29, 11 August 2006 (UTC)


 * This is not intended to be a non-technical intro. It is a technical intro with the simplest maths possible. As such it actually explains relativity which "simple explanations" are notorious for failing to do.


 * I would caution readers of this "Talk" that there is a vigorous group of people who regard the four dimensionalism of relativity as an entirely incorrect idea, largely for religious and philosophical reasons. Just look at newsgroups on relativity which are plagued with postings from people who are almost violently antagonistic to relativity. The article on presentism provides some insight into the religious background to this debate. Geometer 09:01, 27 September 2006 (UTC)


 * I thought this article did a good job of explaining it - I don't see why there needs to be a replacement. Mo-Al 17:13, 11 August 2006 (UTC)
 * Einstein once said that "things should be as simple as possible, but no simpler". This "simple explanation" is a gross violation of the second part of that edict.  Additionally:
 * The Lorentz transformations are not a correction term, but instead are a replacement of the Galilean transformations of classical mechanics.
 * Applying the Lorentz transformation to "all of Newtonian physics" is an oxymoron. SR is a replacement of Newtonian physics/classical mechanics, not a repair of it.
 * The view that all motion is relativity was orignated by Galileo, not Einstein. It is Einstein's desire to find laws of physics such that Maxwell's equations of electromagnetism and a constant speed of light could co-exist with Galileo's principle of relativity that led to the creation of SR and eventually gane it its name.
 * I could go on, but those are the most major flaws. I assure you that if the older article on which you based this "simple explanation" was at all valid that I would support it.  However, it is poorly organized, misdirected and overly condenses the subject even when it is not just plain wrong.
 * I know that this article is not easy reading, but it will give you a good sense of what is going on. If you want to create a non-technical description of SR, then go ahead, but please use established sources and not that old and incorrect version of the special relativity article.  Look at it this way:  An incorrent and misleading article is worse than no article at all. --EMS | Talk 17:50, 11 August 2006 (UTC)
 * So your point is, that the curent introduction is the simplest we can have? You have written 3 things that are major flaws according to you. Why not correct them in the proposed article and use it?--Herr.Schultze 18:29, 11 August 2006 (UTC)
 * While I agree with many of EMS's points, I have to say that as of this moment, the "simple explanation" seems to me to be a better starting point for improvements to a simple version of the special relativity article than the introduction article. The introduction article jumps right in to trying to explain Minkowski space, which while extremely useful and nice mathematically, particularly in view of how general relativity would follow special relativity, it's also not necessary.  In fact, I think the introduction article eschews some of the physics while spending an inordinate amount of time on Minkowski space and ideas and concepts associated with it.
 * Of course, the simple explanation article at the minimum needs polishing, but I believe it's basic approach, at least in the material it attempts to cover and the way it attempts to cover it, is superior to the introduction article. That's my two or fifty cents.  :) DAG 18:34, 11 August 2006 (UTC)


 * I've seen complaints about the complexity of this article in this discussion. I don't consider it to be a good introduction to the topic as it's very difficult to understand. If people don't understand it, then I can't tell it does a good job of explaining it. The fact, that I can understand some explanation doesn't mean that others understand it. Articles on Wiki are not only for me and are not only for you. Is your argument supposed to be Only a few people don't understand it, so it's a good article?--Herr.Schultze 18:29, 11 August 2006 (UTC)


 * Let's take your gripe apart a bit. In terms of describing Minknowski spacetime, this is a good article.  It is not easy to understand but does what it does well.  OTOH, an "introduction" should be easy to understand, and this text is duplicated in Wikibooks, a place that it is more suited to.  So the issue should not be replacing this article, but rather what it is replaced with.
 * I would not mind seeing a non-technical treatment of SR here. However, I figure that others would be better suited to producing it (or at least the initial treatment) since I know a lot about SR and that makes me a terrible person for writing an article for the general public on it.  (I also have plenty of other projects to deal with and have no time for doing a rewrite of this article anyway.)
 * As for the proposed "simple explanation" above -- Please, please do not use it at all!!! You need to start from a clean sheet of paper, using reasonable insights from this article and the special relativity article itself.  That old Wikipedia article is about as bad as an SR article can be.  Someone needs to just plain start over again and use their own words.  If that does not work, then someone else can give it a shot.  Once someone puts together a good foundation, I can help to flesh it out a bit.  Just realize that Wikipedia articles are a bit like buildings:  You cannot create a good one when you are starting on a bad foundation. --EMS | Talk 20:03, 11 August 2006 (UTC)


 * Lets start with the purpose of this article: It is linked as a non-technical introduction. It is not a non-technical introduction at all. It is labeled as an introduction to special relativity and it's mainly a description of Minkowski spacetime. This article uses mathematics of a certain level, not words to describe the basic principles. Normal people do not use math, when they explain things to each other. It uses SR terminology too much. So it is useless for people with only a general knowledge new to SR. And for the people, who can read it, there's is no reason to read it instead of the primary SR article. So it is mislabeled and incorrectly linked as a non-technical introduction. Is the target audience mathematicians? One of your previous comments about the simplicity seems to imply unless you are a mathematician you cannot understand SR. I do not agree with this approach. People who come to this article are interested in "that famous theory of relativity" and what they get? Minkowski spacetime and load of equations. I strongly doubt they get through the first half of the article.


 * I'm afraid, that using any part of this article in any future version of introduction to SR is a very bad idea. Even the primary SR article gives better SR overview and explanation than this one. This article doesn't try to simplify things, give an overview and explain SR, it just discusses some terms related to SR. If simpifying the SR is a bad thing, then there's no reason for any introduction and we can tell all the people who are just curious, what it is about, to go away, that they cannot grip it without understanding the math behind it.


 * Please try to be more specific about the proposed article. Could you take it by paragraph and write, what is incorrect? Could you describe, what negative result it would have if a person new to the topic reads it?


 * Do you think, that the idea of SR can be described without equations?--Herr.Schultze 08:30, 12 August 2006 (UTC)


 * All that I am going to say about the proposed article is that it is a complete piece of trash. Nothing more needs to be said about it.
 * "Can SR be described without equations?" The answer to that is "No".  At the least, it cannot be described well without equations.  But can the use of equations be minimized?  Can the equations be explained for a non-mathematical reader?  For that I would say "yes".
 * If you want an outline for an introductory SR artcle, here it is:
 * What is SR? (It is a theory of space and time created by Einstein in 1905.)
 * What are its postulates? (The principle of relativity and the constancy of the speed of light.)
 * What inspired SR? (Note the incompatibility of Maxwell's equations with Newtonian physics, and the failure of the luminiferous aether model due to the Michelson-Morley experiment.)
 * How does it differ from Newtonian physics?
 * Explain the constancy of the speed of light. (Note that for a car moving at 1 m/s towards you, if the driver sees the light from his headlights moving at 299,798,458 m/s, that you should see that light going past you at 299,798,459 m/s. Instead you also see it moving at 299, 798,458 m/s.)
 * Note time dilation. The time dilation equation can be used here.  $$\left[t' = t \sqrt{1-v^2/c^2}\right]$$.
 * Note length contraction. (A similar equation can be used here.)
 * Note the relativity of simultaneity. This is very hard to describe, but is also very, very important.  Perhaps the use of Einstein's railroad exercise is needed here, with illustrations.
 * Compare the Galilean transformations and the Lorentz transformations. At this point, the previous text should have given the reader enough of a gounding so that this will make sense given a careful explanation of the terms (which is what an introduction should be doing).  Also note that the equations should be supported by the text, and not the other way around as is currently the case.  (That will make a big difference alone.)
 * What are the consequences of SR?
 * Note the inability to travel faster than the speed light with respect to another observer.
 * Note the related increase in mass for a moving object.
 * Note E=mc²
 * Note energy and momentum laws.
 * Describe the "twin paradox" and its resolution.
 * Note the user observer dependency of the theory. (You can exchange the "moving" and "stationary" frames of reference.)
 * Note the geometrical nature of the theory. (The Minkowski metric would be presented here, but not dealt with in detail.)


 * Hopefully you now see what needs to be accomplised in this article, and how that proposed "simple explanation" utterly fails to do so. Of course, the current article also fails to do these things by virute of being too technical.  So if someone wants a better article, do some research and build on my outline.  Most importantly, don't bother trying to use the old version of the special relativity article.  If it was any good, a similar article would still be present in Wikipedia.  None is, and I am not going to tolerate the presense of such a thing. --EMS | Talk 19:20, 12 August 2006 (UTC)

(reset indent) - As the article was earlier marked for prod, I have sent it to AfD to generate consensus. Please have your say there. - Aksi_great (talk - review me) 17:41, 13 August 2006 (UTC)

Invariance of time intervals
This article seems to jump to the conclusion that time intervals are invariant. Maybe the explanation is too technical, but shouldn't it at least be suggested? Mo-Al 14:34, 31 August 2006 (UTC)


 * The article says that space-time intervals are invariant. Geometer 09:07, 27 September 2006 (UTC)

Text in images
Many of the images in this article contain images with text in them. New images should probably be created without the text, so that the text can be placed in the article, and will become editable. Mo-Al 14:37, 31 August 2006 (UTC)

This is a less technical introduction, not a non-technical introduction
This should be made clear so that it is not mistakenly removed because it contains complications such as school maths. An introduction that explains SR is essential in any description of the subject. Geometer 09:07, 27 September 2006 (UTC)

I added the sentence that suggests that readers should at least understand Pythagoras' theorem before reading this article. It included a referece to Weyl's famout book, Space, Time, Matter in which he describes SR as an extension of Pythagoras and wrote the "equation": PYTHAGORAS + NEWTON = EINSTEIN. Geometer 10:11, 9 October 2006 (UTC)


 * I removed the first sentence. You can just as well say that special relativity is based on 1+1=2. DVdm 12:27, 14 October 2006 (UTC)


 * The point of the first sentence was to pre-empt discussions such as those in the sections above. People are surprised that SR demands a knowledge of squares and square roots. The introductory paragraph points out that squares and square roots are required. And, yes, SR does require a knowledge of 1+1=2 as well as a knowledge of Pythagoras' theorem but 1+1=2 does not stretch the casual reader whereas Pythagoras' theorem seems to be beyond many.


 * In fact the link to Pythagoras' is more profound than being just a requirement for knowledge of squares and square roots, the differential geometry that describes SR is an extension of Pythagoras' theorem.


 * I am not going to revert the first paragraph again. It would help the casual reader and prevent the comments about the level of treatment being too complex. I believe it really clarifies the text. Perhaps you, or some other editor, could reinstate it? Geometer 18:29, 15 October 2006 (UTC)


 * This is the text that was cut:


 * "Special relativity is a physical theory based on a particular extension of Pythagoras' theorem and an elementary knowledge of the mathematics of squares and square roots is required to understand it."


 * As I'm convinced that to the 'casual reader' that paragraph is bound to give the impression that special relativity can be understood if only one understands squares and square roots, I'm definitely not going to restore it. If you already haven't, do have a quick look at Usenet's sci.physics.relativity. The place is crammed with 'casual readers' who can just handle squares, square roots and Pythagoras' theorem, and therefore think that they can 'improve' upon the theory - if not 'debunk' it altogether, whereas in fact they haven't got a clue about upon what the theory is really based. They just blindly juggle with equations and have no idea what they are doing. Even on these talk-pages we notice this same behaviour.
 * I think that the paragraph you are trying to push lies at the very heart of most of the misconceptions and discussions you want to pre-empt. Special relativity is based on physical postulates, not on elementary mathematical functions and a mathematical theorem. DVdm 20:59, 16 October 2006 (UTC)


 * All that the paragraph says is that SR is a Physical theory and that the reader will need a level of mathematical knowledge suitable for dealing with Pythagoras' theorem. It says that so that people wont be misled into believing that it can be understood without any mathematical insight. It cant! Just look at the entries in this discussion, there are endless gripes that this introduction is too mathematical - the bad news is that SR demands a minimum level of maths such as are needed by school kids to deal with Pythagoras.


 * You say that I am trying to "push" something. Please explain clearly what it is that I am pushing and what the alternative might be. Geometer 22:57, 16 October 2006 (UTC)


 * I think I made that sufficiently clear. I'm not going to comment on it further. DVdm 12:31, 17 October 2006 (UTC)

How is Minkowski space different from Euclidean 4-space?
I am understanding this article until the sentence "It is this difference in metric signature that causes the principal difference between geometry in a four-dimensional Euclidean space and geometry in the four-dimensional Minkowski space." I do not know how to derive the formula for Pythagorus' theorem in four dimensions, but that does not hinder my understanding of Minkowski space thus far. Although it would be nice if you could embed a link to another Wikipedia article explaining how to derive it if one exists. Where I am stuck is how the Pythagorean theorem in Minkowski space is different from the Pythagorean theorem in four dimensional Euclidean space. Perhaps if I can understand this, I can understand the rest of the article.

--Chris256 02:47, 24 October 2006 (UTC)


 * The key idea is that when using the metric (call it $$g_{\alpha \beta}$$), the dot product becomes $$ g_{\alpha \beta} x^\alpha x^\beta$$, using Einstein's summation convention (there's a summation over repeated indices). ((And yes, I know you want to know about Pythagoras, but bear with me... :) )  So, in 3D Euclidian space, the metric is the the kronecker delta $$\delta_{\alpha \beta}$$, or in matrix form it's the identity matrix.  This means the dot product is $$x^2 + y^2 + z^2$$.  The length of a vector is the square root of this (and that's where you get to Pythagoras, which is the length of a vector is the square root of the dot product of a vector with itself).  Now, in Euclidian 4-space the metric is still the kronecker delta (or in matrix form the identity matrix), except including the time component.  That would mean the Euclidian 4-dot product is $$c^2 t^2 + x^2 + y^2 + z^2$$.  However, in Minkowski space, the metric is not the kronecker delta and can't be represented in matric form as the identity matrix.  The metric has a minus one in place of a plus one in the position $$g_{t t}$$ (though actually things work out the same if you make the time part positive and the x, y, and z parts negative...  it's just a convention).  So, the dot product in Minkowski 4-space becomes $$-c^2 t^2 + x^2 + y^2 + z^2$$.  This doesn't change the former assertion that the length of a vector is the square root of the dot product.  So the length of a vector in Minkowski space, which has acquired the name of space-time interval, is just the square root of the dot product $$-c^2 t^2 + x^2 + y^2 + z^2$$ (you can think of this as a kind of Pythagoras's theorem in/for Minkowski space).  I hope this helps.  DAG 03:36, 24 October 2006 (UTC)


 * Another reply to Chris256 (a bit more down to earth):
 * Imagine someone with a clock and a rectangular coordinate system (x,y,z). He measures the coordinates of event1 as (x1,y1,z1) at some time t. He measures the coordinates of event2 as (x2,y2,z2) at the same time t. So, if you like, you could say that the 4D-coordinates of the events are (t,x1,y1,z1) resp. (t,x2,y2,z2). Until a bit more than a century ago we used to think that the quantity $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2$$ between these events was independent of the coordinate system. Since this thing is positive, we can take the square root of it and give it a name. According to Pythagoras' theorem this is the length of the vector between the two places of the simultaneous events. So we thought this length was observer independent. It turned out that this is not the case. By the very way we measure these coordinates (i.e. radar method or system of rods and synchronized clocks, both equivalently assuming the constancy of light speed), we can no longer trust the assumption that the simultaneity of the events is valid for everyone. In general, if event1 and event2 are simultaneous for one observer, they are not necessarily simultaneous for another, and thus the so-called "time coordinate" of an event obviously will depend on the observer who measures it. So for our arbitrary observer, event1 has coordinates (x1,y1,z1) at time t1, and event2 has coordinates (x2,y2,z2) at time t2. Again, if you like, you could say that the 4D-coordinates of the events are (t1,x1,y1,z1) resp. (t2,x2,y2,z2). But that is hardly important. What is important, is that it turns out that the quantity $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2-c(t2-t1)^2$$ is independent of the observer. If it so happened that $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2+c(t2-t1)^2$$ had been invariant, then we would have said that empty "spacetime" was Euclidean. But it isn't. We're stuck with this minus sign. Since Minkowski was one of the first to ponder over this, we ended up talking about Minkowski-spacetime or spacetime with a Minkowski metric, or spacetime with a pseudo-Euclidean metric... Don't let the names we give to things confuse or mislead you... DVdm 10:34, 24 October 2006 (UTC)
 * Imagine someone with a clock and a rectangular coordinate system (x,y,z). He measures the coordinates of event1 as (x1,y1,z1) at some time t. He measures the coordinates of event2 as (x2,y2,z2) at the same time t. So, if you like, you could say that the 4D-coordinates of the events are (t,x1,y1,z1) resp. (t,x2,y2,z2). Until a bit more than a century ago we used to think that the quantity $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2$$ between these events was independent of the coordinate system. Since this thing is positive, we can take the square root of it and give it a name. According to Pythagoras' theorem this is the length of the vector between the two places of the simultaneous events. So we thought this length was observer independent. It turned out that this is not the case. By the very way we measure these coordinates (i.e. radar method or system of rods and synchronized clocks, both equivalently assuming the constancy of light speed), we can no longer trust the assumption that the simultaneity of the events is valid for everyone. In general, if event1 and event2 are simultaneous for one observer, they are not necessarily simultaneous for another, and thus the so-called "time coordinate" of an event obviously will depend on the observer who measures it. So for our arbitrary observer, event1 has coordinates (x1,y1,z1) at time t1, and event2 has coordinates (x2,y2,z2) at time t2. Again, if you like, you could say that the 4D-coordinates of the events are (t1,x1,y1,z1) resp. (t2,x2,y2,z2). But that is hardly important. What is important, is that it turns out that the quantity $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2-c(t2-t1)^2$$ is independent of the observer. If it so happened that $$(x2-x1)^2+(y2-y1)^2+(z2-z1)^2+c(t2-t1)^2$$ had been invariant, then we would have said that empty "spacetime" was Euclidean. But it isn't. We're stuck with this minus sign. Since Minkowski was one of the first to ponder over this, we ended up talking about Minkowski-spacetime or spacetime with a Minkowski metric, or spacetime with a pseudo-Euclidean metric... Don't let the names we give to things confuse or mislead you... DVdm 10:34, 24 October 2006 (UTC)


 * Thanks for the replies. I guess I should have asked the question "why is Minkowski space different from Euclidean 4-space?"  Or why is spacetime not Euclidean?  I want to know how Minkowsi figured out that "ic" is the conversion constant for time to be entered in as just another diminension.  After re-reading the discussion for this article, I think that this question has been posed before.  I just had a hard time accepting the metric tensor without proof.  The Pythagorean theorem has hundreds of proofs.  I want to see a proof of the Pythagorean theorem for Minkowski space.  Moreover, I just want to know why.  It just seems like too many things are coming out of the blue without any explanation.
 * Thanks for the replies. I guess I should have asked the question "why is Minkowski space different from Euclidean 4-space?"  Or why is spacetime not Euclidean?  I want to know how Minkowsi figured out that "ic" is the conversion constant for time to be entered in as just another diminension.  After re-reading the discussion for this article, I think that this question has been posed before.  I just had a hard time accepting the metric tensor without proof.  The Pythagorean theorem has hundreds of proofs.  I want to see a proof of the Pythagorean theorem for Minkowski space.  Moreover, I just want to know why.  It just seems like too many things are coming out of the blue without any explanation.


 * Start from the Lorentz transformation
 * $$\Delta t' = \gamma (\Delta t - v/c^2 \Delta x)\,$$
 * $$\Delta x' = \gamma (\Delta x - v \Delta t)\,$$
 * $$\Delta y' = \Delta y\,$$
 * $$\Delta z' = \Delta z\,$$
 * where
 * $$\gamma = 1/\sqrt{1-v^2/c^2}\,$$
 * and verify in less than a minute that
 * $$ (\Delta x')^2 + (\Delta y')^2 + (\Delta z')^2 - (c \Delta t')^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 - (c \Delta t)^2\,$$
 * and therefore
 * $$ (\Delta x')^2 + (\Delta y')^2 + (\Delta z')^2 + (i c \Delta t')^2 = (\Delta x)^2 + (\Delta y)^2 + (\Delta z)^2 + (i c \Delta t)^2\,$$
 * Perhaps Minkowski figured this out when he noticed that the equations for light velocity
 * $$\Delta x / \Delta t = \pm c\,$$
 * $$\Delta x' / \Delta t' = \pm c\,$$
 * are trivially satisfied if
 * $$ (\Delta x')^2 - (c \Delta t')^2 = (\Delta x)^2 - (c \Delta t)^2\ = 0\,$$
 * DVdm 06:52, 27 October 2006 (UTC)


 * As DVdm pointed out, the Lorentz transformation implies that the Minkowski-space dot-product/spacetime-interval is the way to go. The Lorentz transformation itself was first derived as the transformation under which Maxwell's equations (the equations governing electricity and magnetism) were invariant (e.g. had the same form).  Einstein later derived the Lorentz transformation using only his two postulates, and then proceeded to interpret it in a new way.  So that's how we got to the Lorentz transformation, which implies that the universe (on small scales at least) is a Minkowski space.  As to why it's a Minkowski-space and not a Euclidian 4-cpace, the simple answer I suppose is that it's a Minkowski-space because our laws of physics describe it that way (e.g. it is because it works).  Now if this leaves you rather deflated, as this amounts to it's a Minkowski-space because that's what turns out to give a correct description of things, which is itself a glorified version of "it is because it is", then you're delving down into some rather deep waters.
 * Certainly the Minkowski metric implies that time is a dimension like our usual three spatial ones, yet the minus sign (or the i, if you want), tell us that it's not exactly the same, something which is kind of clear from everyday experience. After all, time doesn't seem to be the same as space (spatially, I can move however I want while temporally I seem to be constrained to move "forward").  Of course, in light of relativity, and getting down to the heart of your question, we can flip this around and instead of wondering how on Earth time could be so similar and linked to space, we can wonder why it's not exactly identical to just another spatial dimension (if it were, then mathematically we would be in a Euclidian 4-space).  Of course, this is fast devolving into a philosophical or meta-physical discussion where it's not clear that there are are answers (or at least, I don't think anyone has answers to these questions at the moment).
 * I hope I've helped your understanding and not utterly killed it. But, as you can tell, you can either answer your question in a relatively superficial way or try to answer it in a deeper and possibly more profound way.  DAG 15:30, 27 October 2006 (UTC)

Relativity Wikiproject
I've suggested at the proposed wikiprojects page that a relativity wikiproject be created. If interested, you can add your name to the list and check out the plan for the project at WikiProject Relativity. MP  (talk) 13:08, 29 October 2006 (UTC)

Re: This is for beginners???
Tom Cod recently wrote above:
 * [This article] should be written on a level not too much higher than that which would allow it to be printed in the back pages of the science section of the New York Times or the Wall St. Journal; that is an educated "general reader" without a current background in math or technology should be able to credibly struggle with this "introductory" treatment.

Your concern is appreciated, but noone seems to be interested in doing the work to rewrite this article. Are you? --EMS | Talk 02:44, 4 November 2006 (UTC)


 * We could create a new article: "Special Relativity for Dummies" :)  Count Iblis 18:08, 4 November 2006 (UTC)


 * The contents to this article are part of special relativity, and really are better suited to that venue. If I had the time, I would take a stab at this rewrite.  As-is the best I can do is suggest an outline (as I did in the "Replace this article" thread above).  This article really should be more accessible. --EMS | Talk 04:34, 5 November 2006 (UTC)

This is not intended for people with no knowledge at all of maths!!!
This article is an introductory text, not waffle. It orients readers who have the minimum equipment to understand physics, such as school maths, so that they can approach the actual theory. Those who want something simpler should write a "brief description of relativity" article which would just explain that there is a theory that proposes several odd things. People who cannot even understand the simple maths of Pythagoras' theorem can never begin to understand relativity.

It is obvious from the comments above that several readers would like something simpler but no-one has produced this mythical "simpler" article. The truth is that this article is the simplest approach that is consistent with understanding. Try writing a "simple" article on Pythagoras' theorem without mentioning squares. 86.14.2.37 12:08, 22 November 2006 (UTC)

Get rid of this article!
This is ridiculous. I tune in 6 months later and the same farcical article is there, unchanged. This is NOT and never will be a Non-technical article. It is highly technical for a general encyclopedia article of any kind, let alone for one that purports to be a "non-technical introduction". And it is stylistically backward to boot. Why does it begin with "It all started with..."? What is all here? - the theory, the world, the universe, the quest for the One Ring?


 * This is not a totally non-technical introduction. It is a description of the way that SR is a modification of Pythagoras' theorem for a particular four dimensional case.  As such it is essential for beginners. If you can describe Pythagoras' theorem without any maths then you can use this skill to create a new article called "a verbal introduction to SR". NOTICE THAT NO-ONE IS DEMANDING A REWRITE OF PYTHAGORAS' THEOREM WITHOUT ANY MATHS!

The syndrome in effect here, and in thousands of similar articles in Wikipedia, comes about because you have an author who knows the background material, and then spends time and effort crafting an article. As a result, they know BOTH the field and what they are trying to say very well indeed. As a result, they vastly underestimate the difficulty the genuine beginner will find in their musings. TO be a good writer of general articles you need to be a good communicator first, not necessarily a great researcher. There is precious little attention paid here to the simple fact that this is not and NEVER WILL BE an article about Relativity that will reach the non-mathematical novice. Until it is ditched, it does no more than occupy the space that an article that could provide this information would fill.

I propose to write this article if no one else will. I'm not an expert. You don't need to be. People looking for "expert" front-line analysis are not going to be hooking into Wikipedia to get it.

Myles325a 11:55, 9 February 2007 (UTC)


 * Please, please go for it! I strongly advise starting the rewrite in your own user space (at User:Myles325a/Introduction to special relativity), and announcing it here when you have a draft ready.  That will give people a chance to comment on your work and even to tweak it a ways before it goes "live" here.
 * I do agree with your comments here. I would work on this myself, but not only am I also an expert but I am way too busy and have higher wiki-priorities than this.  You may want to see the outline I proposed in .  In any case, I wish you well in this effort. --EMS | Talk 16:30, 9 February 2007 (UTC)


 * If you do this you should keep the current article under a new name. The current article allows those who know high school maths to actually understand SR.  Your verbal article will only skate over the surface.

First paragraph wrong
The very first paragraph of this article is wrong. It does not follow from the result of the Michelson Morley experiment that the speed of light is the same regardless of relative speed between the source and receiver of light. It only shows that the earth is not moving through an ether. Without a justification for the claim of the constancy of the speed of light, none of the rest of the article makes sense. 75.32.30.32 23:32, 9 April 2007 (UTC)

Assessment comment
Substituted at 20:33, 3 May 2016 (UTC)