joigus

Are you contemplating the possibility of being both shallow and insane? Or sane but shallow? It's certainly possible. +1

That's probably because you're an architect. I suppose that when you're thinking about buildings, you must be careful that they don't flip in any sense. That would be a liability for a building. The longer a building lasts unchanged, the better. We're all constrained by the theoretical framework of our guild. Physical systems* do flip. An Ising magnet for example, is a physical system that must make a choice (take a decision). Spontaneous symmetry breaking is the paradigmatic example. Some time in the remote past, the Higgs multiplet took what I've called "a decision", thus breaking a symmetry, filling the world with massive gauge bosons and fermions by pointing towards an abstract direction in the configuration space. Edit: So I suppose my point is: Could the direction of time that we perceive be the result of some kind of accidental orientation-taking that we now know to be at the basis of much symmetry breaking in Nature? Could conscience be some version of this kind of symmetry breaking? When you are exposed to the concept of spontaneous symmetry breaking, it just blows your mind. Edit 2: Natural-born physical systems, not programmed, like a building.

I am to you too, and to all of you. @Ghideon caught me a couple of days ago on an important example about tiling the plane with regular polygons I had omitted. Thank you for being sensitive to that. +1 I would agree, had you said: Time is sooo fundamental that it underlies almost everything we do, say, understand, or think.

I'm trying to grope towards a setting in which a mind is not a thing, but a particular condition in the universe that accretes locally. I'm also struggling to make myself clearer. I'm also trying to read everybody and I'm aware of the conversation that's going on involving @michel123456, @Strange, @studiot and yourself about directionality in mathematics. Let's go back to geometry and minds. Let us suppose the geometrical structure of the universe is more symmetrical with respect to the sign in the metric. The simplest model I can think of is: \[ds^{2}=\left(dt_{1}\right)^{2}+\left(dt_{2}\right)^{2}+\left(dt_{3}\right)^{2}-\left(dx_{1}\right)^{2}-\left(dx_{2}\right)^{2}-\left(dx_{3}\right)^{2}\] The forming of a "mind" (robot, human, squirrel...) implies some set of some series of "decision-taking". Please, let me be a bit vague or I won't be able to get it out. Now a "decision" is taken about what is the inside and what is the outside in the particular part of the universe where this "mind" forms. We're all thinking about that inside/outside decision. Look: But what is inside? You can't see your brain, I can't see mine. Nobody can. Own brains are completely out of the picture biologically. They're just not there in the representational parameter space of the world. It's the interior of the box that we can intuit but we cannot see. I think this connects with an observation that @michel123456 has been trying to make for years, that I will re-phrase here at the risk of adulterating it, as follows: You can't see your past worldline, because that is you, and you are not a signal for yourself. Maybe Michel has been a bit naive in not distinguishing carefully enough that this is not a general setting in physics. In particular, elementary particles can "see" themselves by emitting a virtual boson and re-capturing it. In a cartoonish way of speaking they'd go like "look, that's myself a nanosecond ago". We could discuss whether a virtual particle is really a signal, but... Drifting off-topic. The point is brains are extended objects that need to sacrifice most of their internal dynamical states in order to represent what's outside. So they lose focus of what they are, on what's inside (thoughts and some chirps and clicks aside). They need to. Let's go back to our completely signature-symmetric metric. Now something in the physics of your brain has decided what "inside" and "outside" mean. This seems to automatically suggest a decision about what is after and before. In a non-invariant language (why should it have to be? we're trying to represent perceptions of the observer)* we would have two distinguished parameters: \[dr=+\sqrt{\left(dx_{1}\right)^{2}+\left(dx_{2}\right)^{2}+\left(dx_{3}\right)^{2}}\] \[dt=+\sqrt{\left(dt_{1}\right)^{2}+\left(dt_{2}\right)^{2}+\left(dt_{3}\right)^{2}}\] But time now presents itself as some kind of radius in this 6-dimensional geometry. This leaves us with 6 polar coordinates, two to represent orientation outside; and two to represent orientation inside: \[t,r,\theta_{\textrm{int}},\phi_{\textrm{int}},\theta_{\textrm{ext}},\phi_{\textrm{ext}}\] This would leave the t-angular coordinates free to represent the external world by means of constraints: \[\theta_{\textrm{int}}\left(\theta_{\textrm{ext}},\phi_{\textrm{ext}}\right)=0\] \[\phi_{\textrm{int}}\left(\theta_{\textrm{ext}},\phi_{\textrm{ext}}\right)=0\] And now the (t1,t2,t3) coordinates do point to an origin in time the very same way that spherical coordinates point to an origin in space (call it the "self"). This in some crude way would represent that being conscious implies an origin in time. Of course, as @studiot pointed out, angular coordinates have no meaning at any of the loci r=0 or t=0, foreshadowing at the same time, admittedly in a crude mathematical way, why you cannot represent your own position or your mind's birth consistently. You see nothing there. Now, irrespective of how accurate this simple-minded model may be (it's probably not), it shows that, in a universe geometrically richer than we perceive it to be, constraints defining what a conscious system is could account for the familiar (1,3) structure that we perceive on the basis of what a conscious system needs to do to represent the world, rather than what the world is in its intrinsic structure. I may have misinterpreted you completely, Markus, but something like that is what I thought you were referring to. I'm also trying to answer to what @vexspits was asking me about. * It's about charting the universe locally at this point; not about mapping it out globally.

Deal.

Today's best "gotcha"!!! +1 Yes. Where is the line between one and the other?

I'm going to focus on this. I'm interested in its logical structure. Religious belief is based on wishful thinking and misguided intuitions. Less wishful thinking would imply less religious thinking. (What you propose is a little bit like saying "an improved lie is one that lowers the percentage of false information in it". It doesn't sit well with the intuitive idea of what a good lie is. An improved lie would be one that more efficiently conceals the "mis" bit in "misinformation".) Following your premise: The best religion (the most improved) is that that lowers the % of wishful thinking to naught, while actual knowledge takes its place and substitutes the hierarchy of its tenets to completion (tenets gone). Therefore the best religion is no religion. Which clinches the proof.

Oh, but there is: https://en.wikipedia.org/wiki/Donaldson's_theorem https://mathoverflow.net/questions/47569/what-makes-four-dimensions-special#:~:text=A comment is that 4,live in 4-dimensional cohomology. 4-dimensional manifolds codify important topological properties of any n-dimensional manifold. The latter is my clumsy attempt at re-phrasing what I see. There are more special things about dimension 4. I'm no expert. Most technicalities go over my head. My intuition is that 1+3 codifies something very specific about how anything that merits being called an observer (whatever the definition is) needs to "do" to represent the universe around in itself. That's how I understood Markus and that's why his comments drew my attention so strongly. But I'm stepping on very slippery ground. I may be neither making much sense, nor understanding other people's comments here.

So, are we getting closer to an answer to the question? What is time? Some level-the-playing-field work seems to be necessary here. Maybe a less ontologically-loaded question would be: Where does time come from? Let me rephrase: What geometrical context in which some principles to characterize observers can be formulated would allow anybody to guess possible mechanisms from which these observers would see a single parameter emerge as necessary to map observations of the world around them? Something like that. Sorry if I don't make much sense. It's 35 ºC (95 F) here. My brain is about to reach boiling point.

I suppose it's about here: Phillip K. Dick Now, religions have invented a mechanism for fueling themselves on while not bothering too much with facts. Language can accommodate anything. That's why you cannot rely on language alone.

Some of that.

Curiously enough, the picture started to change at about the same time that we realised that we Europeans may have up to a 5% of their genome. We never learn.

Sorry, my mistake. N=6 is the last one. +1

That's your department. Tell me the rules and I'll play.

One important reason why 5-fold approximate symmetry is interesting is that you cannot tile the plane with regular pentagons for a very special reason. It's some kind of peculiar geometrical frustration. If N is the number of sides of a regular polygon. You have, Triangles (N=3) --> You can tile the plane Squares (N=4) --> You can tile the plane N-gones, N>5 --> You cannot tile the plane because angle is too big N=5 is special because you still have angle left, there's no angular "deficit", but there is a mismatch. Penrose re-discovered this tiling, which appears in some mosques and other religious buildings. The idea is that it creates the illusion of symmetry, but the pattern does not really repeat itself. Here's an interesting lecture by John Baez on number 5, and why it is an amazing number: https://www.youtube.com/watch?v=2oPGmxDua2U He mentions Penrose tilings, but it's about number 5 in general. I'm not aware of any practical use, but approximate 5-fold symmetry does appear in Nature. Baez mentions diffraction patterns in some crystals as another example.

You forget mutation (slow) and recombination (fast). In a billion years almost nothing of your "bloodline" will be left because of mutation and recombination alone (half our bloodline genes on average is discarded every time one of our gametes is produced). One billion years up your (and my) family line all our ancestors were minute eukaryotes swimming around in aqueous solution. Natural (man-made included) catastrophes and migrations are just another major factor of change, punctuating evolution, mainly acting as filters or local amplifiers, introducing a bottleneck effect. "Founder effect" it is called. But you're right in your conclusion. (Grand)N-children (N representing the number of generations in a billion years) will probably look nothing like us and won't look nearly as cute as we do in a family picture. 1 billion years is the domain of so-called deep time.

Forget my suggestion. This is much better, and so simple. +1

Yeah, you're right. Now that I think of it, not in French/Italian/Spanish. -ence, -enza, -encia are common morpheme endings, and loosely equivalent to "quality of". OTOH, änd sounds more lexical than functional, while -rung/-ring seem to be function marks, or morphemes. It's the sequence fer-enc fer-enz vër-änd för-änd (that sound so similar) that threw me off. The -fer-/-vër/-ffer- I think you got totally right from Latin fero. As you say, "to carry". I never thought that Romans took loan words from Latin. +1 When you think about it, it's quite natural. Anyway, from what I gather, old Indoeuropean peoples don't seem to have been overly concerned about the difference between change in time and static differences. Or maybe some root has been lost or not identified as yet.

Either that or we're all equally clueless. So don't be smug just yet. Don't think for a moment I'll forget you're the one who set me on a time travel. I think that's because you think I trashed Fermi, which is not true. Fermi is one of my heroes. Anyway... Let's picture maths as an old grandma who never makes a processing mistake, but is totally neutral about the input. It just doesn't even cross her mind to doubt your premises. She only gives you information correlated to whatever mistakes are intrinsic to your language. Good input --> good output; bad input --> bad output. I think we shouldn't hurry to dismiss bad or meaningless (or perhaps, conflicting) output as totally worthless. IOW, garbage in, garbage out, as they say. I think it was Fermat who said that maths is like a mill that gives you good or bad flour depending on the quality of the grain you put in. My suggestion is: Let's not throw away bad output (or input). Let's analyze it. We all share the same fundamentally incurable disease: We live within a time. It is just not given to us to think outside of time. We need sequential thinking. We must do A, then B. Or perhaps B, then A. Grandma maths has no problem with that. She can handle A and B at the same time. We visit her and tell her that we've come up with something called "quantum mechanics", and she starts crunching numbers and operators. After a while she comes back with the answer. We take a look at it and it's full with "topological frustrations", and references to them, all of them around the funny "concepts", \[\frac{1}{2}\left(AB-BA\right)\] and, \[\frac{1}{2}\left(AB+BA\right)\] The commutator and the anti-commutator. Something very funny happens around these two concepts. They somehow represent the limits of our language in terms of "first A, then B". Those are the two references in trying to overcome the fundamental limitation that is inherent to our language and gives back singularities, limitations, or topological obstructions if you will, in terms of our alphabet of A and B. It is very telling to me that this fundamental splitting of the world comes in the alphabet of mathematical operations that can be understood as trying to make our operations simultaneous in the representation space of the world. +1. Maybe even impossible.

Now I think I can safely tell you that you're on a very slippery slope. Interesting linguistic discussion. Here's a clumsy (and totally unreliable, mind you) attempt on my part at finding cognates for the concepts we're talking about. change difference (English) changement différence (French) cambio differenza (Italian) änderung vëränderung (German) cambio diferencia (Spanish) ändring förändring (Swedish) ------------------------------------------ In Spanish there is "andar", which means "to walk". The green ones are probably just wrong. The red and blue ones I'm more confident that may betray semantic connections. Not at all sure that this attempt at finding cognates means anything at all. I'm just pointing out that they all sound similar to a layman in linguistics like myself. I've been trying to find reliable cognates for "to change" and "to differ" in proto-indoeuropean, but haven't been successful so far. I'm totally out of my depth. Puzzingly enough, in Latin there is a very clear word for change in time, which is mutatio, and has no lexeme in common with any of the above. I'd be very interested in the Greek version from @michel123456. Although this is spilling over into other fields very quickly. I'm still suffering a bit of jet lag from the time travel you got me into. I'll try to react to that later. ------------------------------------------ +1. You just got one thing wrong: This is a physics forum. Although eventually it may be subject to change.

I agree that there's nothing you can do by arguing against. So here's an idea, although there is a risk that it might backfire. You learn just enough about the mumbo jumbo of the supposed theory and get back to them with information that it has been confirmed. You must put on your best performance at this point. Once you get them all excited about how their beloved theory has been confirmed by a high-precision experiment, you reveal to them that you've made it all up and say something to the effect of: You see? You can believe anything! It's not about proving or disproving the theory. When people think like that they couldn't care less. It's about making obvious how gullible they are, showing to them how fragile their belief system is. Once a classmate attending an EM class came late and asked me if they had missed anything important in the class. I told them that the teacher had just reported that a new equation of electromagnetism had just been found: The fifth Maxwell equation. It worked!! It should have been two more equations..., but never mind.

There are at least two things connecting with this that I think are worth mentioning. There may be more, but there's only so much one can say. 1) Is the path to building a well-defined unitary S matrix the only sensible approach to quantum field theory? Aren't we leaving out important substance if we use the |in> and |out> unbounded Hilbert space as representation space for all phenomena? Actually I think many physicists are aware of this. 2) Grivov's ambiguity and a proper study/classification of topological sectors. What possible physical variables are (or may be) hidden behind the humongously big arbitrariness that gauge invariance doesn't let us see in the formalism because they don't appear in the gauge-invariant quantities? Are there missing variables to be described in what is normally described as "gauge junk"? Could there be that what we usually throw in the garbage bin has some meaningful invariants in it? The more likely solution I see for the wave-particle duality of elementary particles is that what we see as quantum formalism is only dealing with the propagating factor of a more complete state that involves as a co-factor a topological Lagrangian that codifies in it the "only particle" aspect and, by suitable hypotheses, can be statistically correlated to the evolution of the linear wave in some kind of à la Bohm solution. That's what I like to think when the lights go off. There are other very interesting off-topic subjects in the link that you provided. Thank you. Assembling different space-times makes me much more uncomfortable, but that's just me. It's far over my head. Very nice point. +1. That's more or less what I had in mind when I said T, P (as Markus said, not C) as coming from some kind of homotopy or diff. transformation. Sorry, I didn't make it clear, although I'm sure you know. These diagrams represent the momentum space.

I'm 55 actually, actually. But not even at your most polemical, or personal, are you offensive to me, MigL.

I'm all in favour of enriching the vocabulary to reflect nuances in what we say. I find no reason for strong disagreement here, as I see it. But the very fact that you (or I, or anybody) feel the need to use a substitute for "change" into a timeless (but isomorphically related one) "variation", suggests to me that neither of us can escape time, in the representation space of ideas that constitutes language, if we want to convey meaning, even though our thoughts do not appear sometimes as an ordered sequence, but as a tangled web of ideas. Very interesting (and I think related to what we're talking about here). Listen to Steven Pinker at, 26' 44'': https://www.youtube.com/watch?v=OV5J6BfToSw There's the rub.

I'm a bit hazy about this, because it's been a while. There's a lot that has to do with prescriptions you adopt just because you want your fields to propagate causally. After some investigation, you find out that your Fourier expansion of the fields must contain both, \[e^{-ip_{\mu}x^{\mu}}\] and, \[e^{ip_{\mu}x^{\mu}}\] with the ordering prescription given by, which amounts to prescribing the "positive energies" to propagate forwards in time, and the "negative ones" to propagate backwards. I don't think this is a big deal: After all, you're interpreting what you energy-dimensional parameter E is doing in your physics. So far you're kind of forcing your amplitudes to behave causally (microcausality). If you do all that, you get amplitudes that commute outside of their causal cones (anti-commute, if they're fermions): \[\left[\varphi\left(x\right),\varphi\left(x'\right)\right]=i\delta^{\left(3\right)}\left(\boldsymbol{x}-\boldsymbol{x}'\right)\] provided that, \[\left(x-x'\right)^{2}<0\] (depending on signature criterion). Then you proceed to solve Heisenberg's evolution eq. in the Dirac or interaction picture. \[\varphi_{\textrm{int}}=e^{-iH_{\textrm{int}}t}\varphi e^{iH_{\textrm{int}}t}\] Then you substitute this expression into the Heisenberg evolution equation in the Dirac picture and discover that the solution must include the time ordering given by Dyson's formula: \[\varphi_{\textrm{int}}\left(t\right)=\left[T\exp\int_{0}^{t}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right)\] So far, so good. It's complicated, you have implemented what you know about the world, as well as used the room that the quantum formalism gives you to represent the states (change picture to a unitarily equiv. one). The really weird step, IMO, comes now. If you try to expand this as a Fourier series in harmonic oscillators, you have an infinite sequence of differently-ordered powers of creation and annihilation operators, so you (again, IMO) kind of pull a rabbit out of a hat by re-defining your formal series as, \[:\varphi_{\textrm{int}}\left(t\right):=:\left[T\exp\int_{0}^{t'}dt'H\left(t'\right)\right]\varphi_{\textrm{int}}\left(0\right):\] The colon-bracketing means that everything that has differently-ordered power of creators and annihilators, is re-ordered so that all the creators are to the left (and conv. for the annihilators). When you do that, you don't end up with the same operator. It's a different one! Then comes the use of Wick's theorem, by using the vacuum state. The re-ordering that you've imposed proves now very useful, because the annihilators to the right kill the vacuum, so that you remove a lot of junk. I think, or vaguely remember, that the steps are justified. This is not the way most people learn QFT. In the old days people invested a lot of time in understanding the gradual steps. Today, everything is considered justified and people tend to jump as swiftly as possible to Feynman diagrams, so they can do calculations. I just want to add (and sorry for a lengthy and perhaps obscure explanation) that in order to rigourously get to Feynman graphs, there are quite many (mainly combinatoric) steps farther ahead. Basically you must remove over-counting due to your re-ordering, because, obviously, when you identify expressions like, \[a^{\dagger}aa^{\dagger}\] and, \[aa^{\dagger}a^{\dagger}\] with, \[:a^{\dagger}aa^{\dagger}:=:aa^{\dagger}a^{\dagger}:=a^{\dagger}a^{\dagger}a\] you must keep track of how many times this last term appears by re-ordering operators. Sorry for such a lengthy attempt at an answer, I may not have been very helpful. Take it just as an appetiser, and feel free to ignore it. Sorry if you know many of these things. --------------------------------------------------------------------- I suppose my succinct answer to your question would be: Dyson's time ordering appears to me as quite natural, because it's a step for you to make your solution formally satisfy the evolution eq. But steps come later that, although immensely useful and allegedly "rigorous" by many people, do present fuzzy areas, at least to me. I'd love to understand them better. For me it's a work in progress, maybe a lifetime-long project, to get to understand the fundamentals satisfactorily enough. PD: Both @Duda Jarek and you have made comments about topology that I think are very interesting and point in the direction that I would like the theory to go. AAMOF, it was Gerard 'tHooft, Polyakov, among others, one of the first pioneers to try to develop a more geometric language for QFT. I can't say that's the ticket, but it sounds to me like a much more promising scope. Other things are going on in QFT. Have you guys heard of MHV amplitude calculations? It's a very quickly-developing subject.