Holes and Wrinkles

There is a lot of misconception about two of the more arcane forms of proposed space travel: Warp Drives and Worm Holes. They work on the same principles but function in wholly different ways.

General Relativity explains that any mass or energy can bend space and time. Since there is energy everywhere space and time are already curved. We can there fore tweak with the curvature of space-time in different ways to produce different effects.

For example, Worm Holes are analogous to tunnels. When there is enough mass or energy concentrated at two points, the space-time bends to form a tunnel between the two locations.



This means that we can reach another point before light, not because we are faster, but because we have a lesser “distance” to travel. So for example if a wormhole were to connect earth to the moon, you could step into the wormhole and go to the moon, and then quickly get back. But since light had to travel a longer distance, your image on the moon might reach you when you came back to earth. You would literally be able to make a thousand virtual copies of yourself. However, wormholes are extremely unstable. Some equations predict that they will immediately collapse as soon as something passes through. Negative energy and negative matter will be needed to stabilize a wormhole. Mankind is still far away from producing and using antimatter at a large scale, so worm holes will remain, for the near future, a fantasy.

Warp Drives also use the same principle. However they only distort space and time around the traveler while keeping him in a “bubble” of normal space-time. Imagine a small toy car on a bed sheet. The car can only travel a few centimetres per second. But you want to reach the other end of the bedsheet quickly. So you scrunch up the sheet in front of the car, effectively reducing the distance it has to travel. Once the car has traversed the wrinkles, you stretch out the sheet again. In a sense a Warp Drive is a less extreme version of the Worm Hole. A worm hole is just like the portals in the game Portal: the distance between destinations is effectively zero. But in a warp drive, you still have to cover some distance. Consequently it is also easier to make. But where worm holes can facilitate inter-galactic travel, warp drives are only viable for interstellar journeys.



Image 1, Image 2

Is Cold the New Hot?



A few days back, a friend shared an article with me. It talked of how scientists had managed to achieve temperatures below absolute zero. Does it mean that temperature has to be redefined? Has our understanding of thermodynamics been flawed for the past hundred years. No, it turns out. It is all a matter of semantics.

Absolute Zero. This is the temperature at which a particle has the minimum possible energy. The energy is NOT zero because that would violate the Heisenberg uncertainty principle (that you cannot know the energy and its duration with absolute certainty). However that zero-state energy is a quantum quantity, so for all intents and purposes, the particle itself appears stationary. Classically, it is impossible to go below absolute zero because for all the matter that we know of, it will never have negative energy (because the zero state energy prevents energy from going past zero and into the negative).

Therefore when you talk of temperatures below absolute zero, and you know that there is nothing wrong with absolute zero, then logically there must be something going on with “Temperature”. The layperson will call temperature the hotness of something. Some one more well versed in science will call it the average kinetic energy of the particles. All of these definitions are correct in the same way Newton’s gravity is correct i.e. it works for our observations. But in order to really understand temperature, you need to understand entropy.

Entropy in a sense is the amount of disorder in a system. Imagine making a mound of sand on a table. Now shake the table. The sand particles will spread out as they roll down from the mound. Because the particles are now spread out, the entropy of the system has increased. The farther a particle is from the original position of the mound, the more effectively it has harnessed the energy you gave the system by vibrating the table. If the table was infinitely expansive, the particles would continue spreading out and absorbing the energy you provide and increasing the entropy of the system.

In a system with infinite states, energy and disorder have a positive relationship.

In a system with infinite states, energy and disorder have a positive relationship.

This is temperature, the ratio of energy required to the change in entropy. The greater the energy required for the same increase in entropy, the greater will be the temperature.

But there is a catch: what if you provide more energy to the system but the disorder (entropy) decreases instead. Is it possible to shake the table and make the sand particles more ordered? If it is, then that would mean that the temperature of the system is negative because the change in energy is positive, but the change in entropy is negative, so the ratio (which represents temperature) is negative. Imagine that the table is not infinite. Instead it has little walls on the edges. As you shake the table, the sand particles start to spread out (they gain energy, and increase entropy). The temperature increases. But there comes a point when they reach the edges. Then they start to accumulate again. The more you shake the table, the greater is the particle accumulation on the edges. At that point, an increase in energy of the system is in fact decreasing its disorder. Thus the temperature has become negative.

In a system with finite states, energy and disorder develop a negative relationship.

In a system with finite states, energy and disorder develop a negative relationship.

That is exactly what the scientists mentioned in the article did. They trapped the molecules using lasers and magnetic fields, so that after absorbing certain amount of energy, the barriers created by the magnetic fields and lasers would cause particles to accumulate around the same energies. In the classical sense, the particles were hotter because they had a greater energy, but since the disorder in the system was lessened, their temperature was negative i.e. below absolute zero.

Gravitational Slingshots

I always wondered why doesn’t the sun slow space probes down when they are leaving the Earth for outer planets. Isn’t there a risk that the probe might change its trajectory and fall into the sun? There is. You see, the more distant the space probe gets from the Sun, the more potential energy it gains. However, energy must be conserved at all costs. Therefore the probe loses its Kinetic energy (and therefore its speed) in order to get away from the sun. It is the same as when you throw a rock up into the air.

But there comes a point, as with the rock, when the probe loses all of its kinetic energy. At that time it has reached as far away from the sun as it can. Yes, you could add thrusters to make sure the probe continues its journey. But the extra weight and inefficiency of propellants known to us make it an unsuitable alternative.

Enter the Gravitational Slingshot! Nature’s way of compensating us (very marginally) for all the millions of years we’ve been dragged through the mud in the name of evolution. Through this method, space probes go into a partial orbit around a planet and emerge on the other side with a greater velocity. “No!”, some might say, because it is a violation of conservation of energy. Intuitively it seems that way, but it is all a matter of relativity.


Imagine there is a probe approaching a planet with a velocity ‘u’. To an observer on the planet, the apparent velocity of the probe’s approach will be ‘V+u’, where ‘V’ is the planet’s and ‘u’ is the probe’s heliocentric velocity, i.e. velocity relative to the Sun. It will go into orbit at that speed. Now, when it comes out of orbit on the other side, it is still moving with a velocity ‘V+u’ relative to the planet’s surface. But the planet is also moving in the same direction at velocity ‘V’. So the final velocity as the probe leaves orbit will be ‘V+(V+u)’. Of course, some of that velocity will be reduced due to the planet’s potential, but in the end it will still be greater than the probe’s initial velocity.

If you look at what happened overall, ignoring how it happened, the probe approaches a moving planet at a certain velocity and “bounces off” at a higher velocity. It is just like when you throw a ball at the face of a moving train, the ball bounces off at a higher velocity. Now, the ball changes its momentum (first going in one direction, then another) and transfers that change to the train to ensure conservation. But the train is comparatively so massive that we do not notice the minuscule change in its velocity. That’s the same with planets and probes.

The effective increment in the probe’s velocity is due to the orbited body’s velocity relative to the Sun (analogously, the change in velocity of the rebounding ball depends on the train’s relative velocity to the ground). Of course, the Sun’s velocity relative to itself is zero. Therefore ‘V’ will be zero. So there will be no gravitational slingshot from the Sun (towards planets in its orbit) even though it is the most massive body in the solar system; just like there will be no increment in the velocity of the ball when you throw it at the ground.

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!):


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:


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:


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:


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:


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:


Destination: Black Hole

I like black holes. I like them a lot. They are in the top ten of my bucket list of destinations if I live for a thousand years.

Seems Legit

Seems Legit

Black holes in popular culture are notorious for being very dark objects. I will try enlighten the readers about their shady origins, and hope that people see them in a better light.

Stars run on hydrogen. In the extreme temperatures in their cores, hydrogen nuclei fuse explosively to form helium nuclei. The explosive energy released opposes the force of gravity of the star on itself. Thus the star continues its merry existence, until it runs out of juice, that is. When there is no more hydrogen left to fuse, the temperature at the core decreases, gravity takes over and the star contracts. The contraction again heats up the core to a level where helium fuses into carbon. This reaction is much more powerful than hydrogen fusion, and the explosive output causes the star’s shell to expand, making it a red giant.

If the star is less that 10.5 solar masses then it sheds its outer layers leaving behind a very dense white dwarf star made of oxygen and carbon. the white dwarf star is prevented from collapsing further by the electron degeneracy pressure. However, if the mass of the white dwarf is more than about 1.4 times the mass of the sun, even electron pressure cannot hold back gravity. And so the electrons fuse with protons to become neutrons, thus forming a neutron star. A neutron star achieves stability due to the quantum degeneracy pressure (that particles simply cannot have the same state and so must remain separate).

However, if the mass of the neutron star exceeds 1.5 to 3 solar masses, it collapses again into one of several exotic remnants, one of which is the black hole.