• #### 科普

SCIENCE

#### 英语

ENGLISH

#### 科技

TECHNOLOGY

MOVIE

FOOD

#### 励志

INSPIRATIONS

#### 社会

SOCIETY

TRAVEL

#### 动物

ANIMALS

KIDS

#### 卡通

CARTOON

#### 计算机

COMPUTER

#### 心理

PSYCHOLOGY

#### 教育

EDUCATION

#### 手工

HANDCRAFTS

#### 趣闻

MYSTERIES

CAREER

GEEKS

#### 时尚

FASHION

• 精品课
• 公开课
• 欢迎下载我们在各应用市场备受好评的APP

点击下载Android最新版本

点击下载iOS最新版本

扫码下载译学馆APP

#### 黑洞中的时间是如何转换的

How Time Becomes Space Inside a Black Hole | Space Time

This episode is sponsored by crunchyroll.

Today on Space Time, we’re going to talk about time-space,

or the strange switching in the roles of space and time

that occurs in the mathematics when we drop below the event

horizon of a black hole.
［音乐播放中］
[MUSIC PLAYING]
“空间与时间之间互相转换”这种奇异的说法
What does this bizarre statement, space and time

switch roles, even mean?

Is this space-time dyslexia purely a mathematical quirk?

Or does it correspond to real timey-wimey weirdness?

We’ve been working up to this one.

So you might want to hit pause and check out these episodes

if you think you need some more background.

Let’s get started.

First we’ll think about what the flow of time

looks like without black holes or even spacetime curvature.

When we talked about the geometry of causality,

we saw that this quantity that we call the spacetime interval

governs the flow of cause and effect,

the only reliable ordering of events in a relative universe.

I’m going to show you the math one more time.

And then we’ll get back to doing all of this graphically.

The spacetime interval is defined like this,

for boring old flat or Minkowski space.

Different observers may report that two events are separated

by different distances delta x and by different amounts

of time delta t.

However all observers record the same spacetime interval.

If one event causes a second event,

the spacetime interval must be 0 or negative.

That just means that a lightspeed causal link

may have traveled between them.

You could say that an object at a given spacetime instant

is caused by way of a version of itself

existed an instant earlier.

So world lines of objects have decreasing spacetime intervals.

In fact forward temporal evolution

requires a negative spacetime interval.

In flat space time, that negative sign

in front of the delta t drives that forward evolution.

This makes t, the time-like coordinate,

while x is the space-like coordinates.

For causality to be maintained, the time-like coordinate

must always increase.

Reversing causality means flipping the sign

of the spacetime interval.

In our episode on superluminal time travel,

we saw that in flat space, this means

traveling faster than light, which is, of course,

impossible.

But if we introduce a black hole,

we now have a second way to flip the side

of the spacetime interval.

We’re going to see how this changes the behavior of time

in very strange ways.

Add a non-rotating, uncharged black hole,

and the spacetime interval becomes this.

This comes from Karl Schwarzschild’s solution

to the Einstein field equations, the very first accurate

description of a black hole.

I’ve left out a few terms.

This equation assumes no orbital motion, only motion

towards or away from the center of the black hole, which

is a distance r away.

of the event horizon.

Very far from the event horizon, the Schwarzschild interval

becomes the good old Minkowski interval.

And time and space nicely separated.

But if an object gets close to the event horizon,

so r just a little bit bigger than rs,

that stuff in the two brackets describes extreme warping

of spacetime.

But as long as you are outside the event horizon,

time behaves itself mostly.

A negative spacetime interval still means causal movement.

And the only way to break causality

is still with faster than light travel.

Things change radically below the event horizon

when r gets smaller than rs.

Then both of these brackets become negative.

The entire delta r stuff is now negative.

And the delta t stuff is positive.

Below the event horizon, there is only one way

to maintain the respectable causal progression expected

of a well-mannered temporal entity.

That’s to fall inwards, to have a non-zero delta r.

As it happens, you don’t have a choice.

Space itself is falling inwards faster

than the speed of light towards the central singularity.

It carries you with it and drives your personal clock

forward as it does so.

In the mathematics the coordinate r,

which once represented distance, now grants

the negative sign needed to maintain your causal flow.

It becomes time-like.

It’s uni-directional.

Meanwhile the coordinate previously known as time, t,

lost its negative sign and become space-like.

So it can be traversed in any direction

or not traversed at all.

But what does all of this time-space switching

actually look like?

Let’s fall into the black hole one more time, now graphically

Back out here in the regular universe,

it’s pretty obvious where the past and the future are.

On our ever popular spacetime diagram,

we see a sharp division between the two.

Our past light cone encompasses all of spacetime

that could have influenced us, while that future light

cone shows us the part of the universe

that we might never hope to encounter or influence.

Which direction is the future?

Ahead along our time axis and at right angles

to all of our space axes.

Our future light cone stares fixedly

forwards, encompassing all spatial directions equally.

This is no longer true if we introduce gravity.

Close to a massive object, your future

is no longer at right angles to space.

It becomes slightly tilted in the direction of that mass.

Send out a burst of future defining light rays,

and they won’t spread out evenly because they

bend towards the gravitational field.

As you approach the event horizon of a black hole,

more and more light rays are turned

towards the event horizon.

begin to blur together with the inward radial axis

of the black hole.

At this point, it’s time we switch diagrams.

Close to and within the black hole,

the Penrose diagram is much more useful.

It deals with the extreme stretching of space and time

by compact defined lines of constant space or time

close to its boundaries.

We talked about these diagrams previously.

But an important thing to remember

is that the lines of constant space and time

are curved so that light cones remain upright.

And light always travels at a 45 degree angle,

even inside the black hole.

This entire diagonal line represents the event horizon.

Watch what happens to our view of the universe as we approach it.

Our entire future light cone encompasses more and more of the event horizon.

That last tiny sliver is a narrowing window

directly above that you could escape to at close to the speed of light.

Meanwhile our past light cone now encompasses

light that has been struggling to escape

from just above the event horizon since the distant past.

But we still see nothing from below the horizon.

Yet as soon as we passed the horizon, everything changes.

The outside universe exits our future light cone, which now

just contains the singularity.

We also begin to encounter a new set of photons from the past.

At the moment of crossing, light rays from the event horizon

itself are suddenly visible.

In fact, we plummet through a sea of light

that is eternally climbing outwards but getting nowhere.

of the black hole.

As we fall with the faster than light flow of space time,

we overtake light that is outward pointing.

That light isn’t actually making headway outwards.

It’s trying to swim upstream and failing

against the faster than light cascade of spacetime.

Some of this light might be from the collapsing surface

of the star that first formed the black hole, emitted

long before we entered the event horizon.

It appears to come from below us because it’s

trying to climb upwards.

In fact though, it was emitted at larger radio

than wherever we encounter it.

Also in our past light cone are light rays

that are pointed inwards, some of them coming

from the outside universe.

This light overtakes us as we fall.

This is light that entered the event horizon

after we did and appears to reach us from above.

We can try to move towards either source of light,

down towards light from the black hole’s past

or up towards light from the black hole’s future.

Those directions, those spatial freedoms,

are now described by what was once the time coordinate.

But it’s no longer time-like.

You can traverse in either direction making it space-like.

Doing so isn’t actually traveling in time,

even though there’s a sense of past events in one direction– the collapsing star–

and future events in the other, everything that fell into the
black hole after us.

But remember that future light cone actually just points

towards the singularity.

If we try to accelerate in either direction, up or down,

we just quicken our demise.

Best just to fall.

It’s the last mercy granted by the black hole.

It transports us to our doom by the slowest path

unless we resist.

Below the event horizon, there’s still a sense

of spatial upness and downness.

However the old radial dimension isn’t space-like,

it’s time-like.

Every photon that reaches us was emitted at some larger radius

than wherever we encounter.

Even if it’s old light struggling outwards,

And all possible future directions

In the same way that all world lines move

towards the future in the outside universe,

And r is time-like, uni-directional.

The singularity becomes a future time, not a central place.

In fact the Schwarzschild metric really

gives two separate spacetime maps in a single equation,

one for above and one for below the event horizon.

The coordinates r and t play different roles

in those regions.

There are other coordinate systems in which

that switch never happens.

But this mysterious dimensional flip

does give us some fascinating insight

into how time and space blend together

in what is perhaps the strangest place in all of spacetime.

Thanks to crunchyroll for sponsoring this episode.
Crunchyroll给你带来日本的新动漫
Crunchyroll brings you new anime from Japan

just one hour after its aired.

All episodes are in 1080p HD and can

be viewed across all devices.

I think Space Time viewers would really

enjoy Cowboy Bebop, a Sci-fi noir that

follows the adventures of a gang of space bounty hunters.

So what’s not to love?

Crunchyroll is offering Space Time viewers a 30 day free
Crunchyroll为Space Time的观众们提供了为期30天的免费观看
trial if you go to Crunchyroll.com/spacetime.

Again that’s crunchyroll.com/spacetime.

Hey guys, in our recent Space Time journal club,

we talked about a paper describing a recipe

for making these weird things called time crystals

and about how some researchers have now successfully created them.

Let’s continue the discussion.

A few of you are unsure of what constitutes a time crystal.

At this point, the use of the term is pretty loose.

It refers to any quantum systems whose internal interactions

result in a periodic change from one state to another and then

back again.

The systems that were tested use electron spins, which

pull on each other to cause a cascading flow of flipping

spins the cycles back and forth.

Really though, the term time crystal

is just used to refer to anything

that has a pattern of internal states that repeats over time.

It doesn’t also have to be a regular crystal that has

a repeating spatial pattern.

In fact, it typically won’t be.

Colin Brown asks if the spin flip oscillation

is only dependent on the electromagnetic field

oscillation.

And he also asks why that’s so special.

Firstly yeah, these time crystals

oscillate at an integer multiple of the electromagnetic field

frequency.

So the time crystal oscillation and the EM field oscillation

are in resonance.

For every one, two, three, et cetera cycles

of the time crystal, the EM field gives a little push.

It has to be an integer factor, because if the EM field were

pushing halfway through the time crystal period,

it would be pushing in the wrong direction.

It’s like when you’re pushing a swing,

you don’t need to push every time to keep it going.

But you do need to push at the right time

or you’ll slow it down.

Colin and others also ask why this is so special.

After all, lots of things oscillate, especially when

you push them.

So in Frank Wilczek’s initial idea,

his hypothetical time crystals didn’t require any input energy

to keep them oscillating.

For Wilczek’s time crystals, the oscillating state

is an equilibrium state.

And the oscillations were supposed to go on forever

without any energy inputs.

That would be special and weird, even if the original period

was defined by an external EM field frequency.

It’s now been proved mathematically

that time crystals can exist in equilibrium.

To keep them oscillating, you need to keep putting in energy.

However, the experimental results

are still exciting, because the system

did develop their own internal oscillations that

resisted changes from the outside forcing EM field oscillation.

So the oscillations were, in a sense,

fundamental, just not sustainable.

Is this more interesting than, say, a swinging pendulum?

Well pendulums are pretty cool.

So I don’t know.

They’re a new type of oscillating system

that could have their own uses.

I’d like to thank Dankulous Memelord for what,

for us, spurred a useful discussion

on the comprehensibility of this episode.

We’re always monitoring feedback to improve

the clarity of the show.

It’s worth commenting here that our goal on Space Time

is a little bit different to most science media.

We’re interested in providing a bridge to understanding

the real science that goes a bit further

than an introductory level.

That’s especially true of Space Time Journal Club.

If you’re finding an episode a bit much on first viewing,

it’s often a good idea to also check out

some other sources, which might give a better intro.

But please persist, because understanding our universe

is well worth all of the work.
［音乐播放中］
[MUSIC PLAYING]

Cassic

Y