Markus Hanke

I’d like to throw in another question - given a system consisting of a very large number of constituents which interact via known laws, is there a mathematical prescription that allows us (at least in principle) to determine all global degrees of freedom of said system from its local degrees of freedom? For example, could one derive Navier-Stokes equations from electromagnetism (ie H2O molecules -> water) in a purely mathematical manner? How exactly are these dynamics mapped into each other? What happens if the interaction mechanism is changed - can we predict what global effects this will have? On a more philosophical level - are all large-scale and global degrees of freedom of the universe uniquely determined by its fundamental constituents, or is it the case that nature is actually made up of a hierarchy of laws, with each one applying to a specific length scale only, and each hierarchy being irreducible? For example, is the particle zoo of the SM the only possible choice to obtain a universe that looks like ours on large scales? This is of practical importance, because it would mean that applying certain laws to the wrong level would be problematic. This is obvious in the down-scale direction, but we implicitly assume it’s ok to go up-scale, for example by applying GR to systems with very large numbers of constituents, and expecting the same degrees of freedom as on smaller scales.

Yes, GR simply doesn’t have anything to say about the earliest moments - that’s outside its domain of applicability.

The FLRW metric is a solution to a classical field equation, using classical fluid dynamics as boundary conditions. The problem is that beyond a certain point in the past, quantum effects (both within the primordial plasma, and within gravity itself) become too large to be neglected - hence, taking the FLRW metric beyond that point would mean you are extending GR beyond its domain of applicability. The alternative approach is to treat the universe in its entirety as a quantum wave-function, even if you don’t know the precise laws of quantum gravity; it then satisfies an evolution equation not dissimilar to the Schroedinger equation, which is called the Wheeler-deWitt equation. Finding solutions to this is, for technical reasons, very difficult - however, one solution we do know of is the Hartle-Hawking state. In this state, neither time nor space have a boundary at the beginning, but instead have ‘poles’. These poles do not coincide, so there would have been an initial region that was just 3D space. The poles themselves are not boundaries, in the sense that you cannot extend geodesics ‘beyond’ them, even though geodesic completeness is maintained. What this means for time is that, if you were to extend a geodesic into the past, there eventually comes a turning point past which you can go back no further; instead, whatever direction you choose to go to will be the future again. It’s like the North Pole on Earth, from which all directions are south, without it being a boundary of any kind. In the same way, a pole in time is a point at which all temporal directions are necessarily the future. Something similar would be true for space as well. Hence, in the Hartle-Hawking state, space and time would be unbounded, yet still finite (in the past). Note though that this is only one specific solution to the Wheeler-deWitt equation; others are possible, which lead to different scenarios.

Evidently not. Nonetheless, many of the answers given are genuine, and thus of value to casual readers, if not to the OP No. I already explained this on another thread - metric expansion means that measurements of distances outside gravitationally bound systems are time-dependent, so the outcome of such measurements depend on when they are undertaken. Metric expansion is just a specific example of the absence of time-translation symmetry in a system. There’s nothing that is being physically accelerated by any forces - you could attach accelerometers to each galaxy in the universe (including our own), and they would all read exactly zero. Yet distance between them is measured to be increasing as the universe ages into the future, irrespective of where you are performing the measurement from. Spacetime is not a “thing”, substance or fabric subject to mechanics of any kind. I don’t think comments such as this will help your argument.

The geodesic equations used to obtain free fall orbits are a system of differential equations - meaning any exact solution depends explicitly on initial and boundary conditions. The planets are (roughly) all in the ecliptic plane, because they all formed from the same protoplanetary accretion disk, meaning they all share one common boundary condition. So yes, GR handles this just fine, and so does Newton. The maths of how to obtain orbits in GR for simple Schwarzschild metrics are found in any undergrad GR text; I’ve worked through these calculations myself, and, while cumbersome and tedious, they demonstrably yield the correct results. It’s curvature of spacetime, not just space. In fact, for situations such as planets and stars, gravitation is mostly due to the time part of the metric. Spatial curvature gives you tidal forces, but the ‘downward force’ of gravity is overwhelmingly (by a factor of c^2) due to time dilation, in conjunction with the principle of extremal ageing. Of course, in the geodesic equation you don’t really separate these effects; there’s just a trajectory in spacetime. If you were to take the emotion out of your posts, then people would take you more seriously. Some of the points you make and questions you ask are valid and worthy of discussion, but your approach to argumentation is off-putting and unscientific. You’re sabotaging yourself here.

We do know how light interacts with all the particles of the Standard Model. Furthermore, postulating unknown particles (which would need to have some very strange properties) to explain cosmological redshift is a far bigger step than simply accepting metric expansion, which is a natural consequence of the laws of gravity, and requires no new physics. So you don’t gain anything. Sure, but such scattering processes are wavelength-dependent, so spectral lines are not shifted uniformly. That’s precisely the point - cosmological redshift affects the entire spectrum uniformly, which is how we know it isn’t due to scattering. This has been pointed out multiple times already. There is no physical medium that ‘stretches’ - metric expansion just means that the outcome of length measurements depends on when they are performed, in a specific way. They are not invariant under time translations. Expansion is accumulative, so it depends on total distance. Thus you simply look at what is behind the empty region, and that will tell you the expansion of the entirety of space between you and the observed object. There are no experiments, and there never will be, since metric expansion only becomes apparent on scales of ~MPc. All evidence is observational and large-scale. But of course you can locally test the laws of gravity, of which metric expansion is a direct consequence. This has been done extensively, as I’m sure you know.

I see. My immediate reaction to this would be that the two cases are interchangeable only in the classical domain; once you take into account the quantum fields that make up matter and vacuum (which GR of course does not do), then you will find that neither the strong nor the weak interaction are invariant under scaling of this type, so it is difficult to make sense of ‘rubbery’ measuring intervals. As such, the curved spacetime view is the more general one, as it applies to a wider domain within the real world.

I don’t understand what this is in reference to? The layout of your posts is a mess, and I made no mention of the dark sector anywhere. As I pointed out to you, the concept was abandoned because it is in direct contradiction to observational evidence.

What exactly is meant by “effects on all clocks and rulers”, as opposed to geometry? Do you have a reference to what Kip Thorne actually stated? This doesn’t seem to make a lot of sense to me.

In the absence of a self-consistent model of quantum gravity, we do not yet know the underlying mechanism that makes gravity work the way it does. General Relativity is an effective description of the large-scale dynamics of gravity, and as such it is very successful; but it has nothing to say about the underlying nature of spacetime. That is outside its domain. For the same reason we also don’t know yet what exactly went on prior to about 10^-35s after the BB. This, however, does not cast doubt on the fact that the BB happened, because this is an inference based on extrapolation from current observational data.

You made numerous references to a class of models collectively called tired light, as an alternative to explain cosmological redshift. The trouble with these models is not so much the exact mechanism, but the fact that none of them actually corresponds to available observational evidence. For example, Zwicky’s original scattering model is immediately falsified by the fact that we...well...don’t observe any scattering (which would visually blur distant images). Others are falsified because they are wavelength-dependent, and thus can’t account for cosmological redshift. I don’t know of a single tired light model that is actually consistent with available data. This is why this line of thinking has been pretty much abandoned by the scientific community.

Let me try to explain this a bit more. In a local gauge symmetry, you apply a smooth and continuous transformation to your fields at every point in spacetime, and the parameters of the transformation can vary from point to point (in global gauge symmetries, the parameters are taken to be the same everywhere). You do this by replacing the ordinary derivatives in your Lagrangian by appropriately defined gauge-covariant derivatives. For example, in QED the gauge group is U(1), so the transformation is essentially a rotation by some angle, and the corresponding gauge-covariant derivative introduces a new rank-1 object in the Lagrangian - which is just the electromagnetic vector potential, and thus the photon field. So what does this mean? Local gauge symmetry means that fields have redundant degrees of freedom that allow a very specific type of change to happen in the field configuration at each point. Since the symmetries are continuous, by Noether’s theorem this corresponds to the existence of a conserved quantity (a charge of some kind). Consistent changes in field configuration plus conserved current equals an interaction between fields. So this is the central idea - redundant degrees of freedom (local gauge symmetries), consistently defined across all fields at each point on spacetime, allows for interactions between fields, and the interaction mechanism is itself a new field, as is apparent by the formalism of gauge-covariant derivatives. Without gauge symmetry, fields wouldn’t have any way to interact in this self-consistent manner. Note that in a global sense (accounting for all fields at all points in spacetime) nothing really changes at all, because all interaction currents are made up of conserved quantities - you still have the same Lagrangian after an interaction happens. All you do is ‘shift things around’, so to speak. This is the great beauty of it. This can be very elegantly described as connection forms (called gauge potential) on fiber bundles, so a knowledgable of differential geometry is very helpful here.

Yes, I am familiar with these concepts. As a quick correction though, I meant to say redundant degrees of freedom, not superfluous.

It essentially just means that our description of the physics in question is over-determined, ie that there are superfluous degrees of freedom in the chosen mathematical formalism. These can be either local or global. This is why you can make specific changes to the fields without affecting the physics.

I think you are focussing far too much on a single phenomenon, whereas metric expansion actually serves as a coherent model for a whole host of different observational data points. It isn’t only about redshift by any means. Note that we are talking cosmological redshift here, and not the Doppler effect or any other frequency shifting - my impression is that you haven’t understood the difference. The other thing is that metric expansion is an unavoidable consequence of the laws of gravity - if you feed basic cosmological assumptions into the field equations, then any solution you get out will have an intrinsic tendency to metrically expand (ie some of the metric coefficients will necessarily be time-dependent). This is mathematical fact. So, if you postulate a static universe of any kind, you’ll need to explain how metric expansion does not happen, in addition to those observations that are difficult to explain without expansion. The only way to really do that is to postulate amendments to the laws of gravity, which takes you down into a really, really deep rabbit hole. So, based on current knowledge and data, metric expansion is simply the most coherent explanation that covers the widest range of observations without having to postulate any new physics.

I made up this term, to describe a fluid the constituents of which interact gravitationally, instead of via EM. It’s not an official concept (I think). If this were so, then ordinary matter (interstellar dust etc) should be detectable as it falls into these micro-BH, due to friction. DM clouds should thus be faintly luminous in the X-ray, radio, and gamma spectra. Also, colliding DM clouds should lead to BH mergers, which again should be detectable. I’m not aware of any data supporting this. My thinking is that this is incompatible with high-speed mergers of DM regions, such as the Bullet cluster. Hydrogen would behave like a gas, and thus generate friction and X-ray luminosity; however, observation tells us that in the Bullet cluster the DM region is separate and ahead of the gaseous baryonic region, and not luminous in any spectrum. It behaves differently than baryonic matter, and thus can’t be hydrogen. It’s interaction really is purely gravitational.

Not unless someone really smart finds a way to describe this mathematically in a computable way. And again, it’s just an idea, I’m making no claims - this could quite possibly be another dead end. I wouldn’t go as far as to say it’s not computable in principle. Basically what’s needed is a mathematical method to derive large-scale dynamics from small-scale interactions, given how the constituents interact (ie GR). I don’t know if that is possible, or how one would go about doing that. What’s certainly not possible is to solve a GR n-body problem with n~ 100 billion.

Not that I’m aware of, though Sabine Hossenfelder has once mentioned a somewhat similar idea, albeit not from the perspective of emergence. This is something I kind of came up with myself; I call it a gravitational fluid. As for math, I have been pondering for some time how this could be modelled, but can’t come up with anything. The GR n-body problem for large n is not computable with currently available computational resources, and I doubt it ever will be.

In principle - yes, you could have charged black holes, though they wouldn’t be of the RN kind. In practice, I doubt it would happen, since on large scales you will usually have a roughly equal amount of positive and negative charges impacting the original body over time, so the net charge will tend to be roughly zero. This is why there are no known examples of any astrophysical objects with appreciable net charge.

I still think there are other viable possibilities besides the ones mentioned. I mentioned briefly on another thread the idea that there might be emergent dynamics at play for gravitational systems with large numbers of constituents; these wouldn’t show up in calculations unless one actually derived an exact numerical solution for a discrete system (n-body with large n) rather than a continuum simplification. Unfortunately we don’t have the computational power to do this, not even in principle. In this picture, DM would be an artefact of our own computational limitations, and not any kind of new physics - the discrepancy that leads us to postulate DM would arise because we don’t have the means to use GR correctly for this scenario. After all, the universe is under no obligation to be computable (given current computational power), even if we do know all relevant laws of nature. There are similar problems in QCD as well.

Yes, that’s what I said.

The notion of a singularity is based on General Relativity, which is a purely classical model of gravity. Unfortunately, what happened at and immediately after the BB wasn’t classical - you need a model of quantum gravity for it, which we don’t yet have. However, even if there is a singularity, no physical infinities would occur, because none of the quantities you mention is meaningfully defined there; T=0 isn’t even part of the spacetime manifold. This is why it is defined as a region of geodesic incompleteness. You wouldn’t see anything at all; it would be completely dark. I’m sorry, but I fail to see any of this. What “theory” are you talking about, exactly? What alleged mystery does it address? What evidence are you referring to?

This is a meaningless concept - the BB represents a singularity in (classical) spacetime, so it is a region that is geodesically incomplete. If you were able to “stand” at the BB, all spatial distances would be zero, and no matter what kind of manoeuvre you performed, it would always take you only to the future. Asking what is before the BB is like asking what is north of the North Pole - it’s simply meaningless, because there are no past-oriented world lines there, just as there is no ‘north’ in any direction when standing directly on the pole. Also, once you account for quantum effects, a strong case can be made that smooth and classical spacetime breaks down long before you even reach the BB, so here too the concept of ‘before the BB’ is meaningless.

When you say ‘actually is’ you are assuming the existence of some absolute reference frame - but no such thing exists. Shape is based on measurements of space, which are relational quantities, and thus require an observer to make sense. The best you can do is define ‘actually is’ as being the rest frame of the Earth, but that’s an arbitrary choice; there’s nothing special about that particular frame. By using the appropriate formalism. In relativistic quantum mechanics, the wave function is always a representation of the Lorentz group - for bosons it will be a tensor of a rank equal to their spin; for spin-½ fermions, it will (in general) be a Dirac (bi)spinor. Both tensors and bispinors are covariant objects, meaning everyone agrees on them, and whether or not they describe a superposition of states is an invariant property. Thus, if there is no superposition in the rest frame, there is no superposition in any other frame too. The only thing observers disagree on is how far apart the particles are, but not whether there is a superposition; they’re just looking at the same system from a different angle in spacetime. You continue to be stuck on the idea that there must be some absolute notion of space and time, some way things ‘really are’ in 3D. The highlighted part is the issue, because spacetime isn’t 3D, and it’s not Euclidean. If you use the appropriate 4D description instead, then there is no issue and no contradictions. Until you can mentally perform the 3D->4D paradigm shift, you will remain stuck on this.

It is true that there are quantities in GR that do not depend on choice of reference frame, ie everyone agrees on them. These are tensors and their invariants. However, there are also coordinate quantities, which are those that are based on measurements of space, time or energy in isolation. These depend on the observer, as they are by nature relational quantities. So, whether or not the choice of frame is important will depend on which quantities you want to discuss. Saying that reference frames ‘don’t change anything’ is a bit too simplistic.