Markus Hanke

Well, for me this quantity describes the local relationship between neighbouring points. I think it is really a matter of definition whether this qualifies as 'change' or not. For me it does, without necessitating any reference to time.

I didn't say this. I said that the Standard Model (taken as a whole, or specific parts in it) are not scale invariant. Can you show this mathematically? Again, this isn't about QM, it's about the Standard Model specifically. Different terms (and there are many!) scale differently within the Lagrangian, and most of the coupling constants are dimensionless and don't scale at all. So no matter what you change in terms of the constants, you can't get a consistent scaling for the overall Lagrangian. I'm simply pointing out to you how the maths work - it's up to yourself what you do with that information. Ideally, you shouldn't take my word for it at all, and instead learn to do the maths yourself. Well then, I don't suppose you have any need for my - or anyone else's - input.

It doesn't need to, because it is equally valid in all reference frames, whether inertial or not. Also, the earth is of course never 'in an inertial frame'. Nonetheless, these laws are sufficiently well tested in purely inertial frames as well, e.g. in satellites and the ISS. Evidently, Maxwell's laws work just as well there. The law of gravitation is the field equations of GR, and as a tensorial equation they are also equally valid in all reference frames. The gravitational field equations are a system of differential equations, so they are a purely local constraint on local geometry - hence there are of course no changes in any constants. Exactly. The calculation of probe trajectories is done using GR, and it evidently yields very accurate and precise results. This shows just how accurate the theory of relativity is.

This isn't how the derivative is defined, though - a quantity such as \[\frac{df(x)}{dx}\] does not involve any dynamics, it involves only the calculation of a static limit at a point - it is purely local. In my opinion there are no dynamics of any kind involved here, and no reference to any notion of time is implied. Perhaps a mathematician's input would be helpful on this point @studiot

It is trivially easy to write the Maxwell equations in covariant form, i.e. without reference to any particular coordinate system: \[dF=0\] \[d \star F=\mu_0 \star J\] These are valid for any reference system, both in free space, and in curved spacetimes. The version you gave is one written in terms of 3-vectors, which directly follows from the above when using a Cartesian coordinate system.

So God doesn't play dice, but he punches a calculator?

This would be the case in Newtonian gravity, but in GR it's much more complex than that. Here, the source of gravity is the stress-energy-momentum tensor, which is a tensorial quantity with 16 (not necessarily independent) components. Energy density is in there as well, but so are other things such momentum fluxes, stresses, strains, momentum density etc. Also, it has to be remembered that the GR field equations are a local constraint - so even in the vacuum of free space where there are no local sources of energy-momentum, you still get gravity. Lastly, unlike in Newtonian gravity, the field equations are non-linear, which physically means that in some sense gravity is also its own source, i.e. gravity is self-interacting. You can in fact get gravitational constructs in the complete absence of any sources of energy-momentum. See above - the source term is a rank-2 tensor, not a scalar. Also, in GR gravity is described purely geometrically, it doesn't use the notion of 'force' as such. Some laws of physics may be scale invariant, but most are not. Specifically, the Standard Model is not scale invariant, and there isn't any self-consistent way to make it so. You don't need matter to have gravity. Also, space isn't 'around' matter - spacetime is everywhere, both in the exterior and the interior of energy-momentum distributions. The coupling constants for the three fundamental interactions are dimensionless; they wouldn't scale along with your clocks and ruler. And if they did scale, you would break the weak and strong interactions in the process, because their Lagrangians are not invariant under such changes. You'd have two regions of spacetime where the fundamental interactions work in two different ways. This is obviously not what we observe in the real world. I understand perfectly well, thank you. I'm simply trying to point out that this can't work. I also understand that the complete Lagrangian of the Standard Model isn't invariant under scalings, regardless of how you try to twist the fundamental constants - in fact, because many of the constants have mutual dependencies, and some are dimensionless, it isn't possible to scale them all simultaneously in a consistent manner. When I first participated on online forums, many years ago, the idea of "shrinking matter" was in vogue for a time - the idea was that the universe is actually static, and just appears to be expanding because all matter in it is shrinking in such a way as to be locally undetectable. The mechanism was supposed to be the same - a scaling of local frames. So not only I am familiar with the essential idea of scaling fundamental laws, I've even been through some of the maths to show why it doesn't work (and can't work). As I said already, spacetime curvature is a tensorial quantity (it is in fact a rank-4 tensor) - so how would that work, do you think?

Are all affluent people honest?

This is only true in spacetimes that are at least static and stationary, but not in the general case. The curvature of spacetime is quantified by the Riemann tensor - its formal mathematical definition aside for now, in the context of GR what this quantity measures is geodesic deviation, i.e. the failure of initially parallel geodesics to remain parallel. This is a more general concept than scale invariance. On an even more fundamental level, you cannot capture the dynamics of gravity by a simple scalar quantity (such as a scale factor), since a scalar field would be unable to account for the necessary degrees of freedom. It can be formally shown that you need at least a rank-2 tensor field for that - represented by the metric tensor in GR. If you postulate a graviton, then, as massless spin-2 particles, they can only couple to rank-2 tensors, not scalars. Well, they are empirically not invariant in that way, so I don’t really get the point you are trying to make? This is not true. If the universe had net electric charge and/or angular momentum, then its geometry would be very different from what we observe it to be. Here’s an example of a cosmological solution to the field equations that models a universe with non-zero angular momentum - many such solutions exist, but they don’t correspond to the universe as we observe it, which places a very stringent constraint on global angular momentum. I haven’t seen a solution for a universe with non-zero net electric charge, but I’m sure they exist too, and going by the case of the Reissner-Nordström metric, they’d be quite different from what we observe too.

I don’t think this is a good way to look at it at all, and it is also not what the formalism of QM actually says. If the particle did pass through both slits simultaneously (according to who’s notion of simultaneity?), then you should be able to show this by simply bringing the detection screen close enough to the slits. But no matter how close the screen is, you always get exactly one hit, never two. Crucially, you also don’t get an interference pattern from a single particle - you get a only a single hit on the screen, as one would expect. It is only when you have an ensemble of many individual hits, that you will observe them to be distributed as an interference pattern. So the crucial aspect here is not that it goes through both slits simultaneously (a highly dubious and ill-defined concept), but that there is no information available about which slit it went through; and since the respective probability distributions are wave-like, an ensemble of many successive hits will give an interference pattern. Conversely, if you amend the setup so that it can tell you which of the slits the particle goes through (and you will find it will always go through exactly one slit, and one slit only), then the interference pattern disappears, because there is now certainty about the state of the system, and thus no longer a basis for any interference. So the central concept here is superposition, and thus the availability of information. A superposition does not mean that somehow two states physically occur simultaneously; it’s rather more subtle than that. Even the very notion of the particle taking any trajectory at all between emitter and screen is no longer a trivial thing.

The maths of GR make no prediction about how much mass there ‘should be’ in the universe, and of what type it is. In fact, taken in and of themselves, the maths make very few predictions at all - they are actually just a very general constraint on what forms local spacetime geometry can take. In more technical terms, this constraint is a system of coupled, non-linear partial differential equations. The crucial thing with this is (and too many people don’t seem to realise that), in order to obtain a solution from such a system, you need to first supply a set of initial and boundary conditions; only then does a definitive solution emerge, which allows us to make quantifiable predictions. So in GR, you get out precisely what you put in. If you start with a wrong premise (e.g. the universe is static) and put in boundary conditions to that effect, the GR field equations will return a solution that is consistent with the basic workings of gravity and those boundary conditions. Complaining then that ‘GR predicted a static/expanding/contracting universe’ (e.g.) is a complete non-sequitur, because all it does is apply the basic laws of gravity to boundary conditions that we supply. If you start with flawed boundary conditions, you get a more or less unphysical solution. That doesn’t mean that GR is wrong - it means that we aren’t using it correctly. This distinction is crucial. So if you get a prediction that doesn’t match observations, then either one of two things can be the cause of that: 1. The boundary conditions are wrong 2. The model is wrong You need to realise that physicists are genuinely considering both of these options seriously - dark matter would fall under (1), but at the same time there is also lots of research being done on how GR as a model could be amended to obtain the observational data without the need for anything ‘dark’. The problem here is that we know that GR works extremely well on smaller scales (on the order of our solar system), which places strong constraints on what kind of amendments one can realistically make to it, without violating experiment and observation. At present, no alternative model works as well as GR itself does, so (1) is currently the preferred option by consensus. As a final note, we already know that GR has a limited domain of applicability, so it isn’t the most general model of gravity possible. We are just not entirely sure yet where exactly the limits are, or what a more general model will look like. This is all under investigation.

I think everyone is always responsible for their actions. Whether or not they should be answerable for them is another matter - it essentially boils down to the question of how much choice someone actually had in a given situation. Someone’s social environment, upbringing, mental disposition etc may place strong constraints on their behavioural patterns, so they may not have been as free to choose their actions as we’d think. But then again, this is very difficult to measure objectively, because on the flip side you have plenty of people from extremely difficult backgrounds who are not prone to criminal behaviour at all. So I don’t know what the answer is, but it can’t be a simple one.

I wish I knew more about QFT, I never got past some ‘first introduction’ type texts, so I only know basic concepts and rough outlines. For some reason I am finding the subject difficult - not in terms of understanding the concepts, but in terms of the mathematical formalism, which I just can’t seem to really get my head around. Another peculiar thing about QFT is that for whatever reason it seems to set off alarm bells somewhere within me. I do not for a moment doubt its empirical success as a model, but something just seems off about it. A lot of things in it appear very ad-hoc, very messy, like an ensemble of disjoint Lego pieces that a child has put together. I just can’t, for myself, motivate the framework from fundamental considerations (as is possible to do in GR e.g.), so it seems invented and artificial. Of course I can’t offer a proper objective argument, but my intuition is telling me that we are missing something important here...something just doesn’t sit right, though I can’t put my finger on it why that is. Even the basic concept of an operator-valued field seems somehow dubious to me, and I don’t quite know why. Of course at the moment it is the best framework we have, and it works well, but...

‘Being intuitive’ is not a requirement for models in physics; it’s also not something that can be objectively determined.

Good point. But does it, really? I am not really sure I understand how you get from \(ds^2\) to a notion of event sequencing. Yes, this is essentially what I was attempting to get at - interpreting \(ds^2\) as time isn’t straightforward. I would agree to this, but like yourself I can’t at the moment put my finger onto just why that is. What’s more, I think our concept of “space” is actually equally problematic, albeit in more subtle ways. My - entirely unscientific - intuition is that neither one is really fundamental to the world, which is why I was speculating about other options over on the other thread. Precisely - all our formal systems (languages, maths, computer code etc) are in some way sequential, because all our mental processes are. We think, feel, and reason in linear 1-dimensional ways; we can’t do anything else, because that is how our minds are structured. For me, that may (!) suggest that our models of reality (both our mental representation of the world, and our abstract descriptions of it) simply inherit that structure. In other words, this may (!) suggest that we use ‘space’ and ‘time’ in our models not because they are actual features of the world, but because that’s how our mind (the originator of those models) is structured. So the question is, can we separate the physically relevant structures within our models (i.e. the parts that encapsulate the actual physics) from their spatiotemporal embedding? I have a feeling that we might be able to, which would have pivotal consequences for the ontological status of space and time. For example in QFT, what is the actual fundamental ontology of that framework? I don’t think it’s momentum eigenstates, or any of the operators in themselves, or the S-matrix, or even the concept of ‘particle’ - it seems we need to rather look at the commutator algebras and symmetry structures that underlie them. Which are not spatiotemporal concepts in themselves. When we play around with embeddings in different spacetimes, we then find all kinds of interesting things, like the observer dependence of vacuum states etc. This raises serious philosophical questions about space and time. I’m just think aloud here Wick’s theorem?

No, I am referring to all the many different types of tests that have been performed to test for Lorentz invariance (not just MM type setups), and which are listed in the link I gave you. By your comment I deduce that you haven’t bothered even looking at the link. Very disappointing, but not very surprising. There are no (repeatable, peer-reviewed) instances where violations of Lorentz invariance have ever been observed. The problem has been identified a century ago, namely that non-relativistic physics fail to accurately describe the world around us. The solution is relativistic spacetime. It has already been pointed out multiple times that this is an example of data misinterpretation. The so-called ‘Twin Paradox’ is neither an inconsistency, nor is it a logical paradox; it is an expected and experimentally verified consequence of relativistic physics. Not at all, because all other types of experiments also gave null results. Even without Einstein and his theory of relativity, the idea of an aether would have been completely untenable, and physicists already knew this. I think you really need to start actually reading the links you are being given. Just saying. Of course we can, so long as they all give the same results and agree with observational data. A model in physics is no different than a map drawn of a piece of terrain - there are many different ways to map out the same terrain, and all these maps can be equally correct. There are in fact numerous concrete examples, such as: you can write the gravitational dynamics of anti-deSitter space in terms of a gravitational theory of its bulk, but you can also write it in terms of a conformal field theory on its boundary. These are completely different models, but they describe the same physics. Numerous other such dualities are known to exist.

Well, what you have defined here is an interval between two points on a differentiable manifold. Of course you can interpret this quantity as ‘time’ in some sense (ref the usual maths of GR), but I don’t think that is a necessary, sufficient, or even obvious conclusion. In the physics sense, time is what clocks measure, and unfortunately in a 3D universe no physical clock can ever measure \(ds^2 \), because all physical clocks are stationary and extended objects, just like the tea cup; ie. their world lines are equal to their spatial embedding. This quantity is thus simply a spatial distance in 3D. Also, in our own normal universe (but not in 3D of course), you have physically realisable world lines for which \(ds^2=0 \); does this imply that no time exists? Obviously not - a photon still propagates at a well defined speed and momentum - so there is a notion of change - even though no proper time elapses for it. So I wouldn’t equate this quantity with time in a general sense (even though it can sometimes be useful to do so), and definitely wouldn’t draw conclusions from it as to the existence of time. Indeed - for precisely the reasons pointed out You mean there is a sequence of operations in doing maths? That is of course true, but that sequence isn’t inherent in the structure of maths, at least not in my opinion. Consider for example the two statements \[ y(x)’=y(x) \] and \[y(x)=ae^x +C\] Of course one can - and frequently will - construct a sequence of statements in between these, i.e. solve the equation analytically. However, in structural terms, these two statements about y(x) are exactly equivalent. It’s simply two formally different ways to make the same statement about y(x). So there is no notion of ‘sequence’ or ‘time’ inherent in the maths themselves - only in the process of formally showing the equivalence with pen and paper, which is a different thing altogether. Both of the above statements are true simultaneously, and are simultaneously equivalent.

Local Lorentz invariance (the symmetry that underlies SR and QFT) has been extensively tested by a very large number of experiments, both historical ones and modern high-precision ones. No instances of genuine Lorentz violations have ever been observed by anyone thus far. The Silverstone experiment is a well known instance of the misinterpretation of data. https://en.wikipedia.org/wiki/Modern_searches_for_Lorentz_violation

Hmm, I think I may be misunderstanding what the term ‘qualia’ is conventionally taken to mean. For me, I am aware of pain, and I am also aware of the unpleasantness of it; these two aren’t the same things at all. Pain is simply a sensation, and that is all it is; the unpleasantness of it is how the mind reacts to that sensation, and it is that which I am referring to when I say ‘qualia’. It is quite real to me. Remember the old Buddhist adage : ‘Pain is inevitable, suffering is optional’. That is precisely how I understand qualia, but perhaps that is not how the term is used in the philosophy of mind...? Well, I am also a practicing Buddhist (albeit in a different tradition) and intellectually inclined, but Dennett’s views - to the extent that I am aware of them and understand them - do not seem to resonate with me. But like I said, I am really not qualified to address them formally from within a philosophical tradition. As mentioned above, in my own meditation practice it appears intuitively obvious to me that an object of experience (e.g. pain) is quite separate from what it is like to have that experience (unpleasant). If I was able to intuitively and immediately experience objects just for what they are (e.g. pain as being just a sensation like any other sensation, and just that, and nothing else), then there wouldn’t be an issue - the process of ‘selfing’ (as I call it myself) couldn’t happen, and thus no suffering could arise. Likewise, if the ‘unpleasantness’ was inherent in pain, rather than separate, we’d be trapped - there would be no way out of suffering. But luckily for us this is not so. On the other hand, in some sense Dennett does have a point though, because the way the mind reacts to objects of experience is ultimately conditioned by ignorance, i.e. by wrong view, by not seeing things clearly. So in that sense the ‘unpleasantness’ of pain is illusory, because pain is just pain, it’s by nature neither pleasant, nor unpleasant - the untrained mind doesn’t see it like that simply because it doesn’t know any better, until insight into the issue eventually arises. So qualia are at the same time quite real, but also inherently empty. I guess in Buddhist philosophy the term ‘qualia’ would encompass sañña (labelling) and sankhārā (conditional formations) within the ‘Five Aggregates’ template; we suffer because we identify with these, and fail to see that they are transient, unsatisfactory, and not-self.

‘Satisfactoriness’ is not a property of scientific models; internal self-consistency, empirical testability (in the sense of making testable predictions), and falsifiability are. And QM does rather well in those regards, all of the debates around different interpretations of the formalism notwithstanding. The standard way of modelling ‘delayed choice’ type experiments may appear unsatisfactory to you only because you tacitly (and perhaps unconsciously) think of the world as classical, which is what we as human experience. More precisely, you tacitly assume locality. But embedding a quantum system such as a delayed-choice eraser setup into spacetime is non-trivial, and in particular not possible so long as one demands Einstein locality to hold. However, we know now for pretty much certain (ref Alain Aspect et al) that Bell’s inequalities are violated in quantum systems, so Einstein locality must be violated; when one takes this into account, a self-consistent and testable model of this experimental setup is easy enough to write down. However, such an explanation will always seem non-intuitive and ‘unsatisfactory’ to us, because it has no analogue in the classical domain.

To be honest, I do not really understand Dennet’s argument, it doesn’t make any sense to me. I can see why he would want to argue against the existence of qualia, given his overall views on the science and philosophy of mind and consciousness, but I really don’t follow his claims. It is obvious that those attributes - an apple’s redness, a pain’s unpleasantness etc - do not exist separate from the mind; in a physical sense, an apple simply reflects light of certain wavelengths, and neurons simply transmit electrochemical signals. Redness and unpleasantness aren’t properties of the ‘ding-an-sich’, in Kantian terms, and believing otherwise is of course a mistake. However, I don’t experience wavelengths of a certain kind, nor do I experience electrochemical signals - I directly experience redness, and the unpleasantness of pain. That’s the whole point. It is in fact precisely the other way around - it is the very concepts of ‘wavelengths’ and ‘electrochemical signals’ that are in some sense at least the illusory fiction here, because these are abstract ideas created by the mind, and at the same time they do not correspond to direct experience (yet they are also real as mind-objects in themselves). Even a newborn infant knows what it is like to see red, or to feel the unpleasantness of pain, though they know nothing as per yet of colours or sensations (as concepts). They experience redness, but do not know that it is ‘red’; they hurt, but do not know that it is ‘pain’. Even my cat manifestly knows what it is like to be a cat, though she does not know that she is a ‘cat’. Any parent who has ever had to console a colicky infant knows that the unpleasantness of their pain is quite real to them, and they are not shy and very vocal in letting you know! Explaining to someone suffering in a dentist’s chair that it is ‘just electrochemical signals’ isn’t likely to alleviate their suffering in any way. Even ethically, such a viewpoint as Dennet’s is very highly problematic. That qualia are subjective (i.e. mind-generated) and possibly lack a physical correlate is obvious, but that does not make them any less real. For any observer, at any given instant, real is what they experience in that precise moment of consciousness; whether the objects of consciousness have a physical correlate or not is really quite irrelevant to that. Even if one hallucinates, and knows that is a hallucination, then both the experience of the hallucination itself and of their beliefs about it are both real. Reality is inherently subjective and observer-dependent; if it weren’t, in what sense could it be ‘reality’? Unfortunately I do not have the philosophical background knowledge nor vocabulary to formally refute Dennet’s claims, but they don’t ring true to me at all, and they most certainly do not correspond to my own phenomenology of experience. In fact, they sound like a cop-out - it seems he is quite desperately attempting to explain away something the existence of which poses a fundamental problem to the rest of his world view.

You got it That being said, our hypothetical tea cup system here is a stationary system, since nothing else is possible in a 3D universe. Meaning, if the cup is empty, it cannot ever be filled, since that would necessarily require a change with respect to some coordinate other than a spatial one. This would be a pretty boring universe

This is not really correct, because gravity has the right degrees of freedom so that it can propagate in the form of gravitational radiation - and such radiation fields never propagate at more than the speed of light. This is a non-sequitur, because there are fundamental interactions other than gravity happening in the universe.

In Newtonian physics, gravity is a linear interaction - meaning the field does not self-interact, so it is not possible to attribute mass to it. One could thus have guessed at the end result without needing to solve this (really awkward) equation. For a model of gravity that is non-linear, i.e. where the field self-interacts, have a look at General Relativity as well as it numerous off-shoots and alternatives.

Sure why not? Mathematically, instead of having quantities that change with respect to some time coordinate, you can always have quantities that change with respect to one another, without reference to any notion of time. ‘Change’ doesn’t imply time, and time doesn’t imply change. Derivatives (in the calculus sense) with respect to some quantity other than time are well defined and commonly used. For example, imagine you have a purely 3D universe, without time, that contains a tea cup. The handle of the cup has a certain curvature; the interior surface of the cup also has curvature, which is probably numerically different. So the surface curvature changes with respect to spatial coordinates, rather than time. So you have a universe that encompasses changes, but no time. This is perfectly consistent and valid, at least in my mind