Quantum Mechanics and the Principle of Least Time 

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

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

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

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.

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

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

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

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.

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

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.

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!!!

Great video again! I suppose one thing I would add is that another consequence of the probability amplitudes being like you describe is that if we were able to conduct an experiment where we measured the x position at which the photons cross the air-water boundary to within some degree of accuracy, far from the position of minimum time, the probability would be very small as all of the amplitudes at nearby x positions would sum destructively, while the probability near the minimum would be large as the amplitudes would sum constructively :)

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.

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

woah, it all made perfect sense. I knew about Snell's law and that in some sense light took the path of least time, but I never quite understood it. And the best part was how easily it was all merged with qed, given that I was also vaguely aware that it also worked in quantum mechanics but in an even more nebulous way (I remember my professor saying something along the lines of light sort of 'looking ahead' in a causality breaking way, but honestly I can't remember much).

This channel is just so awesome. I really enjoy every video despite the fact that there are sometimes topics that I do not understand. Thanks for the videos and keep up the good work

Its channels like this that make me reconsider the idea of a flipped class room. Flipped meaning, students watch video at home and when they arrive in the classroom they can ask as many questions as they like. Typically this doesn't work because students can tend to be undisciplined and won't watch the videos at their leisure, but this video series plus many other physics channels do such a great job at explaining stuff that its making me think that such a configuration would work very well in this new era. Anyway, love your stuff, I try and always watch your content the moment it is released (hit the bell). Keep it up!

It's not lazy, it's in a hurry. Excellent video

Another great video, honestly made Schnells law interesting, and it makes me wonder why I didn't learn about this. Keep it up!

how you managed to compress so much knowledge into one video is mindblowing..QM is a gift that keeps giving :)

"Pink Expression" is a perfect album name. Great vid, btw.

This is unquestionable the best channel of youtube.. Kids, just skip college and watch this.. I am on the floor in awe..

Glad to see another video so quickly. Hello from Toronto 🇨🇦

As is usual for Feynmann, his explanation, which is the one used in this video is the simplest and most intuitive I have seen that explains how this phenomenon is explained using QED. I recommend that anyone interested in learning more about QED read this book. It is a transcript of a series of talks he gave to non-scientists and is designed to present a complex subject in an understandable manner. You will not be an expert in QED who can do complex calculations, but you should have a good basic understanding of what it is all about.

Can't get enough of this great content! Amazing work!

i think it could be like so: light does take all the routes between A and B, but since the route thats the shortest time "gets there" first, it has a roll of probablility, so a chance to collapse the wavefunction. as more time elapses, more and more rolls are happening. and as only the rolls that are near the fastest route happen, theyre the ones "racking up" the tries, making it more and more likely the actual route will be near shortest time

One if the best videos I seen in a long time. As someone who hasn't sat in a calulus or physics class in a very long time, I found the math was presented with a perfect amount of explanation.

a flavor-full mix of physics, maths, and history that delivers a clear and helpful explanation of some complex concepts. Thank you for your effort. i enjoyed and i learned and i will watch again🙏🏼🙏🏼🙏🏼

22:07 goosebumps, i had seen such diagram related to butterfly effect,but didn't understand it,or never tried to understand it...here too I am unable to get a perfect picture, but I enjoy your videos

Thx. Very enjoyable indeed😊 @ 18.22 curve goes ( continuing its own path ) like going under ground ( below the X-Axis ) than comes up again to the Eye-Level of Observer. Cheers🍻

This is a nice condensed adaptation of some of the arguments from QED. It's nice.

I was shocked by nature's behaviour when I first listened to Richard Feynman's Univ of Aukland lecture video where he talks of vectors going round (zing, zing, zing, ...) and not doing much to the probability amplitude awy from the center and building up near the center (for reflection cases). This is a great video illustrating those concepts. Please talk about what is really happening in scattering inside the water (or glass) as the photons interact with electrons making those materials in a subsequent video. Much appreciated. Gerald

This is a superb video. Certainly one of the best if not the best on principle of least action and its connection to quantum physics

You're one of the coolest physics channels on RU-vid. Please come back and make more videos!!!

Superb content ! As per usual. The 1st time I seen Feynman explain QED, it blew my mind. Still does actually.

Out of all the great physics RU-vid channels available yours is the best. Keep up the amazing work!

It helped indeed! This video gave me a deeper understanding of how things really work. You accidentally explained Feynman path integrals. But there is more. Much much more.

This was one of the best explanations I have ever gotten for this principle. You are a GENIUS!

This is an excellent video, I thought it had been available for a long time but I see it's just been posted last week. Thank you. Your walkthrough of the minimization problem is inspirational.

The pedagogic genius of Feynman is incredible, with a bunch of little graphs is capable of explaining very complicated physics equations and makes you understand it better.

I guess the fastest path principle also explains why light is curved by masses, if time is slower close to a mass.

Although it is commonly referred to as the Principle of Least Time, that is incorrect. Fermat did not say the travel time would be a minimum, what he said was that the "first order variation in the travel time" (the derivative of the travel time with respect to distance) would be zero, meaning the travel time would be either a minimum or a maximum. In most cases it is a minimum, but there are cases in optics and seismology where the travel time is a maximum (that would be a good topic for a followup video). Great graphics, BTW.

I used to be a physics phd student but i left the field to do data science. These videos perfectly satisfy my itch to learn some physics. Instant sub

@Physics Explained Your videos are a real treasure for youtube. Honestly, you should be given an award for the best physics video content creation in youtube. You breathtaking high quality presentation in your videos and unambiguous in depth and detail formal explanations and physical interpretation given, is leaving really no room for misunderstanding and is an amazing achievement. Be sure your videos are not only educational but are being used also as a review material by scholars and academics. People watching your videos not only appreciate more physics but also mathematics and how these two are entangled together the one pushing forward the other and controlled by logic. Really, best physics scholar literature content in long memory currently on RU-vid or any other public electronic media. You have risen the bar to a much higher new level . Bravo!

one of the best physics videos I have ever seen on RU-vid 🔥

Loving the quantity of videos recently! :D

Class, Class ...Classic expression. Nice ......I enjoyed this video in full. What I understood in half becomes full now. Deliver more videos.

I really like the fact that you explain some of the thought processes of discoverers.

I still can't get over how good this guy is. Every video i watch is 10/10 gold dust.

Finally!!! Someone made an explanation vid on Fermat's principle

You’ve helped me become a physics person where not even 6 months ago I self admittedly hated the subject. Thank you so much.

Superb Explanation. Anyone can fall in love with physics if explanation is like this.

Nicely done! As a side note, I never knew Snell's first name was Willebrord!

Other than your explanation for how Ψ is calculated, which is completely opaque, this is very clear presentation throughout.

You are actually forcing me to pass my physics exams with how easy these are to understand! Thank you!

I have that book from Feynman (Theory of Light and Matter)....outstanding book for people at all educational levels. Highly recommended.

Gosh, what a well thought explanation. I wish that this was around when I was studying this stuff. Cheers.

This is about energy surfaces defined by low order differential equations. The upshot is that the fastest roll down the landscape is always an efficient guided series of minimal adjustments.

I am very excited for the next videos!! Great job

A great video for understanding these staffs! Thanks. Take love ❤️

I agree that this is an outstanding collection of physics videos extremely well articulated and illustrated. I would like the author to go further into the realm of Casimir effect. Is it true that outer space is empty vacuum from where particles pop in and out of existence? Or is there a massive isotropic field whose density is 10 to the power 98 gm/cm3? I believe Archibald Wheeler and David Bohm among others have done work in this area. Would be nice to research this more

You are the best ..... again you explain everything so simple....... You are very close to discover and explain Theory of Everything.......🤔😎

Nick Lucid's The Science Aslyum YT channel has an AMAZING video on this topic as well called "Nobody Knows how mirrors work" He highlights how the mirror experiment shows that light takes all paths not just in some mathematical quantum underworld, but also here in this place we call the real world Seeing a small but non-zero amount of photons reach a detector that *SHOULDNT* be reachable blew my mind. Quantum experiments are the friggen insane

Simply brilliant (again).

24 minutes of pleasure 🔥🔥 Thank youuu 😍

Best physics channel

Your series is incredible.Thank you very much. My wish list for future videos would be Dirac's equation, the Higgs Boson, and Feynman diagrams .....

Thank you. This was a very clear explanation.

Oh boy. This is so well explained - incredible. Very clear.

Excellent explanation! Thanks a lot.

Long time listener, first time caller, can you please consider a video on film photography? How lenses work and the interaction and history. Cheers.

Brilliant video. I need to watch it at least twice againg after I've forgotten about it so I may be able to understand...

I had never studied QED at my university, but I have a pretty decent math courses, so I would like to make a guess - is this function psi is a result of some kind of Fourier / Laplace transform? I would love to see this topic covered in details.

Not lazy. Graceful and efficient.

Thank you, after 20 years, I now can really understand why the snells law is like that, thank you, it is better late than never.

your videos are incredible! Can we have more please 😇😇😇 You actually made me pull put a sheet and a pen and do physics again! So inspiring!

this was the best demosntraition of snell's law :)

This was awesome! please continue and dont stop.this was greatly explained .thank you

The fact that from our perspective it looks like elementary particles seem to exhibit spatial-temporal awareness, in a sense "virtually" traveling all available paths simultaneously WITHOUT having to physically traverse those paths, has long baffled me and seems to point to something incredibly deep about the nature of space. If physical extension in space creates the illusion that light travels in bent paths, and yet this "bent" path is the path that requires the least effort, then perhaps physical extension in space is itself the illusion.

Great explanation

As a footnote to the final diagram here -- one might wonder whether you could change the path of light by somehow "knocking out" some of the vectors in those spiraling tails and allowing other vectors which would ordinarily be cancelled out to take a more significant role. And you absolutely can! My understanding (it's been a while since I read QED), is that this is how diffraction gratings work (which among other uses are the underlying technology behind CDs and other optical discs), and also partially explains the rainbows you see in oil slicks...

I would prefer to see a classical description of this. I have read Feynman's explanation, but I don't recall it very well and it wasn't always easy to follow. Although it is expressed in terms of classical waves rather than complex probabilities, the explanation should be similar. The light causes simple harmonic oscillations in valence electrons in the materials. There is some sort of cancellation that occurs between adjacent wavefronts due to the difference in electric susceptibilities of the materials, and the sum turns out to be a wave moving at a different speed and in a different direction that obeys Snell's law.

Gracias por tanto, saludos from Bolivia

Me at 18:00: my mind is blown Physics explained at 18:30: BUT WAIT THERE'S MORE

Wow! Another great video...nice job

Excellent film. There must be a deeper meaning for how EMW end up taking the fastest routh through different materials. It means that in the frame of reference of a photon , time does not exist. Extrapolation, Time is an inverse consequence of velocity. If i could produce pure imaginary velocity , i could travel back in time.

Another exquisite video. BRAVO!

Just found this channel and you earned yourself a sub. Fascinating stuff also glad you don't skip the math even tho I don't understand it it's cool to see for some reason :)

hi i'm brazilian and i really like your content i wanted to know if possible you could make a specific video about the schrodinger equation

Beautifully done. What took are you using to do the technical animations? They're clear and evocative

Do you think any topics in string theory would be accessible enough for this channel? I'm hooked on your vids, somewhat therapeutic tbh

When the photon waves hit the water it will excite the electrons and produce a wave in opposite direction. The outgoing wave is going to slown down the incoming wave, because when you add two waves you produce a third one that is smaller. Because it is smaller we perceive it as taking a shorter path.

Well keep making these videos,upto to my knowledge topics are explained correctly

It's indeed a reamarkable discovery!

I feel like this great change in total time (T) leads to destructive interference between waves and they cancel each other. But at this point, where Time doesn't really change, they don't have this interference and don't cancel each other.

QED incoming POG!

Excellent video! Thank you.

sir can u please make a video on to best books to learn physics(including maths for it) from beginner to expert

Very smart teacher.Marvelous

I find the relativistic principle that light follows, not the shortest path or the shortest time, but a (the shortest) geodesic in spacetime to be very intuitive.