This is very useful. I sense he's taking a sort of plodding, thorough approach here, but I'm getting good out of it. I've read so many treatments of this stuff, but in some sense they're all the same treatment, and they breeze through it all on the way to getting to whatever they're really interested in. Nice to have someone really beat these bushes. Thanks, Dr. Zwiebach!
@@KipIngram yes only as Henri Bacry points out - the de Broglie Law of Phase Harmony is actually noncommutative. I just did a vid upload on it ruclips.net/video/1m38Asft-fw/видео.html thanks
The Galilean transformation is a crucial concept in classical mechanics that helps describe how the observations of an event differ for observers in different inertial frames. When applied to ordinary waves, such as sound or water waves, the Galilean transformation allows us to understand how the properties of these waves, like frequency and wavelength, change when viewed from moving reference frames. Under the Galilean transformation, the velocity of a wave is affected by the motion of the observer. For example, if you have a sound wave traveling at speed \(c\) in a stationary medium, and you observe it from a frame that is moving with speed \(v\) relative to the medium, the observed speed \(c'\) of the wave will be the sum or difference of these speeds, depending on the direction of motion. Thus, if you're moving in the same direction as the wave, you would perceive the wave traveling at \(c' = c - v\), while if you're moving against the wave, you'd perceive it at \(c' = c + v\). However, it's important to note that the Galilean transformation assumes low speeds compared to the speed of light and is not applicable in situations involving relativistic effects. This means that while it provides an intuitive understanding of wave behavior in classical contexts, one must be cautious when considering scenarios involving electromagnetic waves or high-speed phenomena where the principles of special relativity take precedence. In conclusion, the Galilean transformation elegantly illustrates how the speed and other properties of ordinary waves depend on the relative motion of the observer, reinforcing the key idea that measurements in physics are dependent on the frame of reference from which they are made.
Viewing from different frames of motion, the amplitudes of the waves at any point at any time are measured to be the same. Therefore the phases are the same too.
No matter you and your friend are in different frames (at low velocities) if two pedulams are in phases both of you will agree that these pendulums are indeed in same phase
Why should both agree upon instantaneous amplitude when speed of wave is altered by angular frequency. Second thing, what phase contribute in measurement, specially time part of phase. So it doesnt depend upon temporal part so much.
Because no matter where you take a measurement from, the result is a real result, so even in a different reference frame, two people would have to measure something that is consistent with one another. Real stuff can't physically be in two places at the same time, for example
1. prof states that "matter wave", which is characterized by its de Broglie's wavelength \lambda, is a kind of WAVE FUNCTION. 2. prof shows that de Broglie's wavelength is NOT Galilean invariant. 3. then he shows that the wavelength of ORDINARY WAVE must be Galilean invariant. 4. thus the wave function, which by definition has a de Broglie's wavelength, need not to be Galilean invariant and that leads to the statement in ur question.
ZiPan Huo Basically this statement was based on the conclusion from the previous lecture "the two de Broglie wavelengths don't agree." The professor was trying to show or proof us that the de Broglie wave is not an ordinary wave, in lecture 4.1 and 4.2. To proof this, the logic is: 1. Assume de Broglie wave is ordinary wave in both lecture 4.1 and 4.2, so that it follows Galilean Invariant. 2. In lecture 4.1 he showed us that by using Galilean Transformation, the de Broglie wavelengths were not invariant. 3. In lecture 4.2 he showed us by phase analysis under Galilean Transformation, the de Broglie wavelengths were the same. 4. The conclusions from 2 and 3 are logically contradict, so that our assumption is a fallacy. 5. Conclusion: de Broglie wave (or Schoringer's Psi) is not an ordinary wave.
"Unlike the doppler radar case where the ambiguity arose because waves were being used to measure an object with a definite distance and speed; what we're seeing here is the particle IS the wave - so the spread out over space and over momentum is not some artifact of imperfect measurement techniques; It's a spread fundamental to what the particle is: analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note....But to me, equally fascinating is that underpinning Heisenberg's conclusion is that position and momentum have the same relationship as sound and frequency; As if a particle's momentum is somehow the sheet music describing how it moves through space." ruclips.net/video/MBnnXbOM5S4/видео.html Grant Sanderson, Math/science degree, Stanford University
Viewing from different frames of motion, the amplitudes of the waves at any point at any time are measured to be the same. Therefore the phases are the same too.
The way he describes it is a very strange way to describe it, I think. The thing to understand is that the thing that does the measurement is part of the same system of that which is being measured. Which means that you have to factor that in in your calculations. So it is strictly not true that two people agree on the property values of a water wave when measured at the same time and position (the measurers can't be at same time and position) but because the scale is so large compared to the scale of a photon it is negligible. But if you don't keep it in mind that you need to account for the whole system it becomes confusing to think about, at least for me. Or am I wrong about this?
Here is a math professor explaining de Broglie waves ruclips.net/video/MBnnXbOM5S4/видео.html "Unlike the doppler radar case where the ambiguity arose because waves were being used to measure an object with a definite distance and speed; what we're seeing here is the particle IS the wave - so the spread out over space and over momentum is not some artifact of imperfect measurement techniques; It's a spread fundamental to what the particle is: analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note....But to me, equally fascinating is that underpinning Heisenberg's conclusion is that position and momentum have the same relationship as sound and frequency; As if a particle's momentum is somehow the sheet music describing how it moves through space." Grant Sanderson, Math/science degree, Stanford University
@@noneatallatanytime for de Broglie though, he was critiquing relativity, so there is no need for two different observers, but rather think of spacetime itself as a relative observer or reflection. de Broglie called this his "Law of Phase Harmony" and his greatest discovery - too bad it is not taught typically. So in that video from Grant Sanderson - when he uses the particle as a wave of different balls bouncing up and down - the reason that they are changing their frequency relative to the one observer moving toward the ball - is due to a superluminal pilot wave or guidance wave that is from the future and echos backwards in time. This is because of the de Broglie-Einstein equation. lh4.googleusercontent.com/proxy/QM7z22wSfgdJbshGZnZlSWLrAG2vw0nefI_f2iMt5rEAJcgbAlNO2H5TtHRWLKIdcmC6rbWtgaWDbcTejcKlmf1LMV02sL3We46a1Q=s0-d So that link is a gif of the same image that Grant Sanderson uses in his video to explain de Broglie's matter waves. Only notice there is a 2nd wave coming from the opposite direction - that is the superluminal guiding wave. So de Broglie realized as a particle go towards the speed of light then based on quantum physics the frequency increases but due to relativity the time also increases. So de Broglie reasoned since both are true then there HAS to be a reverse time that can not be seen - and a supermomentum from the future, secretly guiding the particle. This explains the double slit experiment. Yakir Aharonov: "There is a non-local exchange that depends on the modular variable....I'm saying that I have now an intuitive picture to understand interference by saying that when a particle moves through two slits, it always goes through one slit or the other, but it knows which other slit, the slit through which it did not go, whether it is open or not, because there are nonlocal equations of motion." Finally making sense of the double-slit experiment (2017, Aharonov): The nonlocal equations of motion in the Heisenberg picture thus allow us to consider a particle going through only one of the slits, but it nevertheless has nonlocal information regarding the other slit.... The Heisenberg picture, however, offers a different explanation for the loss of interference that is not in the language of collapse: if one of the slits is closed by the experimenter, a nonlocal exchange of modular momentum with the particle occurs....Alternatively, in the Heisenberg picture, the particle has both a definite location and a nonlocal modular momentum that can “sense” the presence of the other slit and therefore, create interference." as John Bell states: "Is it not clear from the diffraction and interference patterns, that the motion of the particle is directed by the wave?"
@@noneatallatanytime I compiled 77 plus different scientists giving quotes on de Broglie's Law of Phase Harmony ecoechoinvasives.blogspot.com/2018/01/summarizing-de-broglie-pilot-wave-law.html thanks
His lecture is so different from the previous 8.04 course. I find it a lot more usefull than the other lecture.
This is very useful. I sense he's taking a sort of plodding, thorough approach here, but I'm getting good out of it. I've read so many treatments of this stuff, but in some sense they're all the same treatment, and they breeze through it all on the way to getting to whatever they're really interested in. Nice to have someone really beat these bushes.
Thanks, Dr. Zwiebach!
Yes here is the same conclusion about de Broglie waves but from a math perspective. ruclips.net/video/MBnnXbOM5S4/видео.html
@@voidisyinyangvoidisyinyang885 Right - really any things that are related through Fourier transform exhibit this same kind of mutual uncertainty.
@@KipIngram yes only as Henri Bacry points out - the de Broglie Law of Phase Harmony is actually noncommutative. I just did a vid upload on it ruclips.net/video/1m38Asft-fw/видео.html thanks
The Galilean transformation is a crucial concept in classical mechanics that helps describe how the observations of an event differ for observers in different inertial frames. When applied to ordinary waves, such as sound or water waves, the Galilean transformation allows us to understand how the properties of these waves, like frequency and wavelength, change when viewed from moving reference frames.
Under the Galilean transformation, the velocity of a wave is affected by the motion of the observer. For example, if you have a sound wave traveling at speed \(c\) in a stationary medium, and you observe it from a frame that is moving with speed \(v\) relative to the medium, the observed speed \(c'\) of the wave will be the sum or difference of these speeds, depending on the direction of motion. Thus, if you're moving in the same direction as the wave, you would perceive the wave traveling at \(c' = c - v\), while if you're moving against the wave, you'd perceive it at \(c' = c + v\).
However, it's important to note that the Galilean transformation assumes low speeds compared to the speed of light and is not applicable in situations involving relativistic effects. This means that while it provides an intuitive understanding of wave behavior in classical contexts, one must be cautious when considering scenarios involving electromagnetic waves or high-speed phenomena where the principles of special relativity take precedence.
In conclusion, the Galilean transformation elegantly illustrates how the speed and other properties of ordinary waves depend on the relative motion of the observer, reinforcing the key idea that measurements in physics are dependent on the frame of reference from which they are made.
Absolutely well done and definitely keep it up!!! 👍👍👍👍👍
this is my 1st time learning Quantum mechanics, I quite clearly understand the quantum stuff, but the classical mechanics goes way over my head.
7:46 to 7:50 Is it true for light wave?
When he replaces x by x'+vt, why doesn't he replace also λ by λ' ?
This episode sounds vastly interesting even tho I'm not fully understanding it, yet.
Yes, that makes sense to my intuition: the phase of a classical wave is a galilean invariant. But I am obviously still missing something.
What makes the claim that the phase is Galilean invariant? Can you explain?
Viewing from different frames of motion, the amplitudes of the waves at any point at any time are measured to be the same. Therefore the phases are the same too.
No matter you and your friend are in different frames (at low velocities) if two pedulams are in phases both of you will agree that these pendulums are indeed in same phase
Why should both agree upon instantaneous amplitude when speed of wave is altered by angular frequency.
Second thing, what phase contribute in measurement, specially time part of phase. So it doesnt depend upon temporal part so much.
2:26 to 2:32 I am getting to feel this fact but why is this true ? Why should they agree? Reason !
Because no matter where you take a measurement from, the result is a real result, so even in a different reference frame, two people would have to measure something that is consistent with one another. Real stuff can't physically be in two places at the same time, for example
sir, doesn't the velocity of wave wrt S' change as well.
@8:45, what means that "there 2 people will not agree on the value of the wave function necessarily"?
1. prof states that "matter wave", which is characterized by its de Broglie's wavelength \lambda, is a kind of WAVE FUNCTION.
2. prof shows that de Broglie's wavelength is NOT Galilean invariant.
3. then he shows that the wavelength of ORDINARY WAVE must be Galilean invariant.
4. thus the wave function, which by definition has a de Broglie's wavelength, need not to be Galilean invariant
and that leads to the statement in ur question.
thanks very much
ZiPan Huo Basically this statement was based on the conclusion from the previous lecture "the two de Broglie wavelengths don't agree." The professor was trying to show or proof us that the de Broglie wave is not an ordinary wave, in lecture 4.1 and 4.2. To proof this, the logic is:
1. Assume de Broglie wave is ordinary wave in both lecture 4.1 and 4.2, so that it follows Galilean Invariant.
2. In lecture 4.1 he showed us that by using Galilean Transformation, the de Broglie wavelengths were not invariant.
3. In lecture 4.2 he showed us by phase analysis under Galilean Transformation, the de Broglie wavelengths were the same.
4. The conclusions from 2 and 3 are logically contradict, so that our assumption is a fallacy.
5. Conclusion: de Broglie wave (or Schoringer's Psi) is not an ordinary wave.
"Unlike the doppler radar case where the ambiguity arose because waves were being used to measure an object with a definite distance and speed; what we're seeing here is the particle IS the wave - so the spread out over space and over momentum is not some artifact of imperfect measurement techniques; It's a spread fundamental to what the particle is: analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note....But to me, equally fascinating is that underpinning Heisenberg's conclusion is that position and momentum have the same relationship as sound and frequency; As if a particle's momentum is somehow the sheet music describing how it moves through space." ruclips.net/video/MBnnXbOM5S4/видео.html
Grant Sanderson, Math/science degree, Stanford University
With the relativity, there is problem in galellian and we use lorentz to fix that problem why do we not use lorentz
9:31 Why? Reason! 9:35 What is hint
ruclips.net/video/MBnnXbOM5S4/видео.html Here is another perspective on de Broglie waves
Thanks ❤️🤍
How can we say phase of ordinary waves is invariant? Kindly explain!
Viewing from different frames of motion, the amplitudes of the waves at any point at any time are measured to be the same. Therefore the phases are the same too.
@@green0563phases and amplitude have nothing to do with one another ???
Are these waves Lorentz invariant
The way he describes it is a very strange way to describe it, I think. The thing to understand is that the thing that does the measurement is part of the same system of that which is being measured. Which means that you have to factor that in in your calculations. So it is strictly not true that two people agree on the property values of a water wave when measured at the same time and position (the measurers can't be at same time and position) but because the scale is so large compared to the scale of a photon it is negligible. But if you don't keep it in mind that you need to account for the whole system it becomes confusing to think about, at least for me.
Or am I wrong about this?
Here is a math professor explaining de Broglie waves ruclips.net/video/MBnnXbOM5S4/видео.html "Unlike the doppler radar case where the ambiguity arose because waves were being used to measure an object with a definite distance and speed; what we're seeing here is the particle IS the wave - so the spread out over space and over momentum is not some artifact of imperfect measurement techniques; It's a spread fundamental to what the particle is: analogous to how a musical note being spread out over time is fundamental to what it even means to be a musical note....But to me, equally fascinating is that underpinning Heisenberg's conclusion is that position and momentum have the same relationship as sound and frequency; As if a particle's momentum is somehow the sheet music describing how it moves through space."
Grant Sanderson, Math/science degree, Stanford University
@@voidisyinyangvoidisyinyang885 Yes, that is what I mean. I find Grant's explanations very sensible.
@@noneatallatanytime for de Broglie though, he was critiquing relativity, so there is no need for two different observers, but rather think of spacetime itself as a relative observer or reflection. de Broglie called this his "Law of Phase Harmony" and his greatest discovery - too bad it is not taught typically. So in that video from Grant Sanderson - when he uses the particle as a wave of different balls bouncing up and down - the reason that they are changing their frequency relative to the one observer moving toward the ball - is due to a superluminal pilot wave or guidance wave that is from the future and echos backwards in time. This is because of the de Broglie-Einstein equation. lh4.googleusercontent.com/proxy/QM7z22wSfgdJbshGZnZlSWLrAG2vw0nefI_f2iMt5rEAJcgbAlNO2H5TtHRWLKIdcmC6rbWtgaWDbcTejcKlmf1LMV02sL3We46a1Q=s0-d
So that link is a gif of the same image that Grant Sanderson uses in his video to explain de Broglie's matter waves. Only notice there is a 2nd wave coming from the opposite direction - that is the superluminal guiding wave. So de Broglie realized as a particle go towards the speed of light then based on quantum physics the frequency increases but due to relativity the time also increases. So de Broglie reasoned since both are true then there HAS to be a reverse time that can not be seen - and a supermomentum from the future, secretly guiding the particle. This explains the double slit experiment. Yakir Aharonov: "There is a non-local exchange that depends on the modular variable....I'm saying that I have now an intuitive picture to understand interference by saying that when a particle moves through two slits, it always goes through one slit or the other, but it knows which other slit, the slit through which it did not go, whether it is open or not, because there are nonlocal equations of motion." Finally making sense of the double-slit experiment (2017, Aharonov): The nonlocal equations of motion in the Heisenberg picture thus allow us to consider a particle going through only one of the slits, but it nevertheless has nonlocal information regarding the other slit.... The Heisenberg picture, however, offers a different explanation for the loss of interference that is not in the language of collapse: if one of the slits is closed by the experimenter, a nonlocal exchange of modular momentum with the particle occurs....Alternatively, in the Heisenberg picture, the particle has both a definite location and a nonlocal modular momentum that can “sense” the presence of the other slit and therefore, create interference." as John Bell states: "Is it not clear from the diffraction and interference patterns, that the motion of the particle is directed by the wave?"
@@voidisyinyangvoidisyinyang885 I have to think about that. Thanks for the reply.
@@noneatallatanytime I compiled 77 plus different scientists giving quotes on de Broglie's Law of Phase Harmony ecoechoinvasives.blogspot.com/2018/01/summarizing-de-broglie-pilot-wave-law.html thanks
Phase is wave function
?
This is helpful ❤️🤍
This is a little bit use of technology
Wow 😁
Schools really need to move to all white boards. I know its expensive though.