What is space like and light like interval?
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Suppose we have two events (x1,y1,z1,t1)(x1,y1,z1,t1) and (x2,y2,z2,t2)(x2,y2,z2,t2), then we can define
Δs2=−(cΔt)2+Δx2+Δy2+Δz2Δs2=−(cΔt)2+Δx2+Δy2+Δz2
which is called the spacetime interval. The first event occurs at the point with coordinates (x1,y1,z1)(x1,y1,z1) and the second at the point with coordinates (x2,y2,z2)(x2,y2,z2) which implies that the quantity
r2=Δx2+Δy2+Δz2r2=Δx2+Δy2+Δz2
is the square of the separation between the points where the events occur. In that case the spacetime interval becomes Δs2=r2−c2Δt2Δs2=r2−c2Δt2. The first event occurs at time t1t1 and the second at time t2t2so that cΔtcΔt is the distance light travels on that interval of time.
In that case, Δs2Δs2 seems to be comparing the distance light travels between the occurance of the events with their spatial separation. The definition done is then the following:
If Δs2<0Δs2<0 then r2<c2Δt2r2<c2Δt2 and the spatial separation is less than the distance light travels and the interval is called timelike.
If Δs2=0Δs2=0 then r2=c2Δt2r2=c2Δt2 and the spatial separation is equal to the distance light travels and the interval is called lightlike.
If Δs2>0Δs2>0 then r2>c2Δt2r2>c2Δt2 and the spatial separation is greater than the distance light travels and the interval is called spacelike.
These are just mathematical definitions. What, however, is the physical intuition behind? I mean, what an interval being timelike, lightlike or spacelike means?
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hope this will help
please mark as brilliant
here is Ur answer
###############
Suppose we have two events (x1,y1,z1,t1)(x1,y1,z1,t1) and (x2,y2,z2,t2)(x2,y2,z2,t2), then we can define
Δs2=−(cΔt)2+Δx2+Δy2+Δz2Δs2=−(cΔt)2+Δx2+Δy2+Δz2
which is called the spacetime interval. The first event occurs at the point with coordinates (x1,y1,z1)(x1,y1,z1) and the second at the point with coordinates (x2,y2,z2)(x2,y2,z2) which implies that the quantity
r2=Δx2+Δy2+Δz2r2=Δx2+Δy2+Δz2
is the square of the separation between the points where the events occur. In that case the spacetime interval becomes Δs2=r2−c2Δt2Δs2=r2−c2Δt2. The first event occurs at time t1t1 and the second at time t2t2so that cΔtcΔt is the distance light travels on that interval of time.
In that case, Δs2Δs2 seems to be comparing the distance light travels between the occurance of the events with their spatial separation. The definition done is then the following:
If Δs2<0Δs2<0 then r2<c2Δt2r2<c2Δt2 and the spatial separation is less than the distance light travels and the interval is called timelike.
If Δs2=0Δs2=0 then r2=c2Δt2r2=c2Δt2 and the spatial separation is equal to the distance light travels and the interval is called lightlike.
If Δs2>0Δs2>0 then r2>c2Δt2r2>c2Δt2 and the spatial separation is greater than the distance light travels and the interval is called spacelike.
These are just mathematical definitions. What, however, is the physical intuition behind? I mean, what an interval being timelike, lightlike or spacelike means?
#############
hope this will help
please mark as brilliant
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