Schneibster

Neither Strange nor I has made any discernible difference and I see no further point.

In fact you denied it was two way. I did. I became annoyed when you started questioning their postulates. No mathematician does that without acknowledging that's what they're doing. But you did. Then you made claims about "correctness" and have not yet withdrawn them, when it's been shown that a prominent relativist says you're wrong. Lizzie, if you want to talk about relativity, learn its postulates first. That is my best polite advice. You do not know them and it is painfully obvious. Studiot, likewise, but far more. You simply do not understand spacetime physics if you do not understand relativity, and I'm sorry but you do not understand relativity. Saying "I included time, see, t = t" is risible. Please don't repeat this kind of stuff.

Wow. I "introduced" them. So do you think I invented relativity? Is this supposed to be some sort of unscientific thing I just came up with out of my bowels? Are you seriously questioning relativity or the Lorentz transform? If you are, on what grounds, please? How about if you stick with the hyperbolic trig versions? Are they too difficult for you to understand?

Actually, the hyperbolic trig formulae work fine. They merely require you to abandon your ridiculous prejudice in favor of "velocity" and use real relativistic rapidity instead and start doing real physics with 4d rotations like Lorentz and Minkowski and Einstein told us we were supposed to.

Lizzie, that's not hard math either, and it's reversible like almost all of physics. You were the one who brought it into the topic, and you got pwnt. It's time you admit it and start learning some real physics instead of constantly playing games and trying little digs about how Galilean physics works when you don't understand SR. A transform is a transform. A transform cannot make different things the same; that's not what transforms do. Your refusal to admit that this means that space and time are "essentially the same thing" is without reasonable evidence. You are denying relativity.

Frequency is one over time. And the transforms go both ways. Wikipedia: http://en.wikipedia.org/wiki/Fourier_transform And you really should have known better than that, Lizzie. You actually do, I know for a fact; you have to. You can't do your job otherwise.

Note that Fourier transforms are from the frequency domain to the time domain. Just sayin'.

Lizzie, the Lorentz transform shows that space and time are all one sort of thing. It also shows that the relation of time to space is a light-second of space is transformed to a second of time. (Not exactly; it's a more complex relation than that. But that space is translated to time, no one argues.) This is the canon of relativity, if there can be such a thing- it's all mathematically provable, which is what Einstein is famous for doing.

Ummm, sorry, that's exactly what Lorentz says: you can transform space into time and vice versa. Are you, seriously, denying the Lorentz transform? Really? Not particularly. But I'll put up with it if it's what it takes to teach you.

@Hashirama_Senju : You have re-discovered what Einstein called "Mach's Principle." It's actually more of Einstein than of Ernst Mach, but Mach did revive a really old gedankenexperiment called "Newton's Bucket" to argue it. Interesting stuff. I've given you some search terms in the above paragraph that will lead you interesting places. If you need help with your search-fu, let me know; I will provide terms happily. You will also find a good discussion of Mach's Principle in Brian Greene's book, The Fabric of the Cosmos, which I highly recommend. I can look up the chapter if you like. It's actually a pretty direct proof of the Equivalence Principle.

Yes, you did. You used the Galilei transform. See the Lorentz transform. Post 156. Note that it is not the same as the Galilei transform. Note that it is degenerate with it when the velocity/rapidity is zero. Note that time becomes a more and more important element the faster you go. You treated time as if it has no relation to space when they actually do. That's because you used the wrong transform, one that is outdated, obsolete, and known false. The Galilei transform is incorrect because it does not include the Lorentz factor. The correct transform is the Lorentz Transform. That was proven well over a hundred years ago. You're not going to see any other proof. Everyone knows I'm right. You attempting to prove stuff with the Galilei transform is you admitting you don't understand relativity at all. I really don't think you've understood why and how the twin "paradox" and the constancy of the speed of light really work. And you've been fighting well-established physics a long time now, Lizzie. I really think you need to go do some reading/learning. I can recommend some books. I've recommended them to you before and you've ignored me. I won't put you on ignore for not understanding. Only for willfully denying.

You left out time. The reason the Galilei transform is incorrect is because it fails to correct for the Lorentz factor. It is incorrect because it doesn't include time in the calculations for x. Surely you understand that the Lorentz transform replaced the Galilei transform, except in the limit of low rapidity? Did you realize that? That's why physicists say that relativity "replaced" Newtonian/Galilean mechanics. Basically, you just said you don't "believe in" relativity because Newton. And also Galileo. Also. Too.

Another way of saying this is to say that the Pythagorean distance formula in Minkowski spacetime is d = x2 + y2 + z2- c2t2 Note I bolded the negative in the last term. This definition of "d" is called the "spacetime interval" and is as important in spacetime as the Pythagorean distance d is in space. Note the inclusion of the c coefficient in the time dimension's term. Again, this is why I say we move through time at the speed of light. It says so in plain mathematics right freaking there, no questions, no doubts, no BS.

Sorry, if you can't do the math I won't discuss equations with you. LOL I'm sorry, Lizzie, you too. Learn the math then come back. This is a waste of time. You're just making stuff up to object to in order to harass me. One more like this and you go on ignore. One more try for you both: If you have to remove vt from x, then you have to add it to t. That's how the transform works, mathematically. Perhaps if you think of them as simultaneous equations it will help.

Never mind.

Whose convention? You appear unfamiliar with the mathematics of the Lorentz transform, which are far more basic than relativity. I'm using math from John Baez, who is an expert relativist and mathematician and lectures at the University of California, where he is a professor of mathematics. He's probably best known for his "Crackpot Index," a humorous look at internet nutjobs, but he is also an expert in exactly the areas we're discussing. What "correctness" do you assert John Baez is violating? Or what "conventions?" Please elaborate. So you can't do the math. I don't need to define anything. Do you deny that operation transforms x in to partly x and partly t? Never mind what they mean yet- let's just get the math agreed to. I did. Which is precisely what it should say. If your rapidity is zero in x then your Lorentz transform in x is x' = x. Or in the other notation x → x.

x → √(1 - (v2/c2)) * (x - vt) doesn't look like transforming x in to some x and some t, to you? Really? That's one observer's viewpoint. Not both. You're ignoring the main observer.

Well, I hate to say it but I'm finding you just don't understand the math. You also appear not to understand the meaning of "postulate." Nor the meaning of the fact that time calculations work perfectly when you use hyperbolic trig. And the equations are obviously those of a rotation. How can you "rotate in the xt, yt, and/or zt planes" and not rotate time into space? What do you expect to perceive? If you expect anything different than you see now, you're wrong- unless you look out at the universe. That's the meaning of the Principle of Special Relativity, another postulate of the Theory of Special Relativity. So if you go fast enough, you will "see time," and it will look just like space to you. Time and space are the same thing. This is a fact. We know for sure. It's not some nebulous bunch of BS, it's a solid mathematical theory invented by a math genius in the last century named Einstein. It remains uncontradicted in that time, ever. No experiment has ever caused a continuing question about a postulate, or a theoretical finding, of Special Relativity. It is one of the postulates of the Standard Model of Particle Physics, and of the Standard Model of Cosmology. (In that it exceeds even its progeny, the far more powerful Theory of General Relativity, which has not been integrated into the SM of Particle Physics, along with its more far ranging Principle of General Relativity and Equivalence). If you're waiting for an expert that will tell you any of those things are wrong you'll be waiting a long time, Lizzie. It's not superfluous; velocity is. Rapidity is the way you measure movement in relativity; velocity is outmoded. I suppose you could use β, which is v/c, that is the fraction of c of your "velocity," or γ, which is the Lorentz Factor, √(1 - β2), if you insist on using faux Newtonian physics.

Lorentz transform proves space and time are equivalent by direct transformation. Equations governing transformation of space to time are provided. You cannot transform dissimilar things, period. Please pay attention to the math.

That's simple: it's this fictitious thing called "velocity;" some people think it's somehow "the same" as rapidity, which is rotation in the xt, yt, and zt planes of spacetime. It's kind of obsolete, but we keep converting things to it and pretending space and time are different even though Einstein told us a hundred years ago they're not. Ummm, that didn't help much. You seem to be having a lot of trouble with the math.

Yes, really, if you "believe in" relativity. Lizzy, this is why the light cone is 45 degrees. It's a postulate of relativity. It's like zero, or the meaning of +, or of (). You could maybe get more information from the philosophers but my experience suggests you'll wind up knowing less than you do now.

I'm familiar with dimensional analysis (which is what that's called). Please explain why the Lorentz transform can change time into space and vice versa if they are "different things." It's only a transform; no more, basically, than (for example) changing the angle your x y and z point to, or changing the location of the origin. That's all transforms can do. They can't alter the basic character of things; if you "turn the corner" you won't "turn into a penguin." At least not via a transform. No. The shape of time forms the speed of light; the speed of light defines the shape of time. They are effects of a single cause: our universe obeys special relativity. I can put light-seconds on the t axis if I like. It will work fine. We can update all our time measurements to use light-seconds. And Lizzy, if we do, it will all work. All of science, all of engineering. No problem. Just gotta make all the unit conversions. Of course, having the unit of time be 2.997925x108 might be a bit unwieldy, we've got computers, it's no biggie.

The speed at which future seconds become past seconds. It's one second per second. Which is c.

Let's try another angle: Why is the speed of light constant? I am most very sorry to directly contradict you but in fact the speed of time is defined by the speed of light. You are totally ignoring the math, Lizzie. Go back and look at the Lorentz transforms again. Post 158.156. Studiot used the wrong post number above, I think.

Did you read the traditional Lorentz transform in post 158 156? Read the BTW part at the end. That's what the necessity of that factor of 1/c2 is. That's why it's there. If we were (impossibly) accelerated to the speed of light, we would be rotated so that what appears to everyone not sharing our velocity to be x, appeared to us to be our future or t, and what appears to everyone not sharing our velocity to be t to be the direction we're moving, or x. This is not a matter of perception. It is a matter of the actual character of time and space.