[HN Gopher] January 1928: Dirac equation unifies quantum mechani...
___________________________________________________________________
January 1928: Dirac equation unifies quantum mechanics and special
relativity
Author : thunderbong
Score : 95 points
Date : 2024-11-21 02:17 UTC (20 hours ago)
(HTM) web link (www.aps.org)
(TXT) w3m dump (www.aps.org)
| hdivider wrote:
| If our society were sane, rational, advanced, the headlines would
| be all about scientific and technological progress. The fusion
| power breakthrough of 2022 by Lawrence Livermore National Lab
| would still dominate the news. Large corporations would compete
| to create the first Star Trek replicator (at least for organic
| matter, food, etc) by advancements in nanofabrication.
| Politicians would debate R&D topics and strategy, figuring out
| which path leads to greater broad-sector economic progress.
|
| One can dream. :) Instead, we have a society almost entirely
| dependent on many kinds of technology, and yet very few
| understand any of it, nor care to. Wonder how long this trend can
| persist until some sort of phase transition appears on the
| horizon.
| readthenotes1 wrote:
| Some many years ago some people collected some negative traits
| to describe the foibles of people. Unfortunately, these
| negatives seem to dominate much of the news:
|
| Pride, Greed, Lust, Anger, Gluttony, Envy, Sloth.
|
| If we could somehow dim the influence of these human traits, we
| might get closer to the world you described
| heresie-dabord wrote:
| > Pride, Greed, Lust, Anger, Gluttony, Envy, Sloth
|
| The greatest _popular_ innovation of our time appears to be
| to have extended the above list with Falsehood, Cruelty, and
| Pollution.
| terminalbraid wrote:
| I assure you falsehood, cruelty, and pollution have existed
| long before our time.
| Jensson wrote:
| Falsehood Cruelty and Pollution are results of the 7 sins.
| Cruelty is typically caused by Anger or Envy, Pollution
| from Gluttony and Sloth, Falsehood from Pride and Envy etc.
| ggu7hgfk8j wrote:
| We aren't spherical philosophers in a vacuum. We are emotional
| animals trying our best. This fact requires constant
| consideration and management lest it all come crumbling down.
| winwang wrote:
| Alright, so we're spherical cow-philosophers... (jk, I like
| your point!)
| guerrilla wrote:
| > trying our best
|
| I strongly question this part. Most people just want comfort.
| More is never enough for them.
| antonvs wrote:
| > The fusion power breakthrough of 2022 by Lawrence Livermore
| National Lab would still dominate the news.
|
| If our society were sane, rational, advanced, it would
| recognize that that "breakthrough" was a minor, arbitrary
| improvement in reaction efficiency, that realistically brings
| us no closer to commercially viable fusion power, and doesn't
| prove anything about the possibility of that.
|
| That reaction still consumed something like 100 times the power
| that it produced, and the "power" that it produced was just
| heat energy, which would still entail losses when converted
| into usable form.
|
| On top of that, the nature of the Livermore reaction is not one
| that's even intended or suitable for commercial power
| production.
|
| At this point, we simply don't even know whether controlled,
| commercially viable fusion will ever be able to produce more
| power than it consumes. There's no guarantee that it will.
|
| If you're not aware of what I'm referring to, this article is a
| starting point: "Why the nuclear fusion 'net energy gain' is
| more hype than breakthrough": https://whyy.org/segments/why-
| the-nuclear-fusion-net-energy-...
|
| While this might all seem like an irrelevant aside to the point
| being made above, it's relevant because it shows how pervasive
| misinformation is, even when coming from supposedly scientific
| sources.
| elashri wrote:
| The announcement was correct and precise. I am not sure what
| misinformation you are describing here.
|
| Regarding your 100 more energy claim. It overlooks key facts
| about the NIF breakthrough. The fusion reaction itself
| achieved net energy gain, producing 3.15 MJ compared to 2.05
| MJ of input laser energy - far from consuming "100 times the
| power it produced." While the total facility power usage was
| indeed higher due to laser inefficiencies, this misses the
| crucial scientific achievement. This was basically humanity's
| first controlled fusion reaction producing more energy than
| was directly input to the fuel. Dismissing this as a "minor,
| arbitrary improvement" understates its significance. This
| wasn't just about efficiency metrics - it demonstrated fusion
| ignition was possible, a fundamental physics milestone that
| had eluded scientists for decades. Though challenges remain
| for commercial fusion power, the breakthrough proved a
| critical theoretical concept that many thought impossible.
| Many critics before that were referring to this point as the
| reason why it isn't worth it to keep researching. And they
| were proved wrong.
|
| Trying to redefine the announcement and experiment result to
| mean something else so that you can attack is a dishonest
| behavior.
| roelschroeven wrote:
| Nobody ever doubted that fusion ignition was physically
| possible. It happens in stars all the time, and people have
| achieved it in thermonuclear weapons.
|
| This was the first time fusion ignition was achieved in a
| laboratory setting, i.e. in a controlled fashion. Is that
| seen as a fundamental physics milestone? To me it seems
| more an incremental engineering achievement.
| antonvs wrote:
| > The announcement was correct and precise.
|
| "The" announcement? There were several announcements, with
| varying degrees of scientific rigor.
|
| Here's one typical example:
| https://www.llnl.gov/article/49301/shot-ages-fusion-
| ignition...
|
| Quote: "...achieved fusion ignition -- creating more energy
| from fusion reactions than the energy used to start the
| process."
|
| That is not "correct and precise." In fact, without any
| mention of the additional context that at least 300 MJ of
| power was used to produce 3.15 MJ of not directly usable
| heat energy, it's incorrect, imprecise, and misleading at
| best.
|
| It's also misleading because it doesn't tell you that NIF's
| definition of "ignition" is significantly different, in
| essential respects, from the term's use in other fusion
| contexts. For example, ignition at NIF doesn't mean that a
| self-sustaining reaction has been achieved. As such, the
| use of this term at all is dubious. It has no fundamental
| meaning here, it's just a name being used for an
| arbitrarily defined efficiency target.
|
| Realistically, the term is being used to try to connect
| what NIF is doing, in a facility ostensibly intended for
| nuclear weapons research, to what fusion power research
| efforts are doing. It's a hype-driven word game, it's not
| meaningful.
|
| Back to the quote above: it's carefully worded to sound as
| though it's saying something that not true. No layperson
| without prior knowledge of nuclear fusion issues is going
| to correctly understand that statement - and indeed, most
| of the initial press about this didn't, i.e. the
| journalists reporting it didn't understand what it meant,
| which is what the article I originally linked to was
| responding to.
|
| That brings us to the main point: I didn't say anything
| about an announcement. I responded to someone who was
| talking about what our _society_ would do if it "were
| sane, rational, advanced".
|
| I'm saying that it's extremely unfortunate that our society
| is too scientifically illiterate to correctly report on and
| understand what ultimately was a somewhat routine
| scientific achievement, reaching a defined efficiency
| target that has no particular fundamental meaning in the
| context.
|
| > The fusion reaction itself achieved net energy gain,
| producing 3.15 MJ compared to 2.05 MJ of input laser energy
| - far from consuming "100 times the power it produced."
|
| It used at least 300 MJ of power to drive the lasers[1].
| 300 / 3.15 = 95. But that factor of 95 would just be to
| reach a break even point with the heat energy produced,
| it's not directly usable energy.
|
| For actual usable energy, according to a 2023 presentation
| at the LLNL High Energy Density Science Seminar[2], "For a
| power plant, gain would need to be increased ~1000x
| relative to current NIF performance."
|
| None of the announcement about this so-called "ignition"
| event mentioned any of this, and nor did most (any?) of the
| mainstream press about it.
|
| The reality here is that in order to maintain public
| interest in nuclear fusion, and keep getting funded, it has
| to be presented as though fusion power is just around the
| corner - "5 years!". What I was pointing out is that "if
| our society were sane, rational, advanced," we would not
| need to play such games. We would not need to continually
| mislead the public, we would not need to pretend that
| facilities being used to do nuclear weapon "stockpile
| stewardship" research have some relevance to fusion power,
| and so on.
|
| I also found it ironic that the commenter who wanted a
| "sane, rational, advanced" society appeared themselves to
| be a victim of the misleading hype around the NIF event,
| saying that it should "still dominate the news." It simply
| wasn't that significant.
|
| > This wasn't just about efficiency metrics - it
| demonstrated fusion ignition was possible, a fundamental
| physics milestone
|
| This is incorrect, as explained above. "Ignition" here is a
| term defined by LLNL to apply to their particular weapons-
| oriented fusion facility. There's nothing "fundamental"
| about it. It's a defined target for experimental
| efficiency, that's all.
|
| > ... that had eluded scientists for decades
|
| And still does, at any facility that's trying to achieve
| nuclear power generation, and not just a weapons research
| facility blasting a pellet with 300 MJ from 192 lasers. The
| NIF result is simply not transferable to any other fusion
| scenario.
|
| > Trying to redefine the announcement and experiment result
| to mean something else so that you can attack is a
| dishonest behavior.
|
| It's not clear that you yet understand the full extent of
| the deception that you've been subjected to, so you're
| trying to shoot the messenger.
|
| [1] https://ww2.aip.org/fyi/2022/national-ignition-
| facility-achi...
|
| [2] https://heds-
| center.llnl.gov/sites/heds_center/files/2023-03... (bottom
| of 59th slide)
| elashri wrote:
| As a fellow scientist, I will go and read the details
| from the research paper that the group published [1].
| Anything else is nonsense for me. it gives a clear view
| on the goals, physics and what was done. Including all
| the details you would get that. I will quote the first
| paragraph from the paper summary
|
| > In summary, the December 5, 2022 experiment on the
| National Ignition Facility, N221204, was the first time
| that fusion target gain was unambiguously achieved in the
| laboratory in any fusion scheme. The demonstrated level
| of target gain on N221204 of 1.5 times is a proof of
| principle that controlled laboratory fusion energy is
| possible
|
| And they specifically mention that it is not overall
| facility-wise net gain in the next paragraph
|
| > Notethat G_{target} > 1 does not imply net energy gain
| from a practical fusion energy perspective, because the
| energy consumed by the NIF laser facility is typically
| 100x larger than E_{laser}. The NIF laser architecture
| and target configuration was chosen to give the highest
| probability for fusion ignition for research purposes and
| was not optimized to produce net energy for fusion energy
| applications.
|
| So you don't have to go and claim a deception. You want
| to claim it wasn't significant which is your opinion but
| that is not what the actual scientific community in the
| field (who know more than you) would agree.
|
| [1] https://journals.aps.org/prl/abstract/10.1103/PhysRev
| Lett.13...
| antonvs wrote:
| > So you don't have to go and claim a deception.
|
| I didn't claim a deception in the research paper. I've
| clearly stated what I'm claiming, and you've said nothing
| that changes any of that.
|
| In fact, you originally didn't even mention the research
| paper, you said "the announcement". The deception was in
| every official announcement, none of which included any
| details of the caveat that you quoted. That deception
| continued, mostly unwittingly I'm sure, in all the press
| on the matter.
|
| You're shifting the goalposts to try to support a point
| which is irrelevant to what I've been saying.
|
| > You want to claim it wasn't significant which is your
| opinion but that is not what the actual scientific
| community in the field (who know more than you) would
| agree.
|
| It's not significant with respect to commercial nuclear
| fusion power, which was the entire basis for all the
| reporting about it.
|
| The idea that "the actual scientific community" would
| support your position is an unsupported claim that's
| easily refuted.
|
| For example, Victor Gilinsky, a physicist who previously
| a commissioner for the US NRC, wrote in "What's fueling
| the commercial fusion hype?"[1]:
|
| > "Recent White House and Energy Department
| pronouncements on speeding up the 'commercialization' of
| fusion energy are so over the top as to make you wonder
| about the scientific competence in the upper reaches of
| the government."
|
| That article discusses the NIF experiment among others,
| highlighting out the discrepancies between the official
| announcements and what the experiment actual does. It
| also points out that the experiment "is, in effect, a
| miniature (secondary) thermonuclear bomb, with the lasers
| playing the role of the triggering fission reactions
| (primary)," which helps explain "its lack of promise for
| civilian use."
|
| There have been plenty of similar criticism from other
| scientists, including Daniel Jassby previously of
| Princeton Plasma Physics Lab, and M.V. Ramana at U.
| British Columbia.
|
| In "Clean Energy or Weapons? What the 'Breakthrough' in
| Nuclear Fusion Really Means"[2], Ramana wrote, "without
| the excitement created by these hyped-up statements, it
| would be impossible to get funded for the decades it
| takes to plan and build these facilities."
|
| Again, in a "sane, rational, advanced" society, this
| would not be necessary. And you, and the commenter I
| originally replied to, would not have had clear
| misapprehensions about the experiment as a result. In
| your case, at the very least, you appeared to believe
| that "ignition" was some fundamental physical phenomenon
| in this case, which it is not, in the context of the NIF
| experiment.
|
| > As a fellow scientist
|
| As a scientist, you _should_ be interested in what 's
| true.
|
| --
|
| [1] https://thebulletin.org/2024/02/whats-fueling-the-
| commercial...
|
| [2] https://science.thewire.in/the-sciences/clean-energy-
| weapons...
| mikhailfranco wrote:
| The LLNL fusion result was not a breakthrough. The fusion
| output was about 1% of the energy input. The exaggerated press
| release was just a PR ploy to get support for continued DoE
| funding, which was expiring at the end of 2022.
| orwin wrote:
| And while we talk about fusion, even when the energy output
| surpass the energy input and the reaction is stable enough,
| how to you harness the energy? Because the reaction happen
| within a vacuum, the only way is to capture expelled neutrons
| and make electricity from it somehow.
| mikhailfranco wrote:
| Yes, they forgot that part, so there will be further energy
| losses (at least 70%).
|
| They also have to up the repetition rate from once a week
| to at least 1k /s.
|
| Note that ASML lithography machines accurately dilate and
| irradiate molten tin droplets with lasers at ~ 50k /s.
|
| https://www.asml.com/en/technology/lithography-
| principles/li...
| jojobas wrote:
| NIF is first and foremost a thermonuclear weapons research
| facility. The "breakthrough" you're talking about doesn't bring
| us an inch closer to fusion power.
| 8bitsrule wrote:
| I think that a 'breakthrough' would be to realize that
| harnessing fusion outside of a solar environment is a
| hopeless dream that, carefully fed, is very good at provoking
| research grants.
| bckr wrote:
| Don't worry, we can create a priesthood caste with secret
| knowledge of technology whose purpose is to guide the human
| race toward a brighter tomorrow!
|
| Maybe someone could write a foundational science fiction novel
| about this.
| koolala wrote:
| Anathem by Neal Stephenson?
| bckr wrote:
| I'll have to check that one out
| koolala wrote:
| It's my favorite utopian science book!
| aeonik wrote:
| Foundation Series by Isaac Asimov
| _s_a_m_ wrote:
| No they would not. Not all and probably most progresses are not
| technological. Are you living under a rock?
| exe34 wrote:
| what are you talking about? the most important thing is to make
| sure senators use the correct bathroom!
| teleforce wrote:
| > Yet the technique employed to make the theory useful --
| renormalization -- repulsed Dirac because he found it
| mathematically ugly.
|
| Perhaps if he had used quaternion the solution will not be
| mathematically ugly or can even be beautiful [1].
|
| [1] A quaternion formulation of the Dirac equation:
|
| https://mauritssilvis.nl/research/publications/silvis-rug10....
| elashri wrote:
| Dirac was not working in vaccum . Klein-Jordan equation was the
| simplest and the most obvious extension of Schrodinger equation
| in relativistic manner.
|
| So historically, Dirac was focused on correcting the Klein-
| Gordon equation, which had issues with negative probabilities
| and describing electron behavior. His goal was to find a
| relativistic equation that resolved these problems while
| maintaining consistency with his own matrix mechanics
| formulation of quantum mechanics.
|
| By extending his matrix mechanics formalism, Dirac derived an
| equation that not only addressed the issues with the Klein-
| Gordon equation but also predicted the existence of antimatter.
| I would argue that Dirac's approach was consistent with his
| established framework, and while he found renormalization
| mathematically unsatisfactory, it does not diminish the
| validity of his method in deriving the Dirac equation. I doubt
| he focused on any elegant solutions, he was actually quite
| happy working with matrix mechanics framework.
| jesuslop wrote:
| Bohr was a big shot, Nobel prized establishment authority. In
| Weimberg QFT book he recalls a fragment of Dirac's memoirs:
|
| "I remember once when I was in Copenhagen, that Bohr asked me
| what I was working on and I told him I was trying to get a
| satisfactory relativistic theory of the electron, and Bohr
| said 'But Klein and Gordon have already done that!' That
| answer first rather disturbed me. Bohr seemed quite satisfied
| by Klein's solution, but I was not because of the negative
| probabilities that it led to. I just kept on with it,
| worrying about getting a theory which would have only
| positive probabilities."
| phkahler wrote:
| Is there a relationship between the negative probabilities
| of Klein and the negative energy of Dirac? Did his
| formulation just move the problem? If so, does it imply
| anything? Like are probability and energy related?
| elashri wrote:
| Klein-Jordan equation does have both problems, negative
| probabilities and energies. Dirac equation solved
| negative probabilities and now predicts positive
| probabilities for both positive and negative energy
| states. But the negative energies problem still exists
| and Dirac used different interpenetration to explain them
| and did not get rid of them (which we knew later that
| this was the correct things to do). So he came with the
| famous negative energy solutions interpreted as
| antiparticles.
| superposeur wrote:
| It's worth mentioning that, brilliant as Dirac's "sea of
| filled negative energy states" picture was, no one
| believes that interpretation now. The Dirac equation is
| better seen as the _classical equation of motion_ for the
| Grassmann-valued electron field (just as Maxwell's
| equations are the classical eom for photon field). There
| are only positive-energy states (=quantized excitations
| of the field). I do think popular accounts should begin
| mentioning this in order not to keep reinforcing the old
| Dirac sea interpretation.
| codethief wrote:
| > no one believes that interpretation now
|
| I know of at least one (tenured) person that does, at
| least to some degree: Felix Fenster at Regensburg
| University. When I met him years ago, he said taking the
| Dirac Sea interpretation seriously was what caused him to
| come with his own program for a theory of quantum
| gravity, called Causal Fermion Systems[0]. I haven't
| looked into his theory in detail but I did find a
| reference to the Dirac sea[1]:
|
| > In order to obtain a causal fermion system, we first
| have to choose a Hilbert space. The space of negative-
| energy solutions of the Dirac equation (i.e. the Dirac
| sea) turns out to be a good choice. [...] As a side
| remark, it is worth noting that the Dirac sea vacuum is
| to be seen as an effective model describing a particular
| minimizing causal fermion system. It is one particular
| physical system that we can describe as a minimizing
| causal fermion system. But we should really only think of
| it as an effective description, in the sense that it
| describes only the macroscopic structure of spacetime,
| whereas its microscopic structure on the Planck scale is
| essentially unknown. [...] The idea of the Dirac Sea did,
| however, play an important role in the conception of the
| causal fermion systems framework, and most of the
| existing literature is written with that point of view in
| mind. A more detailed motivation for why it is a natural
| starting point can be found here[2].
|
| [0]: https://causal-fermion-system.com/
|
| [1]: https://causal-fermion-system.com/intro-phys/
|
| [2]: https://causal-fermion-
| system.com/theory/physics/why-dirac-s...
| cornel_io wrote:
| That reformulation doesn't let you avoid renormalization, does
| it?
| terminalbraid wrote:
| No, it doesn't.
| kelseyfrog wrote:
| Thank you for posing the quaternion formulation. It inspired me
| to search for a geometric algebra version of the same equation
| and was happy to find that it also exists[1].
|
| 1. https://fondationlouisdebroglie.org/AFLB-342/aflb342m679.pdf
| JPLeRouzic wrote:
| > _Quaternions_
|
| I know nothing of physics, but it seems to me that rotation
| fingerprints are everywhere in physics. Is this just me or is
| there something more tangible in this remark?
| Ono-Sendai wrote:
| It's not just you. Dirac fields are constantly rotating. In
| fact the solutions are called spinors. (e.g. things that spin).
| There are a _lot_ of rotations at the quantum level. It 's also
| why complex numbers show up a lot in q.m.
| ValentinA23 wrote:
| I've been trying to get an intuitive understanding of why
| multiplying by e^ix leads to a rotation in the complex plane,
| without going into Taylor series (too algebraic, not enough
| geometric). I tried to find a way to calculate the value of e
| in a rotational setting, maybe there is a way to reinterpret
| compound interests as compound rotation. Any insight ?
| dboreham wrote:
| IANAM but I'd go with "it's implicit in how complex numbers
| are defined". Complex numbers are a thing made up by humans
| (as are negative numbers), and we got to define i as "up
| the y-axis". Once you do that, and note that a rotation is
| therefore cos angle plus i sin angle, add in that
| e^something is an eigenfuncion of differentiation, and
| you're pretty much there.
|
| Fwiw I think it's Maclaurin series for this.
|
| Edit: obviously should be j not i.
| empiricus wrote:
| One possibility: take the unit circle, and a vertical line
| tangent to the circle at (1,0). Then e^ix takes that line
| and wraps it around the circle. This
| ColinHayhurst wrote:
| Complex numbers and (Pauli/Dirac) matrices not required if
| you use Geometric Algebra. I highly recommend the book by
| Doran and Lasenby [0], or you can get the details from
| their papers, notably [1].
|
| [0] Geometric Algebra for Physicists, CUP, 2003
|
| [1] https://arxiv.org/abs/quant-ph/0509178
| ValentinA23 wrote:
| https://deferentialgeometry.org/papers/Doran,%20Lasenby%2
| 0-%...
|
| page 28, equation 2.36. Thanks a lot I'll take a dive
| into this
|
| Note: my inquiry was motivated by this:
|
| https://blog.revolutionanalytics.com/2014/01/the-fourier-
| tra...
| ColinHayhurst wrote:
| p281 for Dirac equation. But I suggest you start at least
| from the beginning of Chapter 8. Earlier, obviously if
| you don't know Geometric Algebra. It's worth it; many
| examples but one is that the four Maxwell equations are
| expressed as one compact equation with geometric
| intuition.
| itishappy wrote:
| Euler's formula is a specific case of the exponential map
| from Lie theory. This means e^x can be used with all sorts
| of interesting x types, and it often has surprisingly
| intuitive behavior! When x is a real number you get
| continuous growth. When x is a purely imaginary number you
| get continuous rotation. When x is complex you get
| continuous growth and rotation. When x is a matrix you get
| a continuous linear transformation (growth, rotation, and
| shear). What's the similarity here? Euler's formula treats
| it's argument as a transformation which gets continuously
| applied in infinitesimal amounts. This also explains the
| formula for calculating the value of e: e
| = lim (1 + 1 / n) ^ n where (x -> infinity)
|
| https://en.wikipedia.org/wiki/Exponential_map_(Lie_theory)
|
| https://en.wikipedia.org/wiki/Matrix_exponential
|
| https://www.youtube.com/watch?v=O85OWBJ2ayo
| sparky_z wrote:
| My favorite intuitive explanation was actually written by
| science fiction author, Greg Egan. It takes the exact
| approach you're asking for, reinterpreting compound
| interest in a 2d rotational context on the complex plane,
| and doesn't use more than high school math:
|
| https://gregegan.net/FOUNDATIONS/04/found04.html#s2
|
| Fig. 7 is the money shot.
| cjfd wrote:
| Of course. The solutions of the Dirac equations live in space
| and space has rotation symmetry. These solution have to
| transform in some way under rotations.
| nimish wrote:
| Rotations and spin are deeply tied into the geometrical nature
| of a space. It's not just you. It's core to understanding the
| nature of matter itself.
|
| Cartan had only just invented spinors as an object in
| themselves (ignoring clifford) so a lot of the physics stuff
| was done in parallel or even without the knowledge the
| mathematicians had.
| gsf_emergency wrote:
| Looking for possible citations for
|
| > _... renormalization -- repulsed Dirac because he found it
| mathematically ugly._
|
| I found
|
| https://physics.stackexchange.com/questions/375209/dirac-onc...
|
| (2019) for the "Cosmic Galois group" (edited) as well as Anixx's
| comments/Neumaier's responses
| peter_d_sherman wrote:
| >"Months later, Schrodinger -- inspired by Louis de Broglie's
| idea that matter behaves like a wave -- proposed an entirely
| different, but mathematically equivalent, formulation of particle
| behavior based on the better-known mathematics of waves."
|
| [...]
|
| More surprising results unfurled when Dirac extended his equation
| to describe an electron interacting with an electromagnetic
| field. Experimentalists had confirmed that the electron's
| intrinsic angular momentum, or spin, was equal to 1/2, but
| theoreticians couldn't figure out how to properly incorporate it
| into their theories. With his new equation, Dirac had found,
| almost as an afterthought, that the spin emerged naturally.
|
| [...]
|
| The Dirac equation was simple and elegant, yet dense with
| implications. Perhaps its most profound feature was that,
|
| _instead of producing two components for negative and positive
| spin states, it produced four: a negative and positive spin state
| for each of two particles with positive and negative energy
| states._ "
|
| Related:
|
| https://en.wikipedia.org/wiki/Chirality
|
| https://en.wikipedia.org/wiki/Angular_momentum
|
| https://en.wikipedia.org/wiki/Noether%27s_theorem
| magicalhippo wrote:
| For those enjoying the history of early quantum mechanics, I've
| been following Dr. Jorge S. Diaz on YouTube[1].
|
| He has a great video series going on the people, experiments and
| discoveries that lead to quantum mechanics.
|
| The videos are very accessible, but he does go into some details
| like various key derivations and such. Well worth watching for
| casual physics fans IMHO.
|
| [1]: https://www.youtube.com/@jkzero/
| CamperBob2 wrote:
| Diaz is awesome. For me, he manages to strike just the right
| balance between making the topic interesting in a
| historical/human-interest sense and including enough technical
| detail to cultivate actual insight. Both his Franck-Hertz and
| Stern-Gerlach videos are the best I've run across on YouTube
| (and I see the latter has a part 2 now, so that'll be next on
| my watchlist.)
|
| Hugely underrated YouTuber.
| itishappy wrote:
| I also just love his energy. He's unapologetically excited
| about the stuff that excites him, and even if I don't share
| all his interest, it makes his videos an absolute joy to
| watch.
| NoOn3 wrote:
| I very like this playlist
| https://www.youtube.com/watch?v=xLfFWXUNJ_I It's good
| introduction in quantum mechanics with minimum posible math. It's
| on Russian but as I see It has English subtitles.
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