Part 2 of Schrodinger’s Next Lesson — Taking Duality Seriously
In Part 1, I dove into a web of issues surrounding inertial and non-inertial reference frames. There we cast doubt on how our reference frames have been defined and discovered that our current definition of time was causing a variety of problems. It got pretty intense so I had to pull back a little to keep working on gravity. It’s still in progress.
Back in Statistical Mechanics, I was ready for my next assignment. If you remember from last time, Schrodinger used a cat (probably the most ethical option due to the many lives function) in a thought experiment to highlight what was wrong with the interpretation of the double-slit experiment. As my next assignment, I decided to take another look at the results to see what might be wrong.
To refresh our memory, all physical phenomena can be explained by one of two models. A particle or a wave (an amazing feat of science if you ask me). Although, light and other quantum phenomena don’t fit either model very well for all scenarios. See below.
So, we’ve tried particles and we’ve tried waves. We have also tried a sort of step function approach where we apply one model over the other depending on the situation. But, what about a particle AND wave model? The difference is subtle but a particle and wave model would look like a particle that propagates in the shape of a wave.
Reinterpreting the Double-Slit Experiment
Because of the extensive use and verification of our current configuration of physics, the only real possibilities for discovering any new physics would lie, somewhat invisibly, behind our current models. In other words, any new models or extensions of previous models will need to look and act like what we already have.
Looking at the double-slit experiment more critically, I asked myself what other possible physical models could fit the results we see. I didn’t get much of a chance to come up with a coherent alternative on my own before I stumbled onto an alternative that I couldn’t beat, a helix.
A helix is probably most familiar to us from high school biology. That’s where we learn that our genetic code, DNA, takes the shape of a double helix. Our model here is just a little less fancy. Maybe the universe borrows its own tricks every once in a while and saved the best for last? A self-similar or fractal universe would be immensely convenient but, who knows?
Back to the Double-Slit Experiment
Let’s see how much explanatory power this model has with our existing observations. Like I described earlier, any new model we consider should fit neatly behind our existing models while also giving us more room to move around, i.e. a more precise definition.
- Can it describe the same wave-like interference pattern?
- Can it describe the same particle pattern?
- What happens to superposition?
- How does it address Heisenburg’s Uncertainty Principle?
Superposition, Particle, and Wave Patterns
In the figure above I have the typical view of the interference pattern seen in the double-slit experiment. If light and other particles travel along a spherical path then, for very small slits, half of the possible trajectories will be split between the two slits and still have room to interfere with each other with the circular trajectory. This would create the same interference pattern we see in the original experiment and accounts for both the particle and wave-like nature of light. This would also remove the need for superposition which is not a favorite for physicists with determinism in mind.
The distribution of wave intensity can also be readily explained with helical trajectories. Typically, we find a peak at the center of detection as shown below. Peaks and valleys are found to be periodic along the detection plate.
In the figure above we see that adjacent peaks could be attributed to the same wave for different times. As we move further from the center of detection the peaks decrease in amplitude. This would be due to the helical waves hitting the detection plate at more and more acute angles. In between, we find impacts from all the random collisions of light interfering with itself.
What’s fascinating to me is that light waves may not truly cancel each other but instead “scatter” each other? I wonder if detectors covering the inside of a box would pick up stray photons whose trajectory was changed significantly…
The Uncertainty Principle
Heisenberg’s famous Uncertainty Principle states that position and momentum are impossible to determine at the same instant. If waves propagate along a helical path it would make perfect sense that position and momentum couldn’t be determined at the same instant. Half the wave information is missing because it is on the complex plane.
Remember that we describe all electromagnetic waves using complex numbers containing real and imaginary parts. A helix would simply be the vector product of the two and would give us a real position along with momentum in 3D space. With half the wave hidden we need something like a wave packet to account for all possible positions that were left out. We need superposition here to fill the gap that was inadvertently covered up.
At first glance and not considering measurement error, it is likely that the general width of the uncertainty distribution for any wave function is proportional or identical to the difference in phase between the real and imaginary parts of the wave function. If someone can answer this for me I would be very curious to know the answer!
Ultimately, this would mean that Heisenberg’s uncertainty principle wasn’t describing anything fundamental about reality or waves, it might just describe the size and shape of the hole in our misunderstanding of physics. Einstein, that one was for you. I know you hated this and other spooky stuff so, you are welcome! Also, you’re up in the next article…
Variations to the Double-Slit Experiment
There are some variations to the double-slit experiment which were briefly checked. Fortunately, the helical model still worked. It didn’t help that the results from some of those experiments confounded us further so they didn’t warrant a deep check. I need to finish deleting gravity and replacing it anyway.
Implications and Up Next
I am a bit too close to all this now to have an unbiased opinion but if this model does end up working there will be a lot of joy but it will also ruin a few things. The “bad news” might include losing things like quantum entanglement, because it’s likely to be the very same particle, and perhaps quantum computing since everything is deterministic again.
On the bright side, having a single equation that is continuously differentiable that describes all waves would be a huge win for all of us. Having analytical solutions to a 3D wave equation would make weather prediction less laughable and over the long term save millions of lives with much more accurate flood, tornado, and hurricane predictions.
Additionally, a common model for the basis of most physical phenomena would greatly reduce the overall complexity of physics and its related fields. This would reduce the immense learning curve, and sometimes a barrier, to physics education. A more inclusive physics means a more diverse set of minds being interested in the topic and eventually the development of a lightsaber.
I am still making a mess and picking up the pieces. Up next and in Part 3 I plan to tackle gravity and hopefully patch the chasm between classical and quantum mechanics. Thanks, everyone!