why is t coordinate negative


by dpa
Tags: coordinate, negative
dpa
dpa is offline
#1
Feb14-12, 03:36 AM
P: 149
In lorentz transformation,
why has t -sign
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Matterwave
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#2
Feb14-12, 04:35 AM
P: 2,045
The sign doesn't go on the t but on the v. Depending on direction of your boost you can have either +vt or -vt.
dpa
dpa is offline
#3
Feb14-12, 04:40 AM
P: 149
i mean for the metric,
s2=-t2+x2+y2+z2.

I beg your pardon if i did not get you. Would you mind to clarify.

Matterwave
Matterwave is offline
#4
Feb14-12, 04:55 AM
P: 2,045

why is t coordinate negative


Oh, in the metric the sign is negative because you want a "length" which is preserved under the natural transformations of the space (Lorentz transformations in this case).

ds^2=dt^2+dx^2+dy^2+dz^2 would not be preserved under a Lorentz transformation. The version with the minus sign is. In other words, ds with the minus sign definition is something that all observers would agree on, but ds with the plus sign definition, different observers would measure different ds's.
bobc2
bobc2 is offline
#5
Feb14-12, 07:57 AM
P: 848
Quote Quote by dpa View Post
In lorentz transformation,
why has t -sign
Because it is the leg of a triangle that is being computed, not the hypotenuse. Google "special relativity space-time diagram" to study how to interpret the sketch below. We have red and blue guys moving in opposite directions at the same relativistic speed relative to the black coordinates. The blue guy uses the equation to compute the length of some object in the red guy's coordinates. Then, it's the red leg of the triangle that's being computed.

Given the way the coordinates are oriented for red and blue in special relativity, you can identify a right triangle--then just use Pythagorean theorem and solve for the red length. dX1'^2 +dX4^2 = dX1^2. Or, use vector addition as shown.
dpa
dpa is offline
#6
Feb14-12, 10:43 AM
P: 149
thanks
matterwave and bobc2


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