Quantum Mechanics and the Principle of Least Time

In this short video I would like to tell you about the pioneering work of Pierre de Fermat, who discovered that light is the laziest object in the universe, always preferring to take the path that minimises the amount of time spent travelling between two points. But perhaps what is even more exciting is that Fermat’s principle lies at the heart of one of the most successful scientific theories ever created, quantum electrodynamics. In this video I would like to show you why light is so lazy, and how Fermat’s principle connects with our modern formulation of quantum electrodynamics. So, if you are ready for the ride, let's get started.

References:
Feynman Lectures on Physics - Feynman
QED: The strange theory of light and matter - Feynman
Fermat’s Principle and Hamilton’s Principle:

[nick]

I thinks it's funny that he goes into such great mathematical depth on some of the most complicated topics in physics yet still takes the time to explain what the chain rule is lol

[dodokgp]

Mark my words...this series of videos will one day be archived as a lecture collection for a comprehensive Physics course. Excellent way of explanation.

[momchi]

"Light is the laziest object in the Universe". Ah, so I have a rival then.

[asde]

Next video after only 4 days? Let's go!

[_joac]

I felt in love with physics at an early age, just learning the concepts. At highschool I had an awesome professor that presented to me all the mathematics to understand and enjoy classical physics. Sadly, I was unable to study it at university level. Finding your channel almost 15 years later helped me a lot to reconnect with the joy of understanding nature.
Thanks for all the work you put on this material.

[sphakamisozondi]

Content from this channel doesnt only answer scientific questions using concise explainations and equations, but it also gives historical perspective as well.

[potatobearsmo]

Explaining Snell's Law was great and all, but the highlight was explaining mirages. That was amazing!

[tanvirfarhan]

as a non-English speaker, i can easily understand what you are saying. very glad to get find your channel

[disgruntledwookie]

Sir, you are a legend and I thank you deeply. I only found this channel recently and studied physics until leaving university at the end of the first year but you have already taught me so much, so many details and key pieces of the logical puzzle that were never made clear to me. For example, I had known that the principle of least time was somehow due to the interference of the various wave functions contributions from the possible paths, and heard that it was a result of the non-optimal paths somehow cancelled out, but I didn't understand the mechanism. I assumed it was too complicated for my level and accepted that I would come back to it later. I now see that the reason is straightforward, simple and elegant. No more difficult to grasp than the rest of the math we had to learn. This is about the 10th time you have done this for me already... pointed out a key piece of the puzzle. Sometimes it can be annoying or feel patronising when you take the time to explain/recall things that like Pythagorean theorem or the chain rule, but when I think about it I realise what you're doing is providing the whole argument from first principles, with every detail necessary to understand, so that no one gets left behind no matter their level. It is humbling and wonderful to get to understand something a little deeper, thank you.

[mdahdolan]

I think we all need to appreciate how you manage to create such high quality content with PowerPoint and a microphone.

[novakonstant]

I appreciate you taking your time to explain more 'simple' concepts, such as trigonometry. It gives everyone a chance to follow your contents, and even if some information ends up getting lost, it also provide a clear path on what to check further. Your videos contain an amazing amount of information and I wish to thank you again for making them.

[AnonymousAlcoholic]

Even more weird when you consider light does not experience time, yet it takes the path of least time.

[Richardincancale]

Beautiful description - Feynman would be proud of you!

[LampDX]

I love these videos... Your clear, simple explanations of each step of the derivation process is inspiring. I see people with all levels of mathematical experience in the comments; the care you put into fostering genuine curiosity in each of them is a work of art to me. thank you

[jocelbartolay]

I understand QED in simple terms! That's amazing! You're the one of the best physics explainers in the field!

[elodiehill]

I’m glad to know you’ve managed to find a way to share your amazing explanations with everyone! It’s not quite the same as your in class lectures, but maybe I won’t have to miss your Physics classes as much!! Thank you.

[oasa]

As usual, an amazing way to convey different mathematical perspectives about key physical phenomena. It's worth emphasizing the conceptual clarity, the mathematical rigor, and the understandable explanation. Great work!!! Please keep going!!!

[Misteribel]

This is brilliant, maybe the first time I'm actually understanding the connection between qed, defraction and Snell's laws. Awesome!

[ShadowZZZ]

This is absolutely magnificent! I love how easy it was to understand the begining, deriving snails theorem, and using functional analysis to find the least time. But the quote by feynman at the end was so stunning. Truely awesome to understand reality

[pipertripp]

So elegant and simple... and the derivation of Snell's law is something anyone with calc 1 under their belt.