Puzzle Piece 4: The (other) Heisenberg

Previous puzzle: Puzzle Piece 3: What’s special about Special Relativity?

Let’s talk about Heisenberg –  not Walter White, the real Heisenberg, who came up with the uncertainty principle. The fact that for any particle, one cannot measure location and momentum exactly at the same time.

If we look at this in the context of waves, as in sound waves, then maybe it does not sound so strange. Basically, the principle says that the error in the position (dx) times error in momentum (dp) is larger or equal to ħ/2: \sigma_{x}\sigma_{p} \geq \frac{\hbar}{2},

where ħ is the reduced Planck constant.

So what does that mean in the context of sound? A pure sine tone (say 440 Hz) has an exact frequency, but has no clearly defined starting and ending position:

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Imagine you play this tone on an instrument, say a violin. Then you hear just that one frequency, and there is no beginning or end of that tone (except when the player begins and ends of course). So that sine wave extends in space for as long as the player plays that tone. It is not localized – it makes no sense to talk about location, as it is the same for the entire duration of the sound.

Now what does an exploding balloon sound like? It’s the opposite of a pure sine wave: a popping balloon has quite a specific location, but the frequency of that sound is not one pure tone, but a mixture of many frequencies. How can this be represented? Basically by adding a bunch of sine waves (Fourier) together, to get the shape of the explosion sound: below I added a bunch of cos curves – the more you add, the more localized the sound gets, but the more frequencies are mixed in, so the harder it gets to determine a frequency.

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You can either measure the frequency, but then you can’t tell quite exactly where the sound begins or ends, or else, you measure the location, but then you can’t quite tell what frequency the tone had. In fact, the perfect impulse has an infinite number of frequencies, and it doesn’t even make sense to talk about measuring the frequency in that case, because there is no clearly defined frequency. In the other case, it makes no sense to say where exactly the tone is, because it has no clear beginning or end.

This is true for any kind of wave, whether we talk about sound waves, water waves, light waves or matter waves. If matter is composed of true waves, then maybe the idea that for a “particle”  you can either determine it’s location or it’s momentum, but not both at the same time, does not seem so strange anymore  – it is simply a natural consequence of any wave.

Next puzzle: Puzzle Piece 5: The Doppler Challenge

Summary Table

Space-density Universe
(RED pill)

Space-Time Universe
(BLUE pill)

Tags elastic solid, crystal universe, optical-mechanical analogue, space exists Minkowski, space-time, absolute space does not exist
GR Metric Tensor space-density (space with compression) space-time
Cause of Gravity refraction (density gradient, optical) curvature of space-time
Photon quantized wave, similar to phonon quasiparticles in crystal (vibrational mode), there are no photon “particles” probability density wave function, no “real” wave, probability of finding photon
Double Slit Experiment real waves interfering (like phonons) parallel universes, no real wave, “consciousness” ,probabilistic…
Schrödinger Wave Equation describes real waves, rotational waves in an elastic solid. There are no particles probability of finding a particle, there are no real waves
What is space? An elastic solid (not made of matter). Matter and light moves though space as waves move through a crystal There is no absolute space
Special Relativity Time dilation and length contraction are consequence of any wave system. Any wave has a maximum speed in any given medium. There is no intuitive explanation. It follows from the constancy of the speed of light for each observer
Speed of light c, constant in absolute space. Also c for each observer, due to time dilation c is constant for each observer. There is no absolute space
Twin Paradox No paradox. Whoever moved slower relative to absolute space ages faster. If A is considered to be at rest, B ages more slowly, and vice versa. There is no clear answer as to who ages faster (if cleverly engineered –see post on that)
Uncertainty Principle Natural consequence of any wave system Due to wave property of matter and light (but only probabilistic)

Links

Uncertainty Principle