3 thoughts on “Beyond the Standard Model – sliver of reality?”

1. This article by Paul Sutter clarifies my dissatisfaction with the way gravity is treated by legacy quantum mechanics. The decoupling of quantum field interactions from space-time geometry – a non-relational model. As opposed to something more intertwined, tangled like Wilczek’s layered Grid.

   So, this article (and included video) is an overview of loop quantum gravity à la Rovelli. Spin networks. As an incomplete theory.

   • Space.com > “Loop quantum gravity: Does space-time come in tiny chunks?” by Paul Sutter (February 23, 2022) – What does it mean to quantize space-time?

   One of the most annoying things that general relativity and quantum mechanics disagree about is the role that space-time plays in the physics.

   The play is the thing – Sutter’s metaphor.

   • Background independence – foreground actors and background stage.

   For quantum mechanics, space-time is just a background [in some sense], a stage, a floor, a container for all the interesting interactions that make up the physics [QFT] of the universe. Yes, that stage may bend and warp, and that bending and warping affect the paths of particles — but that’s about it. All physics happens “on top” of that background space-time.

   • An interplay – a tangled drama.

   For general relativity … space-time isn’t a background stage for the actors; it is the actor. General relativity doesn’t assume a background; it creates it. General relativity is the language of the warping of space-time, and that very warping generates the physics of gravity.

   So, in our quest to unite quantum mechanics with gravity, maybe we … really need to seek a quantum theory of space-time.

   He cites two key issues with loop quantum gravity. Both relate to the correspondence principle – that quantum calculations must agree with (reduce to) calculations of General / Special Relativity.

   … the biggest problem is that loop quantum gravity is a theory of strong gravity at small scales, which should automatically also be a theory of weak gravity at normal scales.

   There are other issues, … different observers will have different views of the sizes of the quantized pixels of space-time.

   Sutter mixes the language of gravity in the usual way. In our everyday world, referring to gravity as a force; yet, in a deeper sense an interaction – of energy flux and field gradients (from which “gravity” emerges at the macroscopic level à la center of inertia).

   In his video, Sutter remarks that there are variations of loop quantum gravity. In some formulations, spacetime is (merely) “pixelated” at some (defined) level. Spacetime is no longer smooth (continuous); but otherwise remains conceptually intact (in some sense).

   Other formulations see spacetime as emergent. Fundamentally there’s just relationships between quantum entities, from which the geometry and “ticking” of spacetime arises.

   He also talks about singularities. How the theories prevent infinite scrunching.

2. This article poses an interesting question; otherwise, a fashionable recap [1] of ongoing contemporary physics. For example, research on quantum gravity. And some interesting quotes by Sabine Hossenfelder.[2]

   • Space.com > “Was Einstein wrong? The case against space-time theory” by Colin Stuart (Feb 28, 2022)

   Moving beyond Einstein’s spacetime as a background (in some sense, a stage independent of all the interesting interactions of quantum theory) …

   A. One interesting bit of research:

   … a team of physicists from the UK, France and Hong Kong may soon have another way to test out this idea. They hope to use an ultra-cold gas of several billion caesium atoms existing in a state known as a Bose-Einstein condensate to see if gravity is really quantum after all.

   B. A revisit of detecting spacetime defects via distortions in the gamma ray spectrum of far, far away sources.

   C. Then the same question as Paul Sutter: Is there an alternative to trying to quantize space-time? [3] And introduction of a relational theory in which interactions define spacetime: modular space-time.

   It’s certainly a novel approach, one that looks to “gravitationalize” the quantum world rather than quantizing gravity as in LQG [Loop Quantum Gravity].

   … physicists Laurent Freidel, Robert Leigh, and Djordje Minic … believe space-time doesn’t exist independently of the objects in it. Space-time is defined by the way objects interact.

   If space-time emerges from the quantum world, then being closer in a quantum sense is more fundamental than being close in a physical sense. “Different observers would have different notions of locality,” said [Djordje] Minic [4], “it depends on the context.” It’s a bit like our relationships with other people. We can feel closer to a loved one far away than the stranger who lives down the street. “You can have these non-local connections as long as they are fairly small,” said Hossenfelder.

   Notes

   [1] Good grief, the article keeps using the term particle. In an unqualified manner. I find statements like this one to be misdirections: “The quantum world is notoriously weird. Single particles can be in two places at once, for example.”

   Stuart even revisits Schrödinger’s cat – evading progress in our understanding of decoherence.

   The “here & there” metaphor is used so casually: “quantum physics says matter and energy exist in multiple states simultaneously — they can be both here and over there.” Which appears to conflate (classical) matter and (quantum field theory) energy. Waves indeed are extended in space vs. “here” or “there” points.

   Stuart contrasts the smooth continuum of spacetime with quantum superposition, despite superposition entailing linear continuity – the smoothness of the wave function. Paul Sutter does a better job of describing the real issue.[3]

   [2] The Hossenfelder quotes:

   “A gravitational field cannot be in two places at once,” said Sabine Hossenfelder, a theoretical physicist at the Frankfurt Institute for Advanced Studies. … “So where is the gravitational field?” asks Hossenfelder. “Nobody has an answer to that question. It’s kind of embarrassing,” she said.

   So, not the metric field, of course. That is, where is the “gravitational field” in quantum field theory (QFT)? It’s not in the Standard Model. (Or Wilczek’s Core Theory, I assume.)

   The real point: the quantum (QFT or tangled) structure of space-time.

   [3] A recent article as well on this topic.

   • Space.com > “Loop quantum gravity: Does space-time come in tiny chunks?” by Paul Sutter (February 23, 2022) – What does it mean to quantize space-time?

   [4] Minic is referenced within this Wiki article on Laurent Freidel.

3. This podcast with Sean Carroll re the quest for quantum gravity (cf. his latest book) recaps the technical and conceptual issues, with Laplace’s demon and analogies to fluid dynamics (yeah!) in the mix.

   • Quanta Magazine > “Where Do Space, Time and Gravity Come From?” by Steven Strogatz (May 4, 2022) – my summary from podcast transcript.

   Gravity from Newton to Einstein

   (Carroll) Einstein came up with general relativity [a macroscopic theory]… which was to let space-time be curved, to have a geometry, to be dynamical. It’s the fabric of space-time itself that responds to energy and mass, and that’s what we perceive as gravity. … It’s still a classical theory.

   Quantum mechanics is the theory of how the world works. What happens at small scales is that classical mechanics fails. … We do not yet have a full, 100% reliable way of thinking about gravity from a quantum point of view. … this purported map [the quantization procedure] from classical theories to quantum theories is not very well-defined. … nevertheless, it has worked for electromagnetism, the nuclear forces and everything else.

   [But when quantizing gravity] … the infinities you get in gravity are of a different character, they’re not get-rid-able, they’re not “renormalizable,” …

   [Re conceptual issues] … with everything else, every other theory other than gravity, it’s very clear what’s going on. You have stuff inside space-time. The stuff has a location, right? It has a point in space, it’s moving through time. Even if you have a field, it has a value at every point in space, etc.

   But in gravity, you’re sort of combining a whole bunch of different possible geometries of space-time. And what that means is, you’re not really sure what time is, for one thing, and you’re not really sure where things are in space, …

   [The measurement problem …] … what we call the geometry of space-time, or things like location in space, they don’t exist. They are some approximation that you get at the classical level in the right circumstances.

   Emergence

   [Consider a classical “gas in the box.” Aggregate properties: temperature, density, pressure, mean velocity. Collective behavior. Fluid dynamics, a useful predictive model vs. modeling what every atom or molecule is doing.]

   That’s emergence, when you have a set of properties that are only approximate and coarse-grained, that you can observe at the macroscopic level, and yet you can predict with them. And weak emergence just means, there’s nothing new that happened along the way.

   There’s also strong emergence where spooky new stuff does come in. … I’m not a believer in strong emergence at the fundamental level. So, to me, what the emergence of space-time means is that space-time itself is like, the fluid mechanics. It’s like gas temperature and pressure and things like that. It’s just a coarse-grained, high-level way of thinking about something more fundamental, which we’re trying to put our finger on.

   … you don’t start with space-time and quantize it, okay? … You’re going to have something fundamentally different at the deep micro-level, and then you’re going to emerge into what we know of as space-time.

   Entanglement – “It’s not a rare, special thing.”

   [Re the decay of a Higgs boson, as into an electron and a positron, as one wavefunction for the combined system.] It’s not an independent question, what direction are you going to measure the electron in? What direction are you going to measure the positron in? It’s a statement you need to ask at the same time [as unknown, yet always opposite directions]. That’s entanglement, right there. Entanglement is the fact that you cannot separately and independently predict what the observational outcome is going to be for the electron and the positron. … when you measure the location of one, supposedly the location of the other one is instantly determined. … the way the universe works [seems to work] involves correlations that travel faster than the speed of light … [vs. the notion of locality].

   I think of the wavefunction as the fundamental thing … that’s what exists in reality. And the wavefunction, like the wavefunction of this positron and electron is utterly nonlocal. … my mystery is … not “why is locality approximately or, you know, seemingly violated by entanglement?” It’s “why is there locality at all?”

   The wavefunction

   [Getting back to the topic of emergence and connecting with quantum field theory (QFT) as a model] We just have an abstract quantum wavefunction [in an entangled canvas sans any such words like distance, or fields] and we’re asking, can we extract reality as we know it from the wavefunction? Space-time, quantum fields [including a field for gravity], all of those things, okay.

   … just our current best approximation … what seems to fit the data … because there still are fields even in empty space [abstract space, not spacetime?], you can say, is there entanglement between these two points of space? … And the answer is yes, it is always going to be entangled. … there is a relationship between the distance between two points and their amount of entanglement in the lowest-energy state of a conventional quantum field theory.

   Entanglement between different pieces of the wavefunction – a relational nodal network in Hilbert space

   … when the entanglement is strong, the distance is short. And I’m going to define something called the distance (in this big space in which the wavefunction lives). … do those nodes fit together to approximate a smooth manifold? And if you pick the right kind of laws of physics, they will.

   And then you can ask, if I perturb it a little bit, so I poke it, so it’s not in its lowest-energy state, it has a little bit of energy in it. Well, that’s going to be dynamical. That’s going to stretch space-time, that’s going to change the amount of entanglement. We can interpret that as a change in the geometry of space. [Then using certain assumptions …] Is there an equation that that obeys [such as Einstein’s equation of general relativity]?

   AdS/CFT correspondence, the holographic (so-called) principle, an analogy of “living on the boundary infinitely far away”

   So if there’s a boundary to anti-de Sitter space infinitely far away, it’s one dimension less. Because it’s kind of like, you know, the event horizon of a black hole, it’s wrapped around the anti-de Sitter space. It is itself flat space-time. There’s no gravity there, you can define quantum field theory on it, you have no conceptual issues with quantizing it. It’s good old, well-defined quantum field theory. And Maldacena argued that it is the same theory as quantum gravity in the interior, in what we call the bulk of anti-de Sitter space.

   And then, subsequent to that, people like Mark Van Raamsdonk and Brian Swingle and others pointed out that if you take the theory on the boundary, the theory that we understand, the quantum field theory without gravity, and all you do is you twiddle the amount of entanglement between different parts of the quantum field theory on the boundary, the geometry of the anti-de Sitter space inside responds. It changes in response to that. In some sense, the geometry of that emergent anti-de Sitter space, holographically emergent, is very sensitive to the amount of entanglement on the boundary. So this is the sense in which, in this case, geometry is emerging from entanglement.

   Holography kicks in where gravity is strong, where you either have a black hole or a cosmological horizon or something like that. … I think that the AdS/CFT approach doesn’t really illuminate what goes on in the solar system very well.

   Moving forward …

   The ideal thing, the wonderful thing that would be amazing, is to make an experimental prediction from all this.

   … it goes back to what we said about space and time not being quite on an equal footing. … we’re violating Lorentz invariance [as an emergent-like approximation]. … So, it’s possible that there is an experimental prediction for a tiny violation of Lorentz invariance.

   … science is not just a set of results that are handed down from on high, it’s a process.

Comments are closed.