Κατά καιρούς, όλο και κάτι γράφω στο blog σχετικά με τον Feynman. Λογικό είναι, αφού ο άνθρωπος είχε μοναδική ικανότητα στο να απογυμνώνει την ουσία των πραγμάτων από τις περιττές τεχνικές δυσκολίες και νομίζω ότι αυτό ήταν τελικά που τον έκανε τόσο καλό δάσκαλο της Φυσικής. Χαζεύοντας λοιπόν στο youtube, βρήκα την παρακάτω ομιλία από το TEDxCaltech (Γενάρης 2011), στην οποία ο Leonard Susskind παρουσιάζει κάποιες πτυχές του Feynman, όπως προκύπτουν από τη γνωριμία τους.
Και με αυτή την ευκαιρία, όποιος δεν έχει διαβάσει την διάλεξη που έδωσε ο Feynman κατά την απονομή του βραβείου Νόμπελ, μπορεί να την βρει εδώ και αξίζει να την διαβάσει.
The Development of the Space-Time View of Quantum Electrodynamics
The Nobel Prize in Physics 1965
Sin-Itiro Tomonaga, Julian Schwinger, Richard P. Feynman
Το αγαπημένο μου κομμάτι είναι αυτό όπου ο Feynman, ως μεταπτυχιακός, παρουσιάζει την θεωρία του για το radiation resistance των επιταχυνόμενων ηλεκτρονίων στον επιβλέποντά του, τον John Wheeler, αλλά και το ανέκδοτο με τον Herbert Jehle.
Έτσι, για να βλέπουμε και τις διαφορές από τους διάφορους "μόνιμους διεκδικητές" των Νόμπελ, με τους οποίους θα έκανε party ο Feynman, όπως στην περίπτωση των φιλοσόφων που περιγράφει ο Susskind.
Εμφάνιση αναρτήσεων με ετικέτα Feynman. Εμφάνιση όλων των αναρτήσεων
Εμφάνιση αναρτήσεων με ετικέτα Feynman. Εμφάνιση όλων των αναρτήσεων
Σάββατο 26 Φεβρουαρίου 2011
Δευτέρα 26 Απριλίου 2010
Mass of the photon
Με αφορμή την κουβέντα στο forum.atheia.gr για το Big Bang και όχι μόνο, θυμήθηκα ένα πολύ όμορφο ανέκδοτο του Feynman όπου συζητάει με κάποιον καθηγητή για την μάζα του φωτονίου.
Πέρα από την ουσία της συζήτησης για την μάζα του φωτονίου και πέρα από το ότι ο Feynman ξεδιπλώνει το θεϊκό ταλέντο του, το όλο ανέκδοτο αναδεικνύει κάποια ενδιαφέροντα σημεία που υπάρχουν ή ακόμα και προβλήματα που μπορεί να προκύψουν στην όποια συζήτηση μπορεί να κάνει κάποιος για ένα θέμα Φυσικής (ή οποιοδήποτε άλλο επιστημονικό θέμα). 2 είναι τα μεγάλα προβλήματα σε τέτοιες συζητήσεις. Το πρώτο πρόβλημα είναι το τι θεωρεί ο καθένας ως δεδομένη γνώση και το δεύτερο είναι κατά πόσο "παίζει" με τους κανόνες του "παιχνιδιού".
Υπάρχουν αρκετά ενδιαφέροντα σημεία για να επισημάνει κανείς.
Το αφήνω ως "άσκηση".
:P
--------------------------------
Update:
Υπάρχει ένα πρόσφατο άρθρο στο Reviews of Modern Physics που παρουσιάζει τα όρια που έχουμε αυτή τη στιγμή για την μάζα του φωτονίου και του βαρυτονίου.
Το άρθρο είναι το, Rev. Mod. Phys. 82, 939–979 (2010), "Photon and graviton mass limits", των Alfred Scharff Goldhaber και Michael Martin Nieto. Για όποιον δεν έχει πρόσβαση στο περιοδικό, υπάρχει και στο arxiv.org και είναι το arXiv:0809.1003v4 [hep-ph].
Στο άρθρο αναφέρονται και οι μέθοδοι που επικαλείται ο Feynman παραπάνω.
Πέρα από την ουσία της συζήτησης για την μάζα του φωτονίου και πέρα από το ότι ο Feynman ξεδιπλώνει το θεϊκό ταλέντο του, το όλο ανέκδοτο αναδεικνύει κάποια ενδιαφέροντα σημεία που υπάρχουν ή ακόμα και προβλήματα που μπορεί να προκύψουν στην όποια συζήτηση μπορεί να κάνει κάποιος για ένα θέμα Φυσικής (ή οποιοδήποτε άλλο επιστημονικό θέμα). 2 είναι τα μεγάλα προβλήματα σε τέτοιες συζητήσεις. Το πρώτο πρόβλημα είναι το τι θεωρεί ο καθένας ως δεδομένη γνώση και το δεύτερο είναι κατά πόσο "παίζει" με τους κανόνες του "παιχνιδιού".
In this connection I would like to relate an anecdote, something from a conversation after a cocktail party in Paris some years ago. There was a time at which all the ladies mysteriously disappeared, and I was left facing a famous professor, solemnly seated in an armchair, surrounded by his students. He said, “Tell me, Professor Feynman, how sure are you that the photon has no rest mass?” I answered “Well, it depends on the mass; evidently if the mass is infinitesimally small, so that it would have no effect whatsoever, I could not disprove its existence, but I would be glad to discuss the possibility that the mass is not of a certain definite size. The condition is that after I give you arguments against such mass, it should be against the rules to change the mass.” The professor then chose a mass of 10^-5 of an electron mass.
My answer was that, if we agreed that the mass of the photon was related to the frequency as \omega=\sqrt{k^2+m^2}, photons of different wavelengths would travel with different velocities. Then in observing an eclipsing double star, which was sufficiently far away, we would observe the eclipse in blue light and red light at different times. Since nothing like this is observed, we can put an upper limit on the mass, which, if you do the numbers, turns out to be of the order of 10^-9 electron masses. The answer was translated to the professor. Then he wanted to know what I would have said if he had said 10^-12 electron masses. The translating student was embarrassed by the question, and I protested that this was against the rules, but I agreed to try again.
If the photons have a small mass, equal for all photons, larger fractional differences from the massless behavior are expected as the wavelength gets longer. So from the sharpness of the known reflection of pulses in radar, we can put an upper limit to the photon mass which is somewhat better than from the eclipsing double star argument. It turns out that the mass had to be smaller than 10^-15 electron masses.
After this, the professor wanted to change the mass again, and make it 10^-18 electron masses. The student all became rather uneasy at this question, and I protested that, if he kept breaking the rules, and making the mass smaller and smaller, evidently I would be unable to make an argument at some point. Nevertheless, I tried again. I asked him whether he agreed that if the photon had a small mass, then from field theory arguments the potential should go as \exp{-mr}/r. He agreed. Then, the earth has a static magnetic field, which is known to extend out into space for some distance, from the behavior of the cosmic rays, a distance at least of the order of a few earth radii. But this means that the photon mass must be of a size smaller than that corresponding to a decay length of the order of 8000 miles, or some 10^-20 electron masses. At this point, the conversation ended, to my grate relief.
Richard Feynman
Feynman Lectures on Gravitation
pp. 22-23
Υπάρχουν αρκετά ενδιαφέροντα σημεία για να επισημάνει κανείς.
Το αφήνω ως "άσκηση".
:P
--------------------------------
Update:
Υπάρχει ένα πρόσφατο άρθρο στο Reviews of Modern Physics που παρουσιάζει τα όρια που έχουμε αυτή τη στιγμή για την μάζα του φωτονίου και του βαρυτονίου.
Το άρθρο είναι το, Rev. Mod. Phys. 82, 939–979 (2010), "Photon and graviton mass limits", των Alfred Scharff Goldhaber και Michael Martin Nieto. Για όποιον δεν έχει πρόσβαση στο περιοδικό, υπάρχει και στο arxiv.org και είναι το arXiv:0809.1003v4 [hep-ph].
Efforts to place limits on deviations from canonical formulations of electromagnetism and gravity have probed length scales increasing dramatically over time. Historically, these studies have passed through three stages: (1) testing the power in the inverse-square laws of Newton and Coulomb, (2) seeking a nonzero value for the rest mass of photon or graviton, and (3) considering more degrees of freedom, allowing mass while preserving explicit gauge or general-coordinate invariance. Since the previous review the lower limit on the photon Compton wavelength has improved by four orders of magnitude, to about one astronomical unit, and rapid current progress in astronomy makes further advance likely. For gravity there have been vigorous debates about even the concept of graviton rest mass. Meanwhile there are striking observations of astronomical motions that do not fit Einstein gravity with visible sources. “Cold dark matter” (slow, invisible classical particles) fits well at large scales. “Modified Newtonian dynamics” provides the best phenomenology at galactic scales. Satisfying this phenomenology is a requirement if dark matter, perhaps as invisible classical fields, could be correct here too. “Dark energy” might be explained by a graviton-mass-like effect, with associated Compton wavelength comparable to the radius of the visible universe. Significant mass limits are summarized in a table.
Στο άρθρο αναφέρονται και οι μέθοδοι που επικαλείται ο Feynman παραπάνω.
Πέμπτη 2 Οκτωβρίου 2008
Feynman's Tips on Physics
Ο R. Feynman είναι γνωστός για δύο πράγματα, για την συνεισφορά του στην ανάπτυξη της κβαντικής ηλεκτροδυναμικής (QED) και για την καταπληκτική του ικανότητα να διδάσκει Φυσική. Ο ίδιος φυσικά δεν θεωρούσε τον εαυτό του δάσκαλο, πράγμα που το έλεγε σε κάθε ευκαιρία. Όπως και να έχει, η σειρά των βιβλίων, The Feynmans Lectures on Physics, είναι από τα πιο κλασσικά συγγράμματα φυσικής που υπάρχουν για τον προπτυχιακό φοιτητή. Εκτός όμως από αυτό το κλασσικό σύγγραμμα, υπάρχει ακόμα ένα βιβλίο με συλλογή από διαλέξεις του Feynman που είναι λιγότερο γνωστό, το Feynman's Tips on Physics, το οποίο μπορεί να θεωρηθεί ότι συμπληρώνει την σειρά (για την οποία υπάρχει το πολύ ενδιαφέρον site www.feynmanlectures.info).
Πρόσφατα λοιπόν, έτυχε να παρακολουθήσω μία συζήτηση σχετικά με τη δυσκολία του τμήματος Φυσικής του παν/μίου Αθηνών και το πρόβλημα που δημιουργεί στους φοιτητές. Οι λεπτομέρειες εκείνης της συζήτησης ανήκουν σε άλλο θέμα και δεν θα τις συζητήσω εδώ. Υπάρχει όμως κάτι που θεωρώ ότι έχει ενδιαφέρον γενικά και είναι κάτι που θα πρέπει να το έχει υπόψιν του ο καθένας φοιτητής, δεδομένου ότι ξεκινά και το ακαδημαϊκό έτος με τους πρωτοετείς που έρχονται πρώτη φορά σε επαφή με το παν/μίο.
Στο Feynman's Tips on Physics, υπάρχει λοιπόν μία διάλεξη του Feynman με θέμα την μετάβαση από το σχολείο στο πανεπιστήμιο και το πως αλλάζουν τα δεδομένα εξαιτίας αυτής της μετάβασης. Αυτό το απόσπασμα του βιβλίου θέλω να παραθέσω εδώ, αφού το θεωρώ πολύ χρήσιμο, ελπίζοντας ότι δεν θα με κυνηγήσει κανένας για τα πνευματικά δικαιώματα.
"Now, I am therefore imagining that one of you has come into ray office and said. "Feynman, I listened to all the lectures, and I took that midterm exam, and I'm trying to do the problems, and I can't do anything, and I think I'm in the bottom of the class, and I don't know what to do."
What would I say to you?
The first thing I would point out is this: to come to Caltech is an advantage in certain ways, and in other ways a disadvantage. Some of the ways that it's an advantage you probably once knew, but now forget, and they have to do with the fact that the school has an excellent reputation, and the reputation is well deserved. There are pretty good courses. (I don't know about this particular physics course; of course I have my own opinion about it.) The people who have come out the other end of Caltech, when they go into industry, or go to do work in research, and so forth, always say that they got a very good education here, and when they compare themselves with people who have gone to other schools (although many other schools are also very good) they never find themselves behind and missing something; they always feel they went to the best school of them all. So that's an advantage.
But there is also a certain disadvantage: because Caltech has such a good reputation, almost everybody who's the first or second in his high school class applies here. There are lots of high schools, and all the very best men apply. Now, we have tried to figure out a system of selection, with all kinds of tests, so that we get the best of the best. And so you guys have been very carefully picked out from all these schools to come here. But we're still working on it, because we've found a very serious problem: no matter how carefully we select the men, no matter how patiently we make the analysis, when they get here something happens: it always turns out that approximately half of them are below average!
Of course you laugh at this because it's self-evident to the rational mind, but not to the emotional mind - the emotional mind can't laugh at this. When you've lived all the time as number one or number two (or even possibly number three) in high school science, and when you know that everybody who's below average in the science courses where you came from is a complete idiot, and now you suddenly discover that you are below average - and half of you guys are - it's a terrible blow, because you imagine that it means you're as dumb as those guys used to be in high school, relatively. That's the great disadvantage of Caltech: that this psychological blow is so difficult to take. Of course, I'm not a psychologist; I'm imagining all this. 1 don't know how it would really be, of course!
The question is what to do if you find you're below average. There are two possibilities. In the first place, you could find that it's so difficult and annoying that you have to get out — that's an emotional problem. You can apply your rational mind to that and point out 10 yourself what I just pointed out to you: that half of the guys in this place are going to be below average, even though they've all tops, so it doesn't mean anything. You see, if you can stick out that nonsense, that funny feeling, for four years, then you'll go out into the world again, and you'll discover that the world is just like it used to be - that when, for example, you get a job somewhere, you'll find you're Number One Man again, and you'll get the great pleasure of being the expert they all come running to in this particular plant whenever they can't figure out how to convert inches to centimeters! Il's true: the men who go out into industry, or go to a small school that doesn't have an excellent reputation in physics, even if they've been in the bottom third, the bottom fifth, the bottom tenth of the class - if they don't try to drive themselves (and I'll explain that in a minute), then they'll find themselves very much in demand, that what they learned here is very useful, and they're back where they were before: happy, Number One.
On the other hand you can make a mistake: some people may drive themselves to a point where they insist they have to become Number One, and in spite of everything they want to go to graduate school and they want to become the best Ph.D. in the best school, even though they're starting out at the bottom of the class here. Well, they are likely to be disappointed and to make themselves miserable for the rest of their lives being always at the bottom of a very first-rate group, because they picked that group. That's a problem, and that's up to you - it depends on your personality. (Remember, I'm talking to the guy who came into my office because he's in the lowest tenth; I'm not talking to the other fellows who are happy because they happen to be in the upper tenth - that's a minority anyway!)
So, if you can take this psychological blow, if you can say to yourself, "I'm in the lower third of the class, but a third of the guys are in the lower third of the class, because it's got to be that way! I was the top guy in high school, and I'm still a smart son-of-a-gun. We need scientists in the country, and I'm gonna be a scientist, and when I get out of this school I'll be all right, damn it! And I'll be a good scientist!" - then it'll be true: you will be a good scientist. The only thing is whether you can take the funny feelings during these four years, in spite of the rational arguments. If you find you can't take the funny feelings, I suppose the best thing to do is to try to go somewhere else. It's not a point of failure: it's simply an emotional thing.
Even if you're one of the last couple of guys in the class, it doesn't mean you're not any good. You just have to compare yourself to a reasonable group, instead of to this insane collection that we've got here at Caltech. Therefore, I am making this review purposely for the people who are lost, so that they have still a chance to stay here a little longer to find out whether or not they can take it, okay?
I make now one more point: that this is not a preparation for an examination, or anything like that. I don't know anything about the examinations - I mean, I have nothing to do with making them up, and I don't know what's going to be on them, so there's no guarantee whatsoever that what's on the examination is only going to deal with the stuff reviewed in these lectures, or any nonsense of that kind."
Αυτά...
Πρόσφατα λοιπόν, έτυχε να παρακολουθήσω μία συζήτηση σχετικά με τη δυσκολία του τμήματος Φυσικής του παν/μίου Αθηνών και το πρόβλημα που δημιουργεί στους φοιτητές. Οι λεπτομέρειες εκείνης της συζήτησης ανήκουν σε άλλο θέμα και δεν θα τις συζητήσω εδώ. Υπάρχει όμως κάτι που θεωρώ ότι έχει ενδιαφέρον γενικά και είναι κάτι που θα πρέπει να το έχει υπόψιν του ο καθένας φοιτητής, δεδομένου ότι ξεκινά και το ακαδημαϊκό έτος με τους πρωτοετείς που έρχονται πρώτη φορά σε επαφή με το παν/μίο.
Στο Feynman's Tips on Physics, υπάρχει λοιπόν μία διάλεξη του Feynman με θέμα την μετάβαση από το σχολείο στο πανεπιστήμιο και το πως αλλάζουν τα δεδομένα εξαιτίας αυτής της μετάβασης. Αυτό το απόσπασμα του βιβλίου θέλω να παραθέσω εδώ, αφού το θεωρώ πολύ χρήσιμο, ελπίζοντας ότι δεν θα με κυνηγήσει κανένας για τα πνευματικά δικαιώματα.
"Now, I am therefore imagining that one of you has come into ray office and said. "Feynman, I listened to all the lectures, and I took that midterm exam, and I'm trying to do the problems, and I can't do anything, and I think I'm in the bottom of the class, and I don't know what to do."
What would I say to you?
The first thing I would point out is this: to come to Caltech is an advantage in certain ways, and in other ways a disadvantage. Some of the ways that it's an advantage you probably once knew, but now forget, and they have to do with the fact that the school has an excellent reputation, and the reputation is well deserved. There are pretty good courses. (I don't know about this particular physics course; of course I have my own opinion about it.) The people who have come out the other end of Caltech, when they go into industry, or go to do work in research, and so forth, always say that they got a very good education here, and when they compare themselves with people who have gone to other schools (although many other schools are also very good) they never find themselves behind and missing something; they always feel they went to the best school of them all. So that's an advantage.
But there is also a certain disadvantage: because Caltech has such a good reputation, almost everybody who's the first or second in his high school class applies here. There are lots of high schools, and all the very best men apply. Now, we have tried to figure out a system of selection, with all kinds of tests, so that we get the best of the best. And so you guys have been very carefully picked out from all these schools to come here. But we're still working on it, because we've found a very serious problem: no matter how carefully we select the men, no matter how patiently we make the analysis, when they get here something happens: it always turns out that approximately half of them are below average!
Of course you laugh at this because it's self-evident to the rational mind, but not to the emotional mind - the emotional mind can't laugh at this. When you've lived all the time as number one or number two (or even possibly number three) in high school science, and when you know that everybody who's below average in the science courses where you came from is a complete idiot, and now you suddenly discover that you are below average - and half of you guys are - it's a terrible blow, because you imagine that it means you're as dumb as those guys used to be in high school, relatively. That's the great disadvantage of Caltech: that this psychological blow is so difficult to take. Of course, I'm not a psychologist; I'm imagining all this. 1 don't know how it would really be, of course!
The question is what to do if you find you're below average. There are two possibilities. In the first place, you could find that it's so difficult and annoying that you have to get out — that's an emotional problem. You can apply your rational mind to that and point out 10 yourself what I just pointed out to you: that half of the guys in this place are going to be below average, even though they've all tops, so it doesn't mean anything. You see, if you can stick out that nonsense, that funny feeling, for four years, then you'll go out into the world again, and you'll discover that the world is just like it used to be - that when, for example, you get a job somewhere, you'll find you're Number One Man again, and you'll get the great pleasure of being the expert they all come running to in this particular plant whenever they can't figure out how to convert inches to centimeters! Il's true: the men who go out into industry, or go to a small school that doesn't have an excellent reputation in physics, even if they've been in the bottom third, the bottom fifth, the bottom tenth of the class - if they don't try to drive themselves (and I'll explain that in a minute), then they'll find themselves very much in demand, that what they learned here is very useful, and they're back where they were before: happy, Number One.
On the other hand you can make a mistake: some people may drive themselves to a point where they insist they have to become Number One, and in spite of everything they want to go to graduate school and they want to become the best Ph.D. in the best school, even though they're starting out at the bottom of the class here. Well, they are likely to be disappointed and to make themselves miserable for the rest of their lives being always at the bottom of a very first-rate group, because they picked that group. That's a problem, and that's up to you - it depends on your personality. (Remember, I'm talking to the guy who came into my office because he's in the lowest tenth; I'm not talking to the other fellows who are happy because they happen to be in the upper tenth - that's a minority anyway!)
So, if you can take this psychological blow, if you can say to yourself, "I'm in the lower third of the class, but a third of the guys are in the lower third of the class, because it's got to be that way! I was the top guy in high school, and I'm still a smart son-of-a-gun. We need scientists in the country, and I'm gonna be a scientist, and when I get out of this school I'll be all right, damn it! And I'll be a good scientist!" - then it'll be true: you will be a good scientist. The only thing is whether you can take the funny feelings during these four years, in spite of the rational arguments. If you find you can't take the funny feelings, I suppose the best thing to do is to try to go somewhere else. It's not a point of failure: it's simply an emotional thing.
Even if you're one of the last couple of guys in the class, it doesn't mean you're not any good. You just have to compare yourself to a reasonable group, instead of to this insane collection that we've got here at Caltech. Therefore, I am making this review purposely for the people who are lost, so that they have still a chance to stay here a little longer to find out whether or not they can take it, okay?
I make now one more point: that this is not a preparation for an examination, or anything like that. I don't know anything about the examinations - I mean, I have nothing to do with making them up, and I don't know what's going to be on them, so there's no guarantee whatsoever that what's on the examination is only going to deal with the stuff reviewed in these lectures, or any nonsense of that kind."
Αυτά...
Εγγραφή σε:
Αναρτήσεις (Atom)