In our universe, when you change from a non-moving perspective to a moving one, or vice versa,
that change of perspective is represented by a what's called Lorentz transformation,
which is a kind of squeeze-stretch rotation of spacetime that I've mechanically implemented
with this spacetime globe.
A quick reminder - spacetime diagrams plot position on the horizontal axis and time on
the vertical axis, and something moving as time passes traces out a path through spacetime
called a worldline.
One of the first things you might notice about Lorentz transformations is that events that
were at different places at the same time before the transformation aren't at the same
time after the transformation.
This means that from the perspectives of people going different speeds, simultaneous events
for one person won't be simultaneous for the other, and vice versa.
For example, if from my perspective these two boxes spontaneously combust at the same
time, and you're moving at a third the speed of light to my right, then from your perspective,
that is, the perpective from which you're not moving so your worldline is purely vertical,
from your perspective the box on the right will combust first, and the box on the left
will combust second.
The takeaway here is that our universe has neither an absolute notion of time nor an
absolute sense of simultaneous events, and that simultaneity breaks down more the farther
away from each other two things are – a box even farther to the left that from my
perspective simultaneously spontaneously combusts with the others will, from your moving perspective,
be even farther out of sync with the box on the right.
This is described by the time part of the Lorentz Transformation equations, the part
that says t new = gamma times t minus v times x over c squared).
Because of the x in there, the farther away an event is from you, the more its time from
the new perspective will be out of sync with events closer to you.
Though because of the factor of c squared in the denominator, which is huge, it's hard
to notice anything being out of sync until either your speed or distance to the object
in question are really really really big – like, you'd have to be going half the speed of light
and be comparing things farther apart than the earth and moon before things would become
more than 1 second out of sync.
But in that case, events that were simultaneous from my perspective really would be out of
sync for you!
As surprising as this may seem, it might feel more familiar and comfortable when you remember
that this “getting out of alignment” phenomenon happens to points at the same place in space,
too, which is literally what we think of as defining motion – from my perspective, this
box is at the same position at different times – that is, it's not moving; maybe, “simulspacious”–
but from your moving perspective it's at different positions at different times – it is moving.
Relativity of simultaneity is just the other side of the coin – the fact that events
that happen at the same time at different spatial positions happen at different times
when viewed from a moving perspective.
All together, in our universe, the takeaway is this: events that were previously either
all at the same place or all at the same time get out of alignment with each other when
you change to a moving perspective.
A big thanks again to Mark Rober for making the spacetime globe a reality, and to dive
more into the details of relativity of simultaneity, I highly recommend heading over to Brilliant.org's
course on special relativity that they've been developing simultaneously with this video
series (well, at least, simultaneous from my perspective).
There, you can explore custom scenarios and do actual puzzles and problems that help you
build on what you learned in this video, like figuring out how laser tag would work at relativistic
speeds!
The special relativity questions on Brilliant.org are specifically designed to help you go deeper
on the topics I'm including in this series, and you can get 20% off of a Brilliant subscription
by going to Brilliant.org/minutephysics.
Again, that’s Brilliant.org/minutephysics which gets you 20% off premium access to all
of Brilliant's courses and puzzles, and lets Brilliant know you came from here.