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Markus Hanke

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Everything posted by Markus Hanke

  1. Yes, perhaps. My original impulse was actually to just use a function or a field that does not explicitly depend on time, but I thought it would have been too abstract. Hence the tea cup in a 3D universe. But perhaps my first impulse would have been better, as those things have an explicit set-theoretical definition. I think it must be that our thought processes are fundamentally different. For me, it is difficult to understand how someone can not see a notion of spatial change in that picture, just as it is hard to see why change should be in any special way connected to time. But perhaps that's just me and my autistic mind But then again, the concept of change without reference to space or time is fundamental to some models in physics, notably attempts at quantum gravity that are background-independent, such as LQG and CDT. Even in ordinary quantum physics, time does not play the same central role as it does in the classical world. So I'm certainly not the only one finding value in it. Perhaps it is best to leave it at this, since my intention hasn't been to convince anyone of anything; it was mostly to explore the meaning of 'time' a bit more, and hopefully get the reader to go beyond what might seem obvious at first glance.
  2. In a way yes, in the context of Theravada. Ajahn Chah was a bit of a reformist, in that he attempted to cut through all the elaborate ritual, magic spells etc etc that tends to proliferate once any system of thought becomes a folk religion. He wanted people to go back to doing the actual practice, rather than attach themselves to form and ritual. He was very clear on that anyone can find liberation in this lifetime, given sufficient dedication, effort, and the right way of practice. He was also a simple village boy by background, so the way he taught was very down to earth and no-nonsense - in fact his style was very similar to that of the Zen masters of old. Unfortunately, in recent years, as the Ajahn Chah lineage became more popular, it too began to ossify and ritualise again. But I suppose that's the way it goes, once anything becomes institutionalised. This where one needs to take responsibility for one's own practice, and try to focus on what actually matters. I take from the tradition what I find useful, and come up with ways to peacefully coexist with the rest. I will be relocating to Thailand for that, I have already been formally accepted into a monastery of one very well known and respected (in Thailand) teacher within the tradition. He is one of the original students of Ajahn Chah, and the Thai people consider him fully enlightened. I figured if I do this thing I might as well do it right, and learn the original form. It will be a challenge, as I do not as of yet speak any Thai, but hey...life becomes boring if it is too easy So I'll be back and forth between Thailand and Ireland for a few years, but, once the 'junior monk' period is over, I am hoping to be based somewhere in Europe, as all my family is here of course. Absolutely. For me these are the most prominent forms of suffering, as my body is still largely cooperating; but being on the autism spectrum can be tough, and then of course you have all the other usual vicissitudes of life.
  3. No, the second law follows directly from fundamental considerations of statistical mechanics and some basic maths, and as such is not in contention. It also follows more or less directly from \(Z_2\) symmetry and unitarity, so it is fundamentally motivated by manifest symmetry considerations. Essentially, in a world where unitarity holds for quantum systems (as is evidently the case in our universe) you can't not have the second law of thermodynamics, if that makes sense. I am not sure what the point of all this really is, since the setup you have there is not an isolated system in the thermodynamics sense - so what does it have to do with the second law at all? Note also that the second law is a global statistical statement, and as such it does not contradict temporary (even long-lasting) local decreases in entropy. What exactly are you attempting to show here?
  4. Yes, I agree with this. It's just that the act of observation isn't what the discussion is about - I think it is fair to say that we all agree that in the absence of time, there can be no observation. This is not in contention (but it actually has interesting implications, if you think about it...but that's for another thread). So that leaves us with this: if change in itself (not its observation) does not need to involve a process, and thus does not reference time either implicitly nor explicitly, how can it be defined? Here is where I would argue that the best way to do so is via set-theoretical considerations, as detailed earlier. Essentially, I understand it as a relationship between elements in a set (or even between sets of comparable type). Surely that is not an unreasonable (albeit admittedly counterintuitive) position? To be honest, having slept over this whole thing, I am not sure whether I should. Since the tea cup universe has proven so controversial, the implications of a purely temporal universe might set off a riot Perhaps a shout-out to the other participants here is in order - how do you feel about this discussion? Should we continue on, or agree to disagree (which is fine)? I think even from the little bits we have been talking about, it is quite clear that time does not just equal change.
  5. No, the law of reflection does not hold at relativistic velocities.
  6. Yes, the point is precisely to arrive at a suitable definition for the notion of 'change'. I for one would say that 'change' is implied by the non-identity of entities, and is thus not a spatiotemporal concept. It is the failure of a set of entities to be homogenous. So by this definition, a universe that has no time dimension(s) must be perfectly homogenous in all aspects, purely on account of there being no time? In what way is 'change' ontologically identical to 'observation of change'? That's like saying a tree is the same as the act of observing it - your are postulating the identity between a static entity and a (quite separate) process, which is dubious at best. P.S. Very interesting discussion so far, fair play to everyone But wait...the real fun starts when we raise the stakes a little - what happens when we have a universe that consists of only time dimensions, e.g. a (0+3)-dimensional universe? And would you believe it when I said that such a universe might be entirely indistinguishable from a (3+0)-dimensional one
  7. Ok...and that's all I've been doing, really. But no one has been saying this...? I don't really understand where this statement is coming from - neither the definition of functions nor of derivatives involves any notion of changing variables. Functions are formally defined as relationships between the elements of domains and codomains (which are sets), and derivatives are functions that involve limits evaluated at a single point, so they are also relationships between elements in sets. This is the textbook definition. So we are talking about relationships here, not processes or actions of any kind. This is what I have been trying to point out all along.
  8. On a manifold that has both spatial and temporal dimensions, these will indeed by inseparable, and in the sense that they both make an appearance in the metric with opposite signs. A purely spatial 3D universe wouldn't be locally Lorentz invariant since the metric signature must be either {+,+,+} or {-,-,-}, so GR does not apply here. GR does not in any sense establish concepts of space and time - it is simply a constraint on the form local geometry can take, given local sources of energy-momentum and appropriate boundary conditions. All I can say here is that GR - as being a tensor equation - does not demand any specific number of dimensions nor metric signature (i.e. mix of spatial and temporal parts) to be valid. So there is nothing from stopping you e.g. to write GR with 17 spatial and 6 temporal dimensions, the field equations would look exactly the same. Whether what is described then bears any resemblance to our own universe is a different question. But again, this is actually irrelevant, because I didn't demand GR (or any other specific law) to hold in my toy universe. I find it hard to explain my thought process on this point, as I lack both the formal philosophical background knowledge and the necessary vocabulary to do so. Essentially I am of the opinion that while observation requires existence in the ontological sense (something needs to exist first before anyone can observe it), the reverse is not true in my opinion - I don't see any logical reason why the absence of observers should imply that nothing can exist. Hence, while the tea cup universe is undoubtedly physically unreasonable, it is not philosophically inconsistent. Again, the ontology of existence does not, to me, necessarily imply persistence - but persistence always implies existence. Of course my toy universe is not physical - I never claimed that it is. It's simply a philosophical thought experiment. There can be no observer whatsoever in such a universe, neither internal nor external, and I did not postulate one in my original example. This is simply a universe with a single tea cup in it, and otherwise complete empty (vacuum). I also do not require it to be embedded in anything. My point was this: 1. Consider the hypothetical universe as an ordered, uncountably infinite set which consists of all physical locations/points (just like ordinary spacetime manifolds, only in 3D) 2. Each element in the set be of type boolean, i.e. either of value 0 (meaning it is vacuum) or 1 (meaning not vacuum) 3. Not all elements of the set are of value 0, because of the tea cup 4. Because not all elements within the set have identical value, this implies a concept of 'change' 5. Since the elements of the set are abstract entities (it is irrelevant what they physically correspond to), the notion of 'change' introduced here is purely a relationship between elements of an abstract set, and thus neither spatial nor temporal in nature Whether or not this change is observed by anyone is irrelevant, because it makes no difference to the structure of this mathematical set, or the relationships between its elements. I am simply saying that there is nothing special about 'time', so far as change is concerned - you can have change with respect to time, as well as change with respect to any other quantity. Change simply isn't spatiotemporal, it is an abstract, relational concept - in my opinion. So change does not logically imply the existence of time, and conversely time also does not logically imply any change (you can have a complete empty universe without any processes taking place, that nonetheless has temporal dimensions). Why? When the early universe formed, there was no one to observe that (it was too small and dense to contain any observers, it didn't even contain particles), but the change obviously still happened. Of course that was a change with respect to both time and space, but nonetheless is happened without observers, so the above statement is clearly inconsistent. Again, the example was specifically about a 3D universe that contains only a tea cup, and nothing else. Postulating an observer would have been pointless, since without a temporal dimension, no act of observation is possible. This does not however negate the existence of the tea cup and the vacuum - which aren't identical.
  9. Schrödinger hated cats He was very much a dog person, which is why he came up with such a cruel thought experiment... Besides - my own cat definitely exists on both sides of the door simultaneously, as it is impossible to keep her out of the kitchen. Indeed. And that’s the crucial point - the cat should be in a state of superposition, but when we look at it, it never is. And this is true for any observation we make, be it on a quantum system, or on something macroscopic - we never observe any superpositions, only definite outcomes. So how does the system prior to observation, which demonstrably is in a state of superposition, get to take on precisely one definite state when we look at it? This is essentially what is called the ‘measurement problem’.
  10. Ah I see - I misunderstood the accepted meaning of the term so. Thanks for clarifying Sure...it’s the Theravadin Thai Forest tradition, in the lineage of Ajahn Chah. I have plans to ordain as a monk in this tradition, sometime next year. Completely agree, that is the (very effective) evolutionary purpose of pain. Nonetheless, I do believe it is possible to relate to the experience in a way that doesn’t involve automatic suffering. Otherwise I wouldn’t be a practicing Buddhist Yup, sounds reasonable - though I still don’t think I fully understand the intended meaning of ‘quale’. I’ll have to do more reading on this subject.
  11. I think we’ll have to disagree on this Which is fine of course, this being just a philosophical exchange. To me, the term ‘static’ (I think it should have been ‘stationary’ actually, I often confuse them) implies precisely the absence of any kind of reference to time, be in implicit or explicit. This is called a ‘parametrisation’, and it is not what I am doing or suggesting at all. Note also that there is no necessity whatsoever to interpret a parametrisation parameter as ‘time’ - that’s just an extra ad-hoc assumption. Furthermore, note also that generally there is more than one way to parametrise the same curve. So you would say that the hypothetical 3D universe with only a tea cup in it is entirely homogenous (i.e. devoid of changes) in all physical aspects? I definitely (but in a friendly, intellectual way) disagree There is of course no observer in such a universe, since no act of observation is possible - but does that imply that the tea cup cannot exist? Does existence (in the ontological sense) require a temporal dimension? I think not. True, but this issue wasn’t about the observation of change; it was about whether, for two quantities which are not themselves spatiotemporal in nature, one can meaningfully define a notion of ‘change’ of one quantity with respect to the other, and whether this implies a notion of ‘time’ in the physical sense. I think you have answered this correctly in the first part of the above sentence. I think we can all agree that no act of observation is ever possible without physical time, but that isn’t really the point here. The point is rather that, if there is not some concept of ‘change’ in our hypothetical tea cup universe, then that universe would by definition need to be homogenous in all physical aspects. Clearly that isn’t the case though, because at the very least you have the spatial region occupied by the tea cup, and then vacuum for all the rest of that universe. Whether there is anyone there to observe this is irrelevant, in my opinion. To me, ‘change’ in this particular scenario is equivalent to non-homogeneity, i.e. it is simply the failure of all spatial regions of that universe to be identical. It isn’t a process, it’s a relationship.
  12. Interesting, I haven’t heard this term before!
  13. But what if we think of f(x) as an (uncountably) infinite set of real numbers (which it is, mathematically speaking)? Or better still - a 1-parameter family of real numbers? That set would be a static construct, as would be the relationship between the elements in the set. Of course you could externally impose a notion of “going from one element to another”, but I don’t think that is inherent in the set itself.
  14. My original thought experiment was about a tea cup in a hypothetical (!) universe that only had 3 spatial dimensions and no temporal ones (and isn’t embedded into anything higher-dimensional), so speaking of “simultaneity” is meaningless there. You can only slice up such a universe into slices that are purely spatial. Studiot’s choice of words ‘present together’ was very apt in that regard - two points are ‘present together’ if they share the same spatial slice. Crucially, on a manifold that is purely 3D, all pairs of arbitrary points share a common spatial slice, so the entire manifold is ‘present together’. At the same time, two arbitrary points A and B are generally not identical, because geometrically you have \(ds^2 \neq 0 \) unless A=B. So essentially, my way of thinking is this - if you have a pair of entities of the same type {A,B} which are not related by an identity relation, then this defines a notion of ‘change’, to be understood as a relationship between A and B. ‘Entity’ (I couldn’t think of a better term) is to be taken in its most general sense. To put it very succinctly - change is simply the failure of entities of the same type to be identical. Not only does defining it like this avoids any reference to time, it also does not make reference to space; change (again, in my thinking) is not fundamentally a spatiotemporal concept at all. There is no reason why it needs to be, other than our human intuition, which is not a very objective criterium. I think it is better understood as a set-theoretical notion. Yes, you can apply it to points on a differentiable manifold, but you can also apply it to any other kind of entity, be it mathematical or not. For the specific example of the tea cup, evaluating some measure of curvature (e.g. Gaussian curvature) at the handle and at the base of the cup will yield different results in general, so the relationship between them is one of non-identity - so there is a notion of change of Gaussian curvature with respect to spatial coordinates, even though the manifold is purely 3D. I make it clear again that this is only my own thinking on this matter - personal philosophising, if you so will. It is not intended as any kind of claim - it’s more of a ‘thinking aloud’ kind of thing.
  15. The quote in the previous post by ruibin.niu isn’t actually from me - I don’t know how my name got on that. This just for the record.
  16. Here’s a little experiment for you which you can do yourself - jump off a diving board into a swimming pool, and carry an (waterproof) accelerometer with you when you do that. What you will find is that while you are in free fall, the accelerometer reads exactly zero at all times (you might need to account for air resistance though). Since F=ma=m*0=0, there is no force - and yet gravity acts on you, because you are falling, and approaching your terminal velocity. Also notice that funny feeling you get in your stomach while you fall - that is the absence of any force acting on you. Or observe those astronauts floating about on the ISS - no force acts on them, yet the ISS obviously remains gravitationally bound in its orbit around the Earth. Just some food for thought.
  17. The model contains coupling constants that define the relative strengths of the various interactions. They are dimensionless themselves, but are related in specific ways to other fundamental constants that do have dimensions. This (along with boundary conditions in the Euler-Lagrange equations) defines a unique scale for the model as a whole, that cannot be changed without affecting physically detectable changes. Of course you can express the SM in inches, if you are so inclined - but that is not the same as resling the Lagrangian. When you scale something, you are scaling the actual dynamics of the system, which is a physical change; using different units just means expressing the same physics in a different way. Today's temperature can be 20 celsius or 68 fahrenheit - this isn't a scaling, because it refers to the same physical temperature. You can say 'this house's temp is 20C' and 'that house's temp is 68F', and there is no difference whatsoever between them. No, what I am trying to say is that all atoms of the same kind have the same structure regardless of where and when they are, because their fundamental constituents are subject to the same laws and dynamics. And you can't keep those laws and dynamics the same if you rescale them. It's about the dynamics of the system. As for relativity, the Standard Model is CPT invariant, which implies Lorentz invariance, so compliance with the laws of relativity is both guaranteed and required. Essentially, the dynamics of a system isn't the same as its spatiotemporal embedding. Actually, all this if off-topic, because the original question was whether GR can be rewritten in terms of just a scalar field. The answer to this is "no", because a scalar field (irrespective of what it physically refers to) cannot capture all the dynamics of gravity. Even a vector field can't. You need at least a rank-2 tensor field. You can see this most clearly if you consider that gravity can propagate as gravitational radiation fields - such fields have two polarisation modes (+ and x) that are distinct, so you will need at least a rank-2 tensor to fully capture all its degrees of freedom. A scalar field simply can't do the job, which can even be formally proven.
  18. I think in a very general sense, I am referring to the relationship between quantities, regardless of what they are - if there is a relationship other than identity between them, I see no reason why one quantity can't change with respect to another one without needing any temporal dynamics. For spacetime in particular, 'space' and 'time' are on equal footing anyway, so if something can 'change' with respect to time, it can also 'change' with respect to any other quantity. But like I said, I suppose in the end it is a matter of definition / convention.
  19. The Lagrangian contains very many terms - some of them contain units of space and time, others do not; some contain mixes of different parameters, others contain higher powers of some dimensions, but not others. If you simply scale units, then some parts of the Lagrangian change, whereas other parts do not, so the overall Lagrangian is never the same. That's the point - because the Lagrangian is so complicated, it is simply not possible to adjust everything in such a way that it remains overall invariant. Especially the weak and strong interaction parts will cause problems here. And then of course, even if it did somehow remain invariant, you still can't recover the dynamics of gravity from a simple scalar field. You need at least a rank-2 tensor.
  20. 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.
  21. 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.
  22. 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.
  23. 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
  24. 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.
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