Faster-Than-Light Travel

Since humanity first went into space, we've always wondered if there is a way for us to travel to the distant stars faster than the light from those stars reach us. Faster than light travel has been a mystery to us and something we want to figure out if we ever want to go beyond our own Solar System.

What is faster-than-light travel? Basically, it going faster than the speed of light which is 300,000 km/s or 671 million miles per hour. At that speed, we could reach Jupiter from Earth in a little under an hour. Neptune, at 2.795 billion miles from the Sun, could be reached in about 4 hours, the flight time from New York to Dallas. To reach the closest star, Proxima Centauri, would still take 4.22 years. Knowing this, is it possible we could achieve faster-light-travel?

Probably not because when we think of faster-than-light travel, we think of traveling through normal space using the known laws of physics. The one theory that will control whether or not we can travel faster than light is special relativity. This is Einstein's theory that describes the physics at travels at or near the speed of light. Hendrik Lorentz found that as the speed of an object increases, so does it mass. At low speeds, i.e. speeds we achieve on Earth, this increase in mass is negligible. However, at near light speeds, the mass increases so much that when an object travels at the speed of light, its mass becomes infinite. This is given by

where γ is the Lorentz factor given by:

As you can see, as the velocity increase, the Lorentz factor decreases, until at v = c (the speed of light), γ = 0. And anything divided by 0 is infinite. So, sorry, we will never be able to travel through normal space at velocities greater than the speed of light.

So what about science fiction? They show spacecraft travelling faster than the speed of light, right? Well, technically, no. They have apparent faster than light velocity. What this means is that they follow laws of physics about which we do not know much. These laws that could, theoretically, allow apparent faster than light travel. I'm going to focus on two: warp drive in Star Trek and hyperdrive in Star Wars.

Warp drive describes exactly what it does: it warps space. A warp drive in a Star Trek ship creates a "warp bubble" around the ship allowing space in front of the ship to be compressed and the space behind it to be expanded. This allows the ship seemingly to travel faster than light.

via http://physics.stackexchange.com/questions/13444/getting-back-out-of-an-alcubierre-warp-bubble

This is called a Alcubierre drive, which is essentially a warp drive.

Star Wars, however, uses something a little more exotic. It uses something called hyperdrive, which is essentially creating a wormhole in space to allow the ship to travel across vast distances via a shortcut in hyperspace. Think of it as taking a piece of paper and folding it in half so that the two ends are about an inch apart. If an ant wanted to travel from a point on the top half of the sheet to a point on the bottom half of the sheet, it would have to travel the whole length of the sheet. Now, imagine that that ant could create a hole in the top half and a hole in the bottom half and is able to link those two holes together. The ant has created a wormhole allowing it to travel much faster between points than taking the conventional way.

via Space.com

These two methods of faster-than-light travel may someday be achieved. But the physics and engineering of how to accomplish them are not well understood, and for that which we understand, it requires a form of energy that we do not have the ability to create at this time. Both methods require negative energy which may be discussed at a future time.

Special Relativity

Previously, we briefly discussed General Relativity and how it expands Newtonian Mechanics to include the interaction between mass and space(time). Today, we are going to talk a little bit about Special Relativity in that what happens to physics when we approach velocities near the speed of light.

There are two postulates that Albert Einstein proposed make up Special Relativity.

1.      All Laws of Physics are invariant in all inertial systems - basically, the laws of physics must remain the same for all reference frames that are not accelerating.

2.      The speed of light in a vacuum is the same for all observers, regardless of the motion of the observers. In other words, the speed of light, c, is the same for a stationary person and a person moving at any speed, up to the speed of light (which is impossible).

One of the amazing things about Special Relativity is the idea of time dilation. It means that for any body travelling at any speed, time is not constant. To a stationary observer, it would appear that the clock for the moving object slows down, but for the observer in motion, the clock of the stationary person speeds up. In both cases, each observer sees the clock in his or her reference frame as moving normally. How does this work?

We have to use math to show this. There is an equation that describes how time is relative using the Lorentz transformation:

Where  is the time for the moving observer,  is the time for the stationary observer, and  is the Lorentz factor given by , where v is speed of the moving observer and c is the speed of light (3x10⁸ m/s). Since v is always less than the speed of light, is always greater than one, therefore Δt’ > Δt. For the stationary observer, the clock of the moving person is slow, while for the moving observer, the stationary person has a fast clock. For velocities much smaller than the speed of light, γ is virtually 1 and the times are equivalent. However, we have seen for objects moving near the speed of light (particles with little mass), this actually holds true. An example is a muon. A stationary muon would decay in only 2.2 μsec; however, when a muon is travelling near the speed of light will last much longer than 2.2 μsec (to a stationary observer).

Another strange feature of special relativity is the idea of length contraction. In other words, a moving object will appear shorter than it would be if it were stationary.

Where Δx’ is the length of the moving object and Δx is the length of the stationary object. This again leads to another strange phenomenon: relativity of simultaneity.

Relativity of simultaneity means that something that happens simultaneously in one inertial frame is not necessarily simultaneous in another. The best example given is called the ladder paradox.

Imagine a ladder and a barn. The ladder is just a little bit longer than the length of the barn. Now imagine that the ladder is moving at a relativistic speed. Someone in the barn reference frame will see the ladder shorter than its stationary length, and can close doors at both ends with ladder inside simultaneously. However, to keep the ladder from crashing through the end door, the doors must open up again. For the ladder, however, it sees the end door close first, then the front door close secondly, with the end door opening up before the ladder reaches it. The ladder does not see both doors closed at the same time.

A third phenomenon of special relativity is the idea of infinite mass. For a moving mass, Δm’=γΔm. As v approaches c, you can see that γ nears infinity (v/c approaches 1 and the denominator in the Lorentz factor approaches 0). This is why nothing can reach the speed of light as its mass will become infinite, which leads to another famous equation: E=mc², the energy-mass equivalency. This means in order to accelerate a mass to the speed of light, the amount of energy required goes to infinity.