Tachyons travel backward in time?

DaleSpam

I mean that you cannot rotate in a single dimension.

I am not talking physics here, just geometry. In a single dimension you cannot rotate an object so there is a clear directionality to the two ends of a line. In two or more dimensions there is no longer a clear directionality to the two ends of a line. You can always approach the line from the other side and then the sense of the direction of the line is reversed.

I thought that was the point you were making with your "Why should a timelike worldline in relativity be any more directional than a line on paper?" comment.

peter0302

I've just never heard an explanation as to why a "normal particle backwards in time" model is any less "real" and more of simply a "trick" than a "anti-particle forwards in time" model. Seems to me like people use the latter view just to comfort themselves into believing in the absolute nature of linear time.

I also find it incredibly interesting that a 4-dimensional Euclidean view of Relativity has particles moving faster than the speed of light as moving backwards in time as well. These particles would be indistinguishable from anti-particles. But, again, we don't use that model, and instead use the Minkowski model, simply to keep our minds at ease that time always moves forward.

[Edit] Just wanted to add, in that model,whether the particle is a "real" particle or "anti" particle is frame-dependent. In other words, _all_ of the quantum numbers, not just mass, become frame dependent. Doesn't this make for a simpler unified theory?

JesseM

But what do you mean by "forwards in time" or "backwards in time"? As far as I know particles don't "move" in time in either direction in any meaningful physical sense, they just have worldlines in spacetime. Like I said, maybe in the course of certain mathematical procedures you would integrate along the worldline from one end to the other or something like that, but I don't think there's any reason to take this too literally as some sort of physical reality (and note that even as a mathematical procedure, I don't think you're forced to treat antiparticles as normal particles moving backwards, it just simplifies the calculation, and I imagine you could equally well say antiparticles are moving forwards and normal particles are antiparticles moving backwards.)
The minkowski model doesn't say time moves forward or backward, any more than it says space moves left or right, at least not as far as I can tell. And what do you mean by "4-dimensional Euclidean view"?

JesseM

No, my point was about physics, that there isn't any physical meaning to the notion of something actually physically "moving" in a particular direction in time. And the fact that a line isn't "moving up the page" or "moving down the page" doesn't have any relation to the question of whether or not you can rotate the paper, as far as I can tell--why do you think it would?

peter0302

http://www.physicsforums.com/showthread.php?t=103977

And, as far as the Minkowski model, if you draw the worldlines of various particles moving at relativistic speeds, none are ever moving in the -t direction for any observer. In a 4-dimensional Euclidean relativity, with time on equal footing with space, if you continue to accelerate "past" 'c' relative to an observer you wind up moving backwards in time relative to that observer. By extension, that observer would believe you to be made of "antimatter".

JesseM

That's a lot to look over, but I'll try to get to it sometime.
I still don't know what you're talking about here. What does it mean for a worldline to "move" at all, given that spacetime is completely static? Do you claim that worldlines are "moving in the +t direction" for any observer? If so, in what sense? Can you give a numerical example or something? Perhaps you're talking about the "arrow of time" for macroscopic objects (including the psychological arrow) rather than something that can be applied to individual particles?

peter0302

I really think I'm being obvious, but nonetheless:

Take a two-dimensional Minkowski diagram for any particle, one axis being "x", one being "T", where T=ict. dT/dx is always >= 1 and, obviously, is always greater than 0. That's what I mean by "forward" in time.

JesseM

Why are you multiplying by i here?
Given your definition of T, won't dT/dx be imaginary? Consider the worldline of a particle moving at 0.5c (we can use units of 0.5 light-seconds per second) in the +x direction. Then we'd have x(t) = 0.5 l.s./s * t, meaning that t(x) = 2 s/l.s. * x. In this case if T(t)=ict = it*(1 l.s./s) then T(x) = 2i * x. So, dT/dx = 2i.

peter0302

I thought "ict" was the conversion used in SR for time to space. Maybe there's no 'i'. Either way, same point.

JesseM

But the point doesn't work if you remove the i either. Before I imagined an object moving in the +x direction at 0.5c, now just imagine one moving in the -x direction at 0.5c; if dT/dx (with T = ct) was 2 in the first case, it's -2 in the second case.

DaleSpam

Sure it does. This is pretty basic topology. If you have a line segment in one dimension, and you consider arbitrary smooth transformations (homeomorphisms), the only way to swap the positive end and the negative end is through a degenerate state (a point or an infinitely long segment). In other words, topologically the positive end is always the positive end and the negative end is always the negative end. On the other hand, if you have a line segment in two dimensions, and you consider arbitrary smooth transformations, you can easily swap the positive end and the negative end without passing through a degenerate state.

I'm sorry that I misunderstood your point. The way I misunderstood it was pretty interesting though. I haven't thought about it enough to attach to it any physical significance yet, but I think that there may be something geometrically or topologically different between the two ends of a timelike line and that there is not such a difference between the two ends of a spacelike line. I could easily be wrong on that point, and even if I am right I haven't thought it through to a physical conclusion, but I find it interesting.

JesseM

Yes, obviously if a line comes pre-labeled with a "positive end" and a "negative end", you can distinguish between lines with the positive end up and lines with the negative end up, and in one dimension you can't smoothly rotate one into the other. But if I just draw a line on a piece of paper without any labeling, how are you going to decide whether it's "moving up the page" or "moving down the page"? Likewise, what physical features (not arbitrary decisions about how we humans choose to label things) do you think distinguish a worldline that's "moving forward in time" from one that's "moving backwards in time"?

Magic Man

The fact that diagrams and equations show that something could travel back in time doesn't mean it's a fact, it just shows the maths can go both ways - we developed the maths to explain observed results. Time doesn't exist, it's simply what we measure as the passing of one moment to the next.

Light doesn't govern the passage of time, we base the measurment of time on the speed of light but something travelling ftl doesn't mean it travels back in time. What we observe in experiments involving such particles is not neccessarily what is actually happening - our observations are limited by the speed of light afterall.

peter0302

Ok, then why don't you tell me the mathematical way of saying what you know I'm trying to say?

JesseM

I don't know what you're trying to say, because I don't think there's any physical meaning to the notion of "moving forward in time" vs. "moving backwards in time".

peter0302

Ah, then why don't you go change the past for us?

JesseM

Physicists talk about the notion of time travel without any need for a notion of "moving" in time--they just talk about "closed timelike curves", analogous to a line on a piece of paper which bends around into a loop so two different parts of the line can cross. As long as there are no timelike curves, time travel isn't possible.