Three
Truths That Can Not Be Proved
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Quantum means discrete units rather than a continuous spectrum. If you shine white light at an atom, the atom will only reradiate light at particular frequencies. This phenomenon is because the electrons spinning around the atom must inhabit particular energy levels or orbitals around the atomic nucleus. By absorbing light the atom converts the energy of the light to increase the energy of one of its electrons to a higher energy state. Then when the electron returns to its original lower energy state, it releases the exact amount of energy difference between the two energy levels.
Electrons have a spin like a top that is also quantized. Simply put the spin can be either clockwise or counterclockwise, and the spin can only have exactly one magnitude of energy. Quantum theory states that only two electrons can occupy a single energy level of an atom and that those two electrons must have opposite spins. If somehow one of the two electrons switches spin then the other electron will instantaneously switch spins also. This "connection" that the two electrons share is called entanglement. The nucleus of the atom as a whole also has spin which is quantized as do the protons and neutrons that make up the nucleus. Particles of light, called photons, have a polarity that is also quantized similar to electron spin, which can be one of two possible states.
If an electron is alone in its orbital it can have a spin of either direction. One could set its spin by particular magnetic fields or some other energy source. If one has a sensitive enough detector, one can detect the spin of the electron, although the process of detection may alter its spin. If there are two electrons in a orbital and there is no detector around, then either electron could have either spin. However once someone tries to detect the spin of one of the electrons and measures a particular spin, the other electron will automatically immediately have the other spin. As photons and electrons (and all matter for that matter) can either behave as either particles or waves, while there is no detector and no one setting the spin or polarity, these elementary particles can exist as either particles or waves with either spin or polarity. When "particles" are in this unobserved state, it is called the superposition state. The pair of particles in this state do not have a specific spin/polarity, but instead exist as the possibility of either state. It is only during the measurement of its state will each particle have a definite state and act as particle or wave.
Thus in its superposition state, the particle can be though of as being in both states at once. Also if two photons are entangled and the photons move away from each other, once the polarity of one photon is detected the other photon will immediately have the opposite polarity even if the photons are separated by an extremely large distance. Thus this "spooky action at a distance" as Albert Einstein called it shows that influence, or perhaps more strictly information, can travel faster than the speed of light.
The fact that information can travel infinitely fast could be an argument that the world is actually a simulation. Imagine the ultra-computer running the simulation, and imagine what its inhabitants would experience. While the inhabitants of the simulation are bound by the finite speeds of the physical, the simulator computer would treat the whole simulated world as a type of data matrix with any point equally immediately accessible. Note that the simulator computer would not need to be infinitely fast, because the inhabitants of the simulation can only perceive at the same rate as their world is "updated" or refreshed by the computer. Also the fact that the underlying nature of the world is quantized, or in other words, digital is another big hint that the world is a simulation. Since the world is in essence digital, the world can be thought of purely as information, as one would expect in a computer simulation.
When discussing the workings of computers in general, the superposition state of makes things quite interesting. Today's computers store information in the form of bits. Even though today's computers utilize millions of transistors, which exploit quantum phenomena, they store and utilize the information in discrete units. Therefore today's computers are considered Newtonian or classical. A bit is the smallest piece of information and can have the value of zero or one. Normally a computer represents a bit as voltage of say either zero or five volts. Then someone (usually attributed to Richard Feynman) came up with the idea that if you could store the bit as represented as the spin of an elementary particle, you could theoretically create a very powerful computer. Because when this elementary particle representing a bit is in its superposition state, it does not hold the value of either one or zero, but holds the value of both at the same time. Combine the superposition concept with the concept of entanglement where multiple particles could be entangled and you have a state where instead of a single number being stored in a group of bits, all possible numbers that could be represented by the group of bits are represented.
Welcome to the world of quantum computing. Bits that can exist in the superposition state are called qubits. By performing logical operations on all possible numbers stored as qubits of a given problem at once, instead of one number at a time as regular classical bits, theoretically you would have a computer magnitudes faster than any computer existing today. Although the concept of quantum computers has been proven in the lab using a small handful of entangled bits, no human has yet built a practical quantum computer.