Your Daily Equation #9: De Broglie Wavelength
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- čas přidán 7. 04. 2020
- Episode 09 #YourDailyEquation: Particles and waves collide in quantum physics. In today's episode of Your Daily Equation, Brian Greene discusses the famous double slit experiment and explains the formula that connects particles and waves: the DeBroglie wavelength equation.
Even if your math is a bit rusty, join Brian Greene for brief and breezy discussions of pivotal equations and exciting stories of nature and numbers that will allow you to see the universe in a new way.
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There is a part of me that doesn't want this whole thing to end. Your generosity with your time and explanatory ability is priceless, Prof.
I'm interested to know what this will look like from 20 years down the road, but I'm hoping people will appreciate and remember the role that content creators and distribution platforms played in keeping our minds off of the overwhelming uncertainty.
This is priceless!! Thanks Professor Brian for making it happen!! I'm so grateful for the time you're sharing with us!
The double slit has been one of my absolute favorite expiriments for many years, BUT I'd like to take a step farther down the rabbit hole... In my opinion, the REALLY interesting thing about the double slit expiriment comes when we attempt to measure (aka: observe) which slit the particles travel through. SPOILER: when we measure it, the wave collapses, and the interference pattern disappears. What?!? Yes, it's gone, and you have 2 bands showing on the screen. So... what can we make of this? Lets dissect a bit further... For a particle to behave like this, you need wave, so let's start with a couple of questions: 1) is a particle just a particle traveling on a wave, or 2) is a particle both a particle AND a wave? (Note: the answer to this depends on who you talk to...). More questions: why would measuring/observing the particle cancel the wave function and make it behave like a lone particle? Good question, I'll touch on that in a bit... Let's talk about some options: Option 1: the simple act of observing is magical and changes the direction of the particles (hmmm .. I think not... humans aren't as special as we'd like to believe...) Option 2: the measuring device is somehow influencing/cancelling the wave function (problem here is, the quantum eraser and delayed choice quantum eraser expiriments tend to rule this out to a high degree) .. Option 3: mind blown! Whenever we measure it, there are two bands .. when we don't, there is an interference pattern (which requires the existance of a wave). I wish I were smarter, OR more than that, I wish that I had direct access to someone smarter than I so that I might discuss this in greater detail with them, because this keeps me up at night (seriosuly .. its scary-sad...)! While it's not popular among scientific scholars, I am really interested in Bohm's pilot wave theory (I feel that it's undervalued...) - which was coupled with de Broglie, if I recall correctly. While I am NO scholar, I often wonder whether the pilot wave theory (coupled with gravity effects OR maybe even space-time, itself??? .. my ignorance precedes me here...) is affecting things. Someday we'll know, and I hope I'm still around to hear it explained in full. Loved the video, but I would also LOVE to see the next level from you... Thanks!
Never took a physics class while in school, but since I saw your show Fabric of Cosmos, been a fan of hearing your talks....
No doubt, the more I am watching your lecture, I am being more fan of you. Great Job❤
I've been watching one of these a day as the series title suggests when I wake up in the morning. Usually the first thing I do when I wake up. I'm familiar with all of these so far, have attended lectures on them, worked with them etc. but you're so congenial compared to most physics lecturers. And it's fun to revisit these in detail. It's become a really great part of my day. Thanks doc!
I love the episode of Big Bang Theory where Sheldon Cooper asks Brian Greene if he did not have anything more useful to do than teaching the general public complex ideas of physics. Indeed, Greene is the man! I have learnt a lot from him about string theory, and now with these series. Sorry for the joke, I cannot hold it, it is too funny the episode!
Thank you Brian greene for all of your videos and all of your books. I learned so much about the universe from you. Thank you again for all of your help in my study.
I am 12 years old and therefore had no idea about the debroglie wavelength but i derived it when i was trying to explain why wavelength decreases with increase in mass.
Thank You, Dr. Brian Greene, you are an excellent explainer of these subjects. Enjoy all your Programs !!!
Thank you Professor!!! ❤
Each chapter is even better than the previous
Dear Prof. Greene,
Thank you once again for an excellent exposition of the de Broglie wavelength. At the risk of repetition. I would like to say that some of the very best explanations & visualisations of aspects of Quantum Mechanics, are to be found in the PBS Nova series which you made a few years ago - i.e. “The Fabric of the Cosmos”. I have the DVD of the series and viewed it again recently. It is still excellent and well worth watching again.
And thanks again for this excellent series. I look forward to watching each daily episode with my breakfast, while I’m at home here on lockdown in sunny West Wales (UK).
I love these daily equations. Thank you for your time and generosity. As an aside, watching your podcasts, I find myself wondering, as a psychology professor, if I could/should do something similar in psychology, particularly social psychology which is my field. I think there are many topics that would be of general interest such as aggression, interpersonal attraction, obedience to authority, attitudes, and social influence but I don't know.
You do know Sir and that's why you should.
Social influence is very interesting.. I have come to be very much in doubt of actual free will.. are we 100% a result of our surroundings, even after we are born?
@@rickytomczyk4046 The concept of "free will" is tricky. I won't go into it here but I can say, based on substantial research evidence, that our behaviour is a function of both our inherited tendencies (genetics) and our social environment. Although that is true at a fundamental level, It's a little more complicated than that when you consider the notion of what drives "intentional behaviour."
@@Dr10Jeeps so there is your first topic! intentional behaviour, you will for sure have my view:))
We saw the actual double slit experiment in highschool physics. In 1975. (Vienna, Austria)
Thank you so much !!
Best description of the double slit experiment I have seen... two questions: 1. If we do the experiment with smaller and smaller particles at what point do they start behaving in this quantum manner? 2. Does the thickness of the material from which the slits are made affect anything? I can imagine stuff bouncing off the sides of the slits...
Simply superb explanation of this quantum phenomenon
Thanks for the explanation - yesterday we saw how through the photo electric effect, a wave seems to be able to behave like a particle. Today's double slit shows the other way around as well: a particle can have wave like proprties.
Thank you for the information
Sir i have a doubt.. HUP arises becoz of lack of measuring ability and limit to how much we can know about universe. When you try to measure position of electron you disturb it's both position and momentum. There is no counterintuitive stuff here. Electron is behaving according to the classical laws and it's just our inability to measure it and that's why probability popes out.. So why do physicist feel dizzy about it?
Because we don't know why this it is showing this behaviour
Bcoz it is getting slamed by a photon
The only logical answer is photon
And the wave particle duality of as de brogile said
@@raghav9o9 Pls, de Broglie !
The best teacher , thank you
I just love this man ❣️
Thank you very much
I wish I grew up throwing pebbles into the pond for fun 😔
I live in Canada. The pond is always frozen.
Dr Greene ( some nerdy humor, lest anyone think different)
I love the daily equation, thank you for this series, you've made quarantining more enjoyable and enlightening! ! So for some fun and entertainment how about including the 'Daily interruption' ? I love the phone ringing, the calendar reminder, the real life stuff that happens. Perhaps prior to announcing the daily equation, you could include the daily interruption; a dog bark, a door bell, maybe some thunder or a (fake) earthquake ...some comic relief, a trademark if you will on your great series!
Sorry, this formula is to ephemeral to list out - Thank you !
Thank you, thank you, thank you ...
Schrödinger's waves (wave function) and de Broglie's waves (matter waves) are not the same thing, are they?
I think about for example the wave function of say 1s electron of H atom.
Does it even make sense for example to ask what the wave length of that wave function is?
If we place our two fingers together and make a very small space between them we see parallel black lines if we look at a light source through the space. Is this a form of wave interference as well? Is there a connection with the double-slit experiment? Thanks in advance.
Professor..... I'm stuck at the Euler's identity for the Schrödinger equation and tye absolute value of psi.... What do I do now????
Very interesting. Gives me a flashback to Grade 11/12 physics. But as I watched 3 familiar questions came up for me:
1) How does the measured wave property change with slit width (smaller then height)? If the slit width >> de broglie wavelength then it should act like macro objects, right? So what is the equation for the WaveIntferePattern(wavelength, slit width) function in general? This should tell us something interesting as the slit width approaches the magnitude of the de broglie wavelength.
2) If single electrons, separated in time, make this interference pattern does that mean electrons have an existence spread in time (live in 4 dimensions) that allows them to generate a 4D "water wave interference pattern due to mass collection of water molecules", but not a 3D fluid of water, but a 4D fluid of electrons that we only see a 3D slice of, at each moment in time?
3) Could an interaction with the microscopic nature of the slit material be the cause of the 'single electrons at a time' double slit experiment wave interference pattern? So electrons are not speaking to future amd past versions of themselves, nor do they interact due to living in a 4D existence, but it's simply some random-ish interaction with the slit material (via the various forces) that results in the electron particles moving through the slits _like they were waves_, but they are really just interacting like particles?
Always wondered this stuff since about Grad 12.
Is there a video of the full double slit experiment? Every video i've seen of the double slit experiment only ever shows the interference pattern, they never show just two lines forming if you detect which slit its going through.
Professor you're great in explaining the equations. Can you make video on schrodinger equation
I think it would be interesting if you could do some videos on how these various equations are derived.
I think you should make video on Einstein's Field Equation.
thanx dr B! How is the experiment done so there is no material between the slits to maybe influence the beam?
thank youuuuuuuuuuuuuuuuu awesome
Professor, you didn't mention this, but what about the fact that if the particles going through the slits are measured to verify which slit it went through, the interference pattern disappears? What do you think causes that?
Excuse my ignorance. How is it that particles are fired one at a time? how can you tell?
Hi from Spain and congratulations for this exciting initiative.
QUESTION: I've read a wonderful book called QUANTUM ENIGMA, by Bruce Rosenblum and Fred Kuttner. The basic profound idea described in the book is that in a double slit-like experiment your result depends ultimately on which experiment you DECIDE to make and there physics meet consciousness. It is also said that if a robot is made to decide a series of experiments based on some kind of random generator the series of results would be the same, but you cannot ensure that the decisions of the robot are not infuenced or determined in some way by the result of the experiment itself, and therefore you can only ensure independence if a human being consciously decides which experiment to make. I don't understand this. Could you elaborate a little bit on it?
that inability to choose would be "superdeterminism"
Seems like it's philosophically possible but would destroy all science if true.
Isn't it a lot like the idea that the earth is 6k years old but god fools us by making fossils and putting them in the ground?
You spoke of the Heisenberg uncertainty principle in an earlier segment. Would you care to comment more on what led W. Heisenberg to this conclusion and his equation of the product of change in position and change in momentum being greater than or equal to h/4pi? Also I would like to hear your discussion of Ludwig Boltzmann’s equation on his tombstone S = k(log)W. Which happens to be my license marker plate SKLOGW
I wonder if they try on larger particles ? or with more mass
like finding the pattern why its happens with finding common value
Do ions have the tendency to orbit hence "concentric" type ripple effect? Or out of balance? Being a charged partical causes erratic motion?
Question : Which mass do we consider in de Broglie equation for wavelength of matters???? Is it the rest mass or the relativistic mass??????????? I'm a bit perplexed.
Well if I tread on the line of thinking of prince De-Broglei, I might as well argue that - as electromagnetic waves which have particle nature, wave nature and another nature which is that EM waves have a spectrum that runs from longest wavelength Radio waves to highest energy Gamma rays. So may I speculate that in the same way - particles may have spectrum associated with them? And may be that all the different fundamental particles that we know exist in nature be a part of the spectrum, which would unifie them all with some underlying properties?
At what point does the dual slit transition from double lines to wave pattern? As in how small do you have to go before the experiment produces a wave pattern? What if I'm firing atoms instead of the components of atoms?
Atoms do the same even molecules. At certain size the wave effect vanish. I think you can derive it from this equation.
Question: If I assume spacetime is emergent from entanglement, is it reasonable to think dark matter may be a form of entanglement?
I have a question please. The planck's constant has units/dimensions of angular momentum and considering the fact that how small it is, it must be assumedly the angular momentum of some elementary particle or any particular state of such a particle. But what particle exactly???
The fundamental angular momentum for elementary particles is the so-called spin, which is of the size of Planck's constant. Its value is however not unique for a specific particle. The exact value is square-root{s·(s+1)}·(h-bar), where h-bar is Planck's constant divided by 2·pi, and s is the spin quantum number. For "ordinary" matter particles (electrons, protons, neutrons...), s=1/2, for photons s=1.
@@benno365 really grateful of you for taking the time out for replying. Having just passed out of high school, i have never come across that equation giving the angular momentum of elementary particles and have just witnessed QM from the outset. I cannot interpret that Eq and fail to see how it explains the plancks constant. It just expresses the ang. momentum in terms of h and in order that ang. momentum be equal to h(of some particle), s*(s+1) must be equal to 2pi which would only be if the spin of he particle is either (~2.056 or -3.056). Both these values are of course out of the possible quantized spin number. This is what I can draw from the eq. in light of my extremely scarce understanding of QM.
What is the wave length for a accelerated particle? My another question is can de broglie wave length really apply to normal bodies even though the wave length is too small ? If yes what is waving in first place
yes the deBroglie wavelength can apply to large objects like a molecule or a baseball.
But what if you selected special materials which would absorb or dampin vibrations or resonances of the electrons.
What happens if there is only one slit? And is there any pattern if you just shoot electrons at a surface with no interference?
Could the pattern made by the double-slit experiment be the experiment running both forward and backward in time where the backward direction in time shows the parallel universes that are not our past because we cannot travel to our own past but can to parallel versions of our past?
Matt O'Dowd answered this in a video for PBS spacetime stating a loss of coherence moving forward in time does not allow backwards travel in time.
Nice Nice with Brian we will kicks physics ass
What about De Broglie's idea of electrons as standing waves in atoms?
And the time it explained the discreet photoelectric effect we observe of photons emitted from electrons switching energy levels.
But I hear that nowadays this is "proven" wrong. However I didn't find any info on that "proof".
I only found a counterpoint describing the assumption and calculations of electron orbitals in quantum physics, but to be fair both are assumptions and strictly logically (at least with my limited info) it's impossible to say which is right or wrong.
Mr Brian what if the light particle its itself composed of many other smaller particles but we cannot see/test for them ???
See it then doesn't matter as photon is an elementary particle even if it has an internal waving structure hypothetically.
Here is a dumb question; what if we did this with only one slit? does it still form the same pattern?
What if this double slit experiment was done in a vaccum to avoid any kind of atmospheric interaction; would it still form that pattern?
Another dumb question; if the gun that is fired itself is made up of particles; what if that "gun" was changed to have different material? glass, plastic, wood, metal etc... is there a possibility that the gun itself is having an interaction with the electrons before it even gets fired?
Can u say what is a tensor actually,greene??
Isn't there a connection between de Broglie's wavelength and the radii of the energy level's in Bohr's model of the hydrogen atom? IIRC, Bohr's energy levels for the electron in a hydrogen atom correspond to integer multiples of De Broglie's wavelengths for an electron or something like that? Did I get that right?
yup
(but it's the circumference that has the integer multiples of the wavelength, rather than the radius)
@@nmarbletoe8210 thanks for the clarification. Cheers!
Rocket Equation!
At 18:58 why not relativistic momentum?
Looking forward to this particle wave duality in mathematical form
martijn130370 you’re looking for born’s rule or P=|Psi|^2
@@Adraria8 yes it turned out that that was the case, wonderful idea a complex function
ok, so...QM is about trying to explain the observation in nature of, in this case, how light quanta behave both as a particle and as a wave, which in the macro world is impossible. The macro world and micro world cannot be explained by the same fundamental principles.
hello dr b, thanks for doing this 🍏
Does the firing of single electrons really support quantum mechanisms, or is there just a field (like the water medium which we dont know about) that EMR behavioural particles travel through that cause ripples. The single firing would have to be done in a vacuum at long intervals to ensure that the “ripples” are settled before the next particle is fired. Just seems odd that an interference pattern emerges when theres so called “nothing” to interfere with lol. And how do we know it was the original fired electron that landed on the screen and not just an electron from the slit material. Im starting to think that all matter is made up of wave like features or vibrations that all come together to form the tangible substances that we see around us, due to its effects at proximity, which is necessitated by the small nature of matter. And the combination of these smaller influences lend themselves to the macroscopic nature of what we see. In which case then there is a unified theory of matter, but we just dont “see” it yet. Mind blown
Please do a video on S=k*ln(Omega)
Perhaps the "single" electron has a "pulse"? Is this an example that the relativistic heavy ion collider may show?
yes it would have a pulse, aka a phase that goes up and down like a sine wave
The photons going through the double slit are somehow linked. The question is, what quind of link is it ? For a photon time is stuck and space is... what is again the nature of space at the speed of light ?
How about no slit experiment, can we do that? Let's say we place a mirror behind those two slits, so light never reach the wall but reflect back to the source. Than place a screen behind focused light source and see if pattern can reflect in reverse.
I would speculate there are two systems in play here, light should travel in both ways, even if we see only one result. Wall is also shining back at light source.
My idea is, only certain part of visible light band is pushed trough slits, but rest of light waves are also there. So we see only some sort of excess of certain photons, but can't see matrix of channels produced by other wave lengths and those also bounce both ways.
Would be happy to try experiments my self, but i also lack equipment, i guess.
Theoretical physicists don’t help out the engineers build enough experiment’s equipment. The detector just detects the first total electron or enough of the electrons to have a signal good enough to call it our electron. I believe there’s still more electrons than we r detecting. It’s to coincidental to act like an abundant amount of particles like multiple water molecules.
There are experiments which can only be explained by the matter behaving as wave (like the double split experiment) but are there experiments which can ONLY be explained by the matter behaving as a particle?
I may be wrong but doesn't the wave principle suit ALL experiments (the ones with the wave behavior and the ones with the particle behavior)? (Contrary to the particle theory which is contradicted by the wave experiments)
the photoelectric effect shows particle-like behavior
Thoughts on the question of where does time exist (space-time?)
Pure Logic = mathematics. Mathematics is an absolute science, a formal system of pure logic that can be seen as a language existing without philosophical reasoning; we must attach the philosophical inference (one and one are two, the philosophical reasoning asks two of what). There is no questioning of proven mathematics in this ramble, the question is to philosophical assumptions impinged to pure mathematical logic of “space-dependent time” or space-time, where logical deductions flow to time as matter dependent.
Speed is always relative to the observer because it is a measurement of change in distance over time relative to the observer. The only thing that can change this is the absence of a function in the equation if the function of changing distance is missing there is no speed. If the function of time is missing there is no speed.
What if time exists to the observer but does not exist within what is being measured light? Any velocity of the observer relative to the source would become inconsequential, but the perspective of the observer would be of utmost importance,
The speed of light is a constant and an absolute speed traveling through space unmolested by time, the speed inconsequential to the behaviour of matter, a speed that matter can never reach.
To understand this phenomenon there are three different perspectives one can take.
(1) A perspective from our position of measurement, (we know these answers).
(2) A perspective from within the light.
(3) A perspective from outside the universe looking in.
An argument for where time exists must inevitably lead to ‘what is time’, to find an answer a Gedanken experiment is needed, if it can be backed by experiment philosophical logic may have some weight.
Using perspective (2) a perspective within the light.
If you travelled to 99.99% of C you would still exist as matter, but taking the next step of 0.01% C you would experience a state that is not matter but a state in which only energy can exist “time would stand still”, time standing still this is a deficient statement, if time stands still it ceases to exist, a better description would be to say time does not exist within c. This is borne out in the mathematics, s = d/t if time is cancelled so is speed; there is only distance left or the path, showing a reason why C is a constant and why nothing can travel faster than light is because “at c speed does not exist”. It is really the closest thing to being at rest in this universe.
Philosophy of conscious clarity created in simple logic; if simple logic is lost clarity is lost.
Non-existence of time creates another phenomenon, without time the path of C cannot have position within itself, as position infers time, without position the path can only be the whole, the beginning the end and everything in-between. This phenomenon is proven with these two experiments.
(1) Two slit delayed choice experiment.
(2) Entangled photon experiment
(1) Delayed choice experiment shows once you know information about the path that information changes your perspective, in turn, changes the result. It doesn’t matter at what position within the path you learn the information because the path is always the whole ‘without position’. Perspective is contingent on information and our perspective is a perspective of time, once information is known our perspective is of time, which must have a position.
(2) The entangled photon experiment is analogous to delayed choice. In this experiment, light is passed through two polarising filters, polarising light horizontally and vertical then passing the light through a crystal splitting the single light beam into two paths without breaking the path. Observing the polarization of the light on one path you know the orientation of the second path, it will be opposite to the path measured first, no matter what time has passed from the first measurement. Time and distance makes no difference within the beam of light because it is always the whole, time passes for us but not for the energy within the beam of light, it is position less existing only as the whole.
This shows that we live in a universe where time and position only exist below the speed of light but has no existence at C.
This argument does not show what time is and why it behaves the way it does, that understanding leads back to the origins of the universe.
I love this series of daily equation thank you professor Green.
I would love to hear your thoughts on this ramble.
That's some spooky action right there. So the upshot of all this is that we are beings of energy. And the only reason that we can be seen at all is that light reflects off of us. Ha!
Make this experiment at home find a place where the sun light get in than go behind a door blocking the sun and close that door slowly and let the light beam get smaller and smaller when you reach a point where the door opening get very small you will see the light beam getting spread out and getting bigger again.
I agree. That could be the effect.
Schrodinger equation plz
How about if we think of the electrons that are coming from the gun as stone we are throwing in the water .these electrons are causing the space to act like a wave .just like a stone causes a wave.
We want to know about S= k lnw
Pilot wave theory may be more accurate than first thought if this is just an emergent system like waves on water.
what is the most mind boggling theory in physics according to your perspective?
SuperString theory
What he's talking about right now, the double slit experiment. No one really knows what's going on. There are many interpretations and none of them have been chosen as the best. It's just weird
Has anyone done this experiment and compensated for the gravitational wave
Gravitational wave doesn't affect any of it.
Can please make a video on HIGG-BOSON
Relation between time and dimensions..
Time itself is a dimension what else relation do you want.
@@ShailendraKumar-ug4tn where are you from?
holy smokes...thats the first time ive heard holy smokes
Why doesn't the back screen act as a detector and cause the collapse of wave function right away.
because it does not give "which way" information
01001011110100 --> s1 s2 --> 01010101. Out of randomness comes order. Spooky action.
Chris Field then you don't have kids...this never happens!
@@sebastjanbrezovnik5250 yes boss
Thanks you. And that experiment still amazes me after knowing it for a long time. Professor Lewin demonstrated it once in a lecture. It made me understand the particle/wave dualitty of the photon.
Ok.. from this episodes it sounds very 'Brian Greene'
Just waves..
spaceandmotion
Why can't we assume that it's not atom or electron rather ...more fundamental up. down quark passing through slits..
Are we waves ???
is string theory the theory of everything?
Some people think so some people don't. It's still up for debate. The problem is there's still no really good way of experimentally testing it. So until somebody can test it, it's just a really nifty mathematical model.
Pythagorean theorem
The name of fulfillment of desires is paradise.
On that scale the entropy/complexity is enourmous. No way for even our supervcomputers to conceive.
"Today scientists never admit they discover anything by mistake"
Yes and that's so stupid. Most amazing stuff you'd never imagine is discovered by accident simply because you'd never imagine it. People should be encouraged to not fear accidents... And wear protective gear 😉
They never admit it? But there's an actual word for it
Please read, "Infinity, Time, Death and Thought". A new and compelling take on the anomalies of the quantum realm.
Your derivation if the de broglie equation is incorrect, thats not how de broglie derived his relationship
Question: Have you ever thought about that pattern (of double slits) as is obtained as the effect of the wall (and its gravity - because of his mass) against the trajectory of the electrons?
In other words, the electron is starting his travel from the electron gun, is approaching the slit wall (which has a mass, so its own gravity field), and the trajectory of the electron is just modified (bended) because of that just as the light is bended by gravity of an object.
Or, the wall have some kind of "aerodynamic" effects to the trajectory of the electron?
In this way you'll get the same 5 beam pattern.
It could be that the case?
I did something like this with my beard. I cut a small slit in it lined up with the skin that separates your nostrils, and that the beard has grown. When I stand in the mirror. The light above my mirror cast a shadow of my beard onto my chest. So you,d think you'd get a shadow of a beard with a slit down the middle, but instead you get a shadow of a beard with two slits. Which what i can best describe looks like the head of a three pronged pitchfork
E = pc joke:
The energy of light is a computer. Not a mac.
i wonder how many times Brian explain this... The most click-bait experiment on youtube ever.