uncool

As ydoaPs said, that was the point - Endercreeper has been claiming that this is false, so ydoaPs was using his own logic to demonstrate that Endercreeper was wrong. My correction was along the same lines. Further, you have made an error yourself; namely, that sqrt cannot be defined as "the positive one" on the entire real line; it can only be so defined on the nonnegative reals. That (-1)^3 does not mean the same thing as -1^3; the first means -1*-1*-1 (as I had in my post); the second means -(1*1*1). They come out to the same quantity, but using that misses the point of the question.

I want to point out that that specific error started with EnderCreeper01, and ydoaps was using the (still incorrect) same notation. To correct what ydoaps said in terms of notation: So, root((-1)^3) = (root(-1))^3, right?

I agree with the statement as stated. However, rbwinn seems to be using (in effect) a generalization of the Galilean transform that includes arbitrary time dilation; this group is not inconsistent with an invariant, finite speed of light in a particular direction. It is, however, inconsistent with an invariant, isotropic, finite speed of light (as I have been pointing out), which is not true for the Lorentz transform. =Uncool-

Except that it still isn't. The Lorentz equations are the following: x' = \gamma (x - vt) y' = y z' = z t' = \gamma (t - v/c^2 x) if I haven't made a mistake. It includes time dilation and "shear" in x (i.e. the part with x - vt), which are what yours feature, but also includes length contraction and dependence of t' on x. All of these are necessary, and you have forgotten the last one. This is, in fact, the "fix" that I mentioned before. Not true. Once again, the Lorentz equations don't have an absolute ordering on how "fast" clocks are. No, they are not. Anything that is moving at the speed of light relative to K will be moving at the speed of light relative to K'. K' is one frame of reference, period. So you are once again violating the principle of relativity itself - the foundation of Galilean relativity. So your idea - not theory; that has a specific meaning in science - is that light "reacts at c" relative to every frame, basically? Because that's effectively the same as the premise for relativity that I've stated repeatedly. =Uncool-

No, they don't, because with Lorentz equations you don't have to say that one clock is absolutely faster than another. You are assuming that there is an absolute standard of faster and slower clocks, which is almost exactly what Einstein was pointing out that you cannot do. So you're saying that you've abandoned the idea that the speed of light can be invariant and isotropic? That is, that it must be the same in all directions in all frames? Because if you have, then that's an easy thing to test - and we have tested it. And the evidence points towards it being true. =Uncool-

So for light going in the -x direction, the clock must be slower in K and faster in K'. But for light going in the +x direction, the clock must be faster in K and slower in K', as I will show. +x: x = ct, x' = ct2', x' = x - vt implies ct2' = (c - v) t, or t2' = (c - v)/c t. -x: x = -ct, x' = -ct2', x' = x - vt implies -ct2' = (-c - v) t, or t2' = (c + v)/c t. So in K', we get that t2' = (c - v)/c t = (c + v)/c t. So the clock in K' must be both faster and slower than the clock in K in order for both light beams to keep the speed of light. You keep only considering one light beam at a time. I'm asking you to consider both at the same time. ETA: I have corrected a sign error that I made; I apologize for that. It doesn't affect the outcome, however (since it basically switched v and -v). =Uncool-

Blatantly false. I have directly responded to your answers; I have shown the work behind my answers. So I have neither ignored your answers nor repeated dogma. Do you know what isotropic means? Because you are showing that the speed of light in one direction can remain the same, which is not the same as the speed of light in all directions remaining the same. What I have shown is that in order for the speed of light in one direction to remain the same, the speed of light in the opposite direction must change under these transformations. The response of scientists is to ask you to identify the mistake in the demonstration that the Galilean transformations cannot show that. They show that the speed of light for one light beam is the same. That's not what isotropic means. Isotropy is uniformity in all directions. You have dealt with only one direction. What I will tell you is that you have dealt with only one direction, and pointed out that light going in the other direction will not be moving at the speed of light under the same transformation. At this point alone, you don't understand my objection. I have been using the same two frames as you - K and K' - this entire time. Please learn what isotropic means, and then deal with what I have written. That's not why I asked you to use the quote button. In fact, I remember what I said quite well when I asked you to use the quote button - I asked you to use the quote button so that we can determine which part of what I said you are responding to. No, you said that scientists cannot follow simple instructions. I'm not surprised, since you don't seem to have seen any scientists ever. No one has said this. You are making a strawman again. No one has said this. You are making a strawman again. This is one reason for quoting - so you can actually point out what you are referring to, rather than lying about what other people here have said. It cannot be done such that all light moves at the same speed, as I have already shown you. As it happens, I have asked you to follow simple instructions. Show me where I made a mistake or misunderstood what you meant in the post where I demonstrated that light going in the opposite direction will not stay at the speed of light under your expansion of the Galilean transformation. That's a simple instruction, and you have yet to follow it. =Uncool-

Please stop trying to annoy people here. This statement assumes a distinguished frame K. That's not how any kind of relativity works - Galilean or special. Galilean relativity is named after Galileo because of his discovery that the laws of physics are the same with respect to every inertial frame - you are saying that there is a unique frame "at rest", which can be distinguished by time passing most quickly - that is, that if you have a bunch of caesium clocks moving at different velocities, the one that "ticks" fastest will be the one that is at rest with respect to this frame. That's not what people have been saying. You continue to set up strawmen for yourself. What people have been saying is that they can't account for experimental evidence that has been presented and explained within this thread. I am going to ask again for two things: first, please stop with the insults and condescension. Second, please try to quote what you are responding to. See the "quote" button on the bottom right? Please use it. It's really not difficult, and makes conversations much easier to keep track of. =Uncool-

Polite requests for evidence, for explanations, and for politeness? A willingness to explain why a Galilean transformation can't match up to a Lorentz transformation? Scientists entertaining your notion for pages on end after repeated accusations of dogma, fraud, and the like? Because that's what you've gotten here. And as has been shown using your own equations, the speed of light is not isotropic relative to all frames under your transformations. Which contradicts the evidence, indicating that your idea contradicts reality and therefore that special relativity is a better choice for theory than yours. =Uncool-

You are still using complex numbers - the square root itself is complex. And that's what the page is referring to. And because you are taking the square root of a square and not getting the same number. You're effectively saying that i = -i because i = sqrt(-1) = sqrt(-1*-1*-1) = sqrt(-1)^3 = -i, which is blatantly false. Basically, every number has two square roots; if you restrict yourself to the positive real numbers, you can choose one unambiguously (namely, the positive square root). However, if you add in the negative reals and the complex numbers, you get ambiguity that you can't get rid of. That's how the math works. People have answered your question repeatedly now.

Why? Really? Would you mind pointing out where he made that assumption? Or do you mean that Maxwell did all of his calculations as if there were an absolute frame (called that of the ether)? There is, however, evidence of length contraction and the full Lorentz transformation, as has been shown in multiple experiments that have been named in this thread. You can feel free to believe otherwise, but there will be no reason to take you seriously. "Seems" according to what? The primary complaint is that they contradict the evidence that the speed of light is invariant and isotropic. The fact of length contraction falls out of that premise. Then yes, you have misunderstood the equations. In order for light to travel at c relative to all frames, you need both length and time dilation. No, that is not what I am saying. What I am saying has nothing to do with absolute time. What I am saying is that in order for the speed of light in one direction to be invariant, the speed of light in another direction cannot be invariant under your group of transformations, whereas the speed of light in all directions remains the same under the Lorentz transformations. There is no need to wait. Make your predictions. Scientists have already made predictions and observations for relativity - they have been doing so for more than a century already. rbwinn, before you go on, I'd like to ask you to do something in the future. When responding to someone, please use the quote button to quote precisely what you are referring to. While it may be clear to you what you mean and to whom you are responding, it's not clear to everyone else. The quote button makes it obvious - you can see in my posts precisely what I'm responding to where, etc. =Uncool-

Which isn't the same, period. The length contraction is an integral part of the Lorentz equation that can't simply be disregarded because you don't like it. This isn't even close to the Lorentz equations; it's missing a factor of gamma, and the Lorentz equations do not include that condition. You keep being vague. Which "ideas" are you referring to? After one second in which frame? Or, alternatively, you have misunderstood the equations. Which is more likely? You are setting up your own strawman of relativity by removing length contraction and then demanding that your strawman make sense. You've managed to knock down your misunderstood version of relativity, but as yet you have not addressed what relativity actually says. =Uncool-

As it happens, neither do scientists. Who said that they were? Not that they are incorrect. That they have problems with experiments. The problem is that experiments have shown that the speed of light is isotropic relative to every inertial frame that has been tested. In layman's terms, that means that the speed of light is the same in every direction. So a transformation would have to preserve that property - if something is moving with speed c relative to frame K, then its transform should be something moving with speed c relative to frame K'. Yes, they do. I don't understand your point here. But the speed is still 186000 miles per second. Speed doesn't have a direction - it's simply a number. And experiments have shown that it's the speed of light that is the same relative to every frame, in every direction. The equation you've written here is not what the Lorentz equations say. So no, this is not the same as the Lorentz equations. =Uncool-

I asked you to identify the error in what I posted. You are simply saying that the conclusion is wrong without identifying any mistake I've made. That isn't a sufficient objection. Did I perform your transform incorrectly? Did I make a mathematical mistake somewhere? Did I misunderstand something? Further, the Lorentz equations do not have the same problem - that is, something moving at the speed of light in either (and in fact, any) direction remains at the speed of light after a transform, which is what I just demonstrated your expansion of the Galilean transform can't do. Do you want me to demonstrate? Before answering this question, I'd like to clarify. Which scientists are you referring to? Theoretical (mathematical) physicists? =Uncool-

You have once again managed to fail at mindreading. Please, stop trying. Please quote the specific part where we said this. You have a tendency not to quote what you are referring to, and it means that we have no idea what you are responding to. This makes it very difficult to figure out what you are trying to say sometimes. So please quote what you are referring to. Is this your attempt to use "our equations", or are you answering "Further, how much faster will it go? Can you predict that precisely? " This is here to make sure that the speed of light is the same relative to this frame, right? Actually, they have more problems. Because while you've managed to get the speed of light that is moving in one direction to be invariant, you have not done so for all of them. For example: You've said that t2' = t (1 - v/c); at t = 1 sec, t2' = 1 - 30/186000. Now, let's take a look at light travelling in the opposite direction from the original lightbeam that you looked at. We then have that x = -ct. By the equations that you've repeated and repeated and repeated, x' = x - vt = - (v + c) t = - (v + c) t2'/(1 - v/c) = -c ((1 + v/c)/(1 - v/c))t2'. So at t = 1 sec, we have t' = 1 - 30/186000 sec, x' = -186000 - 30, which gives us a speed that is not equal to that of light. So we actually get that the speed of light relative to this frame is not isotropic, which contradicts everything we've ever tested. What you've basically done is expand the group of transformations allowed to include time dilations without spatial dilations. If we choose one direction, we can preserve the speed of light in that one direction, at a cost of the speed of light in every other direction by using this group - which isn't enough. Of course, I may have misunderstood what you've said, or made a mathematical mistake. Please point out any mistakes or misunderstandings I've made. =Uncool-

You have hidden one assumption there, which is that a meter in K is the same as a meter in K' (which is one of the assumptions of Galilean relativity). If the length of a meter is changed proportionally, then they will not get a faster speed between frames of reference. Even when no one has asked you to. That may be a hint that you should stop doing so and try to figure out what they are actually asking you for. Not ours? Would you mind doing the math using "our equations" to demonstrate that? You have made a claim about relativity; now please back it up. What time will the clock on the airplane show? Further, how much faster will it go? Can you predict that precisely? Relativity can, in terms of the velocity of the airplane. OK, so they are coordinates in (that is, relative to) K'. Why, then, wouldn't a clock in (that is, at rest relative to) K' show those as the time? You aren't a very good mind reader. Please stop trying, and simply answer the questions that have been asked, rather than the imaginary questions you think you've been asked. I know what an equals sign is. Please stop being condescending. This is part of the reason that you get insults - people respond in a way that matches what you do. You've repeated this several times now. It isn't answering the question that you've actually been asked. Please stop repeating until it's actually relevant to the question being asked; it makes trying to have a conversation impossible. =Uncool-

And once again, I don't care. Are you going to answer the question or not? What do x', y', z', and t' represent? Why should we care about them?

Once again, this can easily hide many misunderstandings, and is most likely a strawman of relativity. I know what coordinates are. I know how they work. I am not pretending to not understand how coordinates work. That's not what I've been asking you. What I've been asking you is what x', y', z', and t' represent. You still haven't answered that question. Just because you are repeating something doesn't mean that you have explained it. Why should we care about x', y', z', and t' if they aren't what the clock that is at rest with respect to K' shows? Once again, what do they represent - not what are they equal to, but what do they represent? Then you will struggle in vain. Those who were trying to replace epicycles still had to understand them in order to replace them, and to show how what they were doing made more sense. I am asking you to explain what you are trying to do with Galilean transformations, and you are refusing to do so. I don't care. I'm discussing precisely what you've stated. So once again, I ask you: what are x', y', z', and t'? What do they represent? I'm not asking you what they are equal to, I'm asking you what they represent. Why are they important? I can answer this for special relativity. x', y', z', and t' are the coordinates with respect to frame K'; t' is what a clock that is at rest with respect to K' will show. On a quick side note: From what I've seen here, you are the one who is partaking in insults. Please practice what you preach and stick to the questions, rather than the insults. I've asked a direct question that seems to me to be very relevant. Please attempt to answer it. What do x', y', z', and t' represent? That is, why should we care about these numbers that satisfy the equations you've posted? =Uncool-

I don't think I'm making it difficult. What I am doing is asking you to actually explain what you mean by x', y', z', and t'. What precisely are they supposed to be? I think you mean 1 sec. And while providing examples is generally a good idea, I do understand the Galilean transformation. Do you mean by a clock that is at rest relative to K'? Or do you think that objects are "in" one frame and not another? Further, if t' is not shown by a clock in K', then what is it supposed to represent? Why do we care about it at all? Err. That's not correct, if I've understood you correctly. A clock is supposed to tell us the time coordinate. In other words, a clock that is comoving with K' is supposed to tell us the time relative to K', which is the fourth coordinate. And a transform is supposed to tell us how to transform from one set of coordinates to another - so t', the result of the transform, is precisely what should be on the clock. Well, yes, that's the idea of what a transform is supposed to do, assuming I've understood what you mean by "clock in K'", and as I've shown above. But not for any "standard of space and time". Specifically, they cannot account for the actual first premise of relativity, which is that the speed of light is both isotropic (the same in all directions) and frame invariant (the same relative to all inertial frames). The Galilean transformation that you are suggesting would contradict that, as I can show if you want. This is false; many of the members of this site actually are scientists. You may want to rephrase this. Why is v' 0.3333... light sec/sec? Have you chosen this specifically to deal with the change between t2 and t2'? That is correct; what you are in effect doing is putting in a generalization of the Galilean transformation where you are allowed arbitrary time dilations (but not space dilations). Cannot do what? And what "improper mathematics" are you referring to? I'd prefer that you specifically answer the question about what t' is supposed to be, if it's not the time for a clock that is comoving relative to K'. =Uncool-

The time coordinates of what? Are they both the time coordinate for the same event relative to frame K? So t' is the time coordinate for the event relative to frame K', not to frame K? I have no clue what you are trying to say here. The idea of the Galilean transformation is that it tells you how to "translate" from coordinates relative to one frame to coordinates relative to the other frame. There must be a unique way to do so. But you seem to be describing two different transformations from K to K', if I've read your post right. =Uncool- This way of phrasing it could easily hide many, many misunderstandings. That doesn't mean that it definitively does, but I'd be very careful with it. The premise for SR is that anyone will measure the speed of light to be a constant - approximately 3.0*10^8 m/s. Relativity does presume that clocks are "synchronized" if they are comoving, which excludes "slower and faster" clocks that are comoving, as in this example. "Proper time"? What do you mean by that? There is a meaning for "proper time" in relativity, but it doesn't have the properties that you are ascribing to it. You are setting up a strawman here. This is not what special relativity says. =Uncool-

That defeats the idea of the Galilean transformation equations in the first place. The idea of the transformation equations is to be able to "translate" between the coordinates in each of the frames - you need one for every pair of frames, and they must be self-consistent in some way (namely, when you "translate" from frame A to frame B, and then from frame B to frame C, it must be the same as translating from frame A to frame C; also, transforming from frame A to itself must be trivial). What are x', y', z', and t'? In special relativity, those denote coordinates relative to frame K'; you've said that this is about frame of reference K alone without reference to K', so I have no idea what you mean by this. =Uncool-

I'm not entirely sure I see that Bg4 is devastating. What response is there to 14. Qe4? I looked at 14... Bf3 15. Qe6, but didn't see much beyond there for why it should be a problem for white. The queen and king are precariously placed, but it seems stable enough to me - the rook can't become a threat and in fact is threatened where it is.

Not quite. What I'm saying is there is only one set of 63 different switches, and if you apply all of them, you'll have effectively done nothing. There would be 63 different switches in a row somewhere - so you get the same problem. =Uncool-

Just because this definition doesn't show the beauty or power doesn't make it a bad definition, though. A definition doesn't have to describe every aspect of something.

The way I'd put it is everything that can be proven. Specifically, this includes statements of the form "If we make these assumptions, this is what we can prove".