joigus

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.

Thanks a lot. +1

Baby steps, Hanke, pray you. You're giving me a lot to digest here and in the other thread about CPT. You introduce several very interesting ideas there. Hausdorff dimension. I've sometimes toyed with the idea that fractality may play a part in what conscience, arbitrarily small scales, and in general some of the most intractable problems of science, could need as a framework to be formulated. I wouldn't know what to do with it for the very simple reason that I'm not cut for it. I haven't played much with fractals, or with loop quantum gravity. Somehow it's not me. But that doesn't mean I don't think it's an interesting idea. I will share an intimation here: The very fact that from the basis of mathematics you cannot prove whether there is a cardinality that makes "cardinal, or counting, sense" trapped between the discrete and the continuous, I think could signal to something very fundamental. I also think this connects with @studiot's "obsession" with continuity vs. granularity. It may be precisely because spaces with non-trivial Hausdorff dimension potentially have this kind of algorithmic inaccessibility that they could be very powerful stores of information in finite volumes. I don't know. Just giving you my thoughts here. As to the embedding question, I do have a model only to be taken as a parametric setting of the problem, a framework to discuss these questions, rather than a theory, similar to what @studiot did with his pictographic mesh of events. And because we're starting to know each other somewhat better, maybe it could be shared here with no harm done, no nonsense, and no pressing any point on my part. But I do need to include an observation that @michel123456 made to me yesterday by PM, if he doesn't mind. I would have to adapt his idea a bit, because I think it's not applicable "as is". But that would require some discussion with him for authorship. And, perhaps, with everybody else. PD: Michel, I think your idea does not apply to elementary particles, and thus not in general, but it does apply to extended systems that need to sacrifice some of their own dynamical variables to represent what's going on outside.

OK, Eise. I must tell you I don't find in the least diminishing to use some time to get to understand Dennett's thinking better. There are many gradients of meaning here that are taking me some time to understand. I don't have good ears, but I'm restless. If, after all, it takes me about three months to get a consistent picture of it, it will be time well spent. A good investment of my time, I would say. And I will have mostly you to thank for that. Some people find disagreement spiteful. I don't. It's a fertile ground, when your interlocutor makes sense. And you do.

Panta rhei That's in the nature of things. Changes require adaptations, which bring about further changes, which require further adaptations. Were it football, I would be worried, if I cared about football at all. Education is different. It was there millenia before football, and it will be there long after football becomes a hazy memory.

I don't even have a mirror to show me where I left my glasses 20 minutes ago. So... LOL

I'm all ears.

That was very honest. +1

If I could only tell you how many times. I have no answer for why is that. But the fact that once you solve the equations of evolution for one simple system, you can perform this miracle on a small scale, of seeing the whole histories, that's what's kept me wondering for decades. And still does. I have this nagging feeling that most of us here share this intuition that what appears as time and slices (exterior of cones, rather) of present space is a characteristic of whatever makes some systems (us, conscious beings, other organisms, maybe some machines), and not something particularly intrinsic to the universe. Saying that is one thing; trying to picture a mathematical structure that embeds this illusion, if you will; is quite another. I remember that trend in the 70's[?] when the director showed you what was going on at different places by splitting the different courses of action in simultaneous squares. Airport (1970) was a good representative of that trend. Needless to say it didn't last. @MigL always has a metaphor for physics from movies. I wonder what he thinks of that. That's a very slippery slope. Edit: On second thought... That's very interesting. +1. Silly me. If your coordinates in your self-reference are (0,0,0,0) at any moment, what direction is any direction? In particular, what direction is your time direction? The mathematics of vector spaces suggest, if anything, that that's just a choice.

I'd go with option 2 as the most demographically significant. But I agree with Strange that 1 would probably be very popular among conspiracy nuts. If I were allowed, I'd pick something like a 40 % 60 %, fifty-fifty or the other way. The reason is that people tend to look at the past with the strangest mixture of incredulity and gullibility. Example: It is impossible that an ancient society like the Egyptians 5000 y.a. were able to build the pyramids (incredulity), therefore some alien civilization must have made it (weird, weird gullibility). When things are happening before your eyes, so to speak, I think it's more difficult to be gullible against the facts.

Don't be. If Plato was right and all knowledge is remembering, let me remind you of what you already know. Try to picture your whole life as a chain of "congruences" of events, so to speak (relativity of simultaneity aside). Everything you live from birth to death is there placed in some database. Let's imagine that you can consult this database. Let's go to the day of my graduation. Bzzzz... There it is. You can also see the news of that day, the weather, everything! Someone yelling "taxi!!" 10 meters away, a fly landing on the window, your thoughts at a particular moment. Everything. Because the equations of physics don't allow dynamical states of the whole system to repeat, except for very-long-time recurrences in closed systems, you could use your timeless concatenation of dynamical states to answer any question about what goes on in your life without ever having to use time. Your space of occurrences would have to include positions and momenta, of course. This database describes the whole physics, but time is out of the picture. One last thing: You could use a parameter. You could re-wind the whole movie at any speed you want. Slow it down or speed it up. That would represent the re-parametrizations of an instrumental parameter that moves you back (rewind class of parameters) and forth (forward class of parameters). But that parameter would not be part of the physics. If you think about it, when you solve the equations of motion you're kind of doing the same thing on a small scale. You get access to a small part of that database.

Very good question. +1 A quick scan of, https://books.google.es/books/about/The_Global_Approach_to_Quantum_Field_The.html?id=-LtutgAACAAJ&redir_esc=y (The Global Approach to Quantum Field Theory, Volume 1 By Bryce Seligman DeWitt) Allows you to find only a couple of paragraphs where space and time inversions are introduced on a coordinate-patch basis. Nothing like the predictive power and generality of CPT in flat space-time is suggested. For all I can remember, the context where CPT is really powerful is the S-matrix approach. And defining assymptotic states in a curved space time is problematic, to say the least. Searches on other more modern books, or on Quantum Field Theory in Curved Space-Times, also by Brice DeWitt, haven't produced anything that remotely resembles "CPT". Not even mentioned AFAIK. I do not think there is anything like CPT valid for curved ST that is remotely as robust as it is in flat ST. But I would be very thankful if anybody knows. This is very interesting, because it connects with my question following up on a suggestion by you on the thread about "What is time?" Would you have some licence to consider signature-preserving continuous transformations that re-shuffled the space-time coordinates, of which our T, P transformations were a discrete version?

OK. Not that it's interesting to anybody, but I was raised in a Catholic country, and had to do away with a lot of cultural/religious/mythical/ceremonial baggage. I tend to mistrust my own opinions very often; let alone other's. I did that at a very high price. The brain can be a crook. It likes to show to you pleasing landscapes. It likes to prove you right. It also tends to have you accept propositions just because they will make you fit in socially, or stand out. I don't trust the brain's inertial forces. I suppose I'm just a runaway from belief towards degrees of certainty.

That's not what I said. Here's what I said: Can you read it now? Take some time. Read it twice, three times, if necessary.

You believe too much with too little evidence. AAMOF, you believe I believe something. Not only that; you go on to assert it, as if you were privy to my mental states. You couldn't be farther from knowing how I form my opinions. Which goes to prove that you give too much value to your beliefs. I don't to mine. Neither I do to yours.

Thanks a lot for your drawings and explanations, @studiot. +1 The only reason why I would wait a little bit before totally endorsing your picture would be that, if anything, QFT has shown us that whatever it is that we perceive as space and time must be very deeply connected with the space of charge. After all, it's the composition of the 3 inversions (CPT) that produces a very robust discrete symmetry of Nature. But I see no a priori reason why the "internal" dimension of charge could not be added to your picture. Very interesting your rescuing Eddington's observation. It is so interesting that I will re-type it here: (my emphasis). I couldn't agree more. But, in fact, it amounts to something both you and I (at least) have already (at least) implied: IOW: describing relations between points in space as intrinsic, with no oriented parameter. And, AAMOF, I have implied it too. Here it is: Maybe I didn't say it explicitly, but my point was that it is the first, the implicit picture, that is more objective. The oriented parameter t in this picture would be, let's say, just psychological, instrumental, etc., what have you, and have nothing to do** with what goes on in the physical world at large. That objective reality would be described by the intrinsic interdependence of states. The parameter would be just an artifact you need to introduce if you want to account for your experiencing the world as an ordered sequence of configurations. Nothing more. I wouldn't dare to call it emergent, but maybe immersive (more related to how the observer experiences the world). Now, using the arc-length on the curve gives you a natural parametrization, defined except for its sign and a family of infinitely many re-parametrizations. I think most of us here would be closer to common ground for agreement if we made it as clear as possible what we mean.*** ------------------------------------------------------------- * I shouldn't have said "clear-cut" here. After all it's an infinite family. ** Well, not "nothing to do", but a lot more to do with what goes on in the observer's mind, measuring instruments, etc. *** (Edit): This is rather meant as self-criticism, as I don't think I've been as clear as I could have, going back to my previous posts.

Universe did a pretty nifty job of looking as if it had existed long before any intelligent observers were around. That's all I can say.

+1. Very interesting, meaningful and inspiring conversation going on here. I only wish to emphasize observation by @Duda Jarek that charge symmetry can indeed be formulated either locally or globally.

Maybe of interest: https://www.forbes.com/sites/startswithabang/2017/01/26/how-the-anthropic-principle-became-the-most-abused-idea-in-science/#efcb4a57d690 The anthropic principle is tautological. Tautologies are not necessarily bad in physics. They can never be false. What could be more robust than that? But when you depart from a tautology, you need at least a second assumption that gets you out of the circle. Example: Newton's second law rests on a tautology. Mass and force are introduced at the same time, so you have no way to define mass but as based on force. And force cannot be defined without invoking mass. Were it not for the fact that people* related force to position through the concept of potential energy, and additional assumptions on its parametrics, nobody would have been able to get out of the loop. *Starting with Newton himself.

Looking forward to it. You're probably right. You just can't change the rules. But you can change the names. So, what tells you which one of the four directions is time if you know nothing else? Let us remove any sequential notation that suggests an ordering, like t, x, y, z or a, b, c, d, etc., and make the argument clearer. Let's say your event coordinates are: \[\otimes,\boxplus,\oplus,\boxtimes\] Which one is time? If some "angel" told you the metric is: \[\otimes^{2}-\boxplus^{2}-\oplus^{2}-\boxtimes^{2}\] It would be clear your time must be \[\otimes\] But if you were allowed to continuously change to, \[\otimes^{2}+\boxplus^{2}-\oplus^{2}+\boxtimes^{2}\] now time would be \[\oplus\] ... After thinking about it for a while longer, I think you're right, @MigL. I think the mathematical reason has to do with the fact that the Lorentz group splits into 4 disconnected parts, \[L_{+}^{\uparrow},L_{+}^{\downarrow},L_{-}^{\uparrow},L_{-}^{\downarrow}\] Only one of them is a group, because it contains the identity transformation. The up-arrow ones are called orthochronous, and the + and - have to do with space orientation. The only one that can be continuously connected with the identity is the proper orthochronous. So I guess it can't be done. You can't reshuffle time and space, even if you preserve the metric signature. But it was fun. Edit: Although GR is different. You can move more freely with coordinate changes. I'd like to know what @Markus Hanke, @Mordred or other experts think about that.

OK. Point taken. But that's just another fiduciary or referential choice. I'm not convinced it's that essential, although it could have consequences. What I think Hanke is trying to say (maybe clumsily re-phrased by me) is illustrated with this parable: A very advanced ultra-dimensional civilization makes contact with us. They know we're inquisitive organisms and are very interested in our opinion on foundational questions about physical reality. They somehow develop a code to communicate with us (I'm leaving to them all the hard work). And they ask us: Hi, lot, what does the universe look like for you? Starting with: What dimensions do you see?" And we say, "well, it'll be difficult to explain what we see, but just for a start, we can see three spacial dimensions and one time dimension for describing change in this four-dimensional universe". Reply: "Mmmm. That's funny. We see one spacial dimension and three of what you call time dimensions" They exchange documentation in the form of theories, equations, experimental data, etc. And everything checks. It's only that what we call time, they call radius of a 3-dimensional time around the individual that's perceiving that time; and vice-versa. Who would be any the wiser about what they are calling time or space? The words "time" and "space" would just be arbitrary tags, mathematical dummies. I'm leaving the next idea for later.

I'm glad you mentioned time. We're still on-topic.

Good question. +1. I suppose modern psychometric techniques are getting us closer to it.

Maybe it's a British thing.