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- Thread starter Dorje
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[tex]ds^2 = dx^2 + dy^2 + dz^2 + (icdt)^2[/tex]

If you fix the s and let the x, y, and z terms be insigificant, the time term is dominant. On the other hand, if the x, y, and/or z terms are significant, then the time term must be less significant.

cookiemonster

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I think Brian Greene explains it mathematically at the end of the book, in one of his 'footnotes'!

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The imaginary there is quite outdated. The source of the sign differennce is better understood when it is written in terms of the Pauli matrices including the 2x2 identity matrix [tex]\sigma _0[/tex]:Originally posted by cookiemonster

[tex]ds^2 = dx^2 + dy^2 + dz^2 + (icdt)^2[/tex]

If you fix the s and let the x, y, and z terms be insigificant, the time term is dominant. On the other hand, if the x, y, and/or z terms are significant, then the time term must be less significant.

cookiemonster

[tex](\sigma _{0}dc\tau)^2 = (\sigma _{0}dct)^2 + (\sigma _{x}dx)^2 + (\sigma _{y}dy)^2 + (\sigma _{z}dz)^2[/tex].

The Pauli matrices serve as a description of an orthonormal basis with the 2x2 identity associated with time. Boosts between frames are then described as rotatons in spacetime and this spacetime structure revealing spin half eigenvectors corresponding to rotations in space is then understood as the source of such quantum mechanical phenomenon. The ict concept is as outdated and uninstructive as the "relativistic mass" missnomer.

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Yes. Consider the velocity four-vector, [tex]U^\lambda = \frac{dx^\lambda}{d\tau}[/tex]. The four dimentional speed that he is reffering to isOriginally posted by Dorje

[tex]|U| = [g_{\mu}_{\nu}U^{\mu}U^{\nu}]^{\frac{1}{2}} = c[/tex].

In the correct relativistic description which he is using everything always travels at this speed c in that way following geodesics when unacted on by real forces and all that real forces do is deflect them from geodesic motion. The real forces just rotate their direction in spacetime.

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That's a very poor way to think. This is not "traveling" in the normal sense. To "travel" means that one's position in space changes by the amount dr during a time interval dt and the speed of then said to be dr/dt. Greene is speaking not of a spatial displacement per time interval. He is refering to a spacetime interval, ds, in spacetime during a proper time interval dT. But this is another quite different concept that that of dr/dt.Originally posted by Dorje

Greene is not refering to a spatial displacement dr and he's not refering to a time interval dt. He's refering to a spacetime displacement ds and a proper time interval dT. But moving through spacetime with speed "c" Greene means that if

Let d

d

Then the particle's 4-velocity

Then it follows that

It's highly unintuitive to say the all objects move through spacetime at speed c since the term "motion" brings to mind spatial movement. Even a body at rest has a non-zero value of ds. And when it comes to the speed of light then you can't even assign a speed to it in the sense that Greene is speaking.

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turin

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As much as I don't care for the expositions of Briannne Greeeennnne (I don't know how to spell it), I feel I have to throw my two cents into the pot to say that I think it is a verypmb_phy said:That's a very poor way to think.

I would just make one minor adjustment from "time dimension" to "time direction."

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