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#### 相对同时性——狭义相对论第四讲

Relativity of Simultaneity | Special Relativity Ch. 4

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
“洛伦兹变换”来表达的
what’s called a Lorentz transformation,
“洛伦兹变换”是一种时空的伸缩旋转
which is a kind of squeezed stretched rotation of space-time

that I’ve mechanically implemented with this space-time globe

a quick reminder, space-time diagrams

plot position on the horizontal axis and time on the vertical axis

so something that moves as time passes

traces out a path through space-time

called a world line.

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 1/3 the speed of light to my right.

Then, from your perspective,

that is from the perspective in which you’re not moving,

so your world line 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:
tnew=γ(t – v*x/c²)
tnew equals gamma times t minus v over c squared times x.

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 diatance to the object in question are

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 one 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 that are at the same point in space.

Too, from my perspective,

this box is at the same position

at different times that is it’s not moving.

But from your moving perspectives,

it’s at different positions at different times.

It is moving and it’s no longer in alignment.

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 vedio series.
（至少我觉得是同步的）
(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 %

of Brilliant’s courses and puzzles,

and lets Brilliant know you came from here.

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