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.
Hugely underrated YouTuber.
[...]
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
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....
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.
"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."
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 up 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...
Looks like my auto correction messed up.
1. https://fondationlouisdebroglie.org/AFLB-342/aflb342m679.pdf
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?
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.
e = lim (1 + 1 / n) ^ n where (x -> infinity)
[0] Geometric Algebra for Physicists, CUP, 2003
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...
https://gregegan.net/FOUNDATIONS/04/found04.html#s2
Fig. 7 is the money shot.
Fwiw I think it's Maclaurin series for this.
Edit: obviously should be j not i.
>... 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
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.
I strongly question this part. Most people just want comfort. More is never enough for them.
Maybe someone could write a foundational science fiction novel about this.
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...
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.
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.
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.
"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)
> 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 100× 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/PhysRevLett.13...
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...
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
The greatest popular innovation of our time appears to be to have extended the above list with Falsehood, Cruelty, and Pollution.