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Why is t coordinate negative 
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#1
Feb1412, 03:36 AM

P: 149

In lorentz transformation,
why has t sign 


#2
Feb1412, 04:35 AM

Sci Advisor
P: 2,847

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.



#3
Feb1412, 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. 


#4
Feb1412, 04:55 AM

Sci Advisor
P: 2,847

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. 


#5
Feb1412, 07:57 AM

P: 848

Given the way the coordinates are oriented for red and blue in special relativity, you can identify a right trianglethen just use Pythagorean theorem and solve for the red length. dX1'^2 +dX4^2 = dX1^2. Or, use vector addition as shown. 


#6
Feb1412, 10:43 AM

P: 149

thanks
matterwave and bobc2 


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