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Nobel Prize: Political stunt or the real deal?

Started by Linda Howard4 · · 👁 6 views · 41 replies

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Participants Linda Howard4Jesse Adamsgranitepilot2Linda Hughes88Gregory Howardhollowgardener912George Grant12analogfalcon38copperjackal15northerncyclist9driftingviper29redcyclist33Dana Brooks44granitemarlin4Frank Morgan2goldentrucker17
redcyclist33 redcyclist33 Newcomer
9 messages
joined Jul 2008
#21 ·
Regarding the Nobel Prizes, do you believe that:
- White people are more intelligent or capable than Black people?
- Men are more intelligent or capable than women?
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#22 ·
Jesse Adams said:Pascual Jordan developed Jordan algebra. Honestly? It’s a minor achievement compared to other laureates—you can check that yourself. Maybe he could have shared a Nobel with Born, but that’s debatable since Born’s track record is far more substantial. Not long after, von Neumann algebra came along, which is what everyone actually uses today. Funny how he collaborated so closely with Max Born—who was Jewish—right before turning Nazi.
More info on Jordan:
http://arxiv.org/abs/hep-th/0303241

Tesla famously turned down his Nobel.

So, some people claim there's a bias toward Jewish scientists in the Nobel selections?
Counterpoint:
http://en.wikipedia.org/wiki/Yuval_Ne'eman

Nobel controversies don't stem from international politics—it's about protecting one's own industry and university prestige.

1. Jordan is one of the three canonical authors who structured quantum mechanics (Born, Jordan, Heisenberg) in the seminal paper he largely authored. After the war, Born admitted he owed Jordan to some extent because Jordan entrusted him with work for publication—work where Jordan laid out the principles of what would become Fermi-Dirac statistics (he wrote it before both of them). But Born was in a bind, focused on survival, and simply glossed over the contribution. It remains a mystery why Jordan himself didn't publish his own work to ensure the statistics were called Jordan statistics rather than Fermi-Dirac, given he certainly had the original manuscript. These arguments about functionality are laughable. Bohr's description of the hydrogen atom was rejected long ago, despite his involvement. Newton's calculus of fluxions is inferior to the Leibniz-Bernoulli notation, yet that doesn't diminish Newton's contribution.

2. Tesla didn't "refuse" an award, because awards aren't "offered." They are granted. A recipient can decline them, much like Jean-Paul Sartre did, but that has zero impact on whether the committee decides to select a specific individual. In short: Tesla didn't reject anything.

3. Born was a German physicist. You're clearly confusing him with Niels Bohr.
Dana Brooks44 Dana Brooks44 Newcomer
9 messages
joined Jul 2008
#23 ·
Sure,....for the people who don't walk away with it...but honestly, anyone would kill to have that trophy sitting in their display case.😁
granitemarlin4 granitemarlin4 Member
34 messages
joined Nov 2008
#24 ·
The Nobel Prize feels more like a bit of a joke lately—especially when you look at the Peace category.
Dana Brooks44 Dana Brooks44 Newcomer
9 messages
joined Jul 2008
#25 ·
granitemarlin4 said:The Nobel Prize feels more like a bit of a joke lately—especially when you look at the Peace category.

They should just hand it to the leaders of Iran, Russia, and the US... after all their hard work fighting for peace.👍
hollowgardener912 hollowgardener912 Member
15 messages
joined Sep 2008
#26 ·
George Grant12 said:It would be great if you actually went to San Salvador and asked the people there what they think about Jimmy. Man, you claim to despise Henry Kissinger (likely because of his actions in South America), yet here you are backing this idiot. 🙄

As for calling someone an uneducated fool—that just shows how small-minded you are. I suppose you think "great men" need a fancy degree to be valid? You sound incredibly condescending. Or maybe you're just jealous because he had more backbone than both of you combined.

Man, how pathetic.

Never said I was backing Jimmy Carter. Just said he wasn't as brutal as the other presidents.

As for Walesa, I said what I said because I think he's a moron (I'm allowed to have an opinion, right?), degree or no degree.

P.S. What "two little pebbles"? You low-key staring at my crotch or something?
Frank Morgan2 Frank Morgan2 Member
41 messages
joined Apr 2013
#27 ·
hollowgardener912 said:The Nobel Peace Prize needs to be scrapped. Just look at the track record of winners. Here’s some proof:

1973: Henry Kissinger - Absolute joke. One of the worst war criminals ever...

1979: Mother Teresa - Fine, she didn't do anything evil, but nothing great either. Spreading religion isn't exactly "peace"...

1983: Lech Wałęsa - Since when does every half-wit who starts a strike get an award like this?

1989: Dalai Lama - Just hitting up fancy parties and living like a superstar. Sure, Madonna does that too—at least she actually makes albums, this guy is more like Paris Hilton

1990: Mikhail Gorbachev - Or just any politician incompetent enough to wreck their entire country in a few years...

1994: Yasser Arafat, Shimon Peres, Yitzhak Rabin: They started a war then ended it (well, they just thought about ending it). By that logic, Luđman, Šević, and Izmetbegović should have won too

2002: Jimmy Carter - Okay, this one's fine. He was an American president and didn't start a single war...


And the icing on the cake: THE NOBEL PEACE PRIZE FOR THE UN AND KOFI ANNAN IN 1995!!!

The Nobel Peace Prize is basically just spitting on Nobel's grave and insulting anyone with actual human values.

Later,
Frank Morgan2
goldentrucker17 goldentrucker17 Active Member
57 messages
joined Jul 2010
#28 ·
Dana Brooks44 said:They should just hand it to the leaders of Iran, Russia, and the US... after all their hard work fighting for peace.👍

I mean, if Kissinger and Arafat could pull it off... why wouldn't these guys get some recognition for their tireless pursuit of global stability? 😁
Dana Brooks44 Dana Brooks44 Newcomer
9 messages
joined Jul 2008
#29 ·
goldentrucker17 said:I mean, if Kissinger and Arafat could pull it off... why wouldn't these guys get some recognition for their tireless pursuit of global stability? 😁

Yeah, I agree. That's why I said it. They spent years grinding away at global peace. 🤣
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#30 ·
Gregory Howard said:1. Jordan is one of the three canonical authors who structured quantum mechanics (Born, Jordan, Heisenberg) in the seminal paper he largely authored. After the war, Born admitted he owed Jordan to some extent because Jordan entrusted him with work for publication—work where Jordan laid out the principles of what would become Fermi-Dirac statistics (he wrote it before both of them). But Born was in a bind, focused on survival, and simply glossed over the contribution. It remains a mystery why Jordan himself didn't publish his own work to ensure the statistics were called Jordan statistics rather than Fermi-Dirac, given he certainly had the original manuscript. These arguments about functionality are laughable. Bohr's description of the hydrogen atom was rejected long ago, despite his involvement. Newton's calculus of fluxions is inferior to the Leibniz-Bernoulli notation, yet that doesn't diminish Newton's contribution.

2. Tesla didn't "refuse" an award, because awards aren't "offered." They are granted. A recipient can decline them, much like Jean-Paul Sartre did, but that has zero impact on whether the committee decides to select a specific individual. In short: Tesla didn't reject anything.

3. Born was a German physicist. You're clearly confusing him with Niels Bohr.


1. Three "canonical authors"? What about Schrödinger? Planck? Dirac? Von Neumann? And which "major work" are we talking about here? As far as I know, Heisenberg is the one who developed the core concept with matrix mechanics. Give me some actual references on this Jordan guy! How could he have developed Fermi-Dirac statistics before spin was even discovered?

2. Apparently so.

3. Yeah.
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#31 ·
Jesse Adams said:1. Three "canonical authors"? What about Schrödinger? Planck? Dirac? Von Neumann? And which "major work" are we talking about here? As far as I know, Heisenberg is the one who developed the core concept with matrix mechanics. Give me some actual references on this Jordan guy! How could he have developed Fermi-Dirac statistics before spin was even discovered?

2. Apparently so.

3. Yeah.

1. Without dismissing the massive contributions of Schrödinger and Dirac (which certainly outweigh Jordan's), the reality remains: quantum mechanics was codified in what is widely considered the canonical text by a trio of authors:
http://www.theworldsgreatbooks.com/qm.htm

Three papers that defined a discipline:
The theoretical foundation for quantum mechanics

Heisenberg, Werner. Uber quantentheorestische Umdeutung kinematischer und mechanischer Beziehungen. WITH: Born, Max and Jordan, Pasqual. Zur Quantenmechanik. WITH: Born, Jordan, and Heisenberg. Zur Quantenmechanik II. IN: Zeitschrift fur Physik, Vols. 33, 34, 35. Berlin: Julius Springer, 1925-1926. Octavo, modern three-quarter morocco. Three volumes. $6800.

“In three months of intense work Born, Heisenberg and their colleague Pascual Jordan developed what Heisenberg calls ‘a coherent mathematical framework, one that promised to embrace all the multifarious aspects of atomic physics.’ Quantum mechanics, the new system was called. It fit the experimental evidence to a high degree of accuracy” (Rhodes, The Making of the Atomic Bomb, 117).
........
In the summer of 1925, working alongside Pascual Jordan, Born translated Heisenberg’s mathematical insights into the formal language of matrices, and Born, Heisenberg, and Jordan co-published a complete account of the work, famously known as the ‘three-man paper.’

2, http://x.prat.resina.googlepages.com/storiesinscience

Jordan's statistics found at the bottom of a suitcase.

(Max) Born experienced a deeply unsettling moment upon his return—discovering a paper by Pascual Jordan (his student) tucked away at the bottom of his suitcase. Right before Born left, Jordan had handed it over for potential publication in the journal *Zeitschrift fur Physik*, where Born served as an editor. Born had packed it away, planning to review it during his travels. When he finally opened it and read the contents, he realized Jordan had already uncovered the critical statistical laws that Enrico Fermi had just published in the same journal. Shortly thereafter, Paul Dirac made the same discovery of what we now call Fermi-Dirac statistics. (...) Amidst the heavy tensions surrounding his future relationship with Jordan, Born always carried a sense of guilt, even "shame," feeling he had essentially robbed Jordan of his rightful recognition.

p. 135. N. T. Greenspan. The life and science of Max Born. Basic Books 2005. (A compelling read. It details the discovery of Quantum Mechanics through Max Born's eyes and suggests that Born deserved significantly more credit than he received.
A letter from Heisenberg to Born following the awarding of the Nobel Prize to Heisenberg in 1932

Dear Mr. Born, if I haven't reached out in quite some time or expressed my gratitude for your congratulations, it is partly due to a nagging sense of guilt toward you. The fact that I am to be awarded the Nobel Prize alone, for work performed in Göttingen in collaboration with—you, Jordan, and myself—is depressing. I am at a loss for words. (...) I also believe that any serious physicist understands the magnitude of yours and Jordan's contribution to the architecture of quantum mechanics—and that truth remains unchanged by an external error in judgment. All I can do is thank you once more for the exceptional collaboration, while feeling a certain level of shame. Best regards. Yours, W. Heisenberg.
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#32 ·
@Gregory Howard: I’ll say it again regarding Jordan. His contribution to physics isn't negligible—by today's standards, it's actually massive—but by the standards of his era? It's minor. In my view, he doesn't deserve a Nobel, though obviously, that’s up for debate. That whole "matrix mechanics" thing and Jordan’s algebra were quickly sidelined by Hilbert’s formalism (developed by Dirac) and von Neumann’s algebra (thanks to von Neumann)—which is what modern quantum physics actually runs on. Meanwhile, the work from Bohr and Heisenberg is still very much in use.
I’m still not convinced Jordan was passed over for the Nobel solely due to politics. But even if that were true, he’s an outlier. You can't take the whole Nobel Prize committee and call the entire thing "political maneuvering," regardless of what the OP is trying to imply.
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#33 ·
Jesse Adams said:@Gregory Howard: I’ll say it again regarding Jordan. His contribution to physics isn't negligible—by today's standards, it's actually massive—but by the standards of his era? It's minor. In my view, he doesn't deserve a Nobel, though obviously, that’s up for debate. That whole "matrix mechanics" thing and Jordan’s algebra were quickly sidelined by Hilbert’s formalism (developed by Dirac) and von Neumann’s algebra (thanks to von Neumann)—which is what modern quantum physics actually runs on. Meanwhile, the work from Bohr and Heisenberg is still very much in use.
I’m still not convinced Jordan was passed over for the Nobel solely due to politics. But even if that were true, he’s an outlier. You can't take the whole Nobel Prize committee and call the entire thing "political maneuvering," regardless of what the OP is trying to imply.

Jordan's contribution isn't any less significant than several other founding physicists. If we are judging strictly by "weight," his work holds its own against someone like de Broglie. If we start nitpicking formalisms, then according to that logic, neither Bohr nor half the others should have received anything at all.

Jordan didn't miss out solely because of his Nazi affiliations. Subsequent lobbying—led most aggressively by Eugene Wigner—failed to move the needle. As for "merit" (which shouldn't be tied to politics), look at the history of Physics Nobels. A huge number of winners from before the 1930s are questionable, and many later ones are just as dubious. We're talking about discoveries or experiments that are subject to wildly different interpretations.

With such diverse disciplines, measuring the "statistical weight" of a single discovery is nearly impossible. However, the facts speak for themselves. Men like Hubble, Gamow, von Karman, Tesla, Racah, and Bohm never got it. Chandrasekhar barely scraped by. Meanwhile, Bardeen and Curie managed to snag two. This suggests that, in my opinion, at least 50% of the Physics Nobels are problematic. Not to mention things like the Michelson experiment—brilliant design, certainly—or the discovery of the tau lepton and W bosons, which were essentially just confirming the Standard Model.

So what's the conclusion? The Standard Model functioned perfectly fine without confirmation of the Z and W bosons, just as it works without the Higgs. Ultimately, scientific awards—not even touching medicine or chemistry—can be heavily criticized. It isn't just about politicization, though that exists. It is more about shortsightedness and institutional inertia.
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#34 ·
Gregory Howard said:Jordan's contribution isn't any less significant than several other founding physicists. If we are judging strictly by "weight," his work holds its own against someone like de Broglie. If we start nitpicking formalisms, then according to that logic, neither Bohr nor half the others should have received anything at all.

Jordan didn't miss out solely because of his Nazi affiliations. Subsequent lobbying—led most aggressively by Eugene Wigner—failed to move the needle. As for "merit" (which shouldn't be tied to politics), look at the history of Physics Nobels. A huge number of winners from before the 1930s are questionable, and many later ones are just as dubious. We're talking about discoveries or experiments that are subject to wildly different interpretations.

With such diverse disciplines, measuring the "statistical weight" of a single discovery is nearly impossible. However, the facts speak for themselves. Men like Hubble, Gamow, von Karman, Tesla, Racah, and Bohm never got it. Chandrasekhar barely scraped by. Meanwhile, Bardeen and Curie managed to snag two. This suggests that, in my opinion, at least 50% of the Physics Nobels are problematic. Not to mention things like the Michelson experiment—brilliant design, certainly—or the discovery of the tau lepton and W bosons, which were essentially just confirming the Standard Model.

So what's the conclusion? The Standard Model functioned perfectly fine without confirmation of the Z and W bosons, just as it works without the Higgs. Ultimately, scientific awards—not even touching medicine or chemistry—can be heavily criticized. It isn't just about politicization, though that exists. It is more about shortsightedness and institutional inertia.

He’s a much smaller figure than de Broglie. But let's be real—he was the one who first spotted that the eikonal equation in optics is basically an analogue to the Hamilton-Jacobi equation. That realization essentially kicked off quantum mechanics and paved the way for Schrödinger to actually write his equation. Without that link? Nothing.
Jordan didn't just assist Heisenberg—he basically handed him the blueprint for matrix mechanics on a silver platter.

It’s tough—given how much physics spans different disciplines—to put a "statistical weight" on any single discovery. But let's be real: when you look at the list of people who *didn't* get a Nobel—Hubble, Gamow, von Karman, Tesla, Racah, Bohm—and then see guys like Bardeen or Curie walking away with two? It tells me that, IMO, at least 50% of the Physics Nobels are questionable. Not to mention the stuff where the criteria are totally subjective—like the Michelson experiment, which was brilliant design—or the hunt for the tau lepton and W bosons, where researchers were basically just checking boxes to confirm the Standard Model. Is it actually groundbreaking science, or just confirming what we already suspected?

Look, you're already changing the subject. The real question here—the only one that matters—is whether the Nobel Prize has become nothing more than a political tool.
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#35 ·
Jesse Adams said:He’s a much smaller figure than de Broglie. But let's be real—he was the one who first spotted that the eikonal equation in optics is basically an analogue to the Hamilton-Jacobi equation. That realization essentially kicked off quantum mechanics and paved the way for Schrödinger to actually write his equation. Without that link? Nothing.
Jordan didn't just assist Heisenberg—he basically handed him the blueprint for matrix mechanics on a silver platter.

It’s tough—given how much physics spans different disciplines—to put a "statistical weight" on any single discovery. But let's be real: when you look at the list of people who *didn't* get a Nobel—Hubble, Gamow, von Karman, Tesla, Racah, Bohm—and then see guys like Bardeen or Curie walking away with two? It tells me that, IMO, at least 50% of the Physics Nobels are questionable. Not to mention the stuff where the criteria are totally subjective—like the Michelson experiment, which was brilliant design—or the hunt for the tau lepton and W bosons, where researchers were basically just checking boxes to confirm the Standard Model. Is it actually groundbreaking science, or just confirming what we already suspected?

Look, you're already changing the subject. The real question here—the only one that matters—is whether the Nobel Prize has become nothing more than a political tool.

Let's get something straight. De Broglie didn't contribute much to actual quantum mechanics, just wave mechanics. His approach via Hamilton-Jacobi classical mechanics was simply easier for most people to swallow than the radical nature of matrix mechanics. Even if Schrödinger proved both approaches were technically identical, it doesn't change the fact that Jordan, alongside Heisenberg and Born, was the true pioneer in redefining physical reality.

And let's not forget his significant discovery of Fermi-Dirac statistics, which happened well before either of those two.
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#36 ·
Gregory Howard said:Let's get something straight. De Broglie didn't contribute much to actual quantum mechanics, just wave mechanics. His approach via Hamilton-Jacobi classical mechanics was simply easier for most people to swallow than the radical nature of matrix mechanics. Even if Schrödinger proved both approaches were technically identical, it doesn't change the fact that Jordan, alongside Heisenberg and Born, was the true pioneer in redefining physical reality.

And let's not forget his significant discovery of Fermi-Dirac statistics, which happened well before either of those two.

De Broglie didn't help with quantum? Sorry, but that's not what I was taught in my physics courses. Sure, he moved on to wave mechanics later, but that doesn't erase his original breakthroughs.
So you're basically saying De Broglie and Schrödinger developed dual theory, but they aren't the pioneers? Fine.
Matrix mechanics is radical and flawed—it’s incomplete. The complete version is Hilbert space formalism. You're confusing matrix mechanics with Heisenberg's operator picture, which is identical to Schrödinger's picture—and by the way, Dirac proved that, not Schrödinger. Matrix mechanics falls apart the moment you factor in spin.
I don't know where you're getting your info, because some of this is just flat-out wrong (like that bit about Schrödinger).
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#37 ·
Jesse Adams said:De Broglie didn't help with quantum? Sorry, but that's not what I was taught in my physics courses. Sure, he moved on to wave mechanics later, but that doesn't erase his original breakthroughs.
So you're basically saying De Broglie and Schrödinger developed dual theory, but they aren't the pioneers? Fine.
Matrix mechanics is radical and flawed—it’s incomplete. The complete version is Hilbert space formalism. You're confusing matrix mechanics with Heisenberg's operator picture, which is identical to Schrödinger's picture—and by the way, Dirac proved that, not Schrödinger. Matrix mechanics falls apart the moment you factor in spin.
I don't know where you're getting your info, because some of this is just flat-out wrong (like that bit about Schrödinger).

? What are you talking about? I am stating that Schrödinger demonstrated the equivalence of his approach—via differential equations—to the matrix mechanics developed by that aforementioned trio linked to Heisenberg and Pauli. Dirac's formalism and everything else belongs to much later developments.

It's baffling that such a trivial concept didn't stick during your lectures. If you need it, here is the high school version from Wikipedia, so we don't have to bother with actual academic sites:
http://en.wikipedia.org/wiki/Schroedinger#Middle_years
.....
In 1922, he attended the University of Zürich. In January 1926, Schrödinger published in the Annalen der Physik the paper "Quantisierung als Eigenwertproblem" [tr. Quantisation as an Eigenvalue Problem] on wave mechanics and what is now known as the Schrödinger equation. In this paper he gave a "derivation" of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gives a new derivation of the Schrödinger equation. A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect. A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#38 ·
Gregory Howard said:? What are you talking about? I am stating that Schrödinger demonstrated the equivalence of his approach—via differential equations—to the matrix mechanics developed by that aforementioned trio linked to Heisenberg and Pauli. Dirac's formalism and everything else belongs to much later developments.

It's baffling that such a trivial concept didn't stick during your lectures. If you need it, here is the high school version from Wikipedia, so we don't have to bother with actual academic sites:
http://en.wikipedia.org/wiki/Schroedinger#Middle_years
.....
In 1922, he attended the University of Zürich. In January 1926, Schrödinger published in the Annalen der Physik the paper "Quantisierung als Eigenwertproblem" [tr. Quantisation as an Eigenvalue Problem] on wave mechanics and what is now known as the Schrödinger equation. In this paper he gave a "derivation" of the wave equation for time independent systems, and showed that it gave the correct energy eigenvalues for the hydrogen-like atom. This paper has been universally celebrated as one of the most important achievements of the twentieth century, and created a revolution in quantum mechanics, and indeed of all physics and chemistry. A second paper was submitted just four weeks later that solved the quantum harmonic oscillator, the rigid rotor and the diatomic molecule, and gives a new derivation of the Schrödinger equation. A third paper in May showed the equivalence of his approach to that of Heisenberg and gave the treatment of the Stark effect. A fourth paper in this most remarkable series showed how to treat problems in which the system changes with time, as in scattering problems. These papers were the central achievement of his career and were at once recognized as having great significance by the physics community.

What am I supposed to "get" from the lectures? We're studying physics, not the history of physics.
Bottom line: you're wrong—and so is your Wikipedia source. I can go even deeper if necessary:

"Dirac's Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system."

I don't know exactly what that Wikipedia snippet is getting at—maybe it's implying both Schrödinger’s approach and matrix mechanics yield the same results for the Stark effect.
The point is, proving the equivalence between this:
http://upload.wikimedia.org/math/b/8...d1fd437706.png
and this:
http://upload.wikimedia.org/math/6/3...c3dd05f2fe.png
is impossible without using Dirac’s formalism. If you think you can do it, prove it. Until then, I’m sticking to my guns.
Gregory Howard Gregory Howard Active Member
144 messages
joined Dec 2009
#39 ·
Jesse Adams said:What am I supposed to "get" from the lectures? We're studying physics, not the history of physics.
Bottom line: you're wrong—and so is your Wikipedia source. I can go even deeper if necessary:

"Dirac's Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system."

I don't know exactly what that Wikipedia snippet is getting at—maybe it's implying both Schrödinger’s approach and matrix mechanics yield the same results for the Stark effect.
The point is, proving the equivalence between this:
http://upload.wikimedia.org/math/b/8...d1fd437706.png
and this:
http://upload.wikimedia.org/math/6/3...c3dd05f2fe.png
is impossible without using Dirac’s formalism. If you think you can do it, prove it. Until then, I’m sticking to my guns.

It seems we are talking past each other. I am not discussing how various mathematically formalized approaches—distinct formalisms—are merged into a single unified one (honestly, even Dirac didn't fully unify them, and Von Neumann’s formulation has its own flaws; if I recall correctly, true unification only arrived following the discoveries of Frigyes Riesz decades later). I am talking about presenting the equivalence of these approaches in a way that is satisfying and widely accepted. That means demonstrating that A can be transformed into B and vice versa, rather than claiming A and B are merely components of one unifying formalism. This is basic stuff, and there isn't much else to say:

http://www.oberlin.edu/physics/dstye...M/history.html

In short, just twenty-five years after Planck caught the first glimpse of a new physics, there wasn't just one version of it, but two competing ones! These versions appeared completely distinct, sparking bitter debates over which held the truth. In a footnote to a 1926 paper, Schrödinger admitted he felt "discouraged, if not repelled" by matrix mechanics. Meanwhile, Heisenberg wrote to Pauli on June 8, 1926, stating:

The more I contemplate the physical aspects of Schrödinger's theory, the more detestable I find it. His commentary on visualization makes almost no sense; essentially, I think it's garbage. The primary achievement of his theory is simply the calculation of matrix elements.
Fortunately, the conflict was quickly resolved: in 1926, Schrödinger and, independently, Carl Eckert (then just 24) at Caltech proved that these two new mechanics, despite their superficial differences, were functionally equivalent. [Much like how adding numbers using Arabic numerals differs from using Roman numerals, yet the final sum remains the same.] (Pauli also reached this conclusion, though he never published it.)

That covers everything worth mentioning here:
http://www.aip.org/history/heisenberg/p08.htm
Jesse Adams Jesse Adams Active Member
57 messages
joined Aug 2008
#40 ·
Gregory Howard said:It seems we are talking past each other. I am not discussing how various mathematically formalized approaches—distinct formalisms—are merged into a single unified one (honestly, even Dirac didn't fully unify them, and Von Neumann’s formulation has its own flaws; if I recall correctly, true unification only arrived following the discoveries of Frigyes Riesz decades later). I am talking about presenting the equivalence of these approaches in a way that is satisfying and widely accepted. That means demonstrating that A can be transformed into B and vice versa, rather than claiming A and B are merely components of one unifying formalism. This is basic stuff, and there isn't much else to say:

http://www.oberlin.edu/physics/dstye...M/history.html

In short, just twenty-five years after Planck caught the first glimpse of a new physics, there wasn't just one version of it, but two competing ones! These versions appeared completely distinct, sparking bitter debates over which held the truth. In a footnote to a 1926 paper, Schrödinger admitted he felt "discouraged, if not repelled" by matrix mechanics. Meanwhile, Heisenberg wrote to Pauli on June 8, 1926, stating:

The more I contemplate the physical aspects of Schrödinger's theory, the more detestable I find it. His commentary on visualization makes almost no sense; essentially, I think it's garbage. The primary achievement of his theory is simply the calculation of matrix elements.
Fortunately, the conflict was quickly resolved: in 1926, Schrödinger and, independently, Carl Eckert (then just 24) at Caltech proved that these two new mechanics, despite their superficial differences, were functionally equivalent. [Much like how adding numbers using Arabic numerals differs from using Roman numerals, yet the final sum remains the same.] (Pauli also reached this conclusion, though he never published it.)

That covers everything worth mentioning here:
http://www.aip.org/history/heisenberg/p08.htm

Hold on—how exactly would you prove those two equations are equivalent without leaning on Dirac's formalism?
I don't know. Maybe Schrödinger eventually pulled it off, but I doubt he did it without using Dirac's framework.

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