Heisenberg Uncertainty Principle Derived and Explained | Doc Physics
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- Опубликовано: 8 сен 2024
- One of the most-oft quoted results of quantum physics, this doozie forces us to reconsider what we can know about the universe. Some things cannot be known simultaneously. In fact, if anything about a system is known perfectly, there is likely another characteristic that is completely shrouded in uncertainty. So significant figures ARE important after all!
I should point out that, although my derivation is easy to understand conceptually, it is incomplete and its result is not perfect. A proper (but messier) treatment yields a minimum uncertainty of h/(4*pi).
i love how passionate you are about this, its actually ace.
ASUUUUUUUUUUUUUUUUUUU
YOU ARE GODAMN RIGHT!!!
- Heisenberg
Plzz doc keep up your amazing work! i am addicted to all these science channels on youtube , u guys make science really fun, Thanks a lot :D
better than other videos about principle on RUclips.
Heisenberg's uncertainty principle: Δх * Δр ≥ ħ/2
The Heisenberg's uncertainty principle is correct, moreover, it is fundamental. If the uncertainty principle is incorrect, then all quantum mechanics is incorrect. Heisenberg's justified the ncertainty principle in order to save quantum mechanics. He understood that if it is possible to measure with every accuracy both the coordinate and momentum of a microparticle, then quantum mechanics will collapse, and therefore further justification was already a technical issue. It is the uncertainty principle that prohibits microparticles in quantum mechanics from having a trajectory. If the coordinates of the electron are measured at definite time intervals Δt, then their results do not lie on some smooth curve. On the contrary, the more accurately the measurements are made, the more "jumpy", chaotic the results will be. A smooth trajectory can only be obtained if the measurement accuracy is small, for example, the trajectory of an electron in a Wilson chamber (the width of the trajectory is enormous compared to the microworld, so the accuracy is small).
Heisenberg's formulated the uncertainty principle thus:
if you are studying a body and you are able to determine the x-component of a pulse with an uncertainty Δp, then you can not simultaneously determine the coordinate x of the body with an accuracy greater than Δx = h / Δp.
Here is a more general formulation of the principle of uncertainty: it is impossible to arrange in any way an instrument that determines which of the two mutually exclusive events has occurred, without the interference pattern being destroyed.
It should be immediately said that the Heisenberg uncertainty principle inevitably follows from the particle-wave nature of microparticles (there is a corpuscular-wave dualism is the principle of uncertainty, there is no corpuscle-wave dualism - there is no uncertainty principle, and in principle quantum mechanics, too). Therefore, there is an exact quantitative analogy between the Heisenberg uncertainty relation and the properties of waves.
Consider a time-varying signal, for example, a sound wave. It is pointless to talk about the frequency spectrum of the signal at any point in time. To accurately determine the frequency, it is necessary to observe the signal for some time, thus losing the accuracy of time determination. In other words, sound can not simultaneously have the exact value of its fixation time, as it has a very short pulse, and the exact frequency value, as it is for a continuous (and, in principle, infinitely long) pure tone (pure sine wave). The time position and frequency of the wave are mathematically completely analogous to the coordinate and (quantum-mechanical) momentum of the particle.
We also need to clearly understand that the Heisenberg's uncertainty principle practically prohibits predicting behavior (in the classical sense, since Newton was able to predict the position of the planets), for example, an electron in the future. This means that if the electron is in a state described by the most complete way possible in quantum mechanics, then its behavior at the following moments is fundamentally ambiguous. Therefore, quantum mechanics can not make strict predictions (in the classical sense). The task of quantum mechanics consists only in determining the probability of obtaining a particular result in the measurement, and this is fundamental. That is why the uncertainty principle has such a fundamental meaning (there is no uncertainty principle - there is no quantum mechanics). But this does not mean that we do not know any "laws or variables that are hidden from us", etc. No. It's just the reality. This is analogous to how a particle can exhibit corpuscular and wave properties - just this is reality and nothing more. And even if we know the "hidden parameters" (compare, understand why the wave properties and corpuscular ones are manifested), this reality will not change, and the uncertainty principle will also work, but we will understand it more fully.
It must be added that not all physical quantities in quantum mechanics are measurable simultaneously, that is, they can have simultaneously definite values. If physical quantities can simultaneously have definite values, then in quantum mechanics they say that their operators commute. The sets of such physical quantities (complete sets) that have simultaneously defined values are remarkable in that no other physical quantity (not being their function) can have a definite value in this state. The fully described states (for example, the description of the electron state) in quantum mechanics arise as a result of the simultaneous measurement of a complete set of physical quantities. By results of such measurement it is possible to determine the probability of the results of subsequent measurements, regardless of what happened with the electron before the first measurement.
If physical quantities can not simultaneously have definite values, then their operators do not commute. The Heisenberg uncertainty principle establishes the limit of the accuracy of the simultaneous determination of a pair of physical quantities that are not described by commuting operators (for example, coordinates and momentum, current and voltage, electric and magnetic fields).
Let's add a little history. A. Einstein assumed that there are hidden variables in quantum mechanics that underlie the observed probabilities. He did not like the principle of uncertainty, and his discussions with N. Bohr and W. Heisenberg greatly influenced quantum mechanics and science as a whole.
In the Copenhagen interpretation of quantum mechanics (N. Bohr and followers), the uncertainty principle is adopted at the elementary level, and it is in this interpretation that it is believed that this can not be predicted at all by any method. And it was this interpretation that Einstein questioned when he wrote to Max Born: "God does not play dice." To which Niels Bohr, answered: "Einstein, do not tell to God what to do." Einstein was convinced that this interpretation was erroneous. His reasoning was based on the fact that all the already known probability distributions were the result of deterministic events. The distribution of the tossed coin or rolling bone can be described by the probability distribution (50% eagle, 50% tails). But this does not mean that their physical movements are unpredictable. Conventional mechanics can calculate exactly how each coin will land, if the forces acting on it are known, and the eagles / tails will still be randomly distributed (with random initial forces). But it is unlikely that this experience can be extended to quantum mechanics.
The position of Bohr and Einstein must be viewed as views from different angles of view on one phenomenon (problem), and in the end it may turn out that they are right together. This can be demonstrated by lottery. Despite the fact that theoretically the results of the lottery can be predicted uniquely by the laws of classical mechanics, knowing all the initial conditions (it is necessary only to determine all the forces and perturbations, and to make the necessary calculations), in practice the lottery results are always probabilistic, and only in theory they can be predicted (try win the jackpot :). Even in this simplest case, we will be "inaccessible" to all the initial data for calculations. It is logical to assume that the quantum system will be incomparably more complicated than the lottery, and therefore, if we master the "true" laws of the quantum world, the probabilistic picture will remain, since the microworld is such in essence. Moreover, if you think about it, then our world is also probabilistic. It is deterministic only in theory, and practically, in everyday life, we can only predict, for example, tomorrow (or a second, or a year, or 10 years) with a certain probability (who can guarantee the event of tomorrow with 100% probability?). And what is interesting is that only after having lived it (by making a measurement), we can say what probability was realized. Quantum mechanics in action :).
More see by link: www.quora.com/Is-Heisenbergs-principle-of-uncertainty-wrong/answer/Volodymyr-Bezverkhniy?share=b4884212
Benzene on the basis of the three-electron bond:
REVIEW. Benzene on the basis of the three-electron bond (full version, 93 p.).
vixra.org/pdf/1612.0018v5.pdf
1. Structure of the benzene molecule on the basis of the three-electron bond.
vixra.org/pdf/1606.0152v1.pdf
2. Experimental confirmation of the existence of the three-electron bond and theoretical basis ot its existence.
vixra.org/pdf/1606.0151v2.pdf
3. A short analysis of chemical bonds.
vixra.org/pdf/1606.0149v2.pdf
4. Supplement to the theoretical justification of existence of the three-electron bond.
vixra.org/pdf/1606.0150v2.pdf
5. Theory of three-electrone bond in the four works with brief comments.
vixra.org/pdf/1607.0022v2.pdf
6. REVIEW. Benzene on the basis of the three-electron bond (full version, 93 p.). vixra.org/pdf/1612.0018v5.pdf
7. Quantum-mechanical aspects of the L. Pauling's resonance theory.
vixra.org/pdf/1702.0333v2.pdf
8. Quantum-mechanical analysis of the MO method and VB method from the position of PQS.
vixra.org/pdf/1704.0068v1.pdf
Bezverkhniy Volodymyr (viXra):vixra.org/author/bezverkhniy_volodymyr_dmytrovych
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ОТВЕТИТЬ
Its not only a great explanation but also its funny! :D
I've never thought I would ever understand this. Thanks so much.
Nicely explained, just 4pie instead of 2pie
h-bar divided by 2 I thought?
+Justin P yeah I found that too in my book why??
Just a little mistake I believe
^ This is what Bill Burr is talking about.
Katie L Katie L this is just sad. In the usual form, it is indeed hbar/2, but in its usual form the deltas mean something else than in this derivation. Deltas mean standard deviation, and those are precisely defined, for those it really is hbar/2. Now before you decide and try to be a jerk, think, at least a bit. Clearly he remeberd that there should be a 2 there, and he looked it up in a textbook, to back it up. Notice, that he has a textbook, maybe he studies physics. If that is the case, he probably knows better than you, and it is not a good idea to pick a fight about quantum physics whith him. And he doesn't talk about the derivation, he talks about the ending, which is in fact has this little error. So lets take a look at your argument about uncertainty. Uncertainty principle is not talking about infinitesimal quantities, what is this madness? Don't try to be a smartass, talking about how memorising is bad. It still is better than not knowing, and the assumption that he memorises stuff instead of understanding it is another absurdum.
@@katiel1392 wow what a dick
Thank you ..... from Egypt
wlahy anta btfhm :D
hi tutankhamun how's life?
nvm ur dead
Very good presentation. You made it easy for individuals not well versed in quantum fundamentals to grasp the concept of this principle.
Yeah, you're totally correct according to my memory and wikipedia. Strangely, the textbook I use indeed has h/2pi as the minimum uncertainty. It's using a pretty elementary justification, though, and I'm pretty sure it's wrong. Thanks for the reminder!
Fun idea! My first reaction is that Heisenberg's uncertainty goes deeper than just practical observation matters. It's a question of WHAT CAN BE KNOWN EVER.
Secondly, since you don't know where it is nor how fast it's going, you can't predict how either photon will scatter off the electron. A head-on collision presumes you know exactly where it is in the first case. But I could answer special clever situations all day. Refer back to my first paragraph. Sorry - this is deep.
Dr. Schuster , We have to go back to 1924 ! Thanks for your passion explaining Heisenberg Uncertainty Principle
Best video I could find on RUclips that explains it this well
8:20, thank you for this I finally understand after 1 year of quantum physics 308
Thank you ... from Thailand
8:03 best part. That much I am certain
that moment which I stopped the video to press the like button
I love your videos, keep it up!
This video makes more sense than Arvin Ash’s.
The inclusion of the small angles concept makes the uncertainty principle more graspable because it’s an intuitive reason for why the product of uncertainties has to be >= h
I was looking for stats uncertainties for ML, but watched the whole damn thing because he's so funny and passionate (and clear! that's hard to do with "complicated" math). Loved it.
In de Broglie's terms, the electron's pilot wave propagates through each slit independently of the electron itself. The uncertainty of the electron's momentum is due to the unknown phase angle of the pilot wave at the moment the electron passes through the slit. The reason the pilot wave's phase angle is unknown is because we are unable to directly observe the "imaginary" axis of the complex-dimensional propagation of the pilot wave in QFT state space.
All of my THIS. Pilot wave theory makes more sense and gives you the non-local property needed for globally conserved information about the state of the constituent particles.
This lecture is mindblowing! Thank you for making Physics interesting.
A child's swing has natural frequency of 0.90Hz a) What is the separation
between possible energy values (in joules)? b) If the swing reaches its a vertical height of 45cm above its
lowest point and has mass of 20kg (including the child), what is the value
of the quantum number n? c) what is the fractional charge in energy between
levels whose quantum numbers are n (as just calculated) and n + 1? Would
quantization be measurable in this case?
Yes. Time and energy are two other quantities that have an uncertainty relationship (the fancy language is that they do not "commute" or play well with each other). So, at shorter and shorter time intervals, more and more wild things can exist, since energy can create mass, etc. As long as they don't exist for long, the can be AMAZING!
One example of the Heisenberg Uncertainty Principle is the inequality, (Standard deviation of position) x (standard deviation of momentum) is greater than or equal to (reduced Planck's constant)/2.
A demonstration of this is the observation in this video that when electrons are directed through a wide slit the position is uncertain yet the momentum has a relatively small variability and a narrow bell shaped curve pattern forms on the screen. If the slit is narrow meaning that the electron position is more certain the electrons on the screen form a broad bell shaped curve due to greater variability in momentum. This is attributed to an inherent uncertainty of wave-like systems. But if you consider a) that the electrons are negatively charged and that the narrow slit brings them closer together so that they would be subjected to a greater repulsive force; b) there would be more electron-electron collision; c)there would be more interaction with the edges of the slit ;and d) fewer electrons would go straight to the screen because of the narrow slit then more scatter of electrons on the screen would be expected. Heisenberg did not think of his concept as anything more than the notion that the means used to observe small phenomena also changed them. Maybe we should not take it any further than that.
FIRST YOU THOUGHT ME CALCULUS AND NOW YOU THOUGHT ME THIS MORE CONFUSING THING...........YOU ARE AWESOME!!!!!!!!!!!!!!!!!!
he had fun teaching and he helped me clear some concepts.
Hi ,
A particle moving in a transmission medium.
Kinetic energy of a particle ( charge) moving at the velocity of v has two different values:
Kinetic energy of a particle ( charge)
Tkin id =mc^2 [ln |1-v/c|+ (v/c) / (1-v/c) ] in direction of motion of a particle ( charge)
It is realy as Newton´s kinetic energy,
where v is velocity of a particle ( charge) .
Kinetic energy of a particle ( charge) Tkin ad = mc^2 [ln |1+v/c|- (v/c) / (1+v/c) ] against direction of motion of a particle ( charge)
It is realy as Maxwell´s electromagnetic wave energy,
where v is velocity of a particle ( charge).
Corrected Third Newton's law of motion :
All movements in physics are based on principle of action - reaction and on velocity of stable particles ( e-, p+,n0, D, He-3, α ).
Action, as a motion of stable charged particles ( e-, p+,n0, D, He-3, α ), is characterized speeds up in source along ellipse or quasi- elipse ( excentricity e -> 0 ).
Action creates unstable particles ( leptons μ−, τ−, baryons, mesons ), bosons W +, W-, Z (= particles = β electrons moving at nearly the speed of light )in direction of motion of stable particles ( e-, p+,n0, D, He-3, alfa ).
Reaction creates into transmission medium, the electromagnetic waves, as unstable “particles” - neutrínos νe, νμ, ντ , mesons π0, π+ , π- , η , K and gamma rays (=waves of extremely high frequency >1019 Hz ) - against direction of motion of stable particles ( e-, p+,n0, D, He-3, alfa ).
Accompanying activity of reaction on movement of stable particles in the transmission medium are waves, or “unstable particles“ respectively , i.e. neutrinos and mesons.
vixra.org/author/lubomir_vlcek
Extraordinary proofs:
vixra.org/pdf/1506.0207v1.pdf
New Trends in Physics CD Rom /book, Elementes Pictures, Spheres in Nuclei, Forecasted Nuclei
vixra.org/pdf/1504.0082v1.pdf
One Blink of Electron is the Basis Amount of Kinetic Energy 6.62606957x10-34 Js
vixra.org/pdf/1503.0056v1.pdf
Confirmation of the Theory Under Discussion Wave-Particle Duality as Kinetic Energy Against and in Direction of Motion in Discussion Group Theoretical Physics !!!! Eureka !!!!
vixra.org/pdf/1502.0184v1.pdf
Einstein's Theory of Relativity Can not Explain ...
vixra.org/pdf/1501.0199v1.pdf
Corrected Newton´s Laws of Motion
vixra.org/pdf/1501.0198v1.pdf
Principles for the Theory and Its Agreement with Experiment
vixra.org/pdf/1501.0197v1.pdf
Wave - Particle Duality as Kinetic Energy Against and In Direction of Motion.
vixra.org/pdf/1412.0131v1.pdf
Improvement of Classical Physics
vixra.org/pdf/1412.0125v1.pdf
Kinetic Energy According to Einstein and According the Latest Knowledge
vixra.org/pdf/1411.0533v1.pdf
Form of Intensity of the Moving Charge Electric Field is Asymmetrical.
vixra.org/pdf/1411.0531v1.pdf
Form of the Interference Field is Non-Linear
vixra.org/pdf/1411.0530v1.pdf
Kinetic Energy of a Charge Moving at the Velocity of V Has Two Different Values
vixra.org/pdf/1409.0090v1.pdf
Three Objections to Modern Physics
vixra.org/pdf/1408.0185v1.pdf
Protons Are Perfectly Stable or Their Lifetime is Enormous
vixra.org/pdf/1408.0133v1.pdf
Please Read my Articles in More Detail.
vixra.org/pdf/1405.0355v1.pdf
Movement Principles of Ufo
vixra.org/pdf/1405.0334v1.pdf
Kinetic Energy
vixra.org/pdf/1405.0308v1.pdf
Who is Right?
vixra.org/pdf/1405.0307v1.pdf
What is Quark?
vixra.org/pdf/1405.0237v1.pdf
L.vlcek Vixra, Getcited, Book, CD, Conferences 14.5.2014
vixra.org/pdf/1404.0471v1.pdf
Superheavy Spherical Nuclei. Island of Stability
vixra.org/pdf/1404.0369v1.pdf
Neutrino Oscillations
vixra.org/pdf/1404.0279v1.pdf
Physics is Easy
vixra.org/pdf/1404.0273v1.pdf
Particles, Waves and Trends in Physics
vixra.org/pdf/1404.0268v1.pdf
Physics is Beautiful
vixra.org/pdf/1404.0261v1.pdf
Introduction to my Two Articles Physics is Easy and Physics is Beautiful
vixra.org/pdf/1404.0253v1.pdf
Orbit Radius and Speed of the Sun Around the Center of Gravity of the Solar System
vixra.org/pdf/1404.0248v1.pdf
Spectral line Hα
vixra.org/pdf/1404.0246v1.pdf
Shortened Great Table of Elementary Particles
vixra.org/pdf/1404.0243v1.pdf
Great Table of Elementary Particles
vixra.org/pdf/1404.0238v1.pdf
Movement Principles of the Fast-Spinning Bodies
vixra.org/pdf/1404.0130v1.pdf
Nuclear Fusion
Critical examination of fundamentals in physics
www.trendsinphysics.info/
academia.edu
tuke.academia.edu/LubomirVlcek
L. Vlcek, : New Trends in Physics, Slovak Academic Press, Bratislava 1996,
ISBN 80-85665-64-6.
Presentation on European Phys. Soc. 10th Gen. Conf. - Trends in Physics ( EPS 10) Sevilla ,
E 9. -13 September 1996,
www.trendsinphysics.info/
vixra.org/pdf/1502.0184v1.pdf
Einstein's theory of relativity can not explain ...
Abstract
1. Movement principles of the fast-spinning pulsars, (vixra.org/pdf/1404.0238v1.pdf
Movement Principles of the Fast-Spinning Bodies )
2. Nuclear Fusion , ( vixra.org/pdf/1404.0130v1.pdf )
3. Wave - Particle Duality as Kinetic Energy Against and In Direction of Motion
4. the 4th Maxwell's equation, (2.38) in www.trendsinphysics.info/kniha/2-1.html#2-1-3
5. Lorentz equals without the help of Space-Time,
(2.23) - (2.27) in www.trendsinphysics.info/kniha/2-1.html#2-1-3
6.Confinement of quarks (vixra.org/pdf/1405.0307v1.pdf What is Quark? )
7. Great Table of Elementary Particles ( vixra.org/pdf/1404.0243v1.pdf )
8. Spectral line Hα ( vixra.org/pdf/1404.0248v1.pdf ň
9. Neutrino Oscillations ( vixra.org/pdf/1404.0369v1.pdf )
10. Form of the interference field must be non-linear. ( vixra.org/pdf/1411.0531v1.pdf )
11.Form of Intensity of the Moving Charge Electric Field must be asymmetrical.
( vixra.org/pdf/1411.0533v1.pdf )
12.Kinetic energy of a charge moving at the velocity of v has two different values:
Kinetic energy against direction of motion as wave Tkin ad = mc2 [ln |1+v/c|- (v/c)/(1+v/c)]
Kinetic energy in direction of motion as particle Tkin id = mc2 [ln|1-v/c|+ (v/c)/(1-v/c)]
( vixra.org/pdf/1411.0530v1.pdf , vixra.org/pdf/1405.0334v1.pdf , vixra.org/pdf/1409.0090v1.pdf Three Objections to Modern Physics )
13. Yukawa potential
1905 A.E. : Einstein ´s theory Tkin =mc^2 - mo c^2
1996: Tkin id =mc^2 [ln |1-v/c|+ (v/c) / (1-v/c) ]
Tkin ad = mc^2 [ln |1+v/c|- (v/c) / (1+v/c) ]
Einstein's theory works for v < 0.1c.
v/c.......Tkin ad .................Tkin id ...............Tkin (A.E.)
0.1..... 0.00439 mc^2...0.0057 mc^2....0.0050 mo c^2
0.2.....0.0156 mc^2.....0.0268 mc^2......0.0200 mo c^2
0.3.....0.0316 mc^2.....0.0719 mc^2......0.0480 mo c^2
0.4.....0.0508 mc^2.....0.1558 mc^2......0.0910 mo c^2
0.5.....0.0722 mc^2.....0.3068 mc^2......0.1550 mo c^2
0.6.....0.0950 mc^2.....0.5837 mc^2......0.2500 mo c^2
0.7.....0.1174 mc^2.....1.1293 mc^2.......0.4010 mo c^2
0.8.....0.1434 mc^2.....2.3905 mc^2......0.6670 mo c^2
0.9.....0.1680 mc^2.....6.6974 mc^2......1.2930 mo c^2
0.99...0.1906 mc^2....94.3948 m^c2.....6.9200 mo c^2
1……....0.1931 mc^2..........infinite....................infinite
www.trendsinphysics.info/
Why relativity works in some cases and fails in others ?
Like Newton's theory works for small speeds v
I think not anybody can have the talent to teach and make things understandable. You can have all the necessary knowledge but not the skills to teach as this guy does.
Everything you said in this video seems to make intuitive sense to me, which makes me think (since we're talking about quantum physics), that I don't understand it at all. But your derivation all seemed logical. If we assume that an electron is a wave (quantum physics), then we can apply the theory of diffraction (hard to understand, but I think that the theory of diffraction applied to light is purely classical physics, so the analysis of diffraction is only quantum because we are talking about diffracting electrons, and electrons are waves). I worked for several years as an antenna engineer, and I have a master's degree in antennas and electromagnetics. So, this "slit" to me seems kind of like an aperture, and if we are talking about waves getting through an aperture, I'm thinking we can proceed. Accepting that electrons are waves and not treating them as particles per se, I'm wondering if the math works out the same as if an electromagnetic wave was incident on piece of metal that had a hole in it (aperture or "slit"). Regarding uncertainty, of where the electron ends up on the screen behind the slit, wouldn't that be analogous to asking where the photon shows up on the screen behind the aperture (given my analogy of an EM wave being incident on an aperture)? I'm fine with uncertainty and probability, but I think I'm missing (or perhaps even disagreeing - how dare I!) the interpretation of uncertainty in quantum mechanics. (Let's say I'm misunderstanding, because I am not so obnoxious as to disagree with these intellectual giants, even though Einstein did). My lay understanding of the interpretation of uncertainty is not merely that we don't know, but that there is considerable weirdness going on too. Like, things don't exist if they are not observed? Or Schrodinger's cat is simultaneously dead and alive as long as he is not observed, but once observed, he is one or the other? To me, uncertainty simply means that we are ignorant to a degree. I get it that we can't observe anything without interacting with the thing (light reflecting off the thing and hitting our eyes, and the light hitting electrons are transferring energy and momentum to them, causing them to be photoelectrons). But again, that seems reasonable. And if it seems reasonable, I'm thinking that I'm missing something. What am I missing?
That actually makes sense! It means that there's no flaw to the matter as such that is behaving strange when being observed. The flaw is in our observing method! This is also probably true for the on the quantum level of matter. "The only way to observe the system is to change it"
I always have trouble with the last part of the section.
Ok so a photon hits the electron and changes its speed or direction or both, I get that.
But these interactions must still obey the conservation of momentum. So in principle if I knew what the momentum of the photon was, I could now calculate what the true momentum of the electron is.
So that is not uncertainty!
I think the true uncertainty is only due to the fact that, electrons are never just electrons, but are also waves!
FloatHeadPhysix Nope. You don't know what the momentum of the electron WAS, either. I agree with your last statement, though!
Doc Schuster Thanks for the reply doc :)
Here is what I am thinking. I dunno the initial momentum of electron.. say x
But I can in principle calculate the initial momentum of photon, and also final momentum of the photon. So final momentum of electron is y
So two variables. Use conservation of momentum and conservation of energy to solve them?
but then electron iscattered and you won't get to know where it actually is.
All i need to calculate is, the momentum of the electron before the collision and after the collision, and if you treat them as classical particles, you can in principle calculate them using classical conservation principle.
Its like this, suppose there is marble A heading somewhere, I really dunno where and at what speed it is heading, I will send my own marble (that is my photon), by finding out the speed at which it bounces back (and the angles and everything) I could calculate the initial and final momentum of that marble A
Why first write a "w" for the gap, then a "d" and then again a "w" for the same gap all the time. Very confusing!!!
You are correct. This is certainly a problem. However, my hand-wavey intro motivation (see - I'm not even going to call it a derivation) does not produce that other factor of 1/2. For this lecture, I'm just trying to introduce the IDEA of uncertainty, so I've continued in my sloppiness.
The enthusiasm at 8:01 made this video lol
thanks man, keep up your brilliant videos and i,m l looking forward for more . your videos are way cool and fun to watch
I have a few questions:
1. I've also seen the idea of uncertainty written as σ where sigma represents the standard deviation of a particle's position (or momentum). Can this be thought of as a standard deviation in the sense of a Gaussian probability distribution? If so, how is sigma determined?
2. I've always seen the Uncertainty Principle relate momentum/position to h-bar over two (or h/4pi). Are you describing something else here? Just a bit confused...
3. I've also read that the uncertainty in momentum is not caused by the actual observation of the particle's position but is actually an intrinsic part of its quantum nature. Are you sure about the idea of photons actually knocking an electron off-path? The way I see it, one could "measure" the position in several ways that do not involve a photon. For instance, the single slit "determines" the position without actually touching the electron at all.
Sorry to bombard you... just trying to make sense of things. Thanks!
I am always flabbergasted by Planck's constant and where it shows up.
Is that sin(x)~tan(x)~x, only valid for radians? I still haven't gotten to (but will) all of your videos.
It is only valid for small angles, as you should confirm by plotting sin(theta) vs theta, theta vs theta, and tan(theta) vs theta). For all of these, you can see that as long as theta is small, theta ~ sin(theta) ~ tan(theta).
Well played, Sir! It was the right time to attack, and I'm glad you did. They work from home, indeed.
I'll say a couple things, but your question is now beyond me - perhaps someone else can answer fully. It's the electron itself that is the wave in certain circumstances, and the circumstances depend on "what we're asking it" - but likely all experiments are in the vacuum (wave and particle). Nasty vacuum soup complications seem likely but short-lived, though. Other responses?
At the end, that was a great explanation of why you cannot know where the electron is if you know where it was. Wouldn't that mean that as the electron is traveling in space it is not giving off photons? In other words there is no way of seeing the electron passively. It is not transmitting any readable energy that we can receive?
🤣🤣i like the jokes, Keep it up Doc. How are you doing? Very informative and precise
Beautiful hands, great explanation. Thank you Doc.
It's 4π instead of 2π , nice video
In think 2π for this 2 dimensional problem, 4π for 3 dimensional....no?
@@jeffreygrotts4341 nope
Well explained in an interesting way. Thanks Sir!
Okay, okay. So, in the last couple of years, I learned about the Casimir effect which comes from empty space being awash in a sea of virtual particles that are continuously flowing, everywhere, even within the very protons that make up the nuclei of the atoms that make us. It is a virtual ether, if you please. So, what is the relationship between the double-slit experiment, particles acting like waves, and the Casimir effect? "Certainly," there is a relationship, n'est pas?
ty for this very very very very awesome information! I LEARNED A LOT FROM YOU! :) tyvm!
superb content
I do understand that this video was a much simplified version of the derivation of the uncertainty principle, but shouldn't we use dsin(theta)=(lamda)/2 in this case, since the waves are interfering destructively? that would also give a better approximation! but where does the pie come from....
Nice video except for the end. Yes, the observation principle is the result of some of the uncertainty principle, but many interpretations of quantum mechanics say that this isn't just the observation principle, but wave-particle dynamics itself.
So, while the observer effect is nice to demonstrate to people why they should believe in the uncertainty principle, the converse is actually the reality...
+puellanivis Perhaps I could have been more clear in saying that.
+Doc Schuster I'm not sure how... it's one of those sticky points where two effects converge to the same result... it definitely helps to introduce the concept, as it gives a more intuitive model to most people's brains...
but in the end the Uncertainty principle still applies even in a perfect theoretical model where we could know absolute position and momentum at the same time... and that's why it's considered a deeper effect than just the observer effect.
It's more one of those things where when one is in the know, one says "hey, that's not it!" But then you realize that if it isn't mentioned, some people will have difficulty understanding the concept in the first place. >_
Starting with a full classical point of view (i mean with a classical wave description phenomena of diffraction) and then introducing in it the particule wave duality (De Broglie equation) seems to me as keeping to think classic instead of changing radically the way of thinking. QM is a revolution of the way of thinking physics, not just an evolution.
The derivation is based on the weak magnitude of theta...that leads to the fact that the Heisenberg Principle would be wrong for bigger values...
first time saw such an amazing approach To HEISENBERG 'S UNCERTAINTY PRINCIPLE
really a wonderful work
Wish
ohohoh 🤣😊😝😏😏😏😏😏😜😏😏😊😊😊😊😊😊😊😊
How did you plug 2π in the equation?
Depending on the book you use h-bar is equal to h divided by 2pi or h divided by 4pi.
Shouldn't we find an other way observing particles? Which can avoid observation affecting position or momentum. Seems like a constraint in our knowledge of what exactly is happening at that scale.
what is the reason for division with 2 pi?????
flame on my friend, flame on. great video btw.
Okay, so first my snarky response (gotta do it): If time and energy don't commute, does that mean they're unemployed or do they work from home? Now, seriously, with this Casimir thing, if you've got a photon (or electron, or whatever) passing through a vacuum that's bubbling with these virtual particles, won't some sort of shock wave occur, and could that be the wave effect that we see with the double slit experiment? (I'm a physics dullard; so, please be kind!)
Can you make a video about Quantum Foam??
thats brilliant!!! thank you :)
Sheldon?
hey , most smart guys like me are not cool, im a nerdy guy but you , dude youre awesome and smart at the same time ,youre an inspiration to nerds
Dilrukshi Perera I think nerds are way cooler than people who don't care to understand things. Like - hands down - way cooler. Keep it up.
You're so modest, Dilrukshi.
OMG u r so xlever thnx this video taught me so much
Is this a measurement problem or a physical property of things?
Excellent question. The latter. Or rather - a property of the universe. When some things are known, others cannot be. Whoa.
Thanks for your reply. My personal story is that the universe is all energy. What we call "mass" is a preception of that energy when it "has to" define it's state. Would that be a fair description?
Hmmm. Mass is certainly energy. But energy can also define its state in other forms. Matter could be thought of as condensed or packaged energy, I guess.
The present work shows the inapplicability of the Pauli principle to chemical bond, and a new theoretical model of the chemical bond is proposed based on the Heisenberg uncertainty principle.
Review. Benzene on the Basis of the Three-Electron Bond. See pp. 88 - 104. vixra.org/pdf/1710.0326v1.pdf
The Pauli exclusion principle and the chemical bond.
The Pauli exclusion principle - this is the fundamental principle of quantum mechanics, which asserts that two or more identical fermions (particles with half-integral spin) can not simultaneously be in the same quantum state.
Wolfgang Pauli, a Swiss theoretical physicist, formulated this principle in 1925 [1]. In chemistry exactly Pauli exclusion principle often considered as a ban on the existence of three-electron bonds with a multiplicity of 1.5, but it can be shown that Pauli exclusion principle does not prohibit the existence of three-electron bonds. To do this, analyze the Pauli exclusion principle in more detail.
According to Pauli exclusion principle in a system consisting of identical fermions, two (or more) particles can not be in the same states [2]. The corresponding formulas of the wave functions and the determinant are given in the reference (this is a standard consideration of the fermion system), but we will concentrate our attention on the derivation: "... Of course, in this formulation, Pauli exclusion principle can only be applied to systems of weakly interacting particles, when one can speak (at least approximately on the states of individual particles) "[2]. That is, Pauli exclusion principle can only be applied to weakly interacting particles, when one can talk about the states of individual particles.
But if we recall that any classical chemical bond is formed between two nuclei (this is a fundamental difference from atomic orbitals), which somehow "pull" the electrons one upon another, it is logical to assume that in the formation of a chemical bond, the electrons can no longer be regarded as weakly interacting particles . This assumption is confirmed by the earlier introduced notion of a chemical bond as a separate semi-virtual particle (natural component of the particle "parts" can not be weakly interacting).
Representations of the chemical bond given in the chapter "The Principle of Heisenberg's Uncertainty and the Chemical Bond" categorically reject the statements about the chemical bond as a system of weakly interacting electrons. On the contrary, it follows from the above description that in the chemical bond, the electrons "lose" their individuality and "occupy" the entire chemical bond, that is, the electrons in the chemical bond "interact as much as possible", which directly indicates the inapplicability of the Pauli exclusion principle to the chemical bond. Moreover, the quantum-mechanical uncertainty in momentum and coordinate, in fact, strictly indicates that in the chemical bond, electrons are a system of "maximally" strongly interacting particles, and the whole chemical bond is a separate particle in which there is no place for the notion of an "individual" electron, its velocity, coordinate, energy, etc., description. This is fundamentally not true. The chemical bond is a separate particle, called us "semi-virtual particle", it is a composite particle that consists of individual electrons (strongly interacting), and spatially located between the nuclei.
Thus, the introduction of a three-electron bond with a multiplicity of 1.5 is justified from the chemical point of view (simply explains the structure of the benzene molecule, aromaticity, the structure of organic and inorganic substances, etc.) is confirmed by the Pauli exclusion principle and the logical assumption of a chemical bond as system of strongly interacting particles (actually a separate semi-virtual particle), and as a consequence the inapplicability of the Pauli exclusion principle to a chemical bond.
Heisenberg's uncertainty principle and chemical bond.
For further analysis of chemical bond, let us consider the Compton wavelength of an electron:
λc.е. = h/(m*c)= 2.4263 * 10^(-12) m
The Compton wavelength of an electron is equivalent to the wavelength of a photon whose energy is equal to the rest energy of the electron itself (the standard conclusion is given below):
λ = h/(m*v), E = h*γ, E = me*c^2, c = γ*λ, γ = c/λ
E = h*γ, E = h*(c/λ) = me*c^2, λc.е. = h/(m*c)
where λ is the Louis de Broglie wavelength, me is the mass of the electron, c, γ is the speed and frequency of light, and h is the Planck constant.
It is more interesting to consider what happens to an electron in a region with linear dimensions smaller than the Compton wavelength of an electron. According to Heisenberg uncertainty in this area, we have a quantum mechanical uncertainty in the momentum of at least m*c and a quantum mechanical uncertainty in the energy of at least me*c^2 :
Δp ≥ mе*c and ΔE ≥ me*c^2
which is sufficient for the production of virtual electron-positron pairs. Therefore, in such a region the electron can no longer be regarded as a "point object", since it (an electron) spends part of its time in the state "electron + pair (positron + electron)". As a result of the above, an electron at distances smaller than the Compton length is a system with an infinite number of degrees of freedom and its interaction should be described within the framework of quantum field theory. Most importantly, the transition to the intermediate state "electron + pair (positron + electron)" carried per time ~ λc.е./c
Δt = λc.е./c = 2.4263*10^(-12)/(3*10^8) = 8.1*10^(-20) s
Now we will try to use all the above-mentioned to describe the chemical bond using Einstein's theory of relativity and Heisenberg's uncertainty principle. To do this, let's make one assumption: suppose that the wavelength of an electron on a Bohr orbit (the hydrogen atom) is the same Compton wavelength of an electron, but in another frame of reference, and as a result there is a 137-times greater Compton wavelength (due to the effects of relativity theory):
λc.е. = h/(m*c) = 2.4263*10^(-12) m λb. = h/(m*v)= 2*π*R = 3.31*10^(-10) m
λb./λc.е.= 137 where R= 0.527 Å, the Bohr radius.
Since the De Broglie wavelength in a hydrogen atom (according to Bohr) is 137 times larger than the Compton wavelength of an electron, it is quite logical to assume that the energy interactions will be 137 times weaker (the longer the photon wavelength, the lower the frequency, and hence the energy ). We note that 1 / 137.036 is a fine structure constant, the fundamental physical constant characterizing the force of electromagnetic interaction was introduced into science in 1916 year by the German physicist Arnold Sommerfeld as a measure of relativistic corrections in describing atomic spectra within the framework of the model of the N. Bohr atom.
To describe the chemical bond, we use the Heisenberg uncertainty principle:
Δx*Δp ≥ ћ/2
Given the weakening of the energy interaction 137 times, the Heisenberg uncertainty principle can be written in the form:
Δx*Δp ≥ (ћ*137)/2
According to the last equation, the quantum mechanical uncertainty in the momentum of an electron in a chemical bond must be at least me * c, and the quantum mechanical uncertainty in the energy is not less than me * c ^ 2, which should also be sufficient for the production of virtual electron-positron pairs.
Therefore, in the field of chemical bonding, in this case, an electron can not be regarded as a "point object", since it (an electron) will spend part of its time in the state "electron + pair (positron + electron)", and therefore its interaction should be described in the framework of quantum field theory.
This approach makes it possible to explain how, in the case of many-electron chemical bonds (two-electron, three-electron, etc.), repulsion between electrons is overcome: since the chemical bond is actually a "boiling mass" of electrons and positrons, virtual positrons "help" overcome the repulsion between electrons. This approach assumes that the chemical bond is in fact a closed spatial bag (a potential well in the energy sense), in which "boiling" of real electrons and also virtual positrons and electrons occurs, and the "volume" of this potential bag is actually a "volume" of chemical bond and also the spatial measure of the quantum-mechanical uncertainty in the position of the electron.
Strictly speaking, with such a consideration, the electron no longer has a certain energy, momentum, coordinates, and is no longer a "point particle", but actually takes up the "whole volume" of chemical bonding. It can be argued that in the chemical bond a single electron is depersonalized and loses its individuality, in fact it does not exist, but there is a "boiling mass" of real electrons and virtual positrons and electrons that by fluctuate change each other. That is, the chemical bond is actually a separate particle, as already mentioned, a semi-virtual particle. Moreover, this approach can be extended to the structure of elementary particles such as an electron or a positron: an elementary particle in this consideration is a fluctuating vacuum closed in a certain spatial bag, which is a potential well for these fluctuations.
It is especially worth noting that in this consideration, electrons are strongly interacting particles, and therefore the Pauli principle is not applicable to chemical bond (for more details, see the section "The Pauli Principle and the Chemical Bond") and does not prohibit the existence of the same three-electron bonds with a multiplicity of 1.5.
See pp. 88 - 104 Review. Benzene on the Basis of the Three-Electron Bond. (The Pauli exclusion principle, Heisenberg's uncertainty principle and chemical bond). vixra.org/pdf/1710.0326v1.pdf
Bezverkhniy (viXra): vixra.org/author/bezverkhniy_volodymyr_dmytrovych
reminds me of Zeno's arrow. knowing its position mean not knowing its speed. knowing its speed is not knowing its position
Why is h divided by 2Π when some textbook say it is h divided by 4Π?
Hi, just wondered what if you fired 2 photons from opposite directions at the electron could you observe it without moving it if the collisions were equal and opposite?
Interesting , can top this question ?
But if photons are massless, how does the electron being observed feel a force acting upon it to get deflected?
My question is:why is there an uncertainty, eg~take a billiard ball (m=1kg)initially at rest and enclose it with a object so that it acquire δχ (say 0.5m)and then take h/4π to be equal to one(imagine) . You get INDUCED velocity of 2m/s . What????
Shreyansh P Singh Thats wrong , first of all h/4pi is very small than 1 .
Then what you did is multiplied the momentum with x and equated this with 1 .that gave you v=2. But the formula isnt that. The formula is uncertainty in momentum*uncertainty of position=h/4pi
So you don't know the uncertainty of momentum and position and you are trying to find out velocity .
Say both were given , then you would be able to apply it and get the correct velocity.
This principle works for everything.
It's counter intuitive because we can't observe it in our daily life. The catch is that when we plug in the values from something of macroscopic scale say that ball , the uncertainty comes out to be very very small. That's why we are certain .
But when we apply this to principle to particles which are very small like consider a electron orbiting a nucleus , the uncertainty comes out to be big.
Say we are certain of the position of an electron , the uncertainty of its position will be small. This equation is framed in such way that the the smaller the uncertainty of position , the greater the uncertainty of momentum and vice versa. So in our case the momentum of the electron will be relatively much more uncertain .
Lol this reply is late , so this maybe of no use to you now .
Why does the 2pi (should be 4pi) come from though?
I am the student of physics 2nd year and in my slabus there is no rigrouse derivation of this principle and no any teacher tought me the quantum physics because this subject will come in final year so it is good to me to go with this derivation or not ???
My friend, excellent question. You need my video "Light has Momentum and Kinetic Energy but no Rest Mass." It will cause your brain to explode. Bring a towel.
So, uncertainly principle means uncertainly of everything, that you know nothing or it means uncertainly of one thing, so it would be accurate to say relative uncertainly principle, but not absolutely, since we can know the size, the motion of that size, and the impact of that size to result. So, 1 + 2 = 3. So, we are certainly of bigger size, but at smaller size, we are not uncertainly, right? Higher energy or higher density of something, the more certainly we are, the smaller energy or lower density, the uncertainly we are, so smaller density that is below what we can see at most least, so thru microscope. So, the light that hit at certain slit size, it hits the resist of depth size that is between resist and slit size that is first layer. So, the smaller the slit and does depth size matter or not? So, it creases wider wave length and wider vertical gap of wave length, so there is zero resist thru the gap, so the energy impact to resist is higher, so it produces certain size wave length. So, if the slit size is smaller, and the impact of same light and impact of result to resist wall, so both of wall and gap size is same depth size. So, ya know the summary of uncertainly principle?? The bigger slit, bigger depth and higher resist of wall, will product how far the wide of wave length, I am sure it is not always uncertainly but can be explain by what kind of mass since everything is mass. So, the smaller the energy is and the uncertainly it will be, like I look at light that hit something, it will not show light and dark gap, but different kind, so the eye has energy give out that impact smallest energy which it becomes resist that cause motion or cancel out, so it depends on wave and series of standing wave impact.
After getting good grade in college physics, I realized there were too many angry classmates to continuing studying it.
It was fun to study and play with electronics. I could have build many toys by now.
UnitedPebbles That's a terrible story! Why were they angry?
#Doc_Schuster
so what do you think about the cause*( actually) of the change in direction of P here.
by compton's effect we can think of p of photon causes the change in direction of p of electron while taking the measurement, BUT HERE, we are not hitting the electrons by anything, that's then why it's here? ... one can think of this as natural uncertainty! i think so.
why did you said that there is only one wave in d*sin theta? why not 2, or 3, or "n"? i mean, that must be something related to bragg's law, right?
You're saying, photons traveling through a dust cloud in space (dual-slit & single-slit) diffuse?? Is this why space is dark?
omg g= god + xness x is o ,2 places to the left of n.
It stuck delta is uncertainty ... not change in
There’s probably about a half dozen other very relevant considerations that can explain the weird results obtained in this experiment, none of which are mentioned. That’s the all-important thing about not knowing the precise terms and conditions that the experiment was performed under. If there’s one thing I’ve learned through my decades of performing experiments in the laboratory, “if it don’t look right, it probably ain’t”. Go back and take a much closer look at what you did. Take a much, much closer look at what you did and what assumptions you made.
thanks .why not change in mumentum in x-direction
Isnt it h/4pi for heisenberg principle?
The speed is a function of "two" positions Of course you can't know the "one" position and the "two" positions at the same time What's the big deal with the "uncertainty" ?????
Just a question, how can he relate the sine of the angle as a ratio of the wavelength and the width of the slit @6:19
On my to-do, but never get done list, has been to drag myself up to the local University and have a conversation with one of the physics professors, there. I know what you're saying about these tiny particles acting as both wave and particle, depending on how they are detected, Still after hearing about this Casimir effect, I cannot help but to think that the wave that's expressed comes from those virtual particles, somehow. It's been bugging me for a while (damn that Brian Greene!).
Where did the 2Pi come from?
Why is it sometimes h/4pi?
Hey Doc Schuster, I'm 16 and I have a question concerning this 'derivation'. I do know that this isn't a proper derivation of the heisenberg uncertainty principle,but why? I mean, what didn't you take in consideration in this experiment. What would you need to consider to derive the real Uncertainty Principle? Thank you for your time :)
ps: sorry if my question isn't clear
scott gendy Not annoying at all! You should just look up a full derivation, though.
12:19 - 12:35 lmaooo this part is so sick xDD
I noticed you wrote the equation incorrectly. It should read "h-bar" divided by 2.
and in my book, it says that Dx*Dp>(reduced Planck constant)/2
Hi you don't explain why sin theta is equal to wavelength over w
Everything was great Dr except for h/4π and the last explanation which you gave related to Compton and measurements. It seems that the last explanation is incorrect because According to it HUP is arising due to our tendency to measure things. This is contradictory to the fact that HUP always exists and is an Intrinsic property.
Can someone tell me where the pi comes from
What is darke fringe? Do you have some other word for that? Thank you :)
Who said that Physics is no fun...thanks!
4:05 what is d?
Sky L Distance or width of the slit
Really i didn't get that portion where u tell that sin( theta)=lamda/w...how did u get that...although u got the real cincept behind h.u theory u have not done a proper explanation..its quiet confusing..
From where u get 2 pie