Trous Noirs And trous noirs

For an explanation of the title, see the link at the end.

If you are seriously, irreconcilably frustrated by your significant other (or lack thereof) and you never want to see your significant other (or yourself) ever again, please accept a sincere piece of advice from me: Do not- I repeat: DO NOT throw them(or yourself) in a black hole. That would be a bad idea.

"I wasn't gonna push her!"

“I wasn’t gonna push her!”

Now the sensible will decimate my sagely wisdom because of the sheer improbability of a black hole ever crossing two recently uncrossed star crossed lovers. But the curious(and the willing) will ask: Why?

Because the face of the victim will adorn the cosmos for the rest of your life. That kind of kills the point of throwing someone into a hole which never spits anything out. Why?

In my previous article I wrote about how a black hole is formed. Now I will write about why black holes are great advertisement spots and potential reminders of every regretful thing you did in your life. Einstein pointed out in his general theory of relativity that gravity distorts space and time. So for an observer at an arbitrary distance, a clock near a massive object will appear to run slow. The nearer the clock is to the object’s center, the stronger will be the gravitational field, and the slower it will run (for less massive objects the clock will have just to be nearer to the center). However, there is a problem with heavy objects: they are usually very large. Therefore a clock won’t be able to get closer than the radius of the object. So the effects of time dilation won’t be apparent.

Black holes, however, have a zero radius. So objects can get close enough to experience significant relativistic effects. I will be using the case of you, and your significant other (real or imaginary) who recently lost his/her position of significance (and their balance on the space ship, apparently; sshhhh!):

time_dilation_gravity

In this picture, the green line represents the time measured by the observer(you) away from the influence of the black hole. The red line represents the time measured by the, uh, test subject. According to you, your time proceeds normally (the green line is not warped). The red line, even though it appears distorted to you, appears straight to the subject; just like you only have to walk straight without a care for the earth’s curvature to go to your destination, even though you appear to be moving in an arc to an observer in space. The numbers on both lines represent the hours elapsed since the break-up. Notice that the length between the hour intervals is the same for both green and red.

Now imagine that you both have clocks. Assume that the subject’s clock sends out a signal every hour. Also assume, for the sake of simplicity, that the signal reaches you instantaneously. As the warping of space time increases with decreasing distance to the black hole, you will get consecutive signals at ever increasing intervals, until at one point the next signal will take infinite time to reach you. However according to the subject, time will seem to pass normally because according to the subject, the red timeline is perfectly straight (just like with you and the earth). As you can see from the picture, no matter how far into time you progress, you will still get signals from the clock. That is to say, the simple act of disappearing forever will take your significant other an unimaginable long amount of time; and they wont even notice that you are getting impatient. As I said: bad idea.

To understand how the timelines work click here.

An explanation of the title here.

Relativistic Doodles

This post explains how my illustration of general relativistic time dilation works. This is the parent post.

Here is an image of a simple classical timeline:

timeline_1

There are 2 observers: green and red. They have their own watches. The red observer shoots an arrow towards the green observer. The position of the arrow vs. the time recorded by the two observers looks like the picture above. If we take a trace of the trajectory of the arrow, we get:

timeline_2

If we were to take the trace of a 2 signals 1 second apart that travel at constant speed, and 2 signals 1 second apart and traveling instantaneously, we would get:

timeline_3

You will notice that the components of all 4 traces (like the ones drawn in grey) are parallel and perpendicular to the space-time axes. This is always the case. So even when I distort the edge of the red timeline a bit, I get:

timeline_4

So if I am standing with the red observer, and I see him sending out signals, I will not notice a difference even when the red timeline distorts, because to me, the components of the signals are still parallel and perpendicular to my space and time. In the same way, when an observer is falling into a gravity well (like that of a black hole) and sends out signals, the observer does not notice the relativistic effects of gravity on the signal. However, the observer who is standing far away from such distortions notices an altered signal. So even though the signal at t=8 was instantaneous according to the red observer, it reached the green observer at t=9.

If you understood this, then you will know what is wrong with this set of traces of signals that a red observer sends as she falls into a black hole:

time_dilation_gravity_WRONG

If light travelled really slow…

The speed of light is one of the fundamental constants in the universe (along with the Gravitational constant, permitivitty etc.). Changing any constant even slightly will have deadly consequences. But if we manage to survive (somehow), we would find ourselves in a very ‘interesting’ universe.

The constant for the speed of electromagnetic waves ‘c’ has a value of 300 million metres/second. Imagine that some one hacks the universe’s secure servers and changes ‘c’ to 1. The following is a roughly chronological list of things that would happen in a universal conspiracy to end the human race:

1. We would shrivel up and die

Literally. The speed of light is directly related to the strength of electromagnetic force. This is the same force that prevents you from falling out of your house when you lean against a wall, or from falling through a chair while you are sitting. It also helps you keep you in shape while gravity is doing its best to pull you to the ground. If the speed of light were to suddenly decrease by several orders of magnitude, all matter (or most of it) would start to collapse under its own gravity. The world would literally shrink out of existence.

2. The sun would go out

Again: literally. As matter collapses under its own gravity, its gravitational pull on the surface increases and stuff like rebellious atoms and people who can afford a rocket will need higher speeds to escape a body’s gravity. Eventually the ‘escape velocity would exceed the speed of light. And since classically one cannot productively travel faster than light, including light, all matter with high escape velocities would become black holes, including the sun and the earth and all the planets in the solar system.

3. Time will s l   o    w     d       o        w          n

If by any miracle we are still alive we will notice (that’s putting it subtly) that everything has shrunk. The gravitational field will be extremely strong. And since light is so slow, our every motion will be at relativistic speeds. That means that on a jolly morning when I decide to go out for a walk, I might as well come back to my house to find it in ruins from age. In other words we wouldn’t need to wait an entire week for new episodes of our favourite shows.

4. The world will look W13rD

Take a look at these pictures:

Light captured at super high frame rates,

Light captured at super high frame rates,

Simulated reflection of light at super slow motion.

Simulated reflection of light at super slow motion.

This is what light looks like if it is slowed down. On a post-hacked universe, you could stand behind something heavy and literally make copies of yourself (gravitational lensing, kage bunshin no jutsu! for Naruto fans). Since light will bend under extreme gravity, you will be able to see whats happening on the other side of the earth, or the back of your head for that matter. You could swipe your hand through the ‘air’ and turn your palm into a black hole and deflect bullets with a wave of your hand.

All in good time. In the real world we would just stop existing the moment a single constant was changed. If all universal constants were scaled down proportionally, we might have a chance, but alas we don’t even know all of them. So why did I conjure images of a Matrix/Naruto/Avengers/ Harry Potter universe? Simple. I just got carried away.