Talk:Special relativity/Archive 12

Introduction

The article should start off by saying what special relativity actually is (cf. general relativity) before saying who formulated it. MP (talk) 15:22, 18 June 2006 (UTC)

Nonmaterial energy?

The new intro has as the last sentense of its first paragraph:

Einstein's theory extends Galilean relativity to embrace both material objects such as people and nonmaterial forms of energy such as light.

This is totally incorrect and misleading.

1. Classical mechanics could handle light as well as normal matter (although it did make some incorrect predictions).
2. What makes SR different is the constancy of the speed of light for all observers.

I did an edit that reflected that [1]. I see that edit as being more correct since the constancy of c is a central postulate of SR instead of being a consequence. Kindly explain why you saw fit to revert my edit. --EMS | Talk 17:10, 18 June 2006 (UTC)

On second thought I now see that Harald managed to mangle my edit. That may help to explain things, but the current statement is still unacceptable to me. --EMS | Talk 17:37, 18 June 2006 (UTC)

You must be hallucinating - at least that's my explanation, as I did not mangle that part. And I agree that your version is more correct than Anon's. Harald88 20:20, 18 June 2006 (UTC)

the term"special relativity"

Another editor apparently is ignorant about the maeaning of "special relativity". The termm was introduced by Einstein in 1916, and there as well in his book on the "special and the general theroy of relativity" he explains why. In short, "the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion". Disagreement about its meaning isn't an option. Harald88 20:14, 18 June 2006 (UTC)

Harald - I will warn you now that you already have a history of taking inappropriately narrow views on issues related to relativity. I will not say that you are wrong about SR applying to "uniform motion", and in fact I like that wording much better than "inertial motion" or Einstein's own "uniform translatory motion". However, there is the issue of how to fit such concerns into what this anon is doing in a way that improves that article. Do note that your changes to my wording, while technically correct, did have the effect of making my text more technical and cumbersome. Hence the "mangling" I referred to above. So please try to take a more "global" view here, in which the needs of the article are balanced against the desire for technical accuracy.

One more thing: I chose not to revert earlier since I want to avoid an edit war, and since the anon chose to comment here after he reverted the lead. Discussion needs to be tried first here. While I disapprove of the anon's version of the lead, it is not so egregiously wrong that the issues surrounding it cannot be discussed first. --EMS | Talk 21:37, 18 June 2006 (UTC)

EMS, I will ignore your warning, since what you state about me certainly applies to yourself - but I'm glad that this time you don't go as far as stating that Einstein didn't know what his own definition meant.

So far I don't know what "mangling" you meant - except if you mean my tweeking of "motion" to "linear motion" - corresponding to the mistake that anon had made with his/her rotating planet example. Usually it's not hard to state things correctly without becoming too technical, even schoolkids know what linear motion is! Harald88 22:33, 18 June 2006 (UTC)

If I might suggest a phrasing that perhaps covers a little ground on both sides:

"The theory was given the name special relativity because it only addressed the application of the principle of relativity to the special case of inertial frames of reference. This contrasts with Einstein's theory of general relativity which applies the principle of relativity to all frames, inertial or not, and provides a description of gravity. Special relativity does not account for the effects of gravitational fields, though it can deal with accelerations. Another respect in which special relativity is 'special' is that general relativity reduces to special relativity in the case that there is no gravitational field."

I think this covers both bases ( both of which are true enough, and to some extent equivalent, but I think it's good to spell both points out separately ). Of course, I can't say I'm perfectly happy with the phrasing in some places ( particularly the part about GR describing gravity and the end of the last sentence ). So, comments/ideas? DAG 21:27, 18 June 2006 (UTC)

I can go along with it. I would change "gravity" to gravitation and "inertial motion" to "uniform motion" (although I may link the second phrase to the inertia article). I also suggest making this the second paragraph. Finally, I would like any changes to wait until the anon returns and has a chance to comment. --EMS | Talk 21:47, 18 June 2006 (UTC)

All fine to me; rests the question if this - now longer - paragraph is best a part of the summary lead, or if it may be better in the first paragraph of the body of the article (where it is actually lacking). Harald88 22:33, 18 June 2006 (UTC)

IMO this is needed in a broad-brush treatement of SR. So as long as the lead is not getting too big, it can stay there. Note that a compromise position may be in order: a brief mention in the lead and a fuller treatment in an introduction may work. However, we need to first get this revised lead set up, and then determine what an introduction should look like. So my advice is to go with this fuller paragraph for now and change it later if it should become appropriate to do so. --EMS | Talk 01:16, 19 June 2006 (UTC)

Meanwhile I replace "linear" by " uniform" motion, that's a good idea. Harald88 22:30, 23 June 2006 (UTC)

Careful wording

We must be very careful of the wording in this article as a simple word can break the whole concept of relativity. I recently made a change to the sentence "...and returns to discover that his twin has aged much more rapidly." by removing the word "rapidly". This misleads the reader to think that time was really passing faster for the twin on earth which breaks the concept of relativity. The stationary twin's time didn't pass faster, only more of it passed. Tailpig 08:21, 3 July 2006 (UTC)

Thanks for that improvement. "Time passing faster" is a meaningless concept: time always goes one second per second. —Keenan Pepper 14:14, 3 July 2006 (UTC)

The second postulate

I believe the second postulate should read:

There is an upper limit to the speed of interaction between two physical objects which is constant throughout space and time. This maximum speed is in fact equal to the speed of light in a vacuum.

From the first postulate, it can be then concluded that this maximum speed is the same in all inertial reference frames.

I think as it stands, the second postulate is not sufficient. I'm not sure, but I don't believe that simply saying the speed of light is a constant in all reference frames is enough to imply that the maximum speed of interaction is equal to the speed of light in all reference frames, which needs to be stated somehow either as a postulate or as a derivation. PAR 17:23, 11 July 2006 (UTC)

There have in the not too distant past been extensive discussions on how exactly the second postulate should be worded. Many or most of it is archived, though some is on top of the page. You might want to skim some of that for an idea of what on earth we were all thinking at the time. If I remember correctly, the current wording was something of a compromise. Just a heads up, or a warning to keep your head down, as the case may turn out to be...  ;) :D DAG 18:07, 11 July 2006 (UTC)

Einstein did not postulate a maximum. He postulated that there is a speed c (the speed of light) which is the same is all inertial frames of reference. That this constant speed is a maximum is a consequence of the theory. --EMS | Talk 19:21, 11 July 2006 (UTC)

Nowadays it's becoming popular to postulate a possible limit speed; if that speed is infinity we would get "Galilean relativity", but it was experimentally found that that speed is c. Any of such approaches is sufficient. The second postulate isn't like a commandment. ;-) Harald88 20:26, 11 July 2006 (UTC)

4-D is not able to be scientifically established.

To: Wikipedia
<http://en.wikipedia.org>
28 July 2006

From: Gerald L. O'Barr <globarr@yahoo.com>
6441 Dennison St. (858) 453-0071
San Diego, CA 92122

The following thoughts should appear in any subject where Special Relativity is being presented:

---

As far as it is presently known, it is mathematically impossible for any test to differentiate between the 4-D of Special Relativity (SR) and a reality of simple 3-D where there are changes in lengths of rulers and in the rates of clocks, as was assumed by Lorentz. Thus, the assumption that there is 4-D cannot yet be scientifically supported. It is therefore unscientific to accept 4-D over a simpler 3-D approach, unless or until a test can be made that would properly discriminate between these two approaches, and in which support for 4-D was unambiguously shown.

The study of SR by using 4-D math is acceptable, since it is a very powerful and effective way to solve the math that needs to be solved. But at no time should any interpretation be made that this supports 4-D, since it does not. Math problems can often be solved by using a number of dimensions greater than what is actually involved. It only takes an appropriate number of zeros and/or other inter-relationships to accomplish such actions.

The use of a simple 3-D approach removes all apparent paradoxes. In other words, most of the odd things that appear to occur in SR are mainly the effects of having measurement tools that change in their lengths or rates, and not due to anything odd with the actual physics.

Thanks for reading! -- Gerald L. O'Barr

Um, even classical mechanics has four dimensions. It's obvious there are four dimensions because you need four coordinates to specify where and when an event takes place; for example, latitude, longitude, altitude, and time. Being in the right place at the wrong time is just as bad as being in the wrong place at the right time.

You say "The following thoughts should appear in any subject where Special Relativity is being presented", but that is not true, they're only your thoughts, and they're not notable enough to appear in an encyclopedia article. Publish a paper in a peer-reviewed journal and then maybe we'll mention it. —Keenan Pepper 21:05, 29 July 2006 (UTC)

O'Barr comments:

You are exactly correct: classical mechanics has 4-D. And if you want to add temperature, then of course we now have 5-D. It is exactly because classical mechanics has all this, then the assumption of SR experts that we need something different, like this SR 4-D spacetime continuum, makes it all funny and silly and unscientific. Thank you for agreeing with me. And even though you seem to say that you will be unable to understand me unless I get published, let me assure you that I can understand you, whether you are published or not. Sorry about your inabilities where you appear that you need the help of someone else (a peer review) in order for you to know if what I say is correct or not. Now I feel that all this is in violation of the rules, here. Why did you fail to show the experiment that is used to justify there being a 4-D, and not a 3-D? That was the subject, was it not? There is a place where it is stated that you do not accept 4-D, you accept (3 + 1)-D. This is correct! This is just a sneaky way of saying that you accept Lorentz's approach, without having to say so. Gerald.

Pardon? I didn't say I couldn't understand you, I said your thoughts don't belong in the encyclopedia article, because they're original research and not verifiable. Many experiments have confirmed the predictions of SR with great accuracy: Hafele-Keating experiment, Ives-Stilwell experiment, Kennedy-Thorndike experiment... —Keenan Pepper 22:21, 29 July 2006 (UTC)

O'Barr comments:

You do not show any signs of understanding me. I was not presenting any of ‘my research.’ I was not insisting upon any of ‘my thoughts’ to be presented. And I do not question the accuracy of the results of anyone. SR math is very perfect, in the domain where it applies. SR 4-D math is most perfect. The question is not a math question. The question is, to what extent do we know that our physical reality is a 4-D spacetime continuum, and not a simple 3-D reality?

Let me explain to you some very important things about science, and about theories. The correct presentation of any scientific theory requires, as a minimum, the following:

• Its basic concepts and/or what it does or accomplishes.
• The basic assumptions and/or principles upon which it is based.
• The extent to which it has been established as being correct or found to be useful.
• And last of all, what is its greatest weaknesses and/or criticism.

And if you find any theory where such weaknesses and criticisms are not given, you have a problem on your hands. And I see very little of such discussions in this article. You all like to talk about the accuracies of the measurements, but you rarely mention the fundamental limitations that exist. I was trying to tell you that such a thought, even if it was only one or two paragraphs, should be made, if you are going to be scientific about your article. You are, after all, writing an Encyclopedia, not a research article. And an Encyclopedia has an obligation to scope out both the good and the bad (or the strengths and the weaknesses) of any subject.

I noticed in reading some of the archive on this subject that there have been many criticisms made of SR. But I still do not see any addressed in the actual article. Why is that? Why is it considered to be un-allowed to present valid criticism of this theory? The criticism I presented is not my criticism. It is a very common fact that present testing cannot make this simple separation between SR and LET. This is a weakness to SR. To be scientific, you should address this issue. And it has nothing at all to do with me, or whether I am published or not.

There are many other weaknesses to this theory, and you need to at least mention some of these weaknesses. At least, that is my opinion!

Gerald.

Okay, now we're getting somewhere. You're right, every theory has weaknesses that should be presented, but this article does present them. There is a section Special relativity#Status that links to an entire article Status of special relativity devoted to the subject. Does that satisfy you? You are welcome to add any criticisms or shortcomings that are missing, as long as your additions follow the Wikipedia policies of notability, verifiability, etc. —Keenan Pepper 00:04, 30 July 2006 (UTC)

May I ask Gerald - can you give a hypothetical example of what a test might be that would answer the question of whether we are dealing with a 3-dimensional space or a 4-dimensional space? PAR 00:38, 30 July 2006 (UTC)

FYI - O'Barr is a well known anti-relativitst from the USENET sci.phyics.relativity newsgroup. I counsel against taking him too seriously. I for one strongly doubt that the can offer any useful suggestions for this article. OTOH, as long as he abides by WP:CIVIL and recognizes the limits that WP:NPOV and WP:NOR place on his editing ability in the article space I see no problems with letting him make a case here for now. Howeer, I would like it if he would study the editing rules. --EMS | Talk 02:32, 30 July 2006 (UTC)

O'Barr comments on the above: I fully and completely support SR math and its predictions. I am therefore, to this degree, not anti-SR.

O'Barr comments to the comments above the FYI note:

I read your ‘status’ section. And it is an important section. It is important to point out the domain that SR covers. These domain limitations are in some sense a weakness in this theory, but not really. No theory is expected to cover everything. And it is important to point out the accuracies that the theory is able to achieve. This is certainly a potential weakness for many theories. But with SR, this weakness ends up being our own weakness in the efforts we can make in our testing, not any weakness in SR.

You pointed out specific tests that supports SR. You even pointed out some specific tests that differentiates SR from other theories. All this is good. But let me tell you what this section did not do: It did not point out one test that differentiated SR from LET. And this of course was initially and apparently still is the subject of my posting. And at no time did you present any fundamental problems with SR. So this section does not address the needs that I see. Maybe some of your references do some of these things, but I doubt it.

Now you did ask one question. You asked, ‘can you give a hypothetical example of what a test might be that would answer the question of whether we are dealing with a 3-dimensional space or a 4-dimensional space?’

Thank you for asking! Do you think that question is an important question? That is why I asked this question. Unless and until we (at least one of us) are able to answer this question, then we certainly might have the right to propose a 4th dimension, but it would have no advantage over a simpler 3-D if the 3-D can do everything that your 4-D is able to do.

Now I have written articles about how we determine if we have a 1 or a 2 or a 3 or a 4 dimension reality, and it is very simple. And the steps in going from 1 to 2, and from 2 to 3, they are exactly the same, as all additional dimensions would have to be. But there is no evidence at all when we try to go from 3 to 4. There is no evidence at all as we look for a 4-D world. None! Zero!

So thank you for asking!

Gerald.

O'Barr comments to O'Barr!

Hey! I just found your reference, the 'status of Special Relativity! I thought that 'status' was the section to which you were referring. And in this section you do mention that LET is equivalent to SR. No one can ask for more than this. You are saying that a LET 3-D reality will produce the identical results as a SR 4-D, and this is correct.

I am now sorry that I took so much of your time. Please forgive me!

You really ought to say this at the very start of your article on SR, and not hide it so deep! Gerald.

Steer clear of ict

I have removed the ict notation except for a small note explaining why it shouldn't be used. A good discussion of the reasons is given in "Gravitation" by Misner, Thorne and Wheeler in Box 2.1 entitled "Farewell to ict ". Some of the reasons given are:

• To single out the time coordinate as the only imaginary coordinate, while the others are real is deeply misleading. Spacetime is isotropic, there are no preferred directions, and the implication that time is somehow special is counterproductive. The difference between spacelike and timelike directions is fully and completely contained in the invariant Minkowski metric, where it belongs, and not in the particular choice of coordinate system, where it does not belong.
• To reinforce this - there is no place for this notation in general relativity. Disguising the Minkowski metric to look like a Euclidean metric in general relativity leads to a confusing and unwieldy theory.

There are other reasons given, but I find these to be the most compelling. PAR 00:24, 4 August 2006 (UTC)

Gerald L. O'Barr <globarr@yahoo.com> comments:

What a silly thing to take offense with. The use of ict is mathematically correct, and it produces correct math answers. You seem to have a desire to make, in your mind’s eye, space to be the same as time and time the same as space. You want spacetime to be isotropic. You want a lot of things here. But why? You have no reason to have any of these things, since the math of SR will be just as exact and perfect with or without ict, and therefore there is no mathematical reason to do any of this.

Let me say what needs to be said just as clearly as possible: You did not say that the physics required you to do this. You did not say that the math or the science required you to do any of this. All you could say was that you thought it was compelling. Well, maybe it is compelling to your feelings, but again and again, there really is not one single test or one single test result or one single test analysis of a test result that would be able to support or to discriminate against your actions. It is a non-scientific act. SR is not a physical theory, and cannot speak to such issues.

As a math theory, which SR is, you can formulate the math in a multitude of ways. There is no way that you can say one of these ways is any better than another way, as far as the theory exists. And if you want to state this, then you can change the math in any way you please. But please do not indicate that one form of the math is more ‘compelling’ than another. It is nothing like this at all unless you can show a test that scientifically confirms your position.

At least that is MMHO! Thanks for reading.

Hi Gerald - (Please don't indent your paragraphs! - it looks terrible - I see it has been fixed.) The theory of planetary motion was originally formulated as the planets and the sun rotating in perfect circles around the earth. This was found to be in error, because certain planets seemed to stop and go backwards for a while. This was fixed by adding "epicycles" in which the planets travelled in perfect circles about a point on the orbit, which was a perfect circle. This process could be continued indefinitely, and an accurate theory with the earth at the center of the solar system could be constructed with a sufficient number of epicycles with angels pushing the planets around their epicycles. Another theory is that the sun is at the center of the solar system and the orbits of the planets are elliptical. This also reproduces the observed motion, and falls neatly into place with the Newtonian theory of gravitation. There is no test that can distinguish between the two theories. But I find the second model of the solar system to be more compelling, as do most scientists. PAR 17:14, 8 August 2006 (UTC)

I have to agree with Gerald here. As far as I know, putting an imaginary number in the temporal term doesn't materially affect the actual theory, but is instead a convention. It's the same as choosing the spatial terms to be negative and the temporal term to be positive. Or putting the temporal term before the spatial terms and vice versa. As long as you choose one and stick with it, I'm not sure it matters (though mixing conventions can prove to be quite painful). That being said, everyone has their own opinion as to each of these conventions should be used. I generally don't use ict, put time after the spatial components, and have time be negative. So...

As to planets and such, that's a bit different as there are two different theories being discussed, versus just one. And besides, there is a test that can ditinguish between them, that is give any group of students two tests, one on each theory after a normal course in introductory physics, and see which test has higher scores...  ;) :D Cheers. DAG 18:18, 8 August 2006 (UTC)

Maybe I wasn't clear enough - The problem does not exist so much in special relativity as it does in general relativity. Once you study and learn general relativity, the use of ict will feel like epicycles on planetary orbits. Sure, you can make it work, but you know in your heart its not right. When you see the central importance of the metric tensor and the simplifications that it brings, and then go back to the special case of special relativity, you will see that the insights gained in general relativity can be carried over to a deeper understanding of special relativity itself. Here is the section from "Gravitation" by Misner, Wheeler, and Thorne on the subject. (Emphasis is mine.) PAR 22:24, 8 August 2006 (UTC)

Box 2.1 FAREWELL TO "ict"

"One sometime participant in special relativity will have to be put to the sword: $x^{4}=ict$. This imaginary coordinate was invented to make the geometry of spacetime look formally as little different as possible from the geometry of Euclidean space; to make a Lorentz transformation look on paper like a rotation; and to spare one the distinction that one otherwise is forced to make between quantities with upper indices (such as the components $p^{\mu }$ of the energy-momentum vector) and quantities with lower indices (such as the components $p_{\mu }$ of the energy momentum 1-form). However, it is no kindness to be spared this latter distinction. Without it, one cannot know whether a vector (§2.3) is meant or the very different geometric object that is a 1-form (§2.5). Moreover, there is a significant difference between an angle on which everything depends perodically (a rotation) and a parameter the increase of which gives rise to ever-growing momentum differences (the "velocity parameter" of a Lorentz transformation; Box 2.4). If the imaginary time-coordinate hides from view the character of the geometric object being dealt with and the nature of the parameter in a transformation, it also does something evern more serious; it hides the completely different metric structure (&sect 2.4) of +++ geometry and -++++ geometry. In Euclidean geometry, when the distance betwen two points is zero, the two points must be the same point. In Lorentz-Minkowski geometry, when the interval between two events is zero, one event may be on Earth and the other on a supernova in the galaxy M31, but their separation must be a null ray (piece of a light cone). The backward-pointing light cone at a given event contains all the events by which that event can be influenced. The forward-pointing light cone contains all events that it can influence. The multitude of double light cones taking off from all the events of spacetime forms an interlocking causal structure. This structure makes the machinery of the physical world function as it does (further comments on this structure in Wheeler and Feynman 1945 and 1949 and in Zeeman 1964). If in a region where spacetime is flat, one can hide this structure from view by writing

$(\Delta s)^{2}=(\Delta x^{1})^{2}+(\Delta x^{2})^{2}+(\Delta x^{3})^{2}+(\Delta x^{4})^{2},$

with $x^{4}=ict$, no one has discovered a way to make an imaginary coordinate work in the general curved spacetime mainifold. If "$x^{4}=ict$" cannot be used there, it will not be used here. In this chapter and hereafter, as throughout the literature of general relativity, a real time coordinate is used, $x^{0}=t=ct_{conv}$ (superscript 0 rather than 4 to avoid any possibility of confusion with the imaginary time coordinate)."

I admit my knowledge of general relativity isn't very advanced, though I am vaguely aware of the role of the metric, and that is to say it's pretty big. However, this particular article is on special relativity, and to be fair the ict notation, as weird and possibly unused as it is, exists and is still mooted in classes today, if only as a "oh, yeah, and you can do it this way...". I am in no way saying that it should be the primary notation used in this article - in fact, any other one should be used :) - but it's worth mentioning, probably with the very caveat you have mentioned. Basically it's another way to mathematically express special relativity - and more or less only special relativity. DAG 00:19, 9 August 2006 (UTC)

I agree - it should definitely be mentioned, along with reasons why it was introduced, and along with reasons why, for a theoretically inclined person, it is a dead end. PAR 00:57, 9 August 2006 (UTC)

O’Barr comments:

It does not matter whether you want to talk about SR or GR. These two theories are the same theory. Thus, SR is GR, and GR is SR, in the limit where SR applies. Therefore, if SR is just a math theory, then so is GR. If SR is weak as a theory in the domain that it applies, then so is GR weak in this same domain. What is a true failure for SR, is a true failure for GR. Again, this is true as long as you are in the limit where SR applies. You cannot escape any of these relationships.

Maybe you did not see what I wrote above, where it was clearly explained that SR’s 4-D spacetime continuum is presently not a scientific concept. And I assure you, if SR is nothing but a simple 3-D space, 1-D time reality, then so is GR. It is physically impossible to have reality change from being simple 3-D to being 4-D, just because you have added gravity gradients to your reality.

In reading your article on SR, these 3-D and 4-D relationships, and absolute and relative relationships, are not presented in any scientific way, but in a political way, and it is not good science. Math is very powerful and important, and the use of 4-D math in SR and GR should be taught and used. But no one needs to think that the math is the physics. That is ludicrous, unless and until a test can be found that can distinguish these concepts.

Thanks for reading. Gerald.

It looks to me, from the argumentation above, that you and PAR are on the same page about this: the argument against ict is, if I understand it well, that it simply hides the difference between time and space coordinates, without any benefit. Harald88 07:00, 9 August 2006 (UTC)

Gerald, GR and SR are definitely not the same theory! GR was proposed 12 years after SR, Einstein didn't spend all this time waiting around to publish the same theory. GR is accepted to me a more complete description, from which SR can be used under appropriate circumctances (e.g. no curved space). You cannot make assumptions about GR derived from SR. I would also contend that an accurate mathematical prediction often does say something about underlying physics, and you seem to be wrongly applying Occham's razor by saying that a 3-D universe is simpler. Is that because 3 is less than 4? A 3-D universe which acts exactly like a 4-D universe but isn't, is a more complicated explanation than a 4-D universe. If it acts exactly like 4-D, it is 4-D. You can't assume something different based on you seeing the workd in 3-D, you experience time too. Relativity also makes a distinction between space-like and time-like variables.Jameskeates 08:43, 17 August 2006 (UTC)

Gerald L. O'Barr comments: I was very careful in what I said. I did not say these two theories were the same. I said they were the same in the domain where SR applies. There is a difference in what I said and in what you said. It is sad if you are not able to tell that there was a difference between what I said and in what you said.

It is true that there was a time difference between the introductions of these two theories. But I assure you, that Einstein made a great effort to make these two theories identical in the domain where SR applies. And where SR applies, SR is telling you exactly what GR would tell you under these same conditions.

You contend that an accurate mathematical prediction often does say something about underlying physics. Contend all you want, but science depends upon confirmation by tests, and these confirmations must be capable of discriminating between all competing theories. And so far, SR has nothing that can discriminate itself from LET and its more simple reality. For your information, 3 is less than 4, the last time I checked.

You can, of course, believe what you want. But to be scientific, where is your science? Where is your test that shows how reality really works? Since you have none, then you are only talking.

A 3-D reality is simpler than a 4-D reality, no matter what the math might show. Assumptions are great, but until there are tests that turn your assumptions into solid, repeatable, test results, providing clear separations between alternative theories, then you do not have a good theory or a strong theory. And those who are not willing to understand and to acknowledge such obvious things are not good scientists.

Thanks for reading. Gerald L. O'Barr <globarr@yahoo.com