Simultaneity

DEFINITION

DEFINITION - SPECIAL RELATIVITY

2+ Event occur @ same Time in 1 IRF BUT may NOT occur @ same time in another IRF moving compared the first.
2+ Event are "Simultaneous" IF an observer equally distante FROM them CAN see them occurs @same time for him.

[!example]- Example 1: Train
#ASK
There are 2 IRF in Standard Configuration:

$O$ : IRF integral to Earth
$\tilde{O}$ : IRF integral (in the center) to a train moving w/ Velocity $v$ compare to $O$

@Time $t = 0$ , a light blink in $\tilde{O}$
@ $t > 0$ the train is moving w/ Velocity $≅$ Light Velocity $c$ ⇒

According to $\tilde{O}$ the Wave Front arrives at the train's extremeness @same time → Simultaneity
According to $O$ , the Wave Front arrives first in one extremes than the other → NOT Simultaneity

@t=0@t>0@t>>0

$M^{4}$ REPRESENTATION

2+ events are simultaneous IF 1+ IRF they have same

x^{0}

component ⇒ Line that connects them is

∥

to

x^{1}

axis.

\exists

Line WHEN (CAUSE World Line Properties))

θ < 45 °

ELSE events are Causally-Correlated.

BASimultaneous inBUT NOT inBANEVER Simultaneous>45°

QUESTIONS

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DEFINITION

DEFINITION - SPECIAL RELATIVITY

M4 REPRESENTATION

#h-t LINKED

$M^{4}$ REPRESENTATION