"I don't like it, and I'm sorry I ever had anything to do with it." - Erwin Schrödinger "Anyone who is not shocked by Quantum Theory has not understood it." - Niels Bohr
As strange as relativity may seem, Quantum Mechanics is far more unsettling. It states that at a fundamental level, the behavior of the universe is probabilistic (random).
This goes against all of the beliefs ingrained into students of Physics from the time they begin studying simple projectile motion, to the time they study relativity.
Despite this, Quantum Mechanics is the best theory that the human race has ever come up with for explaining the behavior of the very small (subatomic).
Furthermore, its predictions thus far have all been correct, and it is the basis for much of our modern technology, from Computers to Scanning Tunneling Electron Microscopes.
Its application to Starship design is not as great as Relativity, and therefore it will not be discussed in as much depth, but the general ideas of Quantum Mechanics are outlined below.
Most people have heard light represented as a wave (we often speak of the wavelength of light), and as a particle (we also often speak of "photons").
Quantum Mechanics, though, states that all matter is both a wave and a particle. This is called "wave-particle duality" and is the basis for all of modern Quantum Mechanics.
Before we discuss wave-particle duality, though, the meaning of the word "Quantum" should be discussed.
Many people may be daunted by Quantum Mechanics' rather impressive title. It is mainly impressive because of the word "Quantum", which sounds like something very complicated. In fact, a quantum is really just a discrete unit of something. For instance, the number of apples at a super-market is quantized.
So, we could say that A, the number of apples, is a "quantum number" that describes some aspect of the super-market. In this same manner, various aspects of very small things (such as atoms) are quantized.
Later, how these quantizations came about will be discussed.
The hardest thing to grasp about Quantum Mechanics is the notion of wave-particle duality. Simply stated, Quantum Theory says that all things exist as waves while they are not being observed, but once they have been observed, the wave functions "collapse" in to particles.
Many experiments have been done to show that this is indeed the case, but it is still not clearly understood what constitutes an "observation". In any case, sometimes pieces of matter (such as electrons) behave like waves, and at other times behave like particles.
An experiment that has been done to show that electrons can behave like waves is passing a stream of electrons through a pair of thin slits. If they behaved only as particles, the electrons would simply go through one or the other of the slits and strike the screen. The distribution would be roughly uniform.
This is not what is observed at all. Instead, the electrons pass through both slits and interfere with themselves. Or rather, one should say that the wave function of the electrons (all of the electrons together share one wave function in this case), passes through both slits, and interferes with itself. This is precisely what light does.
Now comes the really strange part. If one attempts to view the electrons individually... to see which slit each one goes through, something remarkable happens. The interference pattern goes away. Since the observer has collapsed the wave function by localizing the electrons, they no longer behave as a wave.
Obviously, a particle can not pass through two slits at the same time, but a wave can. So when the electrons are behaving as a wave, they do pass through both slits and interfere with themselves. When they are behaving as particles (because they are being closely watched), they pass through only one or the other of the slits and no interference occurs.
As strange as this sounds, this is really what happens in experiment. While the reasons given by Quantum Mechanics are, of course, theories; the actual observations described above are undeniably real.
Where the "Quantum" part of things comes into play is not yet clear. Let us examine the case of a particle trapped inside an infinite potential well. Observe figure 3:
The red curve in the figure depicts the wave function of the trapped particle in its lowest energy state. It is important to note here what we mean by an "infinite potential well". This simply means in the outer regions (to the left and right) there is something that is stopping the particle from going there.
What is stopping the particle depends on what the particle is. For example, an electron could be stopped in such a manner by extremely strong electric or magnetic fields. Note also that we say an "infinite" potential well. No such thing exists in nature, of course, but it is a simplified example to aide in understanding.
At any rate, the wave function is obtained by using Schrödinger's equation (which is a differential equation and is therefore difficult to solve in many cases).
The wave function must be continuous (this is entirely logical), and it should (in the case shown above) go to zero at the edges of the well. This is because the square of the wave function represents the probability of finding the particle in that given location.
Obviously, the probability of finding it in the area of infinite resistance must be zero. The solution shown in figure 3 obeys both these criteria. What would happen, however, if the particle was more energetic? Well, it turns out that the wavelength of the particle shortens as it gains energy (just like light).
Remember, though, that the wave function must be zero at the boundaries, which means that a small change in wavelength is not allowed. The wavelength must change sufficiently so that it is still equal to zero at the boundaries. This means that only discrete levels of energy are allowed for this particle!
It is quantized.
An atom is just like a potential well for the electrons (of course, this well is not infinite). Therefore, the allowed energies of electrons are also quantized, hence the "quantum numbers" that describe an electron in an atom.
It is important to realize that these quantizations apply only to trapped particles. A free particle can have any energy in the continuous spectrum.
Of particular interest to us is something called "Quantum Tunneling". Observe Figure 4:
Again, the red curve represents the wave function of a particle. In this case, it is incident on a barrier of some sort (a potential jump). Solving the Schrödinger for such a case yields the startling result depicted above. Instead of simply bouncing off the barrier, the wave function actually passes through the barrier.
A portion of the wave function exists on the other side of the barrier. The wave function is smaller on that side though, indicating that there is a certain probability that the particle will be found on that side of the barrier; but, that probability is less than being found on the side it started on.
The fact that particles can jump from one side of a barrier to the other is extremely important in understanding nuclear decay, and in creating many of today's technologies.
For example, the Scanning Tunneling Electron Microscope (STEM) has a probe that is only one atom thick at its tip. This tip is placed very very close to the surface of a material. When a potential difference is applied to the probe, electrons from nearby atoms will actually tunnel from their atom to the probe. This creates a current.
The stronger the current, the closer the probe is to an atom. By mapping the tunneling current over an area, one can construct a super-detailed image of the surface. The very locations of the individual atoms can be seen!
Unfortunately, Quantum Tunneling is useless for space travel. Although any particle (no matter how massive) has a certain probability of tunneling, the larger the mass, and the greater the tunneling distance desired, the lower the probability becomes. For instance the probability of a human being tunneling to Jupiter (which is even in our own solar system) is on the order of 1 in 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000.
Or 1 in a trillion trillion trillion trillion trillions. In case you couldn't tell... this is so improbable, it is effectively impossible.
