Understanding the Uncertainty Principle with Quantum Fourier Series

But this intuitive, mechanical reality is emergent from underlying reality in which the particles that form matter arise from of the combination of an infinity of possible properties. And forget matter – the vacuum itself is the sum of infinite possible particles. If we fully unravel this idea we’ll be on the verge of tackling things like Hawking radiation. But as you’ll see today, in that unraveling we are led, unavoidably, to Heisenberg’s uncertainty principle.

The Vacuum Catastrophe

Let’s talk about vacuum energy from a theoretical standpoint. From the perspective of quantum field theory, every point in space is represented by a quantum oscillator; one for each elementary particle type. Higher energy oscillations represent the presence of real particles. However even the lowest possible energy oscillation – the one corresponding to the absence of particles – has some energy.

The Nature of Nothing

How do we study nothing? An empty jar still contains something: molecules of air and a bath of infrared light from its warm environment. But what if we suck out every last molecule of air, chill the jar to absolute zero, and shield it from all external radiation? The jar would contain only empty space, but it turns out that empty space is far from nothing.

Absolute Cold

Many experimental physicists have spent their careers trying to cool things to absolute zero. This state of absolute cold is the zero-point on the Kelvin temperature scale, corresponding to -273.15 Celsius. Using lasers and magnetic fields, we’ve now managed to cool certain substances to less than a billionth of a Kelvin. Doing so has revealed some bizarre quantum states of matter. But quantum mechanics may also prevent us from ever reaching absolute zero.

The One-Electron Universe

One-Electron Universe idea: that there exists only one electron, and that electron traverses time in both directions. It bounces in time, eventually traversing the entire past and future history of the universe in both directions, and interacting with itself countless times on each pass. In this way it fills the universe with the appearance of countless electrons. And when the electron is moving backwards in time it is a positron; the antimatter counterpart of the electron.

The Secrets of Feynman Diagrams

Feynman’s path integral shows us that, to properly calculate the probability of a particle traveling from point A to point B, we need to add up the contributions from all conceivable paths between those points – including the impossible paths! In fact we can go even further: according to Feynman’s approach, every conceivable happening that leads from a measured initial state to a measured final state DOES in a sense happen.

Solving the Impossible in Quantum Field Theory

The equations of quantum field theory allow us to calculate the behaviour of subatomic particles by expressing them as vibrations in quantum fields. But even the most elegant and complete formulations of quantum physics – like the Dirac equation or Feynman’s path integral – become impossibly complicated when we try to use them on anything but the most simple systems.

Feynman’s Infinite Quantum Paths

Quantum mechanics seems to imply that ALL possible properties, paths, or events that could reasonably occur between measurements DO occur. Whether or not this is true, a mathematical description of this crazy idea led to the most powerful expression of quantum mechanics ever devised: Richard Feynman’s path integral formulation.

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