The closest we have to a Theory of Everything

Three questions on the theory side of your presentation: >> "Hyperion … interacts with dust and … photons. [These] interactions … slightly shift the crest and troughs of parts of the [moon's] wave-function. This is called 'decoherence' and it's just what the Schrödinger equation predicts. [This] equation is still linear." Q1 — All finite-energy waves have finite-information carrying capacities. Why do the infinitely-expanding Schrödinger waves in the above definition get a free pass? Q2 — Schrödinger wave thought experiments begin with particles in classical states. If chaos makes this impossible at the end of the experiment, why is it possible at the start? >> "[If] measurement collapse [is not] a physical process … quantum mechanics [fails to] describe … observations. But … what is this process? No one knows." Q3 — Do solar sails work as Maxwell predicted? If so, how is the coherent reflection of a photon from the sun to the sail _not_ an enormous collapse of that photon's original solar solid angle wave function, and how is this collapse _not_ associated with imparting linear momentum to the sail? [2022-05-29.23.02 EDT Sun]

Terry Bollinger

"… higher information density of Hilbert space …" Sabine, what kind of nonsense are you letting this Bollinger fellow spout THIS time?!? ... oh wait... that's me... :) My faux pax on this one is an excellent example of how casual, poorly examined biases can impede analysis. Hilbert spaces are infinitely "denser" because they have infinitely more _dimensions_ than 3D or other finite spaces. However, in terms of _data_ that must reside within those infinite dimensions, Hilbert spaces are infinitely dark. As you increase the number of dimensions in a Hilbert space, its information density asymptotically approaches zero as the number of orthogonal states (dimensions) approaches infinity. For example, it's easy to find one black marble in a row of white marbles, more challenging to find it in a tray of white marbles, harder still to find it in a 3D cube of white marbles... and infinitely difficult to find it in an infinite-dimensional hypercube of white marbles, since at that point the ratio of black to white marbles becomes 1 to infinity. For any quantum physics model in infinite-dimensional Hilbert space, the issue thus is not that the model has too much specificity or too high of an information density but how to extract _any_ information out of its infinite darkness (that is, infinite volume). That's where the distribution function concept is helpful [1]. This mathematical technique blurs the data search to include ranges of similar axes (states). However, if you think about that carefully, it's the same as saying the energy scale of the experiment determines the finite number of dimensions needed. The Hilbert formalism becomes an algorithmic pathway for creating more states as needed, such as modeling linear-collider electron-quark collisions. There's a catch even with using distribution functions in Hilbert spaces. Distribution functions, including their famous limit, the Dirac function, are a delightfully obscure and oblique way of introducing the real-world phenomenon of quantum wave collapse into mathematical models. Distribution functions just let you do this without actually _saying_ the unsightly phrase "wave collapse" out loud. Just as a real-world telescope focused on an Einstein ring can pluck one tiny photon out of a photon wave function that arguably occupies a non-trivial fraction of the entire universe's volume, a distribution function model can pluck that same photon out of the infinite darkness of a sizeable fraction of the volume of the entire universe. Distribution functions are also popular because they are infinitely differentiable, which make at least local bits of the universe look smooth and shiny at all imaginable scales. Alas, in the end, all distribution functions — including their famous limit, the Dirac function — achieve this infinite smoothness via piecemeal constructions that bump one-over-infinity discontinuities against bits of genuinely smooth finite functions. Such boundaries always involve _computational_ infinities, even if they look smooth to the human eye. This piecemeal approach to creating smooth distribution functions developed over decades of painful and often paradoxical development, and it helps perpetuate the comforting illusion that everything in physics is infinitely smooth, even though no such smoothness ever exists experimentally ---------- [1] E. P. Xing, Hilbert Space Embeddings of Distributions. Lecture 22 of CMU Course 10-708 Probabilistic Graphical Models (2014). https://www.cs.cmu.edu/~epxing/Class/10708-14/scribe_notes/scribe_note_lecture22.pdf Page 1, para 3,4: "Higher order moments bring increasingly greater resolution power for characterizing arbitrary distributions, which leads to the intuition that an infinite dimensional vector consisting of moments will absolutely capture any distribution. This is, of course, practically infeasible, since storing or manipulating a vector of infinite dimensions is impossible. It however motivates the use of Hilbert Space embeddings, and the kernel trick to solve this infinite dimensional representation scenario." ---------- Terry Bollinger CC BY 4.0 2022-05-25.16:20 EDT Wed https://sarxiv.org/apa.2022-05-25.1620.pdf

Terry Bollinger

Hello Dr Hossenfelder Thank you for taking time to respond to my question. I appreciate it. And if you don't mind I have a question about correlation between The Principal of the last action and curved space.  I mean as far as I am concerned when light encounters heavy and dense galaxies (obstacles), from The Principal of the last action/geodesics, it should take less time to go around the galaxy than through it; and eventually cause gravitational lensing.  In contrast curved space looks as straight as it can get, from the perspective of the proton traveling along it. In other words proton doesn't even encounter anything on its path.  I just don't see connection between this two

Hello Tracy There is no need for sorry. I tried to make my response as short as it was possible and it came out wrong. Sorry about it. Best regards

Even if science can't tell us the difference, I find the discussion interesting. For example, in S. James Gates' Superstring Theory (from The Great Courses) he mentions that while certain string theory math calls for 10 spatial dimensions, there is string theory math that calls for only our experienced three. So, in my unqualified mind, this indicates that math is but an invented tool, otherwise there would be but one string solution, either one or the other as reality has either three or 10 spatial dimensions.

Hi Sabine, Actually I was thinking in terms of the physics - what we observe (direct detect) and measure - not in terms of a particular mathematical representation of the physics. The "future dependence" in the PLA does not appear to accord with any observable or measurable phenomena. So, it seems to me that "future dependence" doesn't convey any meaningful existential information; it is only a characteristic of the math. My sense of your comments is that you regard this "future dependency" as physically meaningful or consequential. Is that correct or am I misreading you? BTW I received an email the other day about a new Chaos-QM video of yours but the link doesn't work, just generates a 404 error from the Patreon server. Regards.

Hi Sabine, Thanks for the intriguing paper reference -- I'll take a closer look. That's a decidedly non-obvious transformation of Feynman's path model, though it sounds familiar... ah, yes: I already have it in my e-library from a post you did some time ago. I'm fascinated because my intuition is the exact opposite. I would anticipate embedding paths in the higher information density of Hilbert space to limit the ability of a model to describe experimental uncertainty correctly, not increase it. I love reading ideas that I know will surprise me! 2022-05-25.10:02 EDT Wed

Terry Bollinger

In our reductionist view, the physical laws are the rules on the lowest level. Not necessarily differential equations. The human view on a higher level (as visible for our eyes) is normally different. Take as a simple example the planetary motion which is circular (or better elliptic) from our view. The physical cause is the gravitational field acting on the planet’s elementary particles – with possibly some further internal forces. Our human structural view detects the orbit and succeeds to define a principle for it. But such principle is not the origin of the physics. Fermat’s principle is another example. We measure and judge the angle of an EM beam. The electrical charges reacting here in a precisely understood physical way do not know anything about an angle. They may follow the momentum law which is a physical law at the lowest-level (present understanding). - Similar the least action principle. Also a human-level understanding. It can also be deduced from lower level reactions; so, why to use it as a principle? It may be a practical means for an easier treatment; but not to be confused with a true law. Also here, the engaged elementary particles do not have any knowledge of this principle, but as well react in a well-defined way.

Basically, yes, that's the idea.

Hi Terry, I think you're right to worry about the uncertainty principle, but this is a rather technical point that I didn't want to elaborate on in the video. In the usual Feynman path integral you use classical paths in space-time. I instead want to use paths in Hilbert-space, so each path has the uncertainty principle built in already. Sandro and I have a paper about this here: https://arxiv.org/abs/2110.07168

Well, well, but the question is what is the "law"? You seem to implicitly assume a law is necessarily a differential equation acting on an initial condition. But this is not how the principle of least action works. It is indeed teleological in its original formulation, odd as this seems.

Hi Bud, Well, you're thinking of it in terms of initial conditions and an evolution law. But this is not how the principle of least action in its integral form works. You really integrate over the entire path. Now, as I say later, we know that we can rewrite the principle of least action into differential equations for classical systems, so the perplexing "future dependence" disappears, but it's arguably there in the original formulation.

Hi Jeffery, Yes, I guess the deeper question is whether mathematics is "there" and we just figure out what mathematics it is that nature abides by, or whether we fumble together some mathematics that works to describe whatever is "there". I'm not sure that science will ever be able to tell us the difference.

Hi George, Sometimes. Depends on what's between the galaxy and us. If there was only the distant galaxy and ours, then the path of the light would be straight. If there are big masses (like other galaxies) in between, they will curve space and bend light around. I didn't discuss this in the video, but, yes, it's also an example of the principle of least action. It follows from the one that gives you Einstein's field equations and Maxwell's equations. (So, a combination of electrodynamics and general relativity.)

Sabine, you say: “The path [of the rock] that minimizes the action turns out to be a parabola, … , but again note how weird this is. It’s not that the rock actually tries all possible paths. It just gets on the way and takes the best one on first try, like it knows what’s coming before it gets there.” I think that this conclusion is not compelling logic. This rock does not follow the “goal” to reach a certain point. This seems to lead to a wrong mindset. Because the rock merely follows a physical law and at the end it reaches a point as a result of this law. So it is on the one hand a funny fact that the path turns out to be an optimal one, but this is not the fulfillment of a goal. If we have this understanding that the laws of physics have the function to fulfill a final goal, we are in the vicinity of a religious understanding, not science. And the idea that the world is based on principles ( … symmetries etc.) is not at all a new one but quite old: the Greek philosopher Plato followed this way. The idea of Isaac Newton on the other hand that natural laws determine the physical world was a great progress which we should not give up.

Yes, a brachistochrone curve can be a path of least action and can be somewhat independent of the curvature of space mostly because the falling "object" is constrained to a path that is not a geodesic. The typical, classical situation for brachistrochrone curves is light moving through a medium with a gradient in index of refraction or a ball rolling down a ramp. In these cases, there is more than just gravity in play, like the normal force of the ramp. I have also seen cases of brachistrochrone curves computed for objects in free fall with only gravity in play (no ramp to follow). In this case, a brachistochrone curve is a geodesic, however, geodesics are not necessarily brachistochrone curves. Sorry about my sloppy response earlier, I was referring only to your original question about galaxies being where we think they are.

Hello Tracy But as far as I am concerned the brachistochrone curve, the shape of the path of the principal of least action, has a curve relative to straight line even in flat space, and the brachistochrone curve has a curve relative to "curved straight line" in curved space. In other words Brachistochrone curve isn't dependent on curvature of the space. Best regards

My pleasure. Theoretical physics was quite different in his day. I wonder if he’d say the concluding paragraph for the mathematician now also holds for the theoretical physicist. Of course, it’s pretty hard to be guided by empiricism when there is no data to look at.

Rad Antonov

re: Let us pause here for a moment and appreciate how odd this is. The ray of light takes the path that requires the least amount of time. But how does the light know it will enter a medium before it gets there, so that it can pick the right place to change direction. It seems like the light needs to know something about the future. Crazy. >>> In classical physics, the assumption is that we are dealing with a wave-front, not a particle. To rationalize with quantum photons, it is only necessary to think of the photons as a spray. The end result works out because the spray samples many trajectories and the resulting distribution conforms to the classical prediction. The parts of the spray that don't are given names like 'glare' and reflectance, and dispersion.

"Let us pause here for a moment and appreciate how odd this is. The ray of light takes the path that requires the least amount of time. But how does the light know it will enter a medium before it gets there, so that it can pick the right place to change direction. It seems like the light needs to know something about the future. Crazy." This comment leaves me completely befuddled. I guess it's what comes of thinking only in terms of math rather than physics. In physics the beam of light has an initial trajectory, when it encounters a new medium (water) its trajectory is altered in a well-understood manner. Any point on that new path can be arbitrarily labeled "b". So what? How is this mysterious or crazy? Maybe the problem is that the principle of least action, which has as its basis the poorly defined concept of action, beclouds the physics. The principle seems to suggest that the body (or light beam) chooses its path in accordance with the principle. Physics does not behave like that. The path of a rock or light beam is determined by their initial trajectory and subsequent interaction with the environment they encounter. It has nothing really to do with the principle of least action, even if the math employs it.

Thanks for that link.

Thanks, Tracey. :)

Hi Tracey, thanks for asking! My right eye is doing great. My eye surgeon gave me full approval for normal activities about a week ago. It's a good thing to, since I was getting frustrated with the bad timing. Some of the chirality issues I've been working on this month require figures and visual grouping, not text and not equations (yet). George, Tracey is right: The angles of light path deviation created by the largest Einstein lenses are tiny indeed, e.g., 54 arcseconds (see https://academic.oup.com/mnras/article/392/2/930/977840, search up -- thus from the bottom -- for "arcsec". The movie Interstellar has a nice depiction of a more extreme gravitational light deviation when it shows the backside of the accretion ring angling up until it resembles a mohawk haircut on top of its giant black hole.

Terry Bollinger

Hey Terry, how are your eyes doing? Better I hope. Yes, galaxy clusters acting as gravitational lenses are great examples of the curving of space due to the presence of mass. There are lots of cool pictures of full Einstein rings and lots of other geometrical effects if the background galaxy is off center from the gravitational lens. Even in this case though, the actual deviation of the background galaxy light is only a couple degrees or so for a dense, compact cluster.

Hi George and Colleen, yes, light follows geodesics, which are paths of least action -- the shortest paths in a curved space. For all that we can tell, space is flat (uncurved) for the most part unless near a body with mass, in which case the degree of the curvature of space depends on the amount of mass and how close you are to the body. Where space is flat, the shortest path is a straight line and where space is curved, the shortest path is a curved line. Specifically answering your points George, 1. curved space cannot have "straight" lines, in a Euclidean sense. Or maybe consider that a geodesic may look straight according to a photon traveling along it. 2. the principle of least action results in a straight path in flat space and a curved path in curved space -- the path of least action is dependent on the curvature of space. 3. Since space is flat, as near as we can measure (except when near a massive body), the galaxies we see really are where we see them.

I thought the 'curved path' of light, a geodesic, would seem more or less straight to us/telescopes unless it hit a gravitational or material snag? Or is that too simplistic?

Hello Tracy Thank you for your response, even though it was somewhat confusing. I mean, as far as I am concerned even curved space has a straight line and the path light takes, according to the "Principal of the least action", isn't straight. In other words regardless wether space is curved or not, the path the light takes is curved relative to straight line. And if the path light takes is curved, then we have to assume that galaxies we are looking at aren't located were we assume. That's what my question was about.  I have other questions associated to your response, but I am focusing only on one.  Thank you for your time and response  Best regards  George

Tracey gave an great answer to George's question, but one small addendum is needed: In the case of Einstein rings, which are gravitational lenses, yes, galaxies show up "around the corner" from their real locations. Action works the same for gravity as for any other energy potential. That's why it's the nearest thing we have to a theory of everything.

Terry Bollinger

Jeffery, you might enjoy von Neumann’s “The Mathematician” essay: https://mathshistory.st-andrews.ac.uk/Extras/Von_Neumann_Part_1/. He is quite humble to start but calls out the “peculiar duplicity in the nature of mathematics.” Amazing stuff! My $0.02 is that what makes physics powerful is predictions. Not just any kind of predictions but ones that are made precise through the use of mathematics, regardless of whether it was discovered or invented.

Rad Antonov

Happy Sunday! This discussion makes me think of the question as to whether mathematics is invented or discovered, as in questioning how the rock "knows" the optimal path. It doesn't. The universe simply works a certain way that we model with the tool "math"; We invent math to create more accurate models to get closer approximations to the structures of mathematics that exist in reality (https://www.youtube.com/watch?v=ybIxWQKZss8 and https://www.youtube.com/watch?v=1RLdSvQ-OF0). However, my guess is that reality actually has a limited number of structures, such as that produced by a gravitational field or the packing of seeds in a flower, while math has the potential for too many more, such as in the mathematical existence of more than the real three spatial dimensions. So mathematics appears to be a modeling game that we need to play to identify those real structures such that we can better explain reality.

Vielen Dank! 💜

It's all _very_ good, ranging from upbeat to haunting. Your music would be a perfect match with a graphic visualizer output projected onto the dome through a fish-eye lens. Perfect!

Hi George, in case Sabine doesn't get back here until Wed to answer your question, yes, general relativity describes the bending of space-time due to the presence of mass. Light takes a curved path in this curved space-time according to the principle of least action. Arthur Eddington performed a famous experiment during the solar eclipse of 1919 that showed the path of light from a background star bending around the Sun in accordance with general relativity. For other examples, you can look up gravitational lensing by galaxy clusters and more recently, the farthest star ever observed was due to a gravitational lensing effect. Generally, the curving of the light path is very tiny and only becomes measurable if the light passes close to a massive body. So, the galaxies we see are, more or less, right where we see them, or rather where they were millions of years ago when the light you now see was emitted from them.

I copied it but forgot to paste... https://soundcloud.app.goo.gl/XN8uZ

Hi Colleen, what's the link to your channel? I'll go and have a listen.

Hi Tracey. I wish I was more like a particle that went straight where it's supposed to, not wandering around trying to figure that out. The journey is proving pretty interesting in some ways though. I'm still interested in making some music for your university's planetarium.q You can have a listen to what I've already got on SoundCloud and let me know what you like, and what you want. 🙂

Hello Dr Hossenfelder If the path light takes between two points is curved according to the "Principal of the least action", does it mean that galaxies we are seeing are located "around the corner" and not directly straight ahead of us? P.S.   Thank you for the essential videos like "The Quantum Eraser Debunked".

Sabine, I gather your idea is to start with a Feynman diagram whose functionals have finite length and resolution since they start in some earlier past (e.g., a lab setup) and end at some later past (e.g., a lab measurement). You extend those functionals to the beginning and end of time, giving them effectively infinite resolution as with any wave train Fourier transform (comms 101). With the added resolving power of infinitely long functionals, the bundle of in-phase functionals shrinks to a diameter of zero in XYZ space, and the whole blurry mess of _probability_ functions disappears. The opportunity for a "pilot wave" also disappears since pilot waves are another way of expressing the fuzziness and uncertainty of Feynman's finite path integrals. Your infinitely tight in-phase functionals eliminate that too. You end up with precisely what Minkowski proposed for relativity, only at the quantum level via your infinite extension of the path integral. Retrocausality, or whatever folks want to call it, is inherent in this approach since those infinite-length functionals convey infinitely precise information in both directions. Your justification for treating the unknown future as known — and it's an excellent one — is that the principle of least action in the quantum domain _works_ by using Dirac's functionals, which are inherently time-embedded.[1] So here's the oddly simple problem: By eliminating all quantum uncertainty, specifically by compressing the in-phase bundle to an infinitesimal diameter in their XYZ slice, you also make each such point infinitely massive. Planck uncertainty doesn't suddenly give you a pass merely because you used path integrals, especially since path integrals and quantum uncertainty are two sides of the same Fourier-transform coin. Yes, I know, renormalization, or this trick, or that trick, whatever. Particle physics, in particular, stopped bothering with deep debugging and regression analysis decades ago, preferring to slap messy fixes on top of bad ideas. Been there, done that. You're still violating quantum uncertainty with all of this. The good news is that your idea is closer to correct than most if you can drop all the Minkowski (and Hilbert, oh my) nonsense about spacetime providing infinite resolution for precisely zero cost. Your model sounds essentially correct _in the non-existent limit of infinite energy_. But observationally — via labs, telescopes, and actual data — our universe doesn't have infinite energy. It would collapse if it did, and notably, it doesn't. The fix is to treat your model as a finite, quantum-limited _approximation_ of a block universe. Does it see into the future? Yes. Does it reach into the past, sometimes doing profoundly weird things? Check. Do simple events here entangle themselves with events in the indefinitely distant future, possibly even billions of years hence (think cosmic photons)? Sure. Is the future fully determined? _No._ It's not even close. For any finite complex system, you can only encode a level of certainty proportional to the total energy of your carrier wave. Our carrier wave is the total positive energy of our universe — the sum of its visible matter, radiation, and dark "matter." This sum is vast, but it's _not_ infinite. That's especially true after you divvy it up for the task of moving around all of those Higgs-mechanism rest-mass fermions that are the true marvels of our universe. Are some items transcendent across ages of time? Sure, though you mostly need to go to the photons and neutrinos for good examples. Are other items locked down so tightly that they see no further than a few millimeters into the past or future? Again, sure. Atoms in warm, dense matter are an excellent example of mundane, minimally transcendent items. Be honest: Were you seriously worried the atoms in your body would suddenly go quantum on you and drift off into the cosmos? [2] Chemistry only works because complex compounds in warm matter only engage in the more localized, less chaotic forms of functional transcendence. Most things having narrow, focused transcendence is a good thing, not a bad one. Finally, in searching for citations on the idea that the universe might simultaneously support an asymptotic version of Sabine's superdeterminism and an uncertain future in which people can still, to some degree, choose their fates, I only found one relevant quote. It's an apt one, though: "I don't know if we each have a destiny, or we're all just floating around, accidental like on a breeze. But I think, maybe, it's both." --F. Gump, 1994 ---------- [1] Dirac's remarkable insight was that such an odd approach would work for quantum mechanics. Oddly, he grew to despise his own idea. He doubled down on using only Hamiltonians and was generally annoyed at Feynman for having so much success with path integrals. I suspect that bothered Feynman since Dirac was one of the few early quantum figures he genuinely respected. [2] Observation is momentum pairs. Atoms do it, and even chemical bonds do it. It's part of how physics is going to become seriously fun again. ---------- Terry Bollinger CC BY 4.0 2022-05-21.23:35 EDT Sat https://sarxiv.org/apa.2022-05-21.2335.pdf

Terry Bollinger

In another branch of the ManyWorlds there exist a large number of antisuperdeterminists who insist that the PLA is absurd and anti-science since it has future input dependence! Fermat, Newton, Maxwell and Einstein were all thrown out of the academy with their super deterministic clap trap PLA theories…

I think I get it now -- retrocausality (or rather future input dependence) is one of the implications of PLA. The QM formalism of PLA is the Feynman path integral which has the future input dependence as the upper limit of the integral. A modified Feynman path integral is one approach to superdeterminism, but instead of a particle taking all possible paths (and then averaging over the probabilities of those infinite number of paths), there is only one optimal path in accordance with PLA. The one optimal path, dependent on the hidden variables of the system, solves the measurement problem.