The de Broglie Equation and Why There Is No Wave-Particle Duality

The wave-particle duality seems to used all the time to explain quantum mechanics to the public, but it is one of my pet peeves. It represents an outmoded way of thinking (old quantum theory), which is replaced by our current understanding of the wavefunction (new quantum theory). I explain how to use the wavefunction to explain one of the most important experiments in quantum mechanics: the double slit experiment.

Update on my life: I'm going to start a PhD! Same place as the masters, on quantum computing. Very very excited. But don't worry, I'm determined to make time for this channel throughout my remaining studies. In fact, expect some videos on quantum comp in the not too distant future (well, at least not too distant compared to the time scales I work on. Don't hold your breath or anything. That will end badly).

[LookingGlassUniverse]

Did anyone notice I completely changed how I produce the videos? No? That's good- I wanted them to have the same style. I no longer draw physical pictures/ write on a whiteboard/ physically move things and take photos. Instead I bought a Cintiq (which I could afford using the Youtube ad revenue I've gotten (I started putting ads on in the last year)), so everything is drawn onto there (in the program Sketchbook Pro) and then hundreds and hundreds and hundreds of these images are edited together in iMovie.

[CheCheDaWaff]

e^(it) := cos(t) + isin(t) isn't just some arbitrary definition. It's the only complex definition of the exponential that preserves its defining property (the derivative of exp is itself) as well as its Talyor expansion.

It's pretty much the only natural non-trivial why of defining exp. That's why any properties it might have are allowed to be interesting.

[tessiof]

You are like the Vi Hart of physics.. I like it.

[le_scienceall]

So happy to see you back on YouTube! I was so afraid you had given up! And as usual, such awesome explanations! The relationship between position space and momentum space is much clearer to me now.
Here's a small comment about the awesomeness of e^{i\pi} + 1= 0. Euler did not define e^{i\theta} as a point on the circle. He defined it based on the Taylor series e^x = 1+x+x^2/2+x^3/3!+..., and by then replacing x by i\theta. Following his footsteps, it is then almost spooky that e^{i\theta} gets to be decomposed into the back-then well-known trig functions. Of course, these days, we have a much more geometrical interpretations, but this interpretation was not really available to Euler.

[manuelodabashian]

It did not sufficiently explain why there is no wave particle duality

[girlscoutfather]

You do a very good job at composing and orating these lectures. I’m not sure why these types of videos suit you so well, but you have a talent for capturing your audiences’s attention and keeping people engaged.

[tone]

You have no idea how excited I was when I got the email alert for this video! I'm pretty sure I managed to follow along with the general premises, although my lack of a calculus background made some of the more technical parts a little tricky. I'll probably have to watch it again at some point...

Also, at 8:26, I totally feel your pain. When we're filming, sometimes my brother accidentally skips a step, and since it's all one take, by the time we notice it's too late to do anything about. Fortunately, the pace we do things at means that it's closer to 4 seconds than 12, but still, it's always a frustrating realization in the editing process.

And the animations look great! I noticed they were a little different, but I just assumed you'd gotten new markers or a new board or something. It's incredible that you got such a similar look to your old style out of an animation program!

Also, congrats and good luck on the PhD! Looking forward to the quantum computing stuff: It's an area I have some vague semi-understanding about, but every explanation I've seen has wound up creating more questions than it answers, so I'd love to see a good deep dive on the topic.

Anyway, all that aside, awesome video, and great to see you back! I hope it's not a 11 more months before your next one!

[rikvandenkerckhove]

Great presentation. This is the first 'Looking Glass Universe
' I see. This has a particular level of mathematics not usually used in You Tube physics videos and I like it. Looking forward for more!

[agmessier]

The paradox comes not from the fact that it looked like a particle with a single slit...waves do the same thing as you described. The paradox comes from the fact that photons come in discrete packets and are measured at a single point, which isn't the behavior of classical waves, which are always continuous.

[Jopie]

Thanks for your awesome video again! I was really hoping you didn't stop making them. They inspire me a lot.

I think the real mystery to QM, that makes people think it sometimes behaves as a particle, is because the energy of a wave manifests itself in a single spot, and not somewhere else. The wave moves through a slit or slits and moves anywhere on the screen with different energy densities anywhere. But then.. it lands on a single spot, and not anywhere else where the wave has been. Now why is that I wonder? Why does this energy wave which is everywhere, suddenly releases all its energy on just a single random spot and not anywhere else?

[levels]

Hi I like your teaching style! The identity e^ix is not just a definition I think though. It is derivable both from the power series representation of e^x, and by relating cosx+isinx to a function "z" taking the derivative and then solving the resulting differential equation. It is not like somebody just said lets define e^ix= cosx+isinx and left it at that. It is a mathematical identity. They are the same function.

[NuclearCraftMod]

Thank-you! I totally agree - this idea of 'wave-particle duality' is not only one which doesn't actually make sense in many cases (where the wave function doesn't look anything like what you would classically call a 'wave'), but it also makes coming to the correct conclusion about certain experiments incredibly difficult.

[olivermorrison]

"I don't know why people get excited about it (e.g. e^ipi = -1)

My heart :'(
You poor poor physicists. If only you were given the chance to stop, sit down and realise the beauty of the equation

[chiknsld]

Your videos are very enjoyable to watch. You allow science to be understood in a meaningful and relatable way like no one that I have ever seen before. What you are doing for the world is more than you will ever know.

[princeofcupspoc]

Why the duality? Because in certain experiments, classical physics can be used to explain the results, and quantum physics can also explain it. This is not the case for most things. I've never been able to calculate the wave function of my cat when she is using the litter box. Maybe the confusion is existential. We want to impress an identity onto what we observe, and waves and particles are thought of as different things. The existence of electrons themselves is only seen indirectly. I can imagine that there are no electrons, but instead a ghost breathing fairy dust. However, I don't have any math that is very useful in describing the ghost. I have useful math for the thing we think of as an electron, so we go with that. And in some cases, two different sets of mathematical formula can explain what's happening in an experiment, one that talks about particles and one that talks about waves. If I could come up with math for ghost fairy dust, then we'd have 3 sets of math.

[paulikeda]

As an occasional viewer, I enjoy your videos as my preferred channel for QM.

One point that I would like to clarify, is that the wave function doesn’t describe a physical model, though in this case, I can surely understand why it seems that way.

To see why imagine if particles were in a probability state instead of a superposition state. To calculate the probability (or coefficient) of each state, you would still be required to treat the problem like a superposition state because that’s the only way we can calculate probability states. i.e. any individual state probability could not be calculated without the context of all possible states that add up to 1.

So you would be using the same wave equations if it was for probability or superposition. Therefore the equation doesn’t define the physical cause and effect of the system.

Mathematical models can only determine results as values despite being a very intuitive model of a wave with all of its states defined. Only logical models can explain understanding of the theory such as requiring superposition.

So as you stated, the dual slit wave interference results were the logical basis for treating superposition as real. The Heisenberg Uncertainty Principle and the mathematical models also helped support the superposition conclusion.

The observer effect was the logical basis for particle/wave duality.

Warning:
Below, is a logical model that can explain QM in a way that may seem absurd at first, but then makes so much sense you will probably feel disillusioned.

It is not accepted science.

The dual symmetry logical model:
At the beginning of time the properties of space and time flipflop at time = 0 at the Big Bang.
⇒ Entangled matter/antimatter pairs were created moving in opposite directions in time but not space.

Applying Noether’s first Therem where conservation laws are the basis for symmetry which CPT (Reverse Charge, Polarity, and Time) symmetry provides:

...-9, -8, -7, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, +7, +8, +9...

Figure 1: New BB model, Dual Light Cones over a dual timeline of positive and negative time.

Opposite time lines seperated by the Big Bang could just be treated as positive timelines since there would be no way to reference the other side. With both domains moving in the directions of increasing entropy. CPT symmetry would tell us that their would be no way for a local oberver to distinguish which domain they were in. Since both time domains are locked in hidden entanglement they would exist like two sides of the same coin, sharing a single determinism and all observers existing in both frames would be controlled by a shared free will and each only ever aware of a single universe.

The particles would interact with opposite charges causing rotations in the same direction as if dual orbiting stars, matter/antimatter particles would act in a virtual dual orbit as if in close proximity with their hidden partners, yet they would be seperated by dimensions of time, safe from self annihilation though interacting through their EM fields and charges, creating EM waves.

To see why they would have the same spin, imagine rotating one cone over the other and you would note that all left/right polarity and spin would synchronize. Also remember that while they exist in 180° time shift, they still occupy the same space as the other, if viewed in the x domain. The only differences between them would be opposite charge and their orbits would be 180° phase shifted from each other.

We can now see that the twisted worldlines create a tightly twisted pair loop, that would be modeled as infinitessimal loops between the pairs in hidden extra dimensions along their world lines just as is the case for string theory.

Ideal for long distance propagation accross the Universe. They would exhibit mysterious properties of spin, magnetic dipole moments, and seem to have wavelike properties when entangled, due to each particle passing through a different slit in their symmetrical domains.

Yet if observed, then entanglement would break, waves would collapse, just like a switch creating an opening in a circuit.

Why the differential loop makes sense out of the Universe in reference to all known Theories.
1. Properties of time and space are flip floped at time = 0 in the BB theory
2. Noether’s first theorem states that conservation laws require a symmetrical differential Universe based on conservation laws which are the conservation of mass, charge, and spin in equal and opposite Universes.
3. CPT Symmetry requires symmetry in all three: +/-charge, L/R polarity, and +/-Time which creates dual universes that are impossible to tell apart by the observers in them.
4. Accounts for the missing antimatter.
5. Explains lack of evidence for matter > anti-matter
6. Provides the logical model that explains Quantum Spin, dipole moments, matter/antimatter properties in the Durac Equation, dual rotation in the Schroedinger equation.
7. It provides the logical model that make sense out of all Quantum weirdness
8. Unifies all Quantum Wierdness effects to the dual Helix model.
9. Dual light cones complete the conics analog.
10. Dual time lines complete the numberline analog.
1. +/-square roots results
2. -1 = +1 using sqrt(i)
3. complex numbers
4. rotation into the complex plane.
11. It provides the logical model that explains
1. Black Hole paradox
2. matter/antimatter annihilation at SoL/EH for conservation of information paradox.
3. negative energy for ER bridge,
4. positive energy for Hawking Radiation
5. Reverse time at FTL speeds in ER Bridge.
12. It provides the logical model for one of the two hidden loop dimensions in string theory.

[C]

It's simple: there are no particles. The electron seems to appear in more than one place because it is a superposition of 3D waves of different wavelengths which form localized wave-packets. During the time evolution of the wave function, these wave-packets would seem to appear in a position where it didn't follow a particle-like trajectory. That dispenses with Max Born's probability nonsense.

[sour]

how can you say wave particle duality isnt a thing, but youre explaining electrons based on their wave function? wave particle duality only means that they ACT as both. if there is no wave particle duality, then you cant assign momentum and speed to light, which means that light is literally nothing at all, no properties like spin, polarization, and no force interactions.

[dylanparker]

i've probably horribly misunderstood (sorry!) but i believe de broglie's wavelength is h / p (but at 8:19, you give it as p / h)

[erikziak]

Welcome back. Great to read about you going for a PhD. You can totally do it! You mixed up the colors blue/red parts at 7:30. Answers: 1. Not now, sorry. I completely lost track of QM, was reading other stuff (Eliezer Yudkowsky). But he confirmed what my feelings about QM were as he briefly wrote about it (as if he were some authority on QM, and as if we should trust "authorities"). 2. Nils was simply wrong in this. 3. I am pretty good again, finished a 36 pages long "paper" as final draft three weeks ago (it took me four months of research and work to finish and since it is no real academic material and I am lazy, I decided not to cite any sources), will present it hopefully until the end of September. I have to prepare another presentation for an event in two weeks, I already agreed to it (which I now regret). I bought a new flat, painted today the last room (ok, kitchen not done yet as well), moving in hopefully soon, lots of work. Finally finished a big project at work and the next one is already lurking behind the corner. No time or money for vacation. I should stop writing.