Why Time and Space swap in a Black Hole

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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.

👍︎︎ 108 👤︎︎ u/AlessandroRoussel 📅︎︎ Dec 06 2021 🗫︎ replies

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.

👍︎︎ 8 👤︎︎ u/010011100000 📅︎︎ Dec 07 2021 🗫︎ replies

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.

👍︎︎ 8 👤︎︎ u/cryo 📅︎︎ Dec 07 2021 🗫︎ replies

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 👏

👍︎︎ 6 👤︎︎ u/azarraga 📅︎︎ Dec 07 2021 🗫︎ replies

This is great animation!

👍︎︎ 6 👤︎︎ u/sfreagin 📅︎︎ Dec 07 2021 🗫︎ replies

Very Good. Thank you!

👍︎︎ 5 👤︎︎ u/glesialo 📅︎︎ Dec 07 2021 🗫︎ replies

Man that was wild, great work! So that means all black holes exist in a time and place in the future?

👍︎︎ 6 👤︎︎ u/mufasis 📅︎︎ Dec 07 2021 🗫︎ replies

Dig it..

👍︎︎ 3 👤︎︎ u/clackersz 📅︎︎ Dec 07 2021 🗫︎ replies

I'm really looking forward to see this, I love this topic in particular.

👍︎︎ 3 👤︎︎ u/silvlub 📅︎︎ Dec 07 2021 🗫︎ replies
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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.
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Channel: ScienceClic English
Views: 371,206
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Id: GQZ3R81iyE0
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Length: 12min 11sec (731 seconds)
Published: Mon Dec 06 2021
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