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30.1 Cause and Effect: A Spacetime Invariant
Discussion
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I have struggled to follow the explanation of this Unit as there seems to be an inconsistency that I cannot understand!
Throughout the introductory sections of Unit 30 it was established that if the invariant interval between two events on a space-time diagram given by the condition: −(c∆t)2 + (∆x)2
is 0 then they can’t, they are causally disconnected
if =0 then they are at a causal boundaryHowever throughout the exercises (30.5) and the problem (30.6) it was stated that the invariant interval was given by: ∆t2 − ∆x2 and that if the resultant value:
is 0 the events can be causally connected
if =0 the events are at a causal boundaryNevertheless I did follow the initial version for the invariant interval to a correct conclusion.
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Sadly my text (above) became scrambled when I copied it across!
However, I am now more enlightened – the original definition of the invariant interval (when c = 1) does readily transpose into (△t)² – (△x)² but, of course, the outcome must also be transposed.
So a negative value (less than 0) that relates to a potential causal connection in the original definition becomes a positive value (greater than 0) for a potential causal connection in the transposed version
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Timelike, spacelike, lightlike separations.
The sad life of a photon actually being invariant.
Study group diagram-
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