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Anonymous Tue 17 Aug 16:31:43 2021 No.13529223 View Reply Original Report

Quoted By: >>13529375 >>13530671

The spacetime interval is defined as s^2 = x^2 - (ct)^2
What is the meaning of there being a minus sign there? The further apart in time the events are the closer they are together? Taking it further, an event 10 light-years in the away and 10 years in the future is a spacetime distance of 0 away?? I don't see how two points so far away could be interpreted as occupying the same point.

Anonymous

Anonymous Tue 17 Aug 2021 16:42:34 No.13529258 Report

Quoted By:

its da light cooone

its says if you are in the cooone, how far apart you are from light coone inside cooooone

Anonymous

Anonymous Tue 17 Aug 2021 16:44:14 No.13529262 Report

Quoted By:

also its s^2=(ct)^2-x^2-y^2-z^2

you cant surprass the coone

the jew has said thou shant not travel faster than the coone

Anonymous

Anonymous Tue 17 Aug 2021 17:13:01 No.13529375 Report

Quoted By:

>>13529223
It's litterally just a property that is preserved by the lorentz transform, wich means that the "distance" between two points in spacetime is the same for all observers. It's a usefull concept and also defines a pseudo remannian metric, we can also use it to meassure the proper time between two events in spacetime aswell as the proper length of objects.
>Taking it further, an event 10 light-years in the away and 10 years in the future is a spacetime distance of 0 away??
No, it means that the proper time on a worldline connecting the two events is zero (that is, time doesn't pass for photons). Essentially, for events within the lightcone, it gives the time that an observer on a straight worldline between two events would meassure,.
>What is the meaning of there being a minus sign there?
It means that contrary to ordinary euclidean geometry where the shortest distance between two events in space is a straight line, the longest distance between two spacetime events is a straigt line (try proving the Lorentzian triangle inequallity)..

Anonymous

Anonymous Tue 17 Aug 2021 17:38:09 No.13529442 Report

Quoted By:

If you look at your picture with the t-axis up and the x-axis sideways, then linear inert motion is lines through that picture.
E.g. if you take the photo of a guy on skateboard, that corresponds to one point
(t0, x0)

If he rolls with a velocity v, then the trajectory is
(t0 + t, x0 + v · t)
where t is the time passed since t0.

In newtonian theory, v can be any real value.
In relativity theory, v is restricted by c, so all motion (lines) are inside the light cone.

The acceleration laws, and consequent coordinate transformation operations (elements of a matrix representation of the Poincare group) are such that "speeding up" any number of times leads to a velocity addition that still doesn't exceed c. If you're moving at half the speed of light, you can't move 7 times at fast. it's not just v \maptso 7˜v I.e. it's a complicated "boosting" law.

El Arcón

El Arcón Tue 17 Aug 2021 17:41:03 No.13529452 Report

Quoted By:

Zero meters of spacetime interval is completely unrelated to a quantity of meters of distance. The units of spacetime interval were chosen as meters purely by artificial convention. The formula for ds^2 could have had any dimensional transposing parameter in it but use "c" is easy and convenient, and it gives the units of spacetime interval in meters.

Anonymous

Anonymous Tue 17 Aug 2021 23:05:24 No.13530671 Report

Quoted By:

>>13529223
>minus sign
It's useful since it divides space-time intervals into positive (space like, ftl), negative (timelike, sub light speed) or zero (light like).

Anonymous

Anonymous Tue 17 Aug 2021 23:06:41 No.13530679 Report

Quoted By:

in english, doc?

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