The Universe Exists Because of Identical Particles.

The universe as we know it, can only exist if certain particles are absolutely identical to each other (assuming also that quantum mechanics is correct...)

Here's a talk I did recently (huge thanks to Reading School for inviting me) discussing this rather interesting concept. We started by considering the structure of atoms. We know that each atom has protons and neutrons in a nucleus, and electrons surrounding this nucleus. The electrons are arranged in shells and orbitals. But why is that?

To answer that, we need to look at quantum mechanics. Quantum mechanics is basically the study of very small objects, such as particles that make up atoms. And because quantum mechanics is not very intuitive, it says that particles behave in rather strange ways. When we do an experiment to find where a particle is, it's not always going to be where we expect it. However we can work out the probability that we'll find our particle at a given point in space each time we are about to try and measure its position. So instead of working with pesky, difficult to track particles, we work with a wave function.

A wave function is a mathematical function that changes smoothly over time, and tells us something about our particle. Most commonly, it tells us the probability of us finding our particle at different points in space. To find this probability, we square our wave function. This means that the square of the wave function is a directly measurable quantity, since we can repeat the experiment and work out the probability of each experimental result for a future experiment. So why deal with the wave function at all, and why not with the square of the wave function? Well that's because the wave function itself contains information that is lost when squaring.

We also look at the wave functions of multi-particle systems. We understand how the probability of each experimental result changes if we swap two particles. For identical particles, the probability does not change because we cannot tell them apart. If this is true for all possible experimental results, then these particles are said to be "indistinguishable". There are two flavors of indistinguishable particles: bosons and fermions.

Electrons happen to be fermions. We see how two fermions with the same spin state can never be found in the same orbital state. In other words, for every orbital in an atom, there can only be two electrons in it - one with spin up, and one with spin down. This is known as the Pauli Exclusion Principle. And it's because of this principle that atoms are arranged the way they are - with electrons being found in shells and orbitals (rather than all being in the same low-energy state).

And it's the atomic structure that enables basically all of chemistry to occur through covalent and ionic bonding, and so on. Which means that the universe as we know it, made up of atoms, would not exist if electrons were not indistinguishable fermions. Neat right?

I really enjoyed giving this talk, pitching it at a level that I felt comfortable explaining to a live audience. This inevitably meant cutting out on some not-very-important but technically correct details. So please let me know if I cut out too much! Thanks again to Reading for inviting me, and to the wonderful students who were so attentive and asked genuinely insightful questions.

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[sarsedacn]

well done. A nice expansion over the Pauli exclusion principle, without which matter would not have volume hence, our universe!

[grayaj]

This is at the perfect level of detail for me. I'd read this before (in one of Brian Cox and Jeff Forshaw's books) and had a vague understanding of it but couldn't recall exactly why it works. That book (forget the title) also coupled this with the uncertainty principle and then IIRC used the two ideas to explain how semiconductors work.

My only comment is that it's hard to get through the audience comment parts because we can't hear what they're saying. Not a huge criticism, because otherwise this was perfect.

[RojinSharma-cl]

very clear explanation. Awesome Parth!

[brucewright]

I'm a little bit confused. You say that psi-squared represents the probability. You also mention that psi-squared is larger than psi. Now a probability is (by definition) less than 1. The square of a number less than 1 is SMALLER than the non-squared number. i.e. psi-squared should be smaller (not larger as you have shown) than psi. Can you please explain to me why you have shown the opposite of what should be happening?

[lemmer]

Hello. the frustrating part for me is related to the Pauli exclusion principle. You said 2 electrons with same spin cannot coexist on same orbital, it is "forbidden". Forbidden by who ? what ? Why would an electron "care" that something is forbidden ? How does an electron "know" that the other electron has spin up, then "decide" that it should have spin down, because "it is forbidden to do otherwise" ? that really makes no sens to me at all

[TheDavidlloydjones]

I forget whether it was Feynman to Wheeler or Wheeler to Feynman, but their suggestion was that the reason all electrons seemed so similar was that in fact there was only one electron in the universe.
Wey-yul, I guess that would be one way of explaining it...

[misterlau]

Heey Psrth! Good to see you! Long time no see, mate! 🤓

I can't hear the students, but it was hilarious when you said "that comes later. You are reading my thoughts, that's cool" 😆

So far so good, I'm in the indistinguishable part

Commute! Commute!

Good teacher indeed you are, Parth!

[zahajek]

please provide more videos with the simple explanation and long time duration like this, as a layperson i really enjoyed with your content

[bonsai]

Your videos helped me on my last semester, its really very impressive how you make these topic of qm. in such a simple way! Tqh parth

[harrygreen]

Could you please do a video on the Alcubierre drive???

[antona]

The ratio of electric force and gravitational force between a proton and an electron is K e^2 / G memp ≅ 2.4 × 10^39. Q. Quantum mechanics doesn’t give the answer to the single most fundamental question: why electrons don’t collide with protons? Although, when it is applied to details it yields certain results… mathematically.

[GeoffryGifari]

from what i've read about him, the thumbnail is hilariously in character for wolfgang pauli lol

[docta]

I want to be like you when I grow up 😭! Such an amazing explanation!

[mcwulf]

Love it. I now want to find out the missing bit - why do fermions have to have opposite spin? (I think it's something to do with angular momentum).

[GooogleGoglee]

Example of Bosons are: uh yep yep mm yep that's the one yep yep
Good job

[foxhound]

I really enjoy your channel, in fact I’m becoming a Patreon donor. I actually learned most of your content 40 years ago, in college. Yes, I’m old. However, I never used this type of content in my chosen field, professional Pilot. As such, I would like to ask a question, to check my understanding. The “wave packet” is the probability of finding the particle in that location. The wave packet is “semi localized “ in that the highest probability of finding the particle is in a fairly small region, but the “tails” of the wave packet trail off towards zero fairly quickly, but never actually ever reach zero. As such, there is very small probability that the particle can be found out by the orbit of Jupiter, however that probability is so vanishingly small as to be practically zero. Is that a correct understanding?

[DuckStorms]

Wait but what if you swap 2 electrons in different orbitals and different spins. With the simplified math shown here both parts would have signs flip, and the wave functions would be identical before and after the switch which we just said wasn’t allowed for a system of 2 identical fermions. So there must be more. What’s missing?

[collapsed_state]

What is the set of books with mathematical practice questions and that will make you expert-ish (gradually, if studied) in the field of quantum physics?

[Wrackey]

The camera wasn't weird... It looks like it just got hit with sunlight as the day progressed.

[mnawari]

I can't hear the students comments and contributions which seems they are part of the lecture.