Welcome back to ScienceClic,
today, light cones and black holes. Imagine lighting a candle. The
candle emits a flash of light that travels in all directions,
forming a bubble that grows. This bubble is in 3 dimensions, and surrounds
us completely. If we are inside this bubble, it is impossible to get out of it because
we would have to exceed the speed of light. Imagine that we only perceive a 2D slice of space. The bubble forms a circle
that grows all around us. If we decompose the situation image by image,
and if we stack the images one after the other, we can construct a diagram in which the bubble of
light, which grows as time passes, forms a cone. This cone widens from the past to the future, and
inside of it, we trace a trajectory through time. The sides of the cone are tilted at 45°, because for any given amount of time, light
always travels a set distance. For example, in one year, light will always travel a
distance of “one light year” through space. This type of object is called a light cone. As
time passes, the cone expands at the speed of light, and whatever we do, our path remains
bounded by it, it’s impossible to escape it. In relativity, these light cones are essential
to understand the structure of the universe. In particular, they restrict
cause and effect relationships. To understand, imagine an event that occurs
far from Earth, such as a supernova explosion. This event won’t be able to affect us
until its light cone has reached Earth. Before that, no information
about the explosion can reach us, since nothing can be
transmitted faster than light. This explosion can only be seen and felt on
Earth as soon as we enter its light cone. “Causality,” the fact that one event can trigger
another, is limited by the speed of light. More importantly, light cones allow us
to understand the profound difference between the notions of “time”, and “space”... What is the difference between time and space
? Through space we can move in any direction, turn around, or trace a path
that loops back on itself... But through time, all objects are
forced to move in the same direction. In time, it is impossible to turn back, we
always move from the past towards the future. Light cones allow us to
clearly see this difference: through space, we are free
to choose any direction, but through time, the successive light
cones force us to always move forwards. We cannot turn around because we are
bound to remain within these lightcones. This property allows us to define rather
rigorously what we called “time”: “Time”, in relativity, is simply the direction
in which the light cones are oriented. It is this direction along which we cannot
turn back. This is the direction towards which all allowed trajectories point,
and in which our future necessarily lies. Space on the other hand is the set of all
other directions, perpendicular to time. In an area where the universe is empty, with no
gravity, its structure, space-time, is straight. Time and space form a symmetric, rectilinear grid,
and the light cones are all aligned in the same direction. We can thus define "time" globally:
in this diagram, time goes from left to right. But imagine now that the universe contains a
very massive body, for instance the Earth. If we drop an apple, the apple will gradually fall
downwards, deflected by the gravity of the planet. However, gravity affects not only matter, but
also light. If the apple emits bubbles of light over time, they will also be drawn
downwards. Close to a massive body, the light cones are no longer aligned with each
other: they curve more and more, bent by gravity. Near a massive body, the direction
of the light cones curves... and in other words, "time" is bent
towards the center of the planet. If the apple falls, although it was motionless at
first, it is because its future points downwards. Mass distorts the geometry of the
universe, space and time become relative, their orientation depending on where
we are, this is “general relativity”. The more massive a body,
the more it bends spacetime. But imagine a massive object that is very compact.
Such a body would generate a curvature so strong that below a certain altitude, all light
cones would be completely oriented downwards. If we were to light a candle in this place,
all light rays, whatever their direction, would be destined to fall towards the
center… this is what we call a black hole. A black hole is a spherical
region of the universe, a sort of bubble, in which the curvature of
space-time drives all objects towards the center. If we consider a 2D slice of space, the black
hole manifests as a circle, which stays static, and traces a cylinder through spacetime. The boundary of the black
hole is called the “horizon”. Above the horizon some light rays can escape,
but below the horizon all light is captured. In a black hole, lightcones force
the path of any object downwards… "Time" itself points towards
the center of the black hole. To understand what a black hole really is, it is
wise to consider two different points of view: that of an astronaut who
falls into the black hole, and that of a distant observer,
stationed at a great distance. For the distant observer, gravity is very weak,
and in his vicinity the grid of spacetime is flat. For him, time flows from left to right. The
horizon of the black hole seems motionless, as it traces a straight line
from the past to the future. But let's now take the perspective
of the falling astronaut. As she gets closer to the horizon,
“time” and “space” curve more and more, bent by the presence of the black hole. When she
finally reaches the horizon of the black hole, the astronaut does not realize it, but, at
this point, time and space are tilted at 45°. For the astronaut, the horizon is not a
horizontal line from the past to the future, it’s a diagonal which rises at 45°…
exactly like the surface of a light cone. While the distant observer sees the black hole
as stationary, for the astronaut at the horizon, time and space are tilted, such that the
black hole behaves like a light cone, which explains why it is impossible to escape. When she crosses the horizon, the notions of
time and space seem swapped around compared to the outside: time is now pointing downwards
- which, before, was a direction through space - the horizon of the black hole is
no longer a place in space, but a moment in our past, and the center of the black hole is
no longer a point, but an event in our future, a destiny we cannot avoid. Below the
horizon, all objects inevitably fall, because it is in this direction
that their future lies. When a massive star collapses in on
itself, it emits one last flash of light, a last bubble that tries to grow, but within a
curved spacetime, bent by the mass of the star, such that the bubble seems
static from the outside. A black hole has formed. It is a light cone...
rendered motionless by the curvature of spacetime. If we straighten back the
diagram, we recover a global direction of time, for flowing from left to right. In this straightened diagram, we see explicitly
that the horizon of the black hole forms a light cone, emerging from the collapsing star, and from
the inside of which it is impossible to escape. Once below the horizon, we are forced to hit
the center of the black hole - a place where the curvature becomes so intense that our models
no longer work. The center of the black hole, is an event… in the future. Finally, if we compactify this diagram, we
get a “Penrose diagram”, in which the outside and the inside of the black hole form two
distinct regions. As soon as we cross the horizon, the rest of the universe is behind us, in our
past. We won’t ever be able to access it again. Our only possible future is to fall…
all the way to the singularity.
Hi! I wanted to share with you my latest video, about light cones and black holes. I hope you like it! It took a lot of effort to make, and I would be interested to have your opinions about it.
This video was a work of research, trying to find the most intuitive depiction of why time and space swap around inside a black hole. I wanted to find a set of coordinates, or a diagram, that would be mathematically accurate from the scientific standpoint, as well as being easily explainable in layman terms for outreach videos.
For this, I have developed a more intuitive (in my opinion) version of Penrose diagrams, which, for those interested, consists in embedding the Penrose diagrams in the complex plane, and applying the conformal transformation z→z². This allowed me to generate a curved grid (used throughout the video, at 6:08 for instance), which is more intuitive than a Penrose diagram in the sense that "motionless" objects still move in straight horizontal lines, while clearly displaying the orientation of "time" and "space" (from Kruskal coordinates), and thus keeping lightcones oriented at 45° everywhere (thanks to the conformal transformation). Btw let me know if you have seen such a diagram before, I personally haven't, which surprises me since the construction is not so difficult to come up with.
Great video but I'd be careful with the title. Time and space don't flip, whatever that would even mean. Timelike curves are still timelike inside a black hole. If they appear to flip it's only because the coordinates we chose to represent time and space weren't actually a good choice of coordinates. There are other coordinates where none of this "flipping" happens.
I think the message that “time and space switches roles” and similar are kinda misleading, since it’s really more a coordinate artifact than anything else.
Awesome video! I love how this video nicely complements your "A New Way to Visualize General Relativity" video which I've watched many many times. Please keep making these videos 👏
This is great animation!
Very Good. Thank you!
Man that was wild, great work! So that means all black holes exist in a time and place in the future?
Dig it..
I'm really looking forward to see this, I love this topic in particular.