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It means that Λ is invertible, which implies that the aforementioned frames A and B are symmetric, see above and below. “Symmetry” means that you apply a transformation to an object in order to obtain a new object; and then apply the inverse transformation to the new object; you end up again with the original object. That’s exactly what you have demonstrated here - ⅛ x 8 = identity. Thank you for confirming this for us (once again). Likewise in physics - you Lorentz-transform a frame A into a frame B; and then you reverse-transform B back into A using the inverse of the original transformation matrix. That’s how symmetry is defined. Physically, it means that all inertial frames experience the same laws of physics, irrespective of their state of relative motion. No, your just repeating this nonsense does not make it any less wrong. Two frames A and B are symmetric iff B=Λ(v)A A=Λ(−v)B=Λ(−v)Λ(v)A=IA Physically speaking, this means simply that all inertial frames experience the same laws of physics, irrespective of relative motion. Once again, here is the experimental evidence for that, which is clear and unambiguous. You are perfectly entitled to your own misconceptions, but not your own physical facts. What I have shown you is elementary linear algebra, and it is not in contention by anyone except people who have agendas that are incompatible with actual science. Then you have wasted your time, because evidently you don’t even understand simple linear algebra - or, more likely, you don’t want to understand it. That being the case, you are really not in any position to argue about SR. The proof has already been provided. Several times, in fact. So far as anti-relativity sentiments are concerned, this was a very underwhelming and childish attempt, I have to say. With this kind of approach you will never be taken seriously by anyone who has even just cursory knowledge of the subject matter. Needless to say you have utterly failed to convince anyone here on this forum. And honestly, given the overwhelming amount of experimental and observational evidence for SR (a small selection of which I have linked above), I will never understand why people like yourself are even wasting your time with this. You might as well argue that a round shape isn’t in fact the best shape for the wheels on a car - this debate has been settled long ago. You aren’t making any kind of valuable contribution to science, you know. Had you used those 10 years you mentioned to actually learn real physics and maths, you might have been able to contribute something of value. It’s a missed opportunity. We really are done here now. Good luck to you.

I don't think there are such concepts as "interval of points" and "interval ends at ..." in math. I have no idea what revolving, breaking, and reattaching segments have to do with numbers and interval lengths. The former are not mathematical concepts, AFAIK. @Boltzmannbrain, I start to suspect that the root of confusion is here: you are talking about an actual physical segment, while the "real number line" is a mathematical concept. The "real" in the latter does not refer to "line", i.e., it is not a "real line." It refers to "number", i.e., they are "real numbers."

Using "nature" to mean "born with" (aka genetics) and "nurture" to mean "learned after birth" (aka environmental factors), I disagree that there's any nature in either. I don't think there's a religion gene, just some genetics that make some more susceptible. You learn about gods and whether they seem credible to you or not, you aren't born that way. You may be born with a curious mind that questions, but what you believe depends on how those questions are answered. Some people get scientific answers, some are told they're lucky, some are told they're worthless, some are given no answers, and some are told about a specific god and its teachings.

I think our nature us to want explanations/answers. We also tend to want neatness. Sometimes we settle for simple and wrong because then no further thought is required.

I agree with main arguments developed by @Genady, @studiot, and @Lorentz Jr. I particularly liked Studiot's summary. I would call his argument about closed and open sets --as well as those that are neither open nor closed-- a "topological approach." A crash course in topology would include concepts such as, Topology: Existence of an inclusion relation in a set, \( \subseteq \) --contains--, \( \subsetneq \) --does not contain. => neighbourhoods of a point. Limit point --o accumulation point--: A point in a set that has neighbouring points also in the set that are arbitrarily close to it. Interior of a set: All its point are limits points of the set --if I remember correctly--. Boundary of a set: The set of all the limit points of its exterior Closure of a set: The union of the set and ist boundary ... etc. With these rigorous topological definitions, when applied to the real numbers, we can prove they constitute a topological space, and, eg, the set \( \left[0,2\right]=\left\{ x\,\textrm{in}\,\mathbb{R}\,\textrm{such that}\,0\leq x\leq2\right\} \) contains its boundary --and it is, therefore, closed; while the set, eg, \( \left(0,2\right)=\left\{ x\,\textrm{in}\,\mathbb{R}\,\textrm{such that}\,0<x<2\right\} \) does not contain its boundary --and it is therefore, open. https://en.wikipedia.org/wiki/Topological_space

The word point is much overused. I debated with myself how to avoid it as far a possible to avoid confusion. Totally agreed. But I do not like the use of the word end in relation to lines as it can be imprecise. An open interval has no end. I am sorry you missed my main point (there is that word again, but with a different meaning this time) So it means that my explanation was not good enough so I will try to do better. But it is difficult to know what you know as you obviously have met the idea of open and closed intervals before since you used an alternative notation in your responses. I carefully avoided [0,2) etc because it is easy to overlook which bracket is which and you can never be sure whether the writer meant it or not. The reversed square bracket stand out, don't you think ? Also curved brackets are used to denote sets. Anyway you clearly understand that part. My main point was that lines and numbers are not the same, although they have some properties in common, which allows one to exemplify the other when only the common properties are of concern. But sets of numbers have lots of other properties where they cannot be represented as lines. So mathematicians seek more general approaches. If there is a number that is greater than any other number is the set then the set is bounded. In fact we say it is bounded above and can say (similarly it is bounded below if there is a number less than any other number in the set.) So the set (1, 2, 3, 4, 5, 6) is bounded above by the numbers 6, 7, 8, 9, 10... We call any of these an upper bound. Also the upper bound may be an element of the set or it may not. When the upper bound is an element we call it the maximum of the set. Now there is a theorem, which I will not prove, called the least upper bound theorem. "If any set of numbers is bounded above it has a least upper bound" In our example 6 is the least upper bound of our set and is also the maximum. But our set is also finite so it is easy to see this. Finite sets means that the count of elements is finite: Infinite sets have an infinite count of elements. The boundedness theorems apply to finite and to infinite sets, (But not the max and min) Infinite sets can also be bounded. The set of all the elements of the negative exponential e-x, from x=0 to x = ∞ is bounded above by 1 and bounded below by 0, although the set is infinite becasue the count of x values is infinite. Note the x = ∞ 'end' is never reached or as I prefer there is no right hand end to this line. So this line has no minimum. The left hand end depends whether we include or exclude x = 0 in the set (closed or open ) If we include x = 0 then the upper bound of 1 is also the maximum, But if we exclude it then again the upper bound is never reached and the set has no maximum either.

I am a relativity amateur, but this one is even clear to me: you should of course use the same dimension for velocity for v and c: both in m/s, or both in km/h. But if you set c = 1, then you should express v as a fraction of c. This is such a beginner's error, that I don't have to take the rest of your exposés seriously.

-1. You would be well advised to stop insulting people and clean up your own house. Neither one of us is "dominant in the world of science." As to you, you are nowhere near the world of science. Reported.

^^^ maybe a consequence of ->

The numbers are not normalized by cost of living. Rice, for example, costs ~4x as much in the United States as it does in Vietnam. So an expenditure that is 4x higher does not mean they are eating 4x more. https://www.numbeo.com/cost-of-living/country_price_rankings?itemId=115

It's a good start for General Philosophy though.

Owls are amazing in this particular department. http://www.instantshift.com/2014/12/12/hidden-camouflage-owls/

I can't say i noticed but its an interesting thought. I can say that the older persons in the group expressed a slight bias towards nature, whilst the younger appeared more open to the idea of nurture. That (my bold) did make me chuckle, I was sipping on my morning coffee while reading it and spat half out all over my pc key board. I was watching a documentary following the lives of teenage Mormons who were heading off to missionary college. One teenage lad even after years of in doctrine, decided to abandon the religion because he wanted to peruse gay relationships. His sister did continue on to the missionary college though she did find some of the expectations difficult, especially so when in social groups from other religious/culture backgrounds .To be fair to the parents they were very accepting (at least on the face of it) of their son's decision. I wonder though if the fact that their daughter was willing to continue on, helped with this acceptance. Personally though I never understood why some religions or cultures were and continue to be unaccepting of gay relationships. People should be free to love whom ever they like, and not feel persecuted or discriminated for it.

I think what folks have not realized is that our knowledge in functional genomics has turned the entire nurture vs nature debate on its head. In the past, there was often a kind of genetics first assumption, in which certain traits conditions etc. where often assumed to be genetic. If for example a certain ethnic group showed something different, genetics was a plausible explanation. This was also a reason why GWAS were eagerly anticipated and were hoped to reveal the basis for many diseases, conditions and traits. This has fizzled out somewhat, and our improved understanding of functional genetics (and its dynamics) played a big role in explaining why that is the case. Realistically and increasingly folks would actually provide more stringent evidence of a genetic basis (after all, we finally can do that) before claiming a strong genetic basis. At minimum, the basic assumption should realistically be both, with a bit more bias on the nurture side, when it comes to dynamic behaviour.

Seriously? You pay $6 for a bowl of oatmeal with fruit on top? Nice berries, but it's still oatmeal! If you don't like oatmeal, just eat some fruit. Buy whole grain bread and put jam on your toast. Nobody has to eat oatmeal (though I suddenly feel like making some, with brown sugar and allspice); there are other wholesome grains, and other ways to incorporate oats into your diet. No, restaurant food doesn't tell you anything about healthy food. The point of going to a restaurant is to step out of routine, indulge yourself and let somebody else do the work. (Unless you fall for the meal-kit scam, where you overpay for the ingredients and still do the work.) If you want to eat well, buy wholesome groceries, get recipes off the internet, like this https://www.eatingwell.com/recipes/ and just do it. You might even try piling different fruits and nuts on your oatmeal. I think you'd better take her out pretty soon.

Slender filefish:

Oh yes, they are. The Lorentz transformation leaves the metric invariant: \[g_{\mu \nu } =\Lambda _{\sigma }^{\mu } \Lambda _{\rho }^{\nu } =g_{\sigma \rho }\] Rewrite this in matrix notation: \[\Lambda ^{T} g\Lambda =g\] Take determinant on both sides: \[det\left( \Lambda ^{T}\right) det( g) det( \Lambda ) =det( g)\] Since none of these determinants is ever zero, and since the determinant of the transpose equals the determinant of the original matrix, you get: \[det( \Lambda )^{2} =1 \] which implies that \(\Lambda\) is always invertible. Thus, inertial frames related via Lorentz transformations are always symmetric. ! Moderator Note It is against the rules of this forum to post personal theories into the main physics section, let alone onto an existing thread. If you wish to discuss this, you must open your own thread under “Speculations” and explain your thoughts there (don’t just give links).

Trying to summarise: We need something massive/abundant enough. We need something that doesn't interact at all in any other way, except gravitationally. We need something that clusters significantly --very unlike photons, has some mass--, but not too much -> little dissipation --very unlike ordinary matter. From what I gather, this leaves no alternatives but: (1) Exotic particles that are not coupled to anything in the standard model and are massive, copiously produced during the big bang, or combination of massive and copiously produced, so as to yield the desired gravitational effect. And stable once they've been produced -> existence of lightest exotic particle. Or --a quite conservative, but more compelling idea, IMO, (2) Massive right-handed neutrinos that give a very small mass to the left-handed neutrinos as per see-saw mechanism, via interaction with the Higgs + plausible mechanism why one of the 3 RH neutrinos cannot decay. The first alternative requires going beyond the SM in a significant and adventurous way. One would have to find different fits with mass/abundance to make it work. The second one requires generalising the SM ever so slightly. And there exists a proposal for it that's being developed and which predicts that one of the three LH neutrinos must be massless. N. Turok, L. Boyle, K. Finn et al. https://arxiv.org/abs/1803.08930 https://arxiv.org/abs/1803.08928 https://www.youtube.com/watch?v=d-hPmjjjC-I (Public Lecture) I hope I didn't forget anything important.

(The answer in my emphasis.)

Too late chum. Your comment was entirely inappropriate so welcome to my blocked list. You've nothing to say worth hearing.

@Markus Hanke is absolutely right. When one talks about something being symmetric or not, one must specify what is symmetric --the object-- with respect to what --change of POV, transformation, etc. What Markus has shown to you is that, assuming two observers assign respectively coordinates \( \left(t,x,y,z\right) \) and \( \left(t',x',y',z'\right) \), the metric --given by \( t^{2}-x^{2}-y^{2}-z^{2} \) doesn't change --it's the same in the primed coordinates and the unprimed ones. It might be that what you mean is that the law that user with primed coordinates uses to correlate his observations with those of user with unprimed coordinates is not the same with \( \boldsymbol{v} \) replaced by \( -\boldsymbol{v} \). But it is. Both relative velocities are obviously collinear, so, \[ x'=\frac{x-vt}{\sqrt{1-v^{2}/c^{2}}} \] \[ ct'=\frac{ct-vx/c}{\sqrt{1-v^{2}/c^{2}}} \] \[ y'=y \] \[ z'=z \] (simple Lorentz transformations in one direction, AKA 'boosts') Introducing the definitions, \[ \gamma=\frac{1}{\sqrt{1-\beta^{2}}} \] \[ \beta=v \] The reciprocal ones obviously are, \[ \gamma'=\gamma \] \[ \beta'=-\beta \] and you get, \[ \left(\begin{array}{cccc} \gamma & -\beta\gamma & 0 & 0\\ -\beta\gamma & \gamma & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array}\right)\left(\begin{array}{cccc} \gamma & \beta\gamma & 0 & 0\\ \beta\gamma & \gamma & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array}\right)=\left(\begin{array}{cccc} \gamma^{2}\left(1-\beta^{2}\right) & \beta\gamma-\beta\gamma & 0 & 0\\ \beta\gamma-\beta\gamma & \gamma^{2}\left(1-\beta^{2}\right) & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array}\right)= \] \[ =\left(\begin{array}{cccc} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0\\ 0 & 0 & 0 & 1 \end{array}\right) \] which more compactly reads, \[ \Lambda\left(-\boldsymbol{v}\right)=\Lambda^{-1}\left(\boldsymbol{v}\right) \] In what other sense you might want it to be more symmetrical, I don't know.

No. It was your claim that I asked questions about. I did not make a claim. So that's not a burden of proof fallacy. The burden of proof is on you Arete. Very good. So you agree that you can't prove it. In that case, why would you make a claim you cannot prove? Or is your claim misunderstood? Not at all. It depends on who made the claim. This is just a red herring. If you claim this thing about fairies, it is only fair to ask for some form evidence. The burden of proof is on the claimant.

You changed your statement with an edit. Now it's completely different. So could you point out where I made a "positive claim"? Thanks.

None of this is relevant to me. This is all a strawman effort. I questioned you on your claim and your claim only. The burden of proof lies on the claimant, not on the questioner. It's absolutely simple. Have a great day.

β=v in any system of units such as light-years per year, light-seconds per second, etc. That is, any system of units in which c=1 . I thought you understood that, @Abouzar Bahari.

You have provided incoherent nonsense. You're boring us, Mr. Bahari. Please post something funnier. 😄 Length contraction: [math]L' = {x'}_2 − {x'}_1 = \gamma(x_2 − vt)−\gamma(x_1 − vt)=\gamma(x_2 − x_1)=\gamma L[/math] Time dilation: [math]\displaystyle{\Delta t' = {t'}_2 − {t'}_1 = \gamma\left({t_2} −\frac{vx}{c^2}\right)−\gamma\left({t_1}−\frac{vx}{c^2}\right)=\gamma\left(x_2 − x_1\right)=\gamma\Delta t}[/math] No dependence on the sign of v. 😉

I don't know what you mean by "it's a physical parameter, and not a mathematical one." A physical parameter, in the usual sense of the term, most definitely it is not. A physical parameter is any quantity that we can vary either freely, or subject to some specified conditions. Eg, the magnetisation of a medium of given magnetic susceptibility, etc. In the context of relativistic physics, c is a universal constant, not a parameter. Theoretically, it is derived from principles of electromagnetismf. Experimentally, it is measured. If you mean otherwise, you should say so. Because I've been studying these things in excruciating detail for many years, I can tell you you're using the poor-man's version of boosts. The grown-up version of it is, \[ \boldsymbol{x}_{\Vert}'=\frac{\boldsymbol{x}_{\Vert}-\boldsymbol{v}t}{\sqrt{1-v^{2}/c^{2}}} \] \[ ct'=\frac{ct-\boldsymbol{v}\cdot\boldsymbol{x}/c}{\sqrt{1-\left\Vert \boldsymbol{v}\right\Vert ^{2}/c^{2}}} \] \[ \boldsymbol{x}_{\bot}'=\boldsymbol{x}_{\bot} \] Where you have to decompose position 3-vector \( \boldsymbol{x} \) as, \[ \boldsymbol{x}=\boldsymbol{x}_{\Vert}+\boldsymbol{x}_{\bot} \] \[ \boldsymbol{x}_{\Vert}=\frac{\boldsymbol{x}\cdot\boldsymbol{v}}{\boldsymbol{v}\cdot\boldsymbol{v}}\boldsymbol{v} \] \[ \boldsymbol{x}_{\bot}=\boldsymbol{x}-\boldsymbol{x}_{\Vert} \] So the expression in the numerator is actually not a positive 3-scalar, but a 3-vector projection in some inertial frame. You don't understand anything, and what's worse, you don't ask. So Markus's noble attempt to help you, my attempt to close down possible loopholes, and other members' attempts to walk you through the logic of Lorentz transformations, is --most unfortunately-- to no avail. Pitty. Good day.

That wouldn't be directed at me, would it? Unsure. You tell me: https://ourworldindata.org/grapher/food-expenditure-per-person-per-year

Both FBI and DoE reviews offered as probable the "lab leak" source based on their review. Please also recall Wuhan work was reportedly conducted in a BSL-2 lab - the limited contamination control standards used typically in micro 101 teaching labs.

Yes, there are many contradictions. Please read the paper first. Thanks This is not as easy as you said. Have a look at these transformations first. They are not symmetrical and I have demonstrated it by mathematics. Read the paper first. Thanks. Your mathematics is not true. First, you mention that β=v, which is not right. then, you mention γ′=γ, which is meaningless. What is meaning of γ′ or β′? did Einstein himself applied such kinds of meaningless terms himself? Your formula only imply that Lorentz transformation leaves the metric invariant. Yes, this is true. However, it does not mean that the Lorentz transformations are symmetrical. You have to refer to the main formula not to the variant, covariant or determinant of these formula to find how they are not symmetrical. Read my paper first. Thanks.

Sorry, I have replied to somebody else. But, the answer to you is that, This is not as easy as you said. Have a look at these transformations first. In the Lorentz equations, the direction of motion is not important. It means, whether the S’ is moving to the right or to the left, the S observer applies the Lorentz relations without changing the sign of 𝑣. Therefore, we could argue that 𝑣 is a scalar not a vector quantity in the Lorentz relations. Hence, when these relations are inverse, only the quantity of 𝑣 is important not its direction and we must not change the sign of 𝑣. Thence, because the inverse equations are different with the main Lorentz equations, we must not consider them as symmetrical with each other. Please look at the images I have attached to this post from the main paper. Thanks.

Please see the images I have attached from the main paper below to this topic. Thanks. No, dear. you just use the main Lorentz equations, regardless the direction of S' motion. It means, if the S' moves to the right, you use 𝑥 = 𝛾(𝑥′ - 𝑣𝑡′), and if the S' moves to the left, you use 𝑥 = 𝛾(𝑥′ - 𝑣𝑡′), again. the amount of V is important, not its direction. That is the key point.

If a parameter is scalar like mass, density, ... it is characterized by magnitude and have no corresponding direction. They are physical quantities that are represented solely by magnitude as well as size. So, it has not a sign (+ or -). if a parameter is a vector, like velocity, acceleration, ... it has a sign. You mentioned the true statement. Here, in the Lorentz formulas, the velocity is not a vector. So, the inverse equations for S' observer is not the same as the main Lorentz equations. in inverse equations you will have +v instead of -v. That is why they are not symmetrical equations. No, the key point is that the velocity is a scalar parameter, not a vector here.

In mathematics, this term you mentioned : Λ(v)Λ(−v)=ΛΛ−1=I does not mean that Λ is symmetrical. For instance, [1/8] is the reverse of [8] in 1D matrix and [1/8].[8]= I. But 1/8 is not symmetrical with 8. Λ is symmetrical when Λ(v)= Λ(−v), which is not in Lorentz equations. See the term "Parity" in physics. In 1 dimension: 𝑥′ = 𝛾(𝑥 - 𝑣𝑡) but the reverse equation is 𝑥 = 𝛾(𝑥' +𝑣𝑡′). They are not equal to each other. Therefore, they are not symmetrical. we can not change the sign of v, when we reverse the equation. Why? Because it is not a vector. It is a scalar parameter. Even if you consider it as a vector, its sign in both of above-mentioned equation remains +v because we defined it as the velocity of S’ direction to the S direction which is to the right (+). it must be mention that we are talking about physical parameters like velocity and it must be a scalar or vector. they are not just mathematics. Your proof is completely wrong, as the others made this mistake. I have provided an easy and understandable of asymmetry of these equations. Please read my paper completely and learn about many contradictions in today's Special Relativity interpretation. I have worked on this subject more than 10 years and know all matters you have mentioned before. Please read my paper. Kind regards, and thanks for your discussion. No, in both of those cases you mentioned, you will use 𝑥′ = 𝛾(𝑥 - 𝑣𝑡), when you want to use Lorentz boost, without applying + or - for v sign, or else, instead of length contraction and time dilation, you will achieve length elongation and faster timing.

I gave you a picture of how much money people in the world spend on food per person when they cook at home. Does a "westerner" have six times bigger the stomach of anyone else in the world? Looking at these numbers from the point of view of restaurant expenditures, it would look even more terrible for overly rich and obese Westerners.. You seem to be a very simple person, simple minded, if my first comment was worthy of neg by you.. Get your nose out of the den and go out into the world. It reminds me of the Taco Bell/Pizza Hut scene from Demolition Man with Sylvester Stallone and Sandra Bullock, when hungry people tried to get a scrap of food at the same time outside (at the end of scene):

I did not put c=1. others who were discussing with me did it, and I replied to them.

..westerners are truly depraved by wealth..

Since the introduction of Special theory of Relativity (SR), Lorentz invariance has been a fundamental part of our description of nature. Over the past decades, this (Lorentz invariance) was tested and verified by many research groups and almost no Lorentz violation has been found. However, when we look at the Lorentz transformations, we can mathematically find that they are not symmetrical relations. In fact, the inertial frames are not symmetrical in relation to each other and as a result, there must be a reference frame. If the inertial frames are symmetrical in relation to each other, as the SR argues, some paradoxes and contradictions are happened. Hence, we need to find the misconceptions in this theory. Many researches up to now, focused on Zero-Point Field (ZPF) as a cause for many physical phenomena like mass, inertia, and gravity. One can argue that the Lorentz transformations can be applied only for the inertial frames, moving inside the ZPF and the inertial frames, being at rest in relation to the ZPF, must not bear the Lorentz transformations. In addition, we have found that the SR and General Relativity (GR) are not two separated concepts. They are one thing and the space-time of them are the same. In both cases, it is the ZPF, which curves around the accelerated body or a gravitational mass, causing changes in the body’s length, time, and mass. The full-length published paper can be available via the following link: Bahari, Abouzar. " Zero-Point Field is the Cause for the Lorentz Transformations and Leads to Find Misconceptions about the Special Relativity" BULETIN FISIKA [Online], Volume 25 Number 1 (5 September 2022), ISSN 2580-9733, https://ojs.unud.ac.id/index.php/buletinfisika/article/view/82042

Do not claim. Prove it, if you can Mr. mathematician. I knew this, but please note that c is a physical parameter, and is not a mathematical one. So, it can be lessen to 1 in mathematical formulas or Minkowski space-time, metrics, etc, but it should not be ignored or lessen to 1, when we discuss about physics or physical parameters.

span widget When the S is stationary and S’ is moving, what you are saying is that the term x'=(x-vt) in the Lorentz formula is in the Galilean-Newtonian mechanics and does not relate to SR. OK, this is true. In Newtonian mechanics, when we use the negative quantities for v, you will use x'=(x+vt), instead. Example: x= 10 m t= 2 s v (S’ velocity) = 3 m/s x'=(x-vt)= 10-(3)(2)=4 m For v= -3 m/s --> x'=(x+vt)=10+(3)(2)=16 m However, in Lorentz transformations, we are not going to use x'=γ (x+vt) and t'=γ(t+vx/c2) in the case that S’ is moving with the speed v to the left (for instance v = -108 m/s) and in any papers, texts, books, etc about the SR, nobody use such terms for Lorentz equations, in the case that S’ is moving to the left. Not Lorentz, nor Einstein, nor any other people. All the times, everybody use the main formulas, whether the S’ frame is moving to the right or to the left. Have you asked of yourself, why? That is because the Lorentz formulations have been invented to consider the light speed to be constant to c when it is propagated spherically for both S and S’ frame: metrics invariance for both S and S’. Before I make an example, I will derive the Lorentz equations when a light signal is propagated spherically : 𝑥 2 + 𝑦 2 + 𝑧 2 − 𝑐 2 𝑡2 = 𝑥 ′2 + 𝑦 ′2 + 𝑧 ′2 − 𝑐 2 𝑡 ′2 = 0 --> x=ct , x'=ct' x'=γ (x-vt) --> ct'=γ (ct-vt) x=γ (x'+vt' ) --> ct=γ (ct'+vt') 𝑦 = 𝑦’ 𝑧 = 𝑧’ t=γt' (1+v/c) t'=γt (1-v/c) t'=γ^2 t' (1-v/c)(1+v/c) γ=1/√(1-v2/c2 ) For instance, suppose the S frame is stationary and the S’ frame is moving to the left with a constant velocity v = 108 m/s. When the center of coordinates (zero point) of these frames is coincided with together, a light signal is propagated from this point spherically (suppose in the figure 1, S' is moving to the left instead of moving to the right). At this moment, the clocks of both S and S’ observers which have already adjusted together, start to work. We want to calculate the light coordinate in both S and S’ frames after 2 ms. In the S frame: t=2 ms x=ct=3×108×2×10-3=6×105 m =600 km In the S’ frame: with employing the Lorentz transformations, we obtain: x'=γ (x-vt)=1.06 (600-108×2×10-3)=424 km t'=γ(t-vx/c2 )=1.41 s Graphically, you can find that the quantities we have achieved with these formulas for the light signal coordinate for S’ is not true quantities for positive axes of x’. However, since the light is propagated spherically, for negative axes of x’, it becomes true. I mean when the x=ct=-600 km --> x'=-424 km Therefore, we can neglect the sign of x and v in Lorentz transformations and always use the main formulas, whether S’ is moving to the right or left. But if you persist to use x'=γ (x+vt), when the S’ is going to the left, it is OK. However, when you reverse the formula to x=γ (x'-vt'), you must not to apply v reversal, as Dr. Rindler says, to make them symmetrical. If so, you would find γ=1/(1+v/c) which is less than 1 and so, your length would be elongated and time becomes faster. Now, you can go and find something funnier. First, the light speed is a universal constant c = 3*108 m/s. It is not equals to 1. So, when you use the c in the equations, if you want to simplify your mathematical equations, you can use c=1 instead. However, when you want it as a physical constant paprameter, you are not allowed to use c=1. For instance, in the Lorentz equations β= v/c is a number between 0 to 1. But if you put c=1, β= v/c is a number equals to v which could be much larger than 1. Therefore, it is wrong to use c=1 in the Lorentz formulas. Second, as a physicist, you are supposed to simplify the equations not to make them more complicated by copy and paste other derivations of them for electrons inside the magnetic fields and we have from the Internet. Yes, absolutely there are other derivations of the Lorentz transformations in 4 dimensions. But, I am using the simple and completely applicable original Lorentz equations only for x direction, intentionally to explain why these equations are not symmetrical: You have the equation x'=γ (x-vt), when you reverse it, you will find x=γ (x'+vt) , these two equations are not the same, so they are not symmetrical. You have the equation t'=γ(t-vx/c2 ), when you reverse it you will find t=γ(t'+(vx')/c2), these two equations are not the same, so they are not symmetrical. We are not allowed to change the v sign, when we reverse the equation. Because we are performing just an arithmetic job, not changing the observer. Third, after a PhD in nuclear physics and Ms. And Bs. In engineering and writing many outstanding papers that published in the ISI journals and teaching several years in the university and 10 years of hard studying about the SR (at least 200 papers and 20 books) and deep thinking and learning, yes I can not understand the bullshits you add to my comments like "Λ(−v)Λ(v)A=IA means the symmetry of two equations" or γ' or other wrong statements of yours. But, what I understand is that I am talking to some young boys who ever in BS or lesser period and try to discuss with others without even study and learn their papers. This is crazy. I taught I am discussing with some literate people not some dogmatic people who try to speak fast and loudly without even studying and hearing the words of the person in front of them. If I knew, I did not discuss with you never. · Please search in the internet and find the symmetry means. If you can prove that Λ(−v)Λ(v)A=IA means the symmetry of two equations, I will accept your words, or else, please shut your mouth and first, study, then talk. · My attempt is not anti-relativity completely. I have accepted the invariant of the Lorentz equations, but, I do not agree with that they are symmetrical. · All the experimental tests agree with the above-mentioned claims. For instance, the atomic clock inside the moving high-speed airplane is dilated with the gamma factor, but the stationary atomic clock on the earth is not dilated. The researchers test the Lorentz formulas for the moving frames and get results for the Lorenz invariance of the inertial frames. However, they have ignored to test the Lorentz formulas from the view of the moving observer who thinks he is at rest according to what the SR says. Therefore, what they actually achieved is the Lorentz invariance not the symmetry of the inertial frames. · My paper after 5 month from its publication by a refereed journal was taken into account much more than I expected. In your forum, you mentors do not allow the others to speak. You just want to speak what you have learnt already in your books. But the real researchers are open- minded persons who do not think that all the matters in the books are true. They are finding the false theories. Just search how many famous scientists are completely or partially against relativity (you can find it in my paper). · About what you said I do not want to understand the negative value in the equation, read my answers to other. · But, whenever, some dogmatic people are dominant on the world of science, they could not be successful to talk and make their theories worldwide spreading. I do not want to say the journals should publish bullshits. But, I want to say the new theories if they are elaborated scientifically, must be published. Recently a published research showed that the velocity of the progress of science decreased rapidly in recent years. The reason is exactly those dogmatic people in the world of science today. Unfortunately, the people like you, when they have not enough logic in their hands (mathematical or physical logic), try to humiliate the person against them. That is the method of not literate and not civilized persons and I am so familiar with such people. I again recommend you to study more and then come and discuss with honorable people. Just search my name then open your mouth and say bullshits.