Why Time Travel Kills Free Will (Part 3)

Image created by Kurzon, 4/15/2014

Image created by Kurzon, 4/15/2014

Why A Working Time Travel Machine Implies That There’s No Such Thing As Free Will

Part 1: Waves and Superposition
Part 2: Basic Quantum Mechanics: Young’s Double Slit Experiment
Part 3: Basic Quantum Mechanics: The Structure of Hydrogen
Part 4: Spacetime and Wormholes
Part 5: The Death of Free Will

Last week I mentioned that the wave-like nature of electrons can beautifully explain the structure of the hydrogen atom; this week, we’re going to explore this idea. Now you may be wondering, “what does this have to do with time travel?” but stick with me; as it turns out, time travel machines and hydrogen nuclei probably have a lot in common!

The Atomic Structure of Hydrogen

For a long time physicists struggled to understand why hydrogen (and other elements) absorbed or released certain colors preferentially when heated under low pressure conditions. In the early twentieth century a physicist by the name of Niels Bohr created a model of the hydrogen atom where the electron circling the nucleus like a planet orbiting the Sun. As light was emitted or absorbed, the electron would change orbits, “jumping” inward or outward depending on whether the light was released or absorbed:

Image created by Kurzon, 4/15/2014

Image created by Kurzon, 4/15/2014

To make it work, however, Bohr had to include an ad-hoc assumption — that the electron couldn’t orbit at any distance it wanted, but only at “acceptable” distances (which he determined experimentally). Unfortunately, he had no idea why this was the case; he couldn’t explain why the electron should suffer any such limitation. Using what we’ve discussed over the past two weeks — about waves, electrons, and wave-particle duality — we can.

In particular, imagine (in the picture above) that the electron isn’t a planet-like ball, but instead is a wave traveling around the circle. Eventually the electron wave will return to where it started; at that point the wave will begin to interfere with itself. Depending on how the electron wave lines up on itself, this interference could be constructive or deconstructive:

Image by CK-12 Foundation, 2/22/2010

Image by CK-12 Foundation, 2/22/2010

If the electron-wave manages to overlap itself perfectly (like the left side of the picture above), then constructive interference will occur. However, if it does not (like the right side of the picture above), then the electron-wave will undergo destructive interference. Physically, the probability of finding the electron on that circle becomes zero — it can not exist there. Even partially destructive interference significantly reduces the chance of the electron hanging around, which means that the places the electron is most likely to show up — the places that it will, in fact, be required to show up — is only along these certain special circles where the electron-wave constructively interferes with itself. That was the secret behind Neils Bohr’s “acceptable” orbits — the electron can only exist in orbits where it doesn’t interfere itself out of existence! When this occurs, the resulting electron-wave isn’t moving anymore — it has become a standing wave — and it’s said to be in a stationary state:

Image created by Yuta Aoki, 11/30/2006

Image created by Yuta Aoki, 11/30/2006

In reality, the situation is more complex than this — mostly because hydrogen atoms are three dimensional, not two. However, the basic idea is correct: electrons are unable to go anywhere that they would destructively interfere with themselves. The same thought process has been applied to protons, entire atoms, and even molecules, so there’s nothing to suggest that this basic idea can’t be applied to larger collections of matter. In general, physical objects should not be able to go anywhere or do anything that causes destructive self-interference.

Now, at this point you may be able to see where I am headed — at least partially. Even still, there’s one more set of ideas that I’d like to introduce before I bring everything together. Therefore, next week we’re going to build a basic time machine using wormholes through space time, as well as discuss some assumptions and limiting cases. See you then!

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