Quantum Mechanics and the Principle of Least Time
Вставка
- Опубліковано 9 кві 2021
- 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:
Does a least action take a least time for happening? - Anderson and Hadi (iopscience.iop.org/article/10...)
You can help support this channel via the Physics Explained Patreon account: / physicsexplained .
You can follow me on instagram: / physics_explained_ig
You can follow me on Twitter: / physicsexplain1
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
Yes and same with trigonometry XD
he literally explained trigonometry for.... what? 5th graders ? okay
Agree with you ....I like His all video's
@@Cashman9111 hey some people are dumb like me let him explain
@@arpitdhukia9026 I don't mind ;), and you are probably not dumb, just... lazy - like light ;)
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.
It is always the Greeks the discover the secret in nature: math, science, philosophy. The Roman Empire lasted 15 hundred year, there was not a single person can match the Greeks. Forget about Greeks, can you find one person in the 15 hundred years can be called mathematician, scientist, or a philosopher? The Roman Empire was utter failure of mankind.
FACTS! Everything this channel does is fantastic, so detailed and so informative!
History should be like science in the sense that it aught to be objective, it aught to be told truthfully not to be used to secure some dominant groups preferred version of society. Nobel Laureate in physics, Dr. Abdus Salam wrote:
“Ibn-al-Haytham (Alhazen, 965-1039 CE) was one of the greatest physicists of all time. He made experimental contributions of the highest order in optics. He enunciated that a ray of light, in passing through a medium, takes the path which is the easier and ‘quicker’. In this he was anticipating Fermat’s Principle of Least Time by many centuries. He enunciated the law of inertia, later to become Newton’s first law of motion. Part V of Roger Bacon’s ‘Opus Magus’ is practically an annotation to Ibn al-Haytham’s Optics.”
UA-cam might flag it for mansplaining but you have a British accent so it'll be fine.
@@seanleith5312 Two words: indoor plumbing
"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.
Yes true true
sorry for highjacking this comment, but whenever i post in root my comments dont go through i think.
Physics Explained: What do you have to say about 1/s in the planck equation.
Next video after only 4 days? Let's go!
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.
Why werent you able to study it in uni if you dont mind answering, just curious
@@auridon lack of rich parents, and having to work fulltime since I have 19.
@@_joac Ah i feel ya, I still went to uni but I work a part-time job and pay for my stuff myself since i have no rich parents either. Without my grants and scholarships, i probably wouldn't have gone to uni either.
@@_joac aw man
@@auridon I just got my grant for college today and it paid for everything!
Explaining Snell's Law was great and all, but the highlight was explaining mirages. That was amazing!
Glad you enjoyed it!
This topics is relatively easier, but unfortunately, the quantum mechanics explanation of Snell Law is a little confusing, maybe because most people never know why the sum of vectors is related to the overall probability of receiving light emitted by A at B?
Even more weird when you consider light does not experience time, yet it takes the path of least time.
Lol that’s right. Light perceives 0 time lol
if Houston used telescopes to look onboard the Enterprise they would see the crew running in slow motion
But everyone experiences proper time. E.g. Picard looks at his watch & he sees it ticking at normal speed. He sees his crew running about at normal speed.
Therefore if light could experience time, it would experience time running at normal speed. It would experience proper time.
@@alwaysdisputin9930 Proper time at light speed is instantaneous.
@@alwaysdisputin9930 Proper time for light is always t = 0 , infact , you'll be travelling at a finite speed in space but an infinite one in time (relative to the observer travelling at light speed) going from andromeda to the milky way would take exactly 0s , but to someone on earth it would still take You millions of years to reach our galaxy
@@renatoandresmartinezrubio8428 Your sentence is unclear. Please can you work on trying to make your sentences more clear. Use full stops. DrPhysicsA is the best IMO. Try to copy him. Also Physics Explained & DrBecky.
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.
I think we all need to appreciate how you manage to create such high quality content with PowerPoint and a microphone.
Faxxxx
as a non-English speaker, i can easily understand what you are saying. very glad to get find your channel
I get what you mean, but if you can understand this I'd class you as an English speaker
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.
Beautiful description - Feynman would be proud of you!
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
Exactly, superbly said
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!!!
Exactly, this is just amazing
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.
Excuse me what
I understand QED in simple terms! That's amazing! You're the one of the best physics explainers in the field!
Wow, thanks!
This is brilliant, maybe the first time I'm actually understanding the connection between qed, defraction and Snell's laws. Awesome!
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
Glad you enjoy it!
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
Glad you enjoyed it!
@@PhysicsExplainedVideos 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 UA-cam or any other public electronic media.
You have risen the bar to a much higher new level . Bravo!
So elegant and simple... and the derivation of Snell's law is something anyone with calc 1 under their belt.
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 :)
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).
Just found this channel and now I'm hooked on these videos! As a creator, I felt truly inspired by how you took the time to explain even the simplest things before diving into the advanced stuff.
That's the kind of channel that I don't miss a single video! Always a beautiful dive in nature
Glad you enjoy it!
@@PhysicsExplainedVideos I wonder if the QED explanation could be applied to the effect seen with gravitational lensing even though the similar visual effects are for entirely different reasons? Also - I don't think Feynman proposed an equivalent explanation using the wave model but I wonder if someone did whether we could say that there is destructive interference everywhere except for the path of least time?
@@chriskennedy2846 I am really liking this channels approach;
Since "remote sources" see gravitational lensing it is concurrent to examine EM ( light ) as QED; If "hard-backscattering" disperses chromatically-as it does-then lensing would have an effect if gravity affects EM which it rather obviously does based on observations ○ My work currently suggests that Gravity is an "effect of" rather than a causal force of it's own ~ The result of that should be that distant EM is chromatically dispersed as it passes the intervening galaxy such as in diffraction as observed on the bench ○ At any scale the wave model holds it is only that at CDM Physics the effect becomes "lines" ( discrete bands of resonance ) which are themselves only resonances as described by Matt Strassler
@@ChiDraconis What do you propose is the actual force behind what we perceive as gravity?
@@chriskennedy2846
Luckily as fate would have it I have been working on related for several years:
*"Gravity is an effect-of not a causal force of it's own"*
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!
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.
Loving all these vids you're making! They're all so good and clear. Thanks
OMG You are uploading so fast! Appreciated man!
This is unquestionable the best channel of youtube.. Kids, just skip college and watch this.. I am on the floor in awe..
much appreciated for going into the mathematical bit for the theory. often, the other yt educators skip the math part. QED, quantum mech, trig, calculus everything in 20 min video and yet comprehensible to people like me who have been away from the field. great 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!
Hi Khalil. I agree. Such preparation would allow students to shine. Lazy kids will not do well, but this is better than the present broken UK system where 50% students get top marks, after years of grade inflation has created a distorted grade distribution. I'd love to be able to enter an informed discussion in the classroom.. these threads are the nearest I'll get. My kids will enjoy the system you describe at University. Old duffer here :)
That's fairly typical for university education in Denmark, the students attend lectures and read material before and then attend a classroom with usually a higher level student where they go over it together. They'll also have smaller groups where each student has to present a problem to the rest of the class.
Superb video. You pack in so much vital, and fascinating, material - and do it so clearly. It makes me want to go back and re-read Feynman's wonderful little QED.
Glad you enjoyed it! Thanks for the kind and encouraging words
Can't get enough of this great content! Amazing work!
"Pink Expression" is a perfect album name.
Great vid, btw.
This channel is such a gem. I'm glad I found it.
Glad to see another video so quickly. Hello from Toronto 🇨🇦
3:56 to 4:48 has a wonderfully visualized explanation involving a Geometric Wavelength.
As always love your videos, I do not understand maths as well as I would like but you are helping so much. I value so much what you do and have just one wish that you keep making video. Excellent work .
Glad the videos are helpful
Out of all the great physics UA-cam channels available yours is the best. Keep up the amazing work!
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🙏🏼🙏🏼🙏🏼
Glad you liked it!
You are answering questions I never asked n I love it. 😂
I am very excited for the next videos!! Great job
it's also a quite nice illustration to lay sine waves over all paths from A to B, because they tend to cancel out (meaning that they have destructive interference at B) for most paths except around the optimum. the most intuitive way to explain Fermat's principle imo
Yeah, destructive interference can be a model to be used in this instance, but you will run into trouble in other circumstances.
But won't you get areas of constructive interference symmetrically arranged around the optimal point?
@@tim40gabby25 the path with the most constructive interference is the optimal one. I cannot really explain in words why, sorry, but when you draw / simulate it, it checks out.
To build some intuition you can think about it this way: we are only interested in interference between "neighbouring" paths (or paths that are very close to each other) and the stronger the phase shift between the neighbouring paths, the stronger the destructive interference. As the phase at the final point is only determined by the duration light takes to traverse the path, the path with the smallest first derivative in time (i.e. the fastest path) will have the lowest amount of interference.
how you managed to compress so much knowledge into one video is mindblowing..QM is a gift that keeps giving :)
This is a nice condensed adaptation of some of the arguments from QED. It's nice.
Superb content ! As per usual. The 1st time I seen Feynman explain QED, it blew my mind. Still does actually.
Glad you enjoyed it!
Wow, this quality content so frequently? Good work man keep it up!
This was one of the best explanations I have ever gotten for this principle. You are a GENIUS!
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🍻
Another great video. One of the best science channels there is!
This was awesome! please continue and dont stop.this was greatly explained .thank you
Thank you! Remarkable clarity. I really wish I had grown up with access to brilliant work like this. I still remember being the one to stick my hand up to ask "how light knew before it setoff how dense the water would be".. he said "all you need to know is it just does ok" 😂
Glad you enjoyed it!
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
Interesting - but could you repost, clarifying your argument, please?
@@tim40gabby25 um... what wasn't clear? 😅I'm sorry... I'm not a physicist
You're one of the coolest physics channels on UA-cam. Please come back and make more videos!!!
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.
Amazing work as always!
A great video for understanding these staffs! Thanks. Take love ❤️
@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 UA-cam or any other public electronic media.
You have risen the bar to a much higher new level . Bravo!
Loving the quantity of videos recently! :D
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 is a superb video. Certainly one of the best if not the best on principle of least action and its connection to quantum physics
This is a very nice derivation of Snell's Law as well as a quick and simple explanation of why Snell's Law works.
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.
one of the best physics videos I have ever seen on UA-cam 🔥
Man I friggin love your videos so much!! Thank you for these!!
Glad you like them!
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
Thank you. This was a very clear explanation.
Amazing content, crystal clear.
Oh boy. This is so well explained - incredible. Very clear.
Gosh, what a well thought explanation. I wish that this was around when I was studying this stuff. Cheers.
You keep making me accidently learn stuff from my A-Level physics.
Glad to hear it!
You are actually forcing me to pass my physics exams with how easy these are to understand! Thank you!
Video was made with high quality and good explications ! I really enjoyed this video, thank you so much
I was waiting for the day where you would talk about the Feynman QED description in his marvelous book ("All we have to do is simply to trace arrows !").
This book is very dear to me, by far my favorite scientific book. It has been a revelation when I first read it and no other physics book came close since then.
But Feynman purposely did not go too much into the details, essentially the mathematics of QED. This is sort of a missing piece for me so I can not wait to see your future detailed video about QED !
Thank you always for this great video, for you work and clarity.
Very nicely explained.
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 :)
Great topic can't wait to watch
I guess the fastest path principle also explains why light is curved by masses, if time is slower close to a mass.
Yes, that seems like a really intuitive way of thinking about it.
Bro! This is fantastic! Please never dumb it down! A little math never hurt anyone!
Simply brilliant (again).
Very interesting explanations, incredibly intuitive
Excellent video! Thank you.
Light isn't lazy. Its efficient.
Excellent content. Respect.
Thank you so much for this brilliant video
Wow! Another great video...nice job
Class, Class ...Classic expression. Nice ......I enjoyed this video in full. What I understood in half becomes full now.
Deliver more videos.
Awesome channel thank you just got done watching all the videos and left wanting more.
A couple in the pipe line
I still can't get over how good this guy is. Every video i watch is 10/10 gold dust.
Excellent Explanations. You should have 10 million subscribers
Excellent video! Thanks!
Glad you liked it!
Excellent video.
Really enjoyed this! It would be great to see a more detailed follow-on.
Nicely done! As a side note, I never knew Snell's first name was Willebrord!
I had the same reaction.
brilliant exposition!
Excellent explanation! Thanks a lot.
You are welcome!
Great explanation
SIncerly one of the best videos I've ever seen
Superb Explanation. Anyone can fall in love with physics if explanation is like this.
Thanks for the encouraging feedback, very much appreciated!