Ethan Siegel wrote a blog post this week called This Is Why Quantum Field Theory Is More Fundamental Than Quantum Mechanics. I read it and sighed, because so much of it is misleading. This sort of thing has been in the air recently, because Lee Smolin gave a lecture on Einstein’s unfinished revolution. Smolin said quantum mechanics was incomplete, then doubled down and said it was wrong. I think he’s right, only more than he knows. So I thought I’d use Siegel’s post to show just how wrong quantum mechanics is, and quantum field theory. I’ll go through it step by step, giving his text in blue. He starts with a gif depicting virtual particles popping in and out of existence. Note the caption:
Visualization of a quantum field theory calculation showing virtual particles in the quantum vacuum. (Specifically, for the strong interactions.) Even in empty space, this vacuum energy is non-zero. As particle-antiparticle pairs pop in-and-out of existence, they can interact with real particles like the electron, providing corrections to its self-energy that are vitally important. On Quantum Field Theory offers the ability to calculate properties like this. (DEREK LEINWEBER)
The trouble with this is that virtual particles are not short-lived real particles. They are virtual. As in not real. They aren’t the same thing as vacuum fluctuations. The electron is not some point-particle with an infinite self-energy that’s corrected by particle-antiparticle pairs popping in and out of existence. Renormalization is a kludge. It was needed because Heisenberg and Pauli adopted Frenkel’s point-particle electron instead of Schrödinger’s wave in a closed path. Because Schrödinger was the enemy. Anyway, Siegel starts proper with something about what’s truly fundamental:
If you wanted to answer the question of what’s truly fundamental in this Universe, you’d need to investigate matter and energy on the smallest possible scales. If you attempted to split particles apart into smaller and smaller constituents, you’d start to notice some extremely funny things once you went smaller than distances of a few nanometers, where the classical rules of physics still apply.
No, you don’t start to notice some funny things. Especially since the electron’s field is what it is, so the electron isn’t actually small. Nor is the photon. It takes many paths just like a seismic wave takes many paths. Siegel carries on by saying reality becomes strange and counter-intuitive:
On even smaller scales, reality starts behaving in strange, counterintuitive ways. We can no longer describe reality as being made of individual particles with well-defined properties like position and momentum.
However it isn’t strange or counter-intuitive when you appreciate that particles are waves. They aren’t billiard balls. The Heisenberg uncertainty principle is “inherent in the properties of all wave-like systems”, and “arises in quantum mechanics simply due to the matter wave nature of all quantum objects”. Next comes the quantum realm:
Instead, we enter the realm of the quantum: where fundamental indeterminism rules, and we need an entirely new description of how nature works. But even quantum mechanics itself has its failures here. They doomed Einstein’s greatest dream — of a complete, deterministic description of reality – right from the start. Here’s why.
No, they didn’t doom Einstein’s greatest dream of a complete, deterministic description of reality right from the start. Like Lee Smolin said, the Copenhagen school were anti-realists. They rejected all attempts to understand or describe what was really going on in subatomic physics. For example, they rejected electron spin, despite the evidence of electron and positrons tracing opposite curves in a magnetic field. Despite the evidence of the Stern-Gerlach effect. Despite Schrödinger. They won the day, they doomed Einstein’s dream, and here we are to this day. Moving on:
If we lived in an entirely classical, non-quantum Universe, making sense of things would be easy. As we divided matter into smaller and smaller chunks, we would never reach a limit. There would be no fundamental, indivisible building blocks of the Universe. Instead, our cosmos would be made of continuous material, where if we build a proverbial sharper knife, we’d always be able to cut something into smaller and smaller chunks.
That’s what we can do. Our cosmos is made of a continuous material called space, and like Einstein said, the contrast between space and matter would fade away. Space is not made out of chunks. A photon is a wave in space, and it doesn’t approach you in steps.
That dream went the way of the dinosaurs in the early 20th century. Experiments by Planck, Einstein, Rutherford and others showed that matter and energy could not be made of a continuous substance, but rather was divisible into discrete chunks, known as quanta today. The original idea of quantum theory had too much experimental support: the Universe was not fundamentally classical after all.
That’s wrong. Planck came up with the quantum nature of light. His constant of action is the h in photon energy E = hc/λ. It doesn’t mean light is made of discrete chunks. A photon has a wavelength, and it can have any energy you like. See Leonard Susskind talking about Planck’s constant in demystifying the Higgs boson. At 2 minutes 50 seconds he rolls his whiteboard marker round saying angular momentum is quantized. Think like this: ”roll your marker round fast or slow, but roll it round the same circumference, because Planck’s constant of action h is common to all photons regardless of wavelength”. The dimensionality of action can be expressed as momentum times distance. It’s like all photons have the same amplitude, that’s all. Take a look at some pictures of the electromagnetic spectrum. Note how the wave height is always the same regardless of wavelength. That’s Planck’s constant, hiding in plain sight. What’s next?
For perhaps the first three decades of the 20th century, physicists struggled to develop and understand the nature of the Universe on these small, puzzling scales. New rules were needed, and to describe them, new and counterintuitive equations and descriptions. The idea of an objective reality went out the window, replaced with notions like: probability distributions rather than predictable outcomes, wavefunctions rather than positions and momenta, Heisenberg uncertainty relations rather than individual properties.
Yes, reality went out of the window, because people like Niels Bohr willfully rejected any attempt to describe what a photon was, how pair production worked, and what an electron was. The wave nature of light and matter somehow morphed into some kind of probability wave for point-particles. It still thought of in such terms today, 8 years after work by the Lundeen lab that showed that wavefunction was real.
The particles describing reality could no longer be described solely as particle-like. Instead, they had elements of both waves and particles, and behaved according to a novel set of rules.
Not true. Pascual Jordan solved the issue of wave-particle duality in 1925. Particles are waves. That’s why we can diffract photons, electrons, neutrons, and other particles. See Pascual Jordan’s resolution of the conundrum of the wave-particle duality of light by Anthony Duncan and Michel Janssen dating from 2007. Read up on the double slit experiment. There’s no mystery to it once you know that detection involves something akin to a Fourier transform.
Initially, these descriptions troubled physicists a great deal. These troubles didn’t simply arise because of the philosophical difficulties associated with accepting a non-deterministic Universe or an altered definition of reality, although certainly many were bothered by those aspects.
They didn’t trouble physicists for long. The matter was settled by 1925. But in 1926 Heisenberg and Pauli adopted Frenkel’s point-particle electron, and it was downhill all the way after that.
Instead, the difficulties were more robust. The theory of special relativity was well-understood, and yet quantum mechanics, as originally developed, only worked for non-relativistic systems. By transforming quantities such as position and momentum from physical properties into quantum mechanical operators — a specific class of mathematical function – these bizarre aspects of reality could be incorporated into our equations.
There’s nothing bizarre about waves. What’s bizarre is turning your back on understanding and forgetting that the Schrödinger equation is a wave equation. Siegel then gives a gif of a particle in a box. The particle looks like a red billiard ball. That’s the wrong picture. Because the particle is a wave. Standing wave, standing field:
Trajectories of a particle in a box (also called an infinite square well) in classical mechanics (A) and quantum mechanics (B-F). In (A), the particle moves at constant velocity, bouncing back and forth. In (B-F), wavefunction solutions to the Time-Dependent Schrodinger Equation are shown for the same geometry and potential. The horizontal axis is position, the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. (B,C,D) are stationary states (energy eigenstates), which come from solutions to the Time-Independent Schrodinger Equation. (E,F) are non-stationary states, solutions to the Time-Dependent Schrodinger equation. Note that these solutions are not invariant under relativistic transformations; they are only valid in one particular frame of reference. (STEVE BYRNES / SBYRNES321 OF WIKIMEDIA COMMONS)
Then we have a little rewriting of history. Siegel suggests quantum mechanics faced some kind of existential threat because it wasn’t initially relativistic. That really wasn’t a big deal. I know this, because I’ve investigated the history of quantum mechanics, and the nature of time:
But the way you allowed your system to evolve depended on time, and the notion of time is different for different observers. This was the first existential crisis to face quantum physics.
It wasn’t an existential crisis, special relativity is straightforward. The real existential crisis was the problem of infinities. Again, that occurred because Heisenberg and Pauli were determined to adopt Frenkel’s point-particle electron instead of Schrödinger’s wave in a closed path. Because Schrödinger was the enemy. What’s next?
We say that a theory is relativistically invariant if its laws don’t change for different observers: for two people moving at different speeds or in different directions. Formulating a relativistically invariant version of quantum mechanics was a challenge that took the greatest minds in physics many years to overcome, and was finally achieved by Paul Dirac in the late 1920s.
Greatest minds in physics? Have you ever actually read any of Dirac’s papers? They are absolutely awful. In Dirac’s beautiful mathematical world, light doesn’t interact with light, light moving in a straight line is stationary, stationary waves have no energy, and there’s an infinite number of non-existent zero-state photons waiting to jump into existence. Sadly all of this nonsense sidelined Charles Galton Darwin’s 1927 paper on the electron as a vector wave. Siegel then gives some hyperbole on the Dirac equation:
The result of his efforts yielded what’s now known as the Dirac equation, which describes realistic particles like the electron, and also accounts for: antimatter, intrinsic angular momentum (a.k.a., spin), magnetic moments, the fine structure properties of matter, and the behavior of charged particles in the presence of electric and magnetic fields.
The Dirac equation explains nothing. Dirac really didn’t have a clue what an electron was. He still though of it as a point-particle in 1938, and in 1962 he thought it was a charged shell. In 1930 he came up with a theory of electrons and protons. That’s where space consists of an infinite number of negative-energy electrons per unit volume, some of which have infinite negative energy. All these negative-energy electrons are of course completely unobservable, just like the angels on the head of the pin. As for antimatter, Graham Farmelo talked about that in his 2010 article did Dirac predict the positron? He says Dirac’s “close friend Patrick Blackett, one of the leading players in the story’s denouement, denied it”. And that “very few physicists took Dirac’s hole theory seriously”. He also says “Victor Weisskopf later recalled the idea ‘seemed incredible and unnatural to everybody’”.
This was a great leap forward, and the Dirac equation did an excellent job of describing many of the earliest known fundamental particles, including the electron, positron, muon, and even (to some extent) the proton, neutron, and neutrino.
The Dirac equation doesn’t describe the electron at all. Or any other particle. If you beg to differ, describe the electron to me. And it definitely doesn’t apply to the neutron. Or to photons. But to his credit, Siegel includes a picture with a caption that says the Dirac equation doesn’t describe photon-photon interactions. If you don’t describe the photon, or the photon-photon interaction that creates the electron and the positron, you have no foundations. Especially when you don’t describe the electron either.
A Universe where electrons and protons are free and collide with photons transitions to a neutral one that’s transparent to photons as the Universe expands and cools. Shown here is the ionized plasma (L) before the CMB is emitted, followed by the transition to a neutral Universe (R) that’s transparent to photons. The scattering between electrons and electrons, as well as electrons and photons, can be well-described by the Dirac equation, but photon-photon interactions, which occur in reality, are not. (AMANDA YOHO)
Also to his credit, Siegel says in his own text that the Dirac equation doesn’t describe the photon or the photon-photon interaction:
But it couldn’t account for everything. Photons, for instance, couldn’t be fully described by the Dirac equation, as they had the wrong particle properties. Electron-electron interactions were well-described, but photon-photon interactions were not. Explaining phenomena like radioactive decay were entirely impossible within even Dirac’s framework of relativistic quantum mechanics. Even with this enormous advance, a major component of the story was missing.
The above is a paragraph I agree with. But I will say this: a major component of the story is still missing. Even to this day, quantum electrodynamics doesn’t describe the photon, or pair production, or the electron. Even to this day, there’s a hole in the heart of quantum electrodynamics. How does a photon interact with another photon? By exchanging photons? No. How does it interact with itself and stay tied up as an electron? By exchanging photons? No.
The big problem was that quantum mechanics, even relativistic quantum mechanics, wasn’t quantum enough to describe everything in our Universe.
That isn’t the big problem. The big problem is that quantum mechanics wasn’t quantum enough to describe anything in our universe. Siegel then gives a picture that talks about a point particle and an electric field:
If you have a point charge and a metal conductor nearby, it’s an exercise in classical physics alone to calculate the electric field and its strength at every point in space. In quantum mechanics, we discuss how particles respond to that electric field, but the field itself is not quantized as well. This seems to be the biggest flaw in the formulation of quantum mechanics. (J. BELCHER AT MIT)
That’s misleading, because the electron is not a point particle. Its field is what it is. And that field is the electromagnetic field. Siegel then talks about classical electromagnetism:
Think about what happens if you put two electrons close to one another. If you’re thinking classically, you’ll think of these electrons as each generating an electric field, and also a magnetic field if they’re in motion. Then the other electron, seeing the field(s) generated by the first one, will experience a force as it interacts with the external field. This works both ways, and in this way, a force is exchanged.
You know, sometimes it feels like Maxwell was never born. No Ethan, the electron is an electromagnetic field construct. It isn’t some point-particle that generates an electric field. And no, if you’re thinking classically you’ll think of each electron as being a dynamical “spinor”, a double-wrapped electromagnetic wave in a spin ½ Möbius configuration with no apparent phase, so it looks like a standing electromagnetic field. Only it isn’t really standing, it’s more like an optical vortex, and two co-rotating vortices move around one another and away from one another.
This would work just as well for an electric field as it would for any other type of field: like a gravitational field. Electrons have mass as well as charge, so if you place them in a gravitational field, they’d respond based on their mass the same way their electric charge would compel them to respond to an electric field.
This is wrong because the massless photon responds to a gravitational field. And because the electron is an electromagnetic field construct – it doesn’t actually have an electric field, so electric charge is actually a misnomer.
Even in General Relativity, where mass and energy curve space, that curved space is continuous, just like any other field.
General relativity is not a theory where mass and energy curve space. Does nobody know how gravity works? Has nobody read Einstein’s Leyden Address? A concentration of energy, usually in the guise of a massive star, “conditions” the surrounding space, making it “neither homogeneous nor isotropic”. A gravitational field is inhomogeneous space where light curves because “the speed of light is spatially variable”. The inhomogeneity is non-linear, hence spacetime curvature. The electromagnetic field is curved space – see what Percy Hammond said in the 1999 Compumag: “We conclude that the field describes the curvature that characterizes the electromagnetic interaction. Siegel then gives a picture where the caption gets gravitational blueshift wrong. Electron-positron annihilation at a lower elevation results in lower-energy photons, because of the mass deficit. If you include the kinetic energy of a falling electron-positron pair the photon energy is the same due to conservation of energy.
If two objects of matter and antimatter at rest annihilate, they produce photons of an extremely specific energy. If they produce those photons after falling deeper into a region of gravitational curvature, the energy should be higher. This means there must be some sort of gravitational redshift/blueshift, the kind not predicted by Newton’s gravity, otherwise energy wouldn’t be conserved. In General Relativity, the field carries energy away in waves: gravitational radiation. But, at a quantum level, we strongly suspect that just as electromagnetic waves are made up of quanta (photons), gravitational waves should be made up of quanta (gravitons) as well. This is one reason why General Relativity is incomplete. (RAY SHAPP / MIKE LUCIUK; MODIFIED BY E. SIEGEL)
This error is then used as some kind of justification for quantum gravity. For anybody out there working on quantum gravity, I recommend this course of action: understand gravity first, then electromagnetism, and then start working on something other than quantum gravity. Siegel carries on:
The problem with this type of formulation is that the fields are on the same footing as position and momentum are under a classical treatment. Fields push on particles located at certain positions and change their momenta. But in a Universe where positions and momenta are uncertain, and need to be treated like operators rather than a physical quantity with a value, we’re short-changing ourselves by allowing our treatment of fields to remain classical.
This is wrong too. The electron doesn’t move because some field is pushing on it. It falls down in a gravitational field because it’s like light going round a closed path, and the horizontal component curves downwards because of the gradient in the speed of light. It goes round and round in circles in a uniform magnetic field because it’s a dynamical “spinor” undergoing precession in what is effectively a rotor field. Siegel then gives a picture with a caption that says we expect GR’s successor will contain space that is quantized. Somebody just doesn’t understand gravity.
The fabric of spacetime, illustrated, with ripples and deformations due to mass. A new theory must be more than identical to General Relativity; it must make novel, distinct predictions. As General Relativity offers only a classical, non-quantum description of space, we fully expect that its eventual successor will contain space that is quantized as well, although this space could be either discrete or continuous.
Siegel then talks up second quantization, claiming it was some great advance. Does anybody seriously think that introducing creation and annihilation operators was some kind of substitute for actually understanding what actually happens in pair production and annihilation? I’m afraid the answer is yes. Siegel says this:
That was the big advance of the idea of quantum field theory, or its related theoretical advance: second quantization. If we treat the field itself as being quantum, it also becomes a quantum mechanical operator. All of a sudden, processes that weren’t predicted (but are observed) in the Universe, like: matter creation and annihilation, radioactive decays, quantum tunneling to create electron-positron pairs, and quantum corrections to the electron magnetic moment, all made sense.
It’s Emperor’s New Clothes. Matter is created when photons interact with photons and thence themselves to form fermion pairs of opposite chirality. Annihilation is the reverse process. Pair production is nothing to do with quantum tunnelling. Beta decay only makes sense if you understand the neutron, and know that electron capture does what it says on the tin. Then you pay attention to what James Chadwick said in 1933: “the electric field between a neutron and a nucleus is small except at distances of the order of 10-12 cm”. As for quantum corrections to the electron magnetic moment, they were a retrofit to match the observed value. Siegel then gives a picture of Feynman diagrams with a caption that says “The major way this framework differs from quantum mechanics is not merely the particles, but also the fields are quantized”. Somebody doesn’t know that the electron’s field is what it is. The foundations just aren’t there.
Today, Feynman diagrams are used in calculating every fundamental interaction spanning the strong, weak, and electromagnetic forces, including in high-energy and low-temperature/condensed conditions. The major way this framework differs from quantum mechanics is that not merely the particles, but also the fields are quantized. (DE CARVALHO, VANUILDO S. ET AL. NUCL.PHYS. B875 (2013) 738-756)
In the next paragraph. Siegel seems to be admitting that particle exchange is just a calculation tool, and that Feynman diagrams offer only a perturbative or approximate calculation method:
Although physicists typically think about quantum field theory in terms of particle exchange and Feynman diagrams, this is just a calculational and visual tool we use to attempt to add some intuitive sense to this notion. Feynman diagrams are incredibly useful, but they’re a perturbative (i.e., approximate) approach to calculating, and quantum field theory often yields fascinating, unique results when you take a non-perturbative approach.
However a quick Google makes it clear that Seigel believes in particle exchange. He used the same picture of Feynman diagrams in another post on April 25th. The caption said electromagnetic interactions “are all governed by a single force-carrying particle: the photon”. It isn’t true. Hydrogen atoms don’t twinkle and magnets don’t shine. Siegel also says “the way the strong force works is by exchanging gluons”. Which is a bit tricky when the gluons in ordinary hadrons are virtual. Next:
But the motivation for quantizing the field is more fundamental than that the argument between those favoring perturbative or non-perturbative approaches. You need a quantum field theory to successfully describe the interactions between not merely particles and particle or particles and fields, but between fields and fields as well. With quantum field theory and further advances in their applications, everything from photon-photon scattering to the strong nuclear force was now explicable.
Quantum field theory doesn’t describe the interactions between fields. It doesn’t explain why the electron and the positron move rotationally and linearly in their annihilation dance of death. It doesn’t explain how a magnet works. It doesn’t explain anything. That’s why when I asked Siegel to explain the electron, he gave a non-explanation. Siegel then gives a diagram depicting neutrinoless double beta decay which has never been observed, and never will be:
A diagram of neutrinoless double beta decay, which is possible if the neutrino shown here is its own antiparticle. This is an interaction that’s permissible with a finite probability in quantum field theory in a Universe with the right quantum properties, but not in quantum mechanics, with non-quantized interaction fields. The decay time through this pathway is much longer than the age of the Universe.
That’s because the neutrino is not a Majorana particle, and because it’s a non-sequitur to say neutrino oscillations must mean neutrinos have mass. The get-out clause is in the caption: “the decay time through this pathway is much longer than the age of the Universe”. Very convenient. Next:
At the same time, it became immediately clear why Einstein’s approach to unification would never work. Motivated by Theodr Kaluza’s work, Einstein became enamored with the idea of unifying General Relativity and electromagnetism into a single framework. But General Relativity has a fundamental limitation: it’s a classical theory at its core, with its notion of continuous, non-quantized space and time.
People who promote quantum mysticism are always critical of Einstein, and his desire to actually understand what’s going on. Siegel says Einstein became enamored with unifying general relativity and electromagnetism, and suggested the problem was that general relativity is classical. But electromagnetism is classical too. There’s more:
If you refuse to quantize your fields, you doom yourself to missing out on important, intrinsic properties of the Universe. This was Einstein’s fatal flaw in his unification attempts, and the reason why his approach towards a more fundamental theory has been entirely (and justifiably) abandoned.
The opposite is true. When you believe in quantum field theory to such an extent that you don’t question it, or read up on the history of general relativity and electromagnetism as well as the history of quantum field theory, you doom yourself to pseudoscience. And wasting your time on quantum gravity, which is a castle in the air because it lacks foundation. The people who promote it don’t know how gravity works, and they don’t know how a magnet works. Siegel gives a depiction of quantum gravity:
Quantum gravity tries to combine Einstein’s General theory of Relativity with quantum mechanics. Quantum corrections to classical gravity are visualized as loop diagrams, as the one shown here in white. Whether space (or time) itself is discrete or continuous is not yet decided, as is the question of whether gravity is quantized at all, or particles, as we know them today, are fundamental or not. But if we hope for a fundamental theory of everything, it must include quantized fields.(SLAC NATIONAL ACCELERATOR LAB)
Next we have a touch of quantum snake oil. I am reminded of the myth that the internet was invented a CERN:
The Universe has shown itself time and time again to be quantum in nature. Those quantum properties show up in applications ranging from transistors to LED screens to the Hawking radiation that causes black holes to decay. The reason quantum mechanics is fundamentally flawed on its own isn’t because of the weirdness that the novel rules brought in, but because it didn’t go far enough. Particles do have quantum properties, but they also interact through fields that are quantum themselves, and all of it exists in a relativistically-invariant fashion.
The discovery of the transistor has nothing whatsoever to do with quantum field theory. Ditto for LEDs. And no, quantum properties do not show up in Hawking radiation. Nobody has ever seen any Hawking radiation. Which is no surprise, because when you dig into it you find it features negative-energy particles which don’t exist, and particles travelling back in time which don’t exist. It’s based on a thermodynamic analogy that doesn’t stand up to scrutiny, and it ignores gravitational time dilation. It’s pseudoscience. See Yvan Leblanc’s paper on fake physics: black hole thermodynamics, the holographic principle and emergent gravity. Siegel finishes up talking about a quantum theory of everything along with quantum weirdness:
Perhaps we will truly achieve a theory of everything, where every particle and interaction is relativistic and quantized. But this quantum weirdness must be a part of every aspect of it, even the parts we have not yet successfully quantized. In the immortal words of Haldane, “my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose”.
He quotes John Haldane talking about a universe that’s queerer than we can suppose. Trust me, it isn’t. The only thing that’s queer is quantum physics. Because it’s a pack of lies to children. And because irony of ironies, it’s cargo cult science.