Your Daily Equation #23: Deriving Classical from Quantum Physics: Ehrenfest's Theorem
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- Опубліковано 10 чер 2024
- Episode 23 #YourDailyEquation: Classical and Quantum Physics describe reality in completely different ways. Yet, in 1927, Paul Ehrenfest showed how Newton's equation could be derived from Schrödinger's, establishing a deep continuity in our understanding of the physical universe. Join Brian Greene for a brief explanation of Ehrenfest's essential idea as well as the mathematical manipulations he required to realize it.
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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I don't even understand simple algebra and yet I'm here, just because of professor Greene. He is so articulated makes you think you know what he is talking about 😁.
Same here, but its so interesting I want to change career path!
@Arindam kar 😂
@@andreasmichaeliides7754 this is a good start by listening to professor Greene. I have no doubt you'll do what's best for you. 👍
He usually does, and he often admits when he doesn't, as oppose to a lot of science pundits here on youtube.
@@nihlify he is a great professor. 👏
These are such wonderful sessions! For those who follow the mathematics, it's a dream. For those who don't follow the math, Dr. Greene provides enough simple, every day type of explanation to allow a person to enjoy the sheer beauty of the phenomenon in question. Thank you Dr. Greene.
Professor Greene, as a physician who loves physics and tries to learn maths to progress in understanding your field I cannot overstate how valuable this initiative of yours is to me. Thank you so much.
Thanks for this refresher! It’s been several years since I’ve been in a QM class. This certainly was a clear explanation, thanks!
Thank you professor for your videos. please make an episode on Neother's theorem.
Another awesome depiction of physical equations! Thank you for that, Dr. Greene. When will you do an episode of Maxwell's equations? Eagerly waiting for it.
What an episode!
Best Explanation I have ever seen about transition from quantum mechanics to classical mechanics and vice versa.
Thanks you so much Prof Brain.
Reminds me of Kuhn's Logic Of Scientific Revolutions. I did not know about Ehrenfest's equations that blend two theories into each other. Beautiful. Thanks again prof Greene for another episode well worth the time!
Thanks you very much!
Thank you what a great part of the day!
I love the mathematical visualisation for quantum mechanics
I wish I could do that, I really wish I had some sort of visualization of calculus and quantum mechanics..........but I get lost not so much because of the quantum mechanical equation as a wave, but because of the integration and derivation.
Excellent videos and explanations professor Greene, I really enjoy them! You could also speak about the Boltzmann equation of entropy and the connection between information theory and thermodynamics. Thank you very much!
Thank you for the math part💖.
Great series. I'm really enjoying these little tidbits that seem to cover all of physics.
One thing about when you need quantum physics vs. Newtonian physics vs. General Relativity. It isn't just whether something is very small or very fast or really big. It also is how accurate you need to be. That's why GPS uses General Relativity. It's accurate enough that the small effect of acceleration during its orbit effects the position accuracy.
It also uses Special Relativity.
I sleep very well by watching this series. But when I am awake i like it.
All this is way over my head but I enjoy listening to him anyway.
You have to know basic calculus and linear algebra ... U can do it!!
Wonderful presentations, many thanks.
Thank you, I remarked that you forget the ih bar while replacing the derivate of psi in the the first derivation of . Thank you very much it was correct in the other calculations..
Thank you! This was clear. Two questions: (1) does this derivation directly relate to Dirac's Density Matrix representation collapsing to a diagonal matrix? (2) is this derivation independent of QM interpretation, so that it is equally true in Bohmian mechanics?
This is so awesome! I barely follow the math but the concept that comes out of it is beautiful! Take a very large number of particles each with a probability wave and combine them into the atoms and molecules that are a rock and all those probabilities average to a spike and that spike can be described by classical mechanics. Its as if i am a casino with a million slot machines .. I dont know what the win / loss ratio will be at a single machine but I can definitely calculate what my win / loss ratio will be across ALL of those machines. fantastic!
so your taking slices of the system and expressing where you find the slices most probabilisticly most often and building the model off the fluctuation slices. that's pretty cool.
It would be cool to see the geodesic equation from GR being derived from the classical limit of relativistic QM
Thanks again Prof. Greene, but this time, I must admit, is the first Daily Equation where I have felt really left behind. Probably due to the fact that I never learnt Calculus. I love Physics, but my Maths is not quite up to the task I'm afraid. Also, being in the UK, I always get to watch Your Daily Equation the following morning. Not that that makes any difference. I still look forward to watching each episode - at least once. Maybe Prof. Greene, you could do a basic Calculus lesson one day. Thanks and All the Best.
Prof. Greene I guess you overlooked one subtle detail for the sake of simplicity:
one doesn't really recover classical mechanics just by using peaked wave funcion (in position space).
Doing that, the particle will have a definite position indeed, but its momentum will have many different possible values (all of them in fact).
In order to achieve the classical limit, one would probably need to use wave functions that are (like before) non vanishing in a small region, but heavily oscillating there as well, rather than just peaked. Am I right?
Thank you
@Emanuele Binetti In classical mechanics we measure an object at a time t as being at a particular position AND as having a specific momentum (and acceleration). So I can't agree with your "heavily oscillating" conjecture. It seems to me that as we move toward the classical regime, we can have a sharp peak for the position AND the momentum. I'm not sure I answered your question, but I don't think the answer is so strange. In classical mechanics, there is no nonlocality, and no problem in measuring position and momentum accurately at the same time (no Heisenberg uncertainty).
Professor greene,thank you for this wonderful series named your daily equation. I want to know if your lectures are available on YT till now?
Please make more videos on quantum mechanics
Ok this lockdown needs to end. I actually sat through this entire video and have no idea what the hell he was taking about but was completely fascinated with it. Now I'm seriously reconsidering taking some online physics courses.
Why did you remove your explanation of the pilot wave theory?
If you did have an explanation of the Pilot Wave Interpretation, I hope you didn't stop at de Broglie but went on at least to 1952 with David Bohm. That interpretation doesn't require Born's probability axiom or wave function collapse on measurement, and it isolates nonlocality in the "guidance equation", part of Schrodinger's equation; the path of a particle is deterministic.
Wonderful talk! Could you please say something about quark confinement?? If quark s are confined does this mean the quark field is zero outside of nucleons? Is there enough energy in the vacuum for quark - anti quark pair production? Thanks
Dr. Greene, could you cover the Bekenstein Bound? (and possibly the implications for a holographic theory)
It's really odd, I love this subject these days but hated it at school.
It wasn't well taught, that's why, I believe 😊.
Erwin with his Psi can do
calculations quite a few
But one thing yet to be seen
is what wave functions really mean
Daily equation #24 comes through as “private”. What can I do?
Do String Theory ! Zwiebach wrote a good introduction to it which could be used.
Quantum mechanics is general and classical is special. Principle of correspondence tell us a so some point quantum results parallel with classical ones.
How are the superconducting coil charges time calibrated for proton acceleration in the LHC to compensate for position estimation over distance to achieve near 'C' speeds if the position, acceleration and momentum is considered probabilistic?
Sir it will be very useful if you can do a video on electricity, electrical circuit, and power
Professor Greene, would it not be right to think of classical physics as physics that considers matter and energy relative to spacetime (the fabric of space), while quantum physics considers matter and energy relative to the bacground vacuum and therefore it takes into account spacetime. Consequently, math of the former is only an approximation of the latter, which is taken as a special case only at large scale, so that the larger the scale the better the approximation. It is like when in classical physics one neglects or takes into acoount the effect of the medium through which an object is falling under gravity. Many thanks
When I studied QM many years ago I remembered I was frustrated over "Where the h.ll did the ScHrödinger Equation come from?" It was just stated as an axiom. Full stop. After a while the frustration went away and when we were taught that the Ehrenfest Theorem could be derived from the SHE it was clear that the SHE in one way or other were anchored in reality. After todays Video I looked up the Ehrenfest Theorem on wiki and saw that the SHE can be derived from the Ehrenfest Theorem! Wow! Finally an answer. So my question is: Is the Ehrenfest Theorem more fundamental than the SHE? and is Paul E the real "hero" here?
Are there any QM equations that have been derived that deal with non-ideal situations in Classical Mechanics like friction losses (linear motion, rotational, fluid mechanics, etc)? What would the Least Action principle look like if friction were added to the particle motion?
The principle of stationary action cannot be applied to such cases because it deals with non-conservative forces i.e these forces are dependent on the path you take.
Awesome! Thank you SIR for showing de Bohm (de Broglie, et al.)
It seems "weird" that the Schrodinger Equation (SE) takes derivatives with respect to time (especially since there's also distance). Relativity seems to put space and time on similar footing. Are there different versions of the SE where the derivatives are with respect to some other variable?
The issue you bring up here is exactly one of the reasons why Quantum Field Theory was developed. Since in Quantum mechanics time is treated as a parameter and position is treated as an operator, but then in special relativity as you say they are treated as a 4-vector on equal footing. So in this sense yes they are incompatible, which is where QFT comes in to unify them.
@@stephanpotgieter3236 thank you for the response and for clarifying, what I was meaning to say, with a better description: the time-space 4-vector, operators, and parameters. I have much to learn :_)
Great to listed to you and is a motivation.
If Heizenberg realized that he go beyond, had equipment to measure without intruducing engergy, a super computer and a great programmer team, could he had a chance to take clear images at points of a wave where the heavy and inertia mass at its peak is likely to form a focal point of mass, or will they still be blurred due it rotation and natural resonance of the particle, or could he only watch a fussy cloud of clustering energy at this regions of a wave? If Heizenberg realized that he go beyond, had equipment, a super computer and a great programmer team, could he had a chance to take clear images at points of a wave where the heavy and inertia mass is likely to form a focal point of mass, or will they still be blurred due it rotation and natural resonance of the particle, or could he only watch a fussy cloud of clustering energy at this regions of a wave?
I love all these things, what a nerd I am :-)
This is interesting but how does it apply to fluid mechanics in closed loop piped systems. Darcy equation and assuming pressure is applied like a wave and assuming friction is say 'anti visocity'
*IS THERE ANY POSSIBLE WAY TO UNDERSTAND INTEGRATION INTUITIVELY?* I can understand algebra, geometry, trigonometry, topology in SOME sort of intuitive way, but Calculus.......forget it. I get lost instantly and what is worse........is that I have no intuition about what the integration is even doing. Is there ANYTHING AT ALL that I can do to have a better understanding?
I'm right there with ya on that! A lot of these videos just hit you with "well, you just take the third order derivative and get (insert Charlie Brown's teacher's voice)". Checkout the 3Blue1Brown channel. He has a good series of videos on calculus that are fairly east to keep up with. The key thing is he uses a lot of great graphical illustrations to get the main points across without getting you lost in the notation.
What a wonderful physics professor! Captivated by these talks. Just being pedantic, the derivation at 23:36 is not 100% accurate because a factor of 2 was missing. 2*1/(2m) ...= 1/m....
Sir where is Your Daily Equation #24?
I can't find it
What kind of beings (as in intelligent 'minds') would they have to be to develop qm before cm? Their sensorium would have to exclude macroscopic observations. So they also would have to be immobile within their reference frame. They must have concepts of time, some sort of space-like dimensions and energy. I wonder what kind of math they would discover/invent.
As a layman, I've long been wondering if a way of thinking might be possible where fundamental qm and astrophysical principles are derived and explained easily and naturally (say, like basic trigonometry is to our world view). Kind of a bottom-up derivation of mathematics and physics. Perhaps at the cost of making it harder to describe what is classical to us.
A rock hits the water at a lake...and the ripples of the wave propagate...does It matter how fast the rock hits the water?will it make a faster wave propagation?now imagine that in vaccum will the wave be proportional to the mass that causes gravity?or will the value of gravity effect the vaccum in a different manner?
Do not try to bend the vacuum. That is impossible. Instead only try to realize the truth.
There is no vacuum.
Not faster, that is a function of the medium, in this case water. You will increase the amplitude of the wave.
If Gravity is emergent and related to entropy can it be ‘modified’?
Would it be theoretically possible to generate so called negative gravity? For example could this be done by creating a space of extremely high entropy where matter has been transformed into completely random sub nuclear ‘particles’ or ‘strings’ similar to perhaps the makeup of ‘dark energy’?
This could be the basis of an anti gravity vehicle.
Wow
Ehrenfest Yaegar!
Safadi from Syria ,Sir QM and QFT are crucial for comprehending faith ,Angels and Lucifer could be verified only through these theories .
I hope between what yourself and Sean Carroll are doing during Lockdown that you inspire the Physicists / Mathematicians of the Future.
I am a bit long in the tooth to get all that ye are saying but thanks anyway.
Have you had time to have a look at what Stephen Wolfram is doing re; Physics at the Moment ?
As a philosopher who stumbled upon this theorem... I think it’s safe to say I’m out of my element 😂 well played physicists, when you need justification, I’ll be here waiting
Re; The measurement of the particle not being at the same place after the same duration of time perhaps that duration of time is not actually the same length even though to us it appears to be. Perhaps time is remarkably pliable in quantum mechanics and we humans just don’t understand that.
That's not it, particle not displaying the same position every time you measure it, happens even if the wavefunction you are collapsing doesn't change in time. These kind of wave function exists and are called energy eigenstates: they usually don't have a definite position.
Undulation is the word that came to mind because of the position being variable. Now with consideration of inertia then the undulation causes the impact with the variable of the torque? Maybe? Ha
Probability is connected to observational entanglement. So if u throw a baseball, the world will seem classical because of the entangled properties of the next moment with you as the observer. If you broke the link, the ball could theoretically disappear as if it was never thrown. The paranormal works this way as well. The mind is an entanglement device that moves btwn universes. In fact, all life, on an individual level, is moving btwn different universes that have slightly different histories connected to the present evolution. It’s what we don’t see that gives rise to an alternate history. To us, it’ll just always appear as if it was there all this time. It wasn’t. What we discover tomorrow might not exist today. But tomorrow, it might have existed for years.
14:10 Seems like quantum physics produces classical physics. Is quantum mechanics classical in the sense of time and spatial dilation?
I've always believed we as individuals reach a level of maths we can do, only to hit a brick wall.
Hi from Greece.Your session was great. Still you did not answer the question of when one needs to take relativity or quantum mechanics into account.
As I understand it what matters is how accurate ones calculation's must be depending on the problem one is trying to solve. Newtonian physics are accurate enough to send a rocket to the moon but inaccurate when trying to explain the precession of the perihelion of Mercury.
Exactly.
Got to say, there is something pretty sexy about Brian
Imagine a field of wheat. The wind blows through it, forming ripples of waves. Or what appear like waves. The wind of course is the energy, there is not a wave of energy traveling through the field. There are no wavelike properties within the wheat being expressed, no interference patterns. The tips of wheat are just what we see. If two swirls of wind cancel each other out, we see the result in the wheat. Doesn't the double-slit experiment show light to be like this? The photons are what we see, or the pattern they make on the screen anyway. Or maybe I should stick to creepypastas!
Brian, not a big deal, but your '2' and you partial derivative symbol look the same :)
What’s your name
Anyone else watching this series at 1.5x speed? 😂
So he doesn't really give a practical answer to the question of, at what scales do you really need to invoke relativity or quantum mechanics to get accurate answers, does he? It's a practical question that is asked because it deserves a practical answer. But there isn't one because it depends on how the results will be used (e.g. GPS needs SR, moonshots don't).
Of course he knows the practical answer: whenever the physical dimensions of the system you are considering are close to Plank's constant (quantum mechanics) or to the speed of light (special relativity).
Basically in these situations you can't use classical mechanics, whose formulae are (in a way) those of QM and SR as if, planck's constant is zero and the speed of light is infinite, and that's no longer a good approximation in the scenario I showed you.
Does anyone else feel like Brian looks like a deep fake?
No.
andrewwhaddad I don’t.
No. Are you?
how many students of class 9th are here comment😎😎
Ah, I don't like quantum mechanics so far. Seems warped, no wonder Eisenstein did not like it. Gut feeling of a neophyte. Ha