Your Daily Equation #18: Heisenberg's Uncertainty Principle: Math not Meth

[@gafyndavies]

Not even being a mathematician or a physicist, I was still able to gain much better understanding of exactly how the uncertainty principle works. Thanks Brian, you really are one of the great science communicators.

[@daniel723]

An electron is driving down a motorway, and a policeman pulls him over. The policeman says: “Sir, do you realize you were traveling at 130km per hour?” The electron goes: “Oh great, now I’m lost."

[@Sharperthanu1]

Yes,the electron is like a little person

[@umeshshende7540]

It's uncertainty in momentum becomes 0. And uncertainty in position becomes infinite. Therefore he/ she is lost

[@asage5801]

Policemen: “well, just forget your mass and you will find yourself”

[@saadhassan8813]

@@asage5801 great

[@frankt9156]

If the electron is lost how did the policeman find him? Make no sense.

[@biranchikumarjena8257]

Thank you sir, for your effort to attract students towards law of nature. I am from India, according to Indian time it is 12.06am too late night but I am still waiting for your lecture sir.

[@briangreene6975]

That shows great dedication--exactly what is necessary to understanding nature.

[@jayadityasingh8575]

Where are you from in India

[@kaigordon5746]

Dear Prof. Greene ,thank you for this series and all the others in the World Science Festival. Your talks and the way all these things are explained is so intuitive and easy to understand, that it becomes inspiring. It makes people excited and looking forward to understand more about the mysteries of the universe. Absolutely wonderful!

[@radwizard]

I have a midterm in about 10 hours. This is perfect extra for what we are learning right now. Dr.Greene what is your favorite undergrad book to teach physics out of?

[@Adinga123]

Professor Brian Greene, thanks for the awesome presentation. With warm greetings from Mizoram🙏

[@mikeygallos5000]

I understand absolutely nothing of these vids but really enjoy how he tries to explain them. It's amazing that people like him can comprehend such complex concepts!!

[@Sharperthanu1]

Yes,I know but Brian Greene would have WAY more money if he were less brainy and more like Justin Bieber.

[@blackhole1222]

finally, someone who explain the MATH of the uncertainty principle in an intiuitive and a deep enough level to get an idea of what actually the principle represents. Thanks a lot man!

[@ineuron]

Dear Prof. Greene: Could you please consider explaining the Bell's theorem too. Thanks

[@briangreene6975]

Hmmm....Yes....I can try to do that.

[@alexwilson8034]

Please do this. One of the last quantum feats I don’t understand at all

[@rwood1995]

Poser alert 🚨

[@bikashthapa7316]

yes

[@GiR1854]

@@alexwilson8034 hello. There's a channel called DrPhysicsA where many physics concepts are explained lucidly. Bell's theorem too is there. Enjoy.

[@bruceblosser2040]

The two graphs of X and p at 32 minutes just really makes sense! Thank you!

[@angeleduardoloborojas4626]

Very thank you Brian for taking time to explain all these equations to us

[@theheadscout4356]

Thanks Brian. You are an INSPIRATION. I am not a scientist, courtesy of a terrible teacher at school which caused me to hate the subject. Thirty years later I discovered I have always been in love with it without knowing. You help me find answers to so many questions I have had!

[@johnkechagais7096]

I love how much joy he has in explaining the uncertainty principle

[@laaradee]

Wish all teachers were as good as you.! Thanks. I almost think I understand you, don’t stop! I hope to watch them all over again from the beginning!

[@mountainclimber48]

BTW I’m excited about hearing you may give us a peek next week at the mathematics Einstein used (tensors) in understanding the curvature of space-time!

[@GordonDunbar]

Great! Looking forward to hearing Prof Greene's explanation. Thinking about Heisenberg's Principle, leaves me feeling curiously comforted, - finding in 'the knowledge of this trade-off limitation (and others) deep and fundamental truths built into the fundamental structure of the universe.

[@david203]

Thank you for being one of the first physicists on KZbin to even mention the de Broglie-Bohm interpretation of quantum mechanics! I'm not quite sure you got it right, though, because the essence of Bohmian mechanics is not any kind of refutation of the Uncertainty Principle, which you discussed well, and is a mathematical fact. The essence is adding the initial positions of all particles in the experiment to the Schrödinger equation. When you do that, all particle trajectories become deterministic, as though they were under the influence of a force described by the Schrödinger equation. So you can pass one electron through just one slit in the double-slit experiment, and it goes to the right place on the screen to show an apparent probabilistic wave interference between both slits! Not only that, but you can trace the path of each electron (in effect) and see exactly where it is going, with no lack of precision, from the time it is emitted by the electron source to the time it hits the screen. The precise place on the screen that it ends up is governed by the variation in the positions of each electron with respect to the center of the slit it goes through. The probability pattern is governed by the Schrödinger equation, and is determined by the geometry of the two slits. Hide one slit and the Schrödinger equation changes, so that the probability pattern disappears. It is a way of viewing experimental truth without mystery, thus perhaps not as interesting to physicists. Why else have they resisted this interpretation so strongly since it was first published in Physical Review in 1952? Actually, another reason is that Robert Oppenheimer opposed Bohm, not because of his physics but because he had attended Communist Party meetings in the 1920s. Bohm got a bad name because of Senator Joseph McCarthy and, at least for awhile, had to leave physics. And because of this prejudice, physics has been mired in the many mysteries essential to the Copenhagen Interpretation for all these years.

[@david203]

@-GinΠΓ Τάο I challenge you to provide a reliable reference. I don't recall Bohm ever saying that Planck's Constant was not constant.

[@david203]

@-GinΠΓ Τάο I haven't read Bohm's later stuff, I'm just impressed with his 1952 paper that has been ignored by most physicists. I have no idea what "Em-Tension" is, and I cannot follow your confusing description of a rubber band. I have no idea if his later stuff was warped by his subjective understanding of Self or not. If he said that a constant was not a constant, I would be interested in his reasons. If you don't really understand them, then we'll have to let go of this interesting question.

[@ManuscriptsCHi]

I've seen a couple of explanations prior to this but this one nails it. Thank you Brain 🧠 Greene.

[@intotheunknown8100]

I WILL BE HAPPY TO SEE MY FAVORITE EQUATION.. Thank you Professor Greene.🙃😇

[@briangreene6975]

My pleasure.

[@92587wayne]

0/1

[@dougg1075]

How in the world did these guys figure this stuff out in their time? Amazing.

[@jessedaas6365]

They use the all powerfull tool of mathematics :) But yeah they were brilliant

[@PriyanshuSingh-zf8lp]

Using Measurements, Logic and Mathematics. Just like Gravitational Waves, we did in 21st century.

[@ayushdhingra855]

@@jessedaas6365 what matters apart from maths Is focus Determination Patience Thinking Imagination

[@jessedaas6365]

@@ayushdhingra855 Yes agreed. That's the brilliant part :)

[@burtsigal7230]

After your explanation/illustration, the Uncertainty Principle (for me) becomes almost intuitive!

[@jsbllrt]

Still amazed about this classes! Thanks, Dr. Greene!

[@rlsfrny]

We missed you today, Prof Greene. No doubt you have many other commitments. But still, this is one of the highlights of my day in confinement.

[@briangreene6975]

Many thanks. I will pick it up tomorrow, usual time.

[@daffidavit]

I once read a book, I think it was written by professor Greene who said Dr. Heisenberg didn't like the term "uncertainty" and rather preferred it as the "indeterminacy principle".

[@TraditionalAnglican]

daffidavit - “indeterminacy” sounds like it describes the situation more precisely than “uncertainty”.

[@hyperduality2838]

The time domain is dual to the frequency domain -- Fourier transform. Stability is dual to instability Poles (eigenvalues) are dual to zeroes -- the complex plane Controlability is dual to observability -- Optimized control theory Probability densities are composed of two (dual) amplitudes, wave functions, probability is dual! Amplitudes are rectified into densities, diodes -- rectified currents, AC to DC. Positive is dual to negative.

[@AlphaFoxDelta]

Amazing, absolutely stunning. Great explanation as always.

[@nishronw9549]

Dear prof Greene can you please explain Einstein's picture of Gravity and the mathematical tools required to study them.

[@briangreene6975]

Yes...likely will start to do that next week.

[@martijn130370]

Thank you Brian Greene for this fantastic explanation with the graphs in the beginning, and also in the end - they clearly show the wave vs particle situations that yield either v (p) or x (position) but not both. I never knew that both Fourier transforms and the Gaussian curve could come in this as a school example. Beautiful how all these techniques come together. I loved also the number example that shows how and why uncertainty reigns on atomic scales, plus the implication of what the principle really is. Super!

[@rahul27668]

I am so obsessed with your lectures..thank you for doing this

[@MajidHormati]

This was amazing explanation. Always struggling with the last piece you talked about, now I understand that it depends on what quantum theory you believe in (at least until one of them wins :))

[@saikatsaha8703]

Hello sir I am saikat from India and a big fan of your explaination of complex thing in such a simple and elegant manner...I have watched your almost every lectures which are available in youtube and I have found this platform recently which is a matter of immesnse pleasure for me. Thankyou sir from my bottom of my heart for starting this "Daily equation series". And sir please visit india once. I would be waiting for your reply! Warm regards to you and your family.

[@destinyforreal9744]

Quantum is for the brave. I love how he delights in all that is undiscovered versus other scientists that pride themselves on what is "known".

[@prayogdash3564]

@world science festival. professor Greene, during your years in Princeton university u proved along with your colleagues that the fabric of space and time can be tear and repair. so if it can tear than what material will cause it to repair

[@ShailendraKumar-ug4tn]

Well, prayog while studying calabi yau manifold they came up with so called flop transition. According to which by tearing and rejoining the manifold one can transform one calabi yau into other. So in some sense teared space is replaced by itself or repair itself.

[@briangreene6975]

Space actually repairs itself. Or even more precisely, the rip ("flop" or "conifold" transition) does not yield any problems (singularities) in observable quantities. The rip is no more exotic, in this sense, than the expansion or bending of space. So, in string theory, such tears in the fabric of space are on par with the expansion/contraction/curving of space.

[@PhysicalrealityNet]

@@briangreene6975 Would it be incorrect to think of space as being granular and is defined by a continuum of discrete elements, so that an element, lets say spherical, defines a point in space having a diameter equals the Planck length. As such, a manifold could have any number of dimensions, as a dynamic structure forming from the elements of the fabric and exposing some volume of the background vacuum, which would be considered a singularity within the definable surroundings. That singularity would represent mass. Many thanks for your time and these great episodes of daily equations.

[@666Zim666]

Brian you are one of the best science communicators ever. Greetings from a german engineer =)

[@tomstarr845]

At time 32:30 Brian gets into the difference between the uncertainty principle and what is usually called the measurement-disturbance effect. He refers to this as a "philosophical" and "limiting" way of discussing the uncertainty principle. That way of putting it seems to me to diminish the fact that they are separate. Apart from both being applicable to quantum systems, one has virtually nothing to do with the other. The uncertainty principle is intrinsic, inherent in the wave-particle duality of quantum objects. Even if the measurement-disturbance effect didn't exist, the uncertainty principle would still apply to quantum objects, wouldn't it? If I'm wrong on this, someone please explain exactly in what way I've erred, thanks.

[@schmetterling4477]

You are not wrong, but you are still approaching this from the wrong angle. There is no "uncertainty principle" for single quanta. We can measure the position and momentum of a single irreversible energy transfer (aka "quantum") simultaneously and perfectly well. The uncertainty principle only comes into play at the ensemble level, when we are evaluating an infinite number of these measurements at once. At that point we are doing math, though, and not physics. What is important at the physical side of this is that nature conserves momentum (at least locally), but it does not conserve position. You were never promised that much, not even in classical mechanics. So basically everybody who claims that they are "surprised" has to ask themselves what it is that they are being surprised by? In the end, I would say, it's mostly the mediocrity of their own analytical skills.

[@BHuman2024]

Wonderful explanation. Great Honor for You.

[@shaikhahmed6562]

M really fascinated by ur explainations..the way u explain with exaggerated joy shows ur love towards science and nature..I appeal u to elapsed an hour for relativity... especially general relativity and space-time curvature

[@newlaty72]

32:40. Clearly this was not cleared water. The uncertainty on the color of that water he was drinking was huge. But we know with great confidence it's water cause he said so. Brian purposely inserted some uncertainty on the nature or flavor of that water.

[@tedbates1236]

It looks like lemonade.

[@ushatambat1258]

Sir, when we know the position of the electron precisely( by that dot on the screen in the double slit experiment you’d previously shown us that was carried out at a Hitachi lab) , wouldn’t the dent or the impact that that first electron makes, tell us precisely the momentum, and this would thus disprove the Heisenberg Uncertainty Principle?

[@saishubhankar2895]

Brian sir, I would really like you to speak a few words on Noether's theorem in the daily equations as they have a really deep meaning.

[@tanmaydeshmukh3517]

Math not meth cracked me up😳

[@andreaswc]

I’m not even close to understand Heisenberg’s Uncertainty Principle. Still I find your daily equation videos incredibly fascinating. Thank you professor!

[@Dr10Jeeps]

So interesting, so informative! Thank you once again.

[@petergreen5337]

Thank you very much again for your advice and insights

[@DavidKolbSantosh]

when Brian says, at 6:34 "in quantum mechanics a particle can be located at any position for which there is a nonzero probability a nonzero value of the probability wave and there are so many locations where it therefore can be based upon this wave shape that might extend you know maybe across the entire universe with that wavy shape just repeating over and over again so where is the particle located you can't tell me there are just too many possibilities there isn't a single answer to give for that particular probability wave shape" Isn't that just according to the Copenhagen interpretation...the Bohmian Mechanics would say No to that, that it is in a definite position at all times only we cannot know the momentum and position at the same time due to non-local hidden variables, which are not ruled out by the violations of Bell's inequality proven in the recent nobel winning experiments?

[@DavidKolbSantosh]

I see now that he does mention Bohm at 34:08...but still, I think he is speaking at 6:34 to much like it is a fact instead of an interpretation! Brian speaks with such passion as he explains that Heisenberg has told us that our vision of the world is not true...but the truth of the matter is,and you can verify this, the Heisenberg equation does not say that the movement of particles is non-deterministic, it simply says we are not able to determine at the same time the position and momentum of the particles...it DOES NOT SAY WHY! that part is simply interpretation and there are other interpretations...namely Bohmian Mechanics which says we can not know because it is due to non-local variables...and John Bell favored this interpretation, and formulated experiment to verify non-locality, or at least to rule out local hidden variables, which leaves only one alternative, non-locality...non-local hidden variables. The parts are not separate from the whole, everything is non-locally connected, not separate. What the observed parts do is not random, but is dependent on the state of the whole. We cannot see that non-separateness empirically. so sorry Brian! Anyone want to prove me wrong? I will consider all rebuttals!

[@Epoch11]

Could you explain what you meant when you said it was *related to things already known about sound waves in the 1800's?* I really enjoy knowing how things are related and while my math skills are lacking it is very refreshing and often beautiful when you see all the various intersections between one mathematical formula and another. The next time you do a Q&A, I would love to hear more about this or any OTHER relationships which are not obvious, but which help uncover more profound concepts in Physics. Thank you in advance.................................

[@eyewaves...]

Interesting take on the Uncertainty as you tried to clarify... Lets say, going back to Dposition x Dmomentum uncertainty conjugates - if I were to accurately measure the position or change of particle positions within a specific time interval, to me it implies I was able to accurately measure the velocity or momentum of the particle, though Fourier Inverse Transformation tells me otherwise. What is wrong with my intuitive but logical assumption ? Could it be that I will not be able to measure, lets say a delta function of the position within a specific time interval ? If not why not ?

[@schmetterling4477]

It is pretty obvious to me that you never made a single quantum measurement in your life. We aren't measuring "particles". There are no particles. We are always measuring quanta of energy, momentum, angular momentum and charges. Energy can be measured only once, then it's gone. To talk about the "change of position" of energy is therefor total nonsense.

[@eyewaves...]

@@schmetterling4477 fyi - was involved with plenty of q measurements. Of course the measurements are made of quantum of energy /angular momentum etc... now go back to sleep..

[@schmetterling4477]

@@eyewaves... Dude. You need to stop lying to yourself and us. You are just not that smart. Grow up and live with it like a man. ;-)

[@varshathakkar6574]

Hello sir please make a video regarding Eigen value

[@geoffreyfaust3443]

Besides location and momentum, what are other pairs of qualities whose interdependent probability functions limit one's ability to specify their number with precision?

[@imtiazshinwari4527]

sir, you are great. you are a living legend and one of the best scientists of the present day. Love from Pakistan

[@UmarUmar-bg1fj]

Thank you for the wonderful lecture

[@leonardodagnolo4382]

Dear professor Greene, if delta X times delta P shall be equal or bigger then H bar divided 2 it means that neither delta X not delta P can be equal to zero, so does this mean that is impossibile to remove the incertanty about both X and P? I thought that it was possible to know precisely at least one of the two. Thanks

[@nmarbletoe8210]

we can't know it precisely

[@calvinjackson8110]

Dr. Greene, would you tell me what you are using to write the equations? What tablet are you using and what equipment is needed for your virtual teaching. We are able to see you and your writing board. Your presentation is excellent.

[@asage5801]

Best math-based explanation I’ve ever heard

[@bluefinance153]

Dear Prof Greene, can you please explain how physicists create theories and how do you start?

[@briangreene6975]

You usually start by deeply studying existing works and then introducing small modifications that attempt to address outstanding problems. Unless you are Einstein. Then you just revolutionize thinking in one stroke.

[@bluefinance153]

@@briangreene6975 Thank you very much, that helped me understand how theories are created.

[@thecarpetcrawler1962]

Thanks Professor a very explanational presentation.

[@thecreativescience4]

Great to have you back ❤

[@guenterhuber4422]

Dear Dr Green, I am so happy that you did not follow Sheldon‘s advice („Reading to the Elderly...“) ;-) Having studied Physics some decades ago I finally get insights I never had. I hope that - unlike Corona - you will go on with this series.

[@theodorei.4278]

Prof Greene, could it be that the uncertainty Principal which is something fundamental, lead to the probabilistic nature of quantum mechanics? After all any theory should be verified by observation and experiment. So could it be that this observation led to this probabilistic discription/nature?

[@boclairphysics]

Love this series. Thanks.

[@onderozenc4470]

The parameters in Quantum Physics are, in fact, statistical which means, in genral, we can only measure them with average, rms and std values. Experimentally, what we measure, be it energy conventionally, is nothing but the RMS value of this parameter like the amplitute of an alternative voltage 0.707xVoltage(peak).

[@PetraKann]

You can have two different variables obeying the Heisenberg uncertainty principle - like energy and time. What determines whether two variables are connected or related in this manner? Conjugation? Can we have more than 2 variables obeying the Heisenberg uncertainty principle? (ie plotted on a x,y,z coordinate system)

[@erwinmarschall8879]

Wikipedia (Operators in quantum mechanics): "Physical pure states in quantum mechanics are represented as unit-norm vectors (probabilities are normalized to one) in a special complex Hilbert space. ... Any observable, i.e., any quantity which can be measured in a physical experiment, should be associated with a self-adjoint linear operator." Pairs of non-commuting operators obey the HUP (usually the vast majority of operators are non-commuting). The energy-time uncertainty-relation is special because there is no time-operator in QM!

[@PetraKann]

@@erwinmarschall8879 Can you get a third observable variable which satisfies canonical commutation relations with both position and momentum? That is, a triple of pairwise canonical observable variables which will result in a Heisenberg-type uncertainty relation for the product of three standard deviations. Δ(x)Δ(y)Δ(z) >= h? *I have a Chemical Engineering background so only studied quantum mechanics briefly during my undergraduate studies. Cheers

[@erwinmarschall8879]

@@PetraKann I don't think that such a relation exists. Because of the "limited printout" in this comment section, I recommend that you look up e.g. the commutation relations of the components of angular momentum, position and momentum (e.g. Wikipedia). There you have 3 operators L, p, x with 3 components each (a lot of commutation relations, many are trivial)

[@remcoy1825]

It has to do with the (inverse of) the quantity associated with the distance between peaks of the base functions. In case of a function of x, the difference between two peaks is the wavelengh (lambda), so the inverse 1/wavelengh is de associated property, and because p is proportional to 1/lambda, p can been seen as the "mirror" property.

[@remcoy1825]

if the function is a function of t instead of x, then instead of the wavelength, it is the period (T). thus the inverse is the frequency, and because of E = h * feq, the energy E is the associated quantity.

[@richiethesailor629]

Art and Comedy with Contemplata! Perhaps in ones perspective the precice point location is a variable do to "parallax" of distance between the eyes or even the fact the one eye has dimension whereas a point has "no" dimension? A finding of a"fix" with a compass has variation and deviation but have "faith" it is there! Note; I am also intrigued by this (i) and it's usefulness. I had a guess yesterday, fascinating!

[@mohitmehra7027]

Prof. Can you please explain how the higgs field work in our 3 dimentaional world.....

[@briangreene6975]

Sure...let me put it on the list.

[@mohitmehra7027]

@@briangreene6975 Thank you sir...

[@ShailendraKumar-ug4tn]

@@mohitmehra7027 😂he Is not real Brian Greene.

[@mohitmehra7027]

@divyesh Raj but asking questions is our our motive....

[@jasong546]

Thanks Dr. Greene!

[@david-joeklotz9558]

Something beautiful coming out of the Coronavirus crisis: "Your Daily Equation" :-]]]

[@Archaeometal]

Thank you again, Prof. Greene! 🤯 Peace and long life. -Halifax, Nova Scotia

[@JI77469]

Love the video! Historically, is the Fourier transform "duality" between position and momentum PDFs and the uncertainty principle as an easy consequence of the math of the Fourier transform due to Heisenberg or someone else?

[@georgemolnar7344]

Excellent series. A question: Most "explanations" of this focus on the wave aspect, either particle/wave, diffraction, or the bowling ball-pingpong ball microscope collision, or the Fourier transform conjugates. But everything associated with Heisenberg is typically a "matrix" concept. Are there any explanations/derivations of his thought process in this manner? And I don't mean simply that matrices do not commute in multiplication. That is a separate issue he wasn't even aware of. How did he formulate his uncertainty principle in a matrix structure using his analysis from first principles of observation, the jumps in transition? Many thanks.

[@schmetterling4477]

There is no wave particle duality. That's just an old meme that has to die. It's not a useful physical concept.

[@TimHoustonSB]

Awesome! Thank you so much!!!

[@daffidavit]

Questions: Do all atoms and subatomic particles "vibrate" or "wiggle"? If so is it because of the "uncertainty principle"? Is that the reason we can never get it cold enough to reach absolute zero? If a particle stopped vibrating would that mean its temperature would be absolutely known to be "zero" and that is impossible because it violates the uncertainty principle? In other words, if so would we know the particle's exact location and its temperature? Do these questions follow the uncertainty principle or am I making false assumptions and conclusions?

[@chhetry2010]

Hi, Prof. Greene How can we envision the existence of different fields (EM,E,QFT....), and how they interact with each together to form the nature that we experience? And are these fields embedded in "Space-time dimension"? Also Prof. what is space? Sorry for inconvenience. Thanks..

[@mandeepsingh-fd7mh]

Wao thank you mentioned Sheldon when I saw u in BBT I became even a bigger fan..

[@Riteshghosh1987]

It's just like family and work! If you try to grab one tightly you lose another!!

[@deeprecce9852]

Nicely done Professor!!!

[@roboy1235]

I dont know if you do Wigners friend later? The recent real world version of that thought experiment seems to settle the ontology. there is no physical interaction with one side of the entangled pair and only revealing the spin state to the friend collapses the wave.. what do you think of this?

[@Ozgipsy]

That period in physics was amazing.

[@arisss_333]

Great explanation!

[@laxmanchy4020]

Why some books write h bar rather than h bar divided by 2 in Heisenberg uncertainty principle ?

[@Rayquesto]

Isn’t h bar h/2pi?

[@laxmanchy4020]

@@Rayquesto ∆x∆p> or =h bar or ∆x∆p>or =[h bar]÷2 ? which is correct?

[@georgemolnar7344]

On whatever level - math, physics, quantum, macro, or common sense - WHY should the value of momentum and the probability of that value have ANYTHING to do with location? And vice-versa. Even given that momentum involves "velocity" which is the derivative of location/position, why the inherent link? For example, say I have particle on home plate in Yankee Stadium. What difference does it make as to what its momentum is? I could have one baseball sitting still on home plate and another crossing over it at 90 mph. Same location, different momentum. So where is the link? Thanks.

[@schmetterling4477]

Because you are dealing with a wavelike phenomenon here. There is no such thing as velocity in quantum mechanics. That's just a classical expectation value that can be defined for certain quantum states.

[@johnmckiernan987]

Best explanation.Well done Brian

[@sammycross2701]

Brian I’m a huge fan and I love watching these can you explain string theory and the math?

[@priyashetty1231]

sir could you please explain feynman's path integral formula

[@math_brilliant]

I really aprreciate your Wonderful explanation.

[@monoman4083]

does anyone know series and episode no. for big bang theory. thanks

[@robertfinkel5103]

Question for Dr. Green...as the sun converts mass to energy does its gravitational force decrease, as its mass decreases, and therefore does earths orbit change as a result? Thanks for all you do and teach.

[@nmarbletoe8210]

no but then yes. As the mass gets converted to energy, no this does not change the gravity. Then when the energy leaves the sun and flies away from the solar system, yes the gravity of the sun decreases.

[@mrslave41]

5:54 why can’t you start from an experiment?

[@TheMorpheuuus]

Great episode!

[@fahimabegum9557]

So amazing! Thanks doc Greene; I graduated in chemistry this year and I've actually always been drawn to phys chem. However, my lack of confidence in maths always put me off thinking of pursuing a masters degree in phys chem; any tips or course to improve my understanding of maths? Thanks for your time Prof and I wish you well.

[@willpoolman2204]

Finally, an explanation of Heisenberg's uncertainty principal that I can wrap my mind around..... I think. Maybe not.

[@benjaminbenjamin8834]

Awesome Professor!

[@bkkfootball]

Professor, how does the source code can constantly correct the "h bar" error?

[@stevenmeyerson8466]

But why hbar/2? Is this related to the general Fourier transfom result?

[@kennethchow213]

Instead of being called Uncertainty Principle, it should properly be called Certainty Principle. In the inequality : delta p delta x is greater than or equal to h--bar / 2 , if we let delta x =Planck Length i.e. 1.616 x 10 to the power minus 35 metre and h-bar = 1.0549 x 10 to the power minus 34 joule. second, then delta p, where p= mass x velocity= momentum = Planck mass x c(speed of light) x 2 ( inequality, not an equation) In the other inequality: delta E delta t is greater than or equal to h-bar /2, if we let delta t = Planck time ,i.e. 5.391 x 10 to the power minus 44 second, then delta E = Planck mass x c (light speed) squared i.e., 2.177 x 10 to the power minus 8 Kg. x (3 x 10 to the power minus 8 metre/sec.) squaredx2=1.0549 x 10 to the power minus 34 joule. second/ 2 ( again this is an inequality, not equation) All the quantities involved in these two inequality relation are universal physical constants, hence it should be called Certainty Principle.

[@joemmac]

Dr Greene... can you explain the Pauli exclusion principle and also the fine-structure constant.

[@hyperduality2838]

Exclusion implies duality or boundaries. limits, barriers. Duality is the origin of the Pauli exclusion principle. Positive is dual to negative, action is dual to reaction -- Newton.

[@kamaldey3893]

Thank you Sir.

[@Machobravo]

You try so hard. And it shows and you succeed.

[@A.K04]

No I like your 4 channel sir thank you for your examples.

[@georgemolnar7344]

At 19 minutes he states that the wave function of position and the wave function of momentum are related - the Fourier transform. My question is WHY? HOW? I certainly believe him but where is the evidence/proof/derivation of this relationship? Thanks.

[@BruinChang]

Wow, this remind me of Gabor's time-frequency analysis.

[@jesperswinkels2353]

Hey, great video! There’s just something I don’t get; what does it mean for a probability wave to have a certain momentum? I get it if you tell me like ‘this mass is going at this speed therefore it has this momentum’, but I thought probability waves just represented the likeliness of finding a particle at a certain position. What does it mean for them to have momentum?

[@erwinmarschall8879]

Very simple: That's the probability of finding a particle with a certain momentum.

[@briangreene6975]

Well....just as a "usual" probability wave represents the likelihood of measuring the position of a particle and finding it at a particular location, a "momentum" probability wave represents the likelihood of measuring the velocity of a particle and finding that it has one particular momentum.