Markus Hanke

In order to maximise one’s chances of survival and procreation. For example, if you are in the middle of the Savanna, and come across a hungry lion, it is not in the mind’s interest to create an accurate model of all colour variations in the leaves on that bush, or the fragrance of the morning air, or the patterns of the clouds above you. Instead, it will create a model that is almost exclusively focused on the lion, and what you are going to do about it in terms of self-preservation, and the feeling of fear, anxiety, and being threatened. Everything else gets largely filtered out. That isn’t an accurate representation of the world around you at that moment (which consists of much more than the lion, and doesn’t contain anything that corresponds to the emotions felt), but it is one that serves your evolutionary interests in that particular situation. Would the above example work?

Yes, I agree, especially with the part about enhancing one’s own understanding...I’ve experienced that many times myself. So you are right, sometimes it can be skilful to engage. Not in this instance though, the site referenced in the OP is way too far ‘out there’.

Indeed I think we all were, simply because that is what they are conventionally/historically called. Nonetheless, the formal definition of a function is a relationship between sets, so ‘argument of a function’ would probably be a better term.

Note the word ‘approximation’ in this. It’s valid only for the low-velocity, low energy domain.

Well, in the very first place, the sentence you quoted is completely meaningless word salad - it's a bunch of scientific-sounding terms jumbled up into something resembling a sentence, and is devoid of any meaning. So there isn't actually anything there to be responded to. Don't worry about that, because there's nothing there to be understood - the whole thing is completely devoid of any meaning. The one thing you may be able to respond to is the idea that gravity is somehow electromagnetic in nature, which is an old chestnut amongst the crank community, and occasionally resurfaces on various forums. You could suggest the proponent to step into a large enough Faraday cage, which blocks out EM radiation; by their own claims, they should then be weightless. Evidently this is not what happens. Do remember though that ultimately any discussion with adherents of pseudoscience and crackpottery is a waste of time, you aren't going to get anywhere. You simply can't reason someone out of a position that hasn't been arrived at by way of reason in the first place.

Ok, thank you. It would appear to me - and maybe I am wrong and this is just my own ignorance of the subject - that there are a lot of ad-hoc impositions going on that do not necessarily follow from the model/formalism itself. I don't mean boundary conditions, I mean 'doing things to make things fit' kind of prescriptions. This isn't necessarily meant as a criticism of QFT, which evidently works well enough, but rather as an observation that invokes a sense of QFT either not being fundamental, or of us having chosen a mathematical formalism that just doesn't fit the underlying ontology very well, and thus obscures whatever the fundamental physics actually are. Somewhat like Maxwell's equations written with 3-vectors being an unholy mess that obscures the real physics, whereas same become immediately and intuitively obvious when the equations are written in terms of differential forms. I am not even sure what the fundamental ontology of a quantum field is actually supposed to be - it's clearly not the concept of 'particle', but neither is it the field itself, since an operator-valued field is only a mathematical abstraction. So I don't really know what to make of it. I'm afraid not, no. I don't really follow much of what is going in particle physics, since I am more comfortable with GR. Hm...I don't even think that the excitations of quantum fields are ontologically fundamental to the world. After all, both the concepts of 'vacuum ground state' and 'number of particles in a given region of spacetime' are observer-dependent and not invariants; so how could they be fundamental in any real sense? I think there has to be more going on here, which we don't see at the moment. Perhaps it is hidden by an archaic and messy formalism.

The BU concept is kind of related to this, but I am going a step further by saying that information itself requires neither space nor time - these concepts arise only at the point where one attributes context to that information, which requires the imposition of a structure, which generally will be a spatiotemporal embedding. But I say this is an extraneous thing, and not inherent in the information itself. Ok, I haven't actually taken it that far For me, a Hausdorff space simply seems a natural way to think of a complex network such as the brain. Another option would be to think of it as a tensor network that maps inputs (sense data) into outputs (brain states? specific behaviours?). Whether or not spacetime itself can be modelled as some kind of Hausdorff space is another matter, albeit an interesting one. It reminds me of a model called Causal Dynamical Triangulations - one result of this model is that, while spacetime has the usual (3+1) dimensions on large scales, it reduces to just 2D with a fractal geometry on small scales. I don't know too much about this model, but it's an interesting concept. Fair enough, but I'd put it the other way around - 'to vary' inevitably implies a process (and thus time) to me, whereas 'change' does not. But that's just convention Exactly - information vs the embedding of it.

Yes, that's true. But then the question arises of course - if there is no 'external' world, why would the mind need to conjure up any models at all? There seems to be no discernible reason for it, if the mind is already all that exists. In the realist view, at least you can pinpoint a practical reason for the mind's building of a world-model, namely to maximise the individual's chances of survival and procreation. Which is in itself an important point: the mind's model of the world is not designed to reflect actual reality, it is designed to ensure survival and procreation. Thus you have all kinds of distortions, filters and overlays going on that have no analogue in the external world, but do serve a specific evolutionary purpose. Overall I would say that there being an external world is the more likely and philosophically less problematic position - but I would also say that the external reality in itself is almost certainly very different from our mind's model of it.

This is a valid point. But I think the chief problem with a world that is purely invented is the fact that everyone shares a roughly similar ‘invented world’. How is that possible, if it is not based on some external reality? It would mean that either everyone shares the same mind (that’s all there is), and the concept of us being separate individuals is an illusion; or that the ways in which the mind can invent things is somehow intrinsically constrained, so that the end result is always similar.

Take that a step further - as thought experiment, imagine that you are carrying some kind of recording equipment 24/7 for the entirety of your life which records what you hear and see, and then save that data on some hypothetical large-capacity DVD-like disc. Now it is immediately obvious that information requires no specific spatiotemporal embedding - your direct experience of seeing and hearing took place in what appeared like (3+1) dimensions; the same information is stored in your brain in a very complex network that can probably be considered a Hausdorff space with some non-trivial number of Hausdorff dimensions; and also on the DVD, which is in itself (2+0)-dimensional. Interesting to note that there is no real distinction between spatial and temporal dimensions in a Hausdorff space, and no notion of time on the DVD at all...even in its real world embedding, all the information about your life exists on the DVD simultaneously (as it is small enough to be considered local). How we construct a play-back device for the DVD is an arbitrary choice. In all cases, the exact same information (roughly at least) is referenced, so clearly information is quite independent from its spatiotemporal embedding. These embeddings are just arbitrary choices on how the same data set is represented - in the same way that a computer’s graphical user interface is an arbitrary choice of how to represented the information (which are just bits) in its memory banks. There’s nothing inside the memory banks that resembles a little “file” icon, or the letter “A”, or even any notion of a two-dimensional screen. None of this is intrinsic to the actual information contained in the computer’s memory; they are just arbitrary conventions imposed from the ‘outside’ in addition to the raw data. This is quite necessary for our mind though, because we would not be able to comprehend the data set in its raw form. So again - could the imposition of a particular spatiotemporal embedding (such as (3+1) of how we experience the world) be something the mind does to structure and order information, and assemble it into a linear and coherent model of the world?

Ok thanks, I expected that. My understanding is that CPT invariance always implies Lorentz invariance and vice versa (a duality?), so it can only ever be a local symmetry. That has interesting implications though, because what it really means - at least in my reasoning - is that one can only meaningfully speak of ‘future-oriented time’ for larger ensembles of particles. For individual particle interactions, I don’t see how the notion of ‘past-to-future ordering’ could possibly be intrinsic. So another technical question to you @joigus: when calculating the Dyson series in order to get to a S-matrix, how does one know the correct order of the terms? It looks like this is a series of nested integrals, so the order of the terms is not in general arbitrary. I know there is such a thing as a time-ordering operator, but my question is - does the ordering somehow follow from the theory itself, or is it imposed ad-hoc? Hopefully this makes sense. I think this would be problematic, because it leaves electric charge unchanged. There will certainly be a large number of scenarios that are TP invariant, but some systems are not, notably anything that explicitly relies on electroweak interactions. Trouble is, unlike T and P, C is not spatiotemporal, in the sense that it doesn’t directly arise from coordinate symmetries. But perhaps C/P/T could be connected to topological invariants somehow? This way one might be able to treat them under a common framework that is independent of particular coordinates or metrics. It would mean though that vacuum spacetime would have to have a very non-trivial topology, even on scales of the Standard Model, which is potentially difficult to reconcile with GR.

Ordinary spacetimes for simple ensembles of particles don’t have a topology of this nature, so I’m not sure how this is relevant...?

What I mean is that CPT symmetry implies and requires Lorentz invariance, and vice versa. We know that Lorentz invariance is a purely local symmetry - it holds across small enough patches of spacetime that can be taken as Minkowskian. However, an ensemble of many such patches of spacetime taken together is generally not guaranteed to remain Minkowskian. At the very least, the same must hence be true for CPT symmetry as well. Just exactly what “local” encompasses will depend on the circumstances - every time you add another particle to the ensemble, the failure of spacetime to be Minkowskian becomes a little less negligible by degrees, and eventually there comes a point where one can’t ignore it anymore, at least not on the characteristic length scales of the interactions in question. Determining where that point is would be quite a difficult undertaking, since the gravitational effects of each particle do not add linearly. One might argue that a very large number of particles is needed, but I am not so sure, because it is also a matter of scale - what is negligible on our scales may already be very significant on QCD and electroweak scales. Perhaps - and I am just speculating here - the second law emerges precisely due to the failure of background spacetime in that region to be exactly Minkowskian. It would seem too strong a correlation to be a mere coincidence. Purely technically, if one was to be really strict, there is no such thing as a pure CPT symmetry in the real world, because the presence of even a single particle already makes the spacetime region non-Minkowskian - we just choose to ignore this, because the deviation is vanishingly small by all practical standards. So maybe it would be better to say that what is CPT symmetric isn’t the physical system as such, but rather its dynamics, i.e. its Lagrangian. Question to you, since you know much more about QFT than I do - is there some version of the CPT theorem that holds in curved spacetime QFTs as well? I don’t see how it could be possible, since in general curved spacetimes there won’t be any time-translation symmetry.

Great, thanks It would appear that his thoughts were very roughly along the same lines as my own thinking on the subject. I shall definitely add this to my reading list

I think the issue with this is that CPT symmetry is a local symmetry, just like is the case with Lorentz invariance. From what I remember (and I am by no means an expert on QFT, it is the one area of physics I am least comfortable with), to calculate the scattering matrix of an interaction, you perturbatively sum all possible Feynman diagrams of all intermediate states into what is called a Dyson series, which then allows you to obtain the overall S-matrix. It is obvious that each individual Feynman diagram is CPT invariant, but it is not obvious whether or not a large ensemble of resulting S-matrices necessarily has this symmetry, especially not after renormalisation. So I think CPT invariance holds only locally, same as Lorentz invariance can and does only hold locally. I think it is precisely this failure of CPT symmetry to hold over larger ensembles that gives rise to the second law of thermodynamics. The other problem is that from what I remember, renormalisation is a procedure that in itself really only works locally. In any case, it would be practically impossible to actually do the maths for anything more than a few particles at a time, in a small region of space.

No I haven’t, but it sounds very interesting. Have you got a link or a reference to this? Really? But what do you do if the object in question is of higher rank or dimension, such as e.g. the rank-4 Riemann tensor? It’d be a bit awkward to write that out as a matrix

This is a really good question, and, I think, one that we don’t have the final answer to. I have been thinking about this for some time as well (see what I did here...) The situation is complicated, because what seems to be happening is that, while CPT symmetry and T-symmetry are formal properties of the laws themselves, they don’t appear to necessarily apply to physical systems described by these laws. For example, each individual microscopic interaction between elementary particles is CPT invariant, but a large thermodynamic ensemble of the same particles isn’t (due to the second law of thermodynamics). Or take the GR field equations - they are trivially T-symmetric, but some solutions of these equations (spacetimes that contain event horizons) are not. I think the basic problem is that we do not have a unified description of the fundamental interactions with gravity, so it is very difficult to see just what is really going on, on a fundamental level.

Very nicely presented, thank you for the time and effort spent on that post! +1 (I’d give more if I could) The answer is of course no, you don’t need time. Neither do you need space. All you need in order to capture all relevant information/dynamics of the system is a suitable network of relationships, as represented by your S-matrix (which should transform as a tensor). This is intuitively obvious for spacetime and gravity, which is explicitly about relationships between events, entirely independent of how we embed these into a spatiotemporal coordinate system (given some basic conditions). The big question, however, is this - can this be generalised for any physical system or model? In other words, is it conceivably possible to formulate all of physics entirely independently from spatiotemporal embeddings, using a suitable ‘language’ such as (e.g.) tensor networks, algebraic topology, etc? I have a feeling it just might be. If it is, then we must seriously ask ourselves in what sense space and time can possibly be ontologically fundamental properties of the world. It is probably obvious by now that I am personally of the opinion that space and time are not fundamental in the sense we usually take them to be; I think they are artefacts of our perception of reality, rather than fundamental properties of reality itself. I think what is fundamental to the ontology of reality are only networks of relationships, which is why I kept going on about that during the discussion on ‘change’. I think it is actually much like functions in mathematics - the fundamental ontology of a function is a relationship between two or more sets; you can then choose to embed these relationships in a spatiotemporal coordinate system of a suitable kind, and draw them as a plot. But the plot is in no way fundamental to the function - only the domain(s) and codomain(s) and their relationships are. The plot is simply a more or less arbitrary way to visualise that information, to embed it spatially, similar to how a computer monitor spatially embeds the non-spatiotemporal information in a computer’s memory banks. Note that such embeddings are not entirely arbitrary though, since the structure of the underlying network constraints (but perhaps not uniquely determines) how it can be represented; so there will be privileged embeddings for specific underlying structures, in terms of how many axis are needed, how they are arranged etc. I am hoping that this perhaps translates into physics - for example, it might eventually be possible to show that we perceive the world as (3+1)-dimensional simply because that is the privileged (or perhaps even only possible?) scheme to consistently embed the underlying network of relationships for gravity and electromagnetism, being the two interactions that are directly relevant on our length scale. So the big question then is - is there a single underlying network that is fundamental to reality? What are its nodes, and how can it be described and represented? There actually seems to be an issue with this. None of the fundamental laws of our universe determine a unique time orientation, except the second law of thermodynamics (the Standard Model is CPT invariant, and GR is T-symmetric). However, because in our (0,3) toy universe there are no spatial degrees of freedom, so there is no consistent notion of entropy in the thermodynamics sense, and hence the second law simply does not exist in this universe (obviously, since there are no ensembles of particles). So even though there is plenty of time here, there is nothing that could pick out a unique ‘future’ direction on any of the axes. There is nothing to even stop ‘future’ and ‘past’ being oppositely oriented on different time axes. Also, the differential equations describing the physics in this universe would contain multiple derivatives with respect to the three time axis, and no spatial derivatives; that makes them elliptical, so what little dynamics there are in this universe would be deterministic, but nonetheless entirely unpredictable. I don’t even see how there could be a consistent notion of causality. Note also that this universe as a whole, even though it consists of only time, is an entirely static block universe

That’s because there isn’t any such ‘problem’. How could there be? The energy-momentum tensor is a local quantity, whereas the self-interaction of the gravitational field is non-local, so of course it doesn’t form part of aforementioned tensor. It can never be a tensorial quantity, because all tensors are local, and any concept of ‘gravitational energy’ is necessarily non-local and observer-dependent. You can, however, define such a quantity as a pseudo-tensor (such as the Landau-Lifshitz pseudo-tensor, or the Einstein pseudo-tensor); this allows you to write down a combined conservation law. The self-interaction of the field is instead encoded in the structure of the field equations themselves; that is why they are non-linear. This is perfectly well understood, both physically and mathematically, so there is no ‘problem’ here.

I’m not an expert on the engineering applications of thermodynamics, so others here are more qualified to address this. I’m more of a theory guy - so in what way do you think this is related to the second law? I don’t see a direct connection, and most certainly not anything that would put the law into question.

I have to say this is one of the worst papers on GR I have ever seen; it is just full of errors and basic misconceptions from beginning to end. Only goes to show that what is on arXiv is to be taken with a grain of salt - it’s a pre-print server after all.

Nice point I never thought of this. Exactly, you got it What distinguishes time from space in the metric signature is only the fact that they have opposite sign - whether the sign itself is plus or minus is arbitrary. My original (3+0)-dimensional tea cup universe had metric signature {+,+,+} OR {-,-,-}...a purely time-like (0+3)-dimensional universe would have a metric signature of {-,-,-} OR {+,+,+). Hence, their metric would be precisely identical. In theory at least, unless I am overlooking something, these universes should be indistinguishable, at least geometrically. Crucially, in both cases they are static and stationary - so not only is change<>time (IMHO), but also time<>change. Interesting...this isn’t really true in German though, at least not directly. There are, in fact, two nouns for ‘change’ - Änderung, which is the concept of non-homogeneity, of something having different attributes as a comparative relationship; and then there is Veränderung or Abänderung, which is the process of making something different. Only the latter has a connotation of implying time, at least in my opinion.

Oh I see I never bothered to fact check this...just come across it here and there. A somewhat more scientific one - it is possible to construct (mathematically) a geometric body that has finite edge length, and infinite surface area enclosing zero volume.

Here's another one - it is actually illegal to bring a Furbie into the Pentagon. It's in fact a criminal offence, punishable by lengthy prison sentences

Does this have any connection to the fact that a fully stretched out (standard shop-bought) slinky is precisely 82 feet long?