Fun with exotic matter
I recently read a short book called How to Build a Time Machine, by Paul Davies, a very interesting book.
One type of time machine is the one that uses a worm hole. In order to have a stable wormhole, one seems to need exotic matter. This is matter that has negative energy, or equivalently, negative mass. This can keep the wormhole from collapsing under the intense gravity. Exotic matter hasn't been observed yet, but theoretically there is no reason why it can't exist.
Note that it isn't the same as anti-matter. Anti-matter has positive energy, and has been observed. In many radioactive processes positrons are formed, which are anti-electrons. If an electron and a positron meet, they annihilate and create two photons, that have the energy of the masses, as the famous formula E=mc2 tells us. If an electron and an exotic electron meet, they might also annihilate each other, but the sum of their energies is 0, so they wouldn't create photons, or photons with low energy from their kinetic energy.
If you think about it some more, exotic matter is funny, and it behaves very counterintuitive. For example, knowing that it has a negative mass, what do you think would happen if you had a ball of exotic matter in your hand (on earth), and let it fall? (Think about it before reading on)
The force that acts on the ball is F = m.g. The mass is negative, so the force points upward instead of downward. But the acceleration of a mass is found by F = m.a, so the acceleration is downward. It falls down just like ordinary matter!
Now suppose that the earth was made of exotic matter, and you had a ball of ordinary matter that you let fall. What would happen now? (Again, think about it before reading on)
Newtons formula of gravity is F = G.m1.m2/r2. So the ball feels a force away from the earth, just like the ball in the previous paragraph. But the ball has a positive mass, so it moves away from earth. At first I thought ordinary matter and exotic matter were symmetrical (just like matter and anti-matter), but this disproves that.
Now suppose you had two balls in empty space (i.e. far away from any planet, star or other heavy object), one made of ordinary matter, the other of exotic matter. Their masses are the same, except for their sign. What happens as a consequence of their gravity? (Again, think about it before reading on)
F = G.m1.m2/r2 tells you that they both feel a force away from each other. The ball of ordinary matter has positive mass, so it moves away from the other ball. The ball of exotic matter has negative mass, so it moves towards the other ball. This means that the distance between the balls stays the same, the ball of ordinary matter starts to move away from the other ball, faster and faster, while being followed by the other ball! Does this violate the principle of conservation of energy? (Again, think about it before reading on)
Not at all. The formula for kinetic energy is E = m.v2/2. The ball of exotic matter has negative mass, so its kinetic energy is also negative. Because the two balls accelerate the same, they'll always have the same speed, so the sum of their kinetic energies is always 0! The potential energy stays the same because the distance between the balls stays the same.
Now, what would happen if you put a ball of exotic matter on a scale that uses a spring? (Again, think about it before reading on)
The force that a spring exerts is given by F = k.x, where x is the distance that the spring is contracted or pulled out (k is a constant, depending on the spring). The bigger this distance, the bigger the force. If an object is placed on it, there is an equilibrium between the force of gravity and the force of the spring. In this case, the force is upward, so the plate of the scale is pulled upward, and it indicates a negative weight. This is very bizarre: the ball wants to move downward, but it actually pulls the plate of the scale upward!
One type of time machine is the one that uses a worm hole. In order to have a stable wormhole, one seems to need exotic matter. This is matter that has negative energy, or equivalently, negative mass. This can keep the wormhole from collapsing under the intense gravity. Exotic matter hasn't been observed yet, but theoretically there is no reason why it can't exist.
Note that it isn't the same as anti-matter. Anti-matter has positive energy, and has been observed. In many radioactive processes positrons are formed, which are anti-electrons. If an electron and a positron meet, they annihilate and create two photons, that have the energy of the masses, as the famous formula E=mc2 tells us. If an electron and an exotic electron meet, they might also annihilate each other, but the sum of their energies is 0, so they wouldn't create photons, or photons with low energy from their kinetic energy.
If you think about it some more, exotic matter is funny, and it behaves very counterintuitive. For example, knowing that it has a negative mass, what do you think would happen if you had a ball of exotic matter in your hand (on earth), and let it fall? (Think about it before reading on)
The force that acts on the ball is F = m.g. The mass is negative, so the force points upward instead of downward. But the acceleration of a mass is found by F = m.a, so the acceleration is downward. It falls down just like ordinary matter!
Now suppose that the earth was made of exotic matter, and you had a ball of ordinary matter that you let fall. What would happen now? (Again, think about it before reading on)
Newtons formula of gravity is F = G.m1.m2/r2. So the ball feels a force away from the earth, just like the ball in the previous paragraph. But the ball has a positive mass, so it moves away from earth. At first I thought ordinary matter and exotic matter were symmetrical (just like matter and anti-matter), but this disproves that.
Now suppose you had two balls in empty space (i.e. far away from any planet, star or other heavy object), one made of ordinary matter, the other of exotic matter. Their masses are the same, except for their sign. What happens as a consequence of their gravity? (Again, think about it before reading on)
F = G.m1.m2/r2 tells you that they both feel a force away from each other. The ball of ordinary matter has positive mass, so it moves away from the other ball. The ball of exotic matter has negative mass, so it moves towards the other ball. This means that the distance between the balls stays the same, the ball of ordinary matter starts to move away from the other ball, faster and faster, while being followed by the other ball! Does this violate the principle of conservation of energy? (Again, think about it before reading on)
Not at all. The formula for kinetic energy is E = m.v2/2. The ball of exotic matter has negative mass, so its kinetic energy is also negative. Because the two balls accelerate the same, they'll always have the same speed, so the sum of their kinetic energies is always 0! The potential energy stays the same because the distance between the balls stays the same.
Now, what would happen if you put a ball of exotic matter on a scale that uses a spring? (Again, think about it before reading on)
The force that a spring exerts is given by F = k.x, where x is the distance that the spring is contracted or pulled out (k is a constant, depending on the spring). The bigger this distance, the bigger the force. If an object is placed on it, there is an equilibrium between the force of gravity and the force of the spring. In this case, the force is upward, so the plate of the scale is pulled upward, and it indicates a negative weight. This is very bizarre: the ball wants to move downward, but it actually pulls the plate of the scale upward!
posted by Mark VP at
2:56 PM
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