joigus

This connection is fleshed out by a theorem (I forget the name now) that relates time-ordering of operators with expected values in the vacuum for normal-ordered products. Irrespective of technicalities, this strongly suggests that time in getting in the way because of its being very very deeply entrenched in our language, or sequential alphabet, or what have you. I hope it's clear what I mean, although I recognize that what I mean is difficult to make explicit in terms of language and symbols.

A must-read for this post. +1

True. +1

Well, I was going for minimal conditions for a time to be possible to define (from a purely mathematical POV, so no operationalism, no clocks at this stage). Another example to add to the ones you provide in which this technique wouldn't quite work are chaotic systems, because for chaotic systems there aren't nearly enough integrals of motion to reduce the dynamics to a clear trajectory that can be pictured as an implicit relation between your dynamical variables of which a one-parameter could be deduced. To me, once you have defined (in clear-enough cases) this one parameter that suggests to you a sequencing of events, you still have the enormous freedom to choose which particular parametrization corresponds to your clocks, how different sets of clocks relate to one another, etc. That would be problematic if one photon were the only thing that exists in the universe (you could always define an affine parametrization for a photon which is what people do to describe the geodesic equation for photons, but the interpretation of such parameter as a time is another matter). In the scenario that I'm talking about, there are more things, and the coordinates of the photon could in principle be included in the aforementioned implicit equations fi(xmatter,pmatter,xphoton,kphoton)=0, so a one-parameter sequencing for the whole system would be possible to define. Now, on the proviso that this sequencing can serve as the minimal condition for a time to be definable, and taking into consideration your caveats about clocks (the question would be pending of what re-parametrization of this emergent parameter to use so that it corresponds to our physical clocks), there's still the subtle matter that it's defined from a metric or pseudo-metric. And these are always based in physics on quadratic forms, and thereby you must chose an orientation for the sequencing parameter to run along. Here I think you took me a little bit too seriously. Mind you, I said: So I was more cautious than you seem to suggest, and just expressing a feeling. This feeling has been seeded through many moments when studying physics, but the strongest one by far is QFT. In QFT you start from very neatly defined state operators in terms of a given coordinate time, write down the Heisenberg evolution equation, and formally solve it in terms of creation and annihilation operators in momentum space. Because Dyson's formula imposes on you a time ordering, you get a sequence of products. For one of these terms, e.g.: \[a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a\] What's the next thing you do before you engage in any calculation at all? Well, you re-define your exact solution to be "better represented" by the normal ordering: \[:a\left(a^{+}\right)^{2}aa^{+}a^{3}a^{+}a:\overset{{\scriptstyle \textrm{def}}}{=}\left(a^{+}\right)^{4}a^{6}\] If nothing else, to me, that very strongly suggests that there's something deeply problematic about time. It may be possible that sequencing of concepts might have consequences, logical consequences, that we simply cannot get rid of within our present system. I'm not saying that every mathematical statement we make has time impregnated in it, but I'm saying that it may well be that we are quite incapable of totally escaping the non-trivial consequences of having a sequential language. Don't pay too much attention to what I'm saying. Maybe I'm just sounding people out about my deepest intellectual insecurities, that's all.

On further reflection, after reading Studiot's comments (+1) carefully, and to correct myself: This definition, while it's very widely used theoretically and very solid, is not universal; and in particular is not useful to assign space coordinates to distant planets. Also, it had nothing to do with the OP's confusion. Sorry, it was late, my reasoning was obfuscated by the phrasing of the question, and consequently I wasn't very helpful.

I see. And what about the switching frames? Did you understand that part?

Nice post. +1. And nice picture. Dinosaurs are a long way away for this solar system.

Exactly! I want the OP to think: How do I measure separation of distant things? By measuring times. Observers cannot read space directly. How can distant "news reporters" at rest with respect to us liaise with us? It takes some time to realise that this is necessary. I hope this sketch clarifies the meaning of coordinates in SR: \[t=\frac{1}{2}\left(t_{1}+t_{2}\right)\] \[x=\frac{c}{2}\left(t_{2}-t_{1}\right)\] So everything, spacial coordinates included, is based on observation times. I'm not sure if that's what confusing you, @can't_think_of_a_name. It looks to me like that may be it. Once it's clear that you've got all of space-time mapped with these x's and t's, you do what Swansont is telling you and apply Lorentz transformations. But you don't get information back from distant events by sending someone back that "switches" inertial frames. It's a matter of sending light rays back and forth what gives meaning to the coordinates, not people on a spaceship with the news. I hope that helped and had to do with the source of your confusion. +1. Thank you. That got me confused too.

I'm having difficulty understanding what you mean. Do you understand how you assign coordinates to events in SR? I don't know what you mean when you say "switching" frames. Jumping from one to another? That's not how you measure time intervals and distances in SR. It's by sending light rays and receiving them back, and then kind of "triangulating", but taking into account that the signal speed is c no matter what inertial frame you're in. Let me ask you a question: How do you picture in your mind that Alice knows Bob has already arrived in planet 2?

Intuitions can mislead you (and they will if you pay no heed to experimental evidence and logical consistency). Aristotle thought that you needed a physical action on a body to make it move at constant speed. This was a wrong intuition that lasted for centuries. Theories (Galilei, Newton) showed us the first inkling that Aristotle's intuition is not correct. Space navigation has proven beyond any doubt that Aristotle's intuition was wrong. Eise has pointed out somewhere (I don't seem to find it now, maybe it was another post) that once you study physics you get better at developing your intuitions and rendering them less naive. When you study quantum mechanics for years, when you watch interference patterns in a laboratory, you eventually get to develop a feel for what physical systems do. And they don't do what you intuitively would expect. There doesn't seem to emerge a picture of a decision-taking anthropomorphic god in that world. Maybe he created the universe and has been in absentia forever after.

Well, I may be wrong. Maybe this notion I have that time is inevitably present in anything we say, even in formal mathematics, is somehow misled. In some demonstrations, e.g., two different results of previous lemmas used in order to prove a theorem could be used in sequence but in interchangeable order. So there may be many flaws or grey areas to what I'm saying. But, if that were verifiable in some sense; namely, that no matter what kind of logical/mathematical argument you make, you cannot help that your concept of time has some bearing on it, contaminates it, then it could well be that time itself is a formidable obstacle to formulate any system of ideas in complete (all encompassing) and completely consistent (free of contradictions) way. IOW, it could be that you can "solve the world" except for this nagging presence of a sequencing parameter that we call time, because it's a constraint of conscience itself, not because it's an especially important (distinguished) variable of the universe. This connects roughly with some comments that @Markus Hanke has made before. I wouldn't go as far as to distinguish a "logical time" and a "reference frame" time. That would be uneconomical to say the least. As to "subjective time"... Well, we must agree that the perception that time goes the same way consistently (in orientation at least) for everybody involved is pretty persuasive.

Are you familiar with the words "not even wrong"?

Or maybe he just spent too many hours in the company of ovine mammals.

Do you know I have this same gut feeling? I would love to discuss this point, whenever you have the time. +1 I'm currently involved in a discussion with a mathematician friend of mine who says it doesn't. I, on the contrary, always have the feeling that in mathematics there's always a sequence of operations, if nothing else, which foreshadows time. Doesn't it? He says no, and I'm not convinced. Edit: That not to mention the concept of probability on a purely mathematical basis, which I think is heavily impregnated with a notion of time by construction.

Fine point, very precise and illuminating. +1 If you define relations between variables (let's call them x, y) as some kind of implicit constraint, \[f\left(x,y\right)=0\] The natural (simplest, obvious, directly related to the pre-defined terms) parameter to describe the sequence of changing is the (class of) proper length parameter(s) given by, \[ds^{2}=dx^{2}+dy^{2}\] There's your time. Defined as a clear-cut class of parametrizations, modulo (except for) its sign. The only sticking point about time is its orientation (the arrow of time). That remaining bit of information cannot be given by implicit relations between the world variables.

Thank you. +1 This connects with your observation on @studiot's post about some standards for good OP's: Please, keep working on it. I'm very interested in coming up with good standards for what aspects of philosophy scientists and engineers (whether they be experimentalists, theorists or computation-driven) would be well advised to be aware of. I know only too well that certain philosophies are too disconnected, too willing to disregard inductive principles, too vague, to be considered of interest for scientifically-minded people. Nothing to be sorry about. Fuzzy thinking has some value. You could even say that any rigorous thinking must start with fuzzy notions. I spent 10+ years living in a small village and became friends with a shepherd. Sometimes we'd start a casual conversation and he'd say, "why are we here?", "what's the meaning of life?" LOL I may be taking the whole for the part, but I think this guy is a representative example that illustrates your point pretty well. I think you're dead right. Your reputation is well deserved. Just one caveat: Some pretty bold, but pretty good, ideas have been trashed and then re-considered. When you think about it, Darwin's dangerous idea () was trashed ad nauseam in its day by a considerable number of people in academia. Who's to say that a new idea is to be trashed? Sorry for the rhetorical question.

Thank you all for very good points. Let me clarify further. The options could be re-phrased as, 0. Philosophy is never worth undertaking or learning about 1. Philosophy is always worth undertaking or learning about 3. Philosophy is worth undertaking or learning about only after a quality criterion has caught your attention in one of its many theories I didn't mean these categories to have Boolean closure, so to speak, but to be demographically/socially/statistically significant. If you think I've left something out that is significant, please tell me. Yes. Although a quantum Boolean Hamlet would have considered "to be and not to be" as a possibility. Or maybe "neither to be nor not to be".

This is actually not very difficult to conceive in principle within the quantum formalism. Quite more difficult is to give a precise and detailed answer. As Eise has told you, a quantum particle, in some sense, sniffs around all of space time. When you see it in a mathematical formula printed on a paper, you see very clearly it doesn't look like the whim of a god. It does look like a precise mathematical pattern of evolution. Now, this evolution, in a quantum theory that includes special relativity, is very puzzling, among other things, in that it includes modes of propagation that are superluminal, subluminal, every which way. Those are called "virtual amplitudes", and they appear in the calculations, although they cannot be measured. They are called "off-shell". The basic reason for this is actually a peculiarity of relativistic kinematics. A real photon satisfies a condition or reality that has the form, \[k^{2}=0\] k is called 4-momentum, and codifies the direction in space-time in which the photon is moving. It's a combination of 4 numbers, the time component and the 3 spacial components: \[k^{2}=\left(k^{t}\right)^{2}-\left(k^{x}\right)^{2}-\left(k^{y}\right)^{2}-\left(k^{z}\right)^{2}\] So it could be negative, positive, or zero in general. Real photons are null. For real photons this quantity must be zero. But you can always decompose this "real" state as made up by the real components plus many other virtual ones, \[k^{2}=\left(k+p\right)^{2}\] These virtual ones have momentum ("direction") p, which is not physical, and in particular could be superluminal or subluminal: \[p^{2}>0\] \[p^{2}<0\] as long as they give you a real photon: \[0=k^{2}+p^{2}+2kp\] I haven't shown you the full-fledged argument in quantum field theory, which goes with amplitudes and so-called Dyson time-ordered formula, but a simplified version of it. It is by no means a foolproof explanation. But here's my question for you: Can you guarantee that the positions where the particle can or cannot land (the not-so-well-known partial reflection paradox is another interesting example) are not set in advance by all the components of the quantum state, including the virtual ones, that make up the Feynman propagation formula?

Neither term would be precise in defining its properties. Dark matter is actually even weirder than transparent. Ordinary matter goes right through. It's not just transparent. Ghostly is more like it. Edit: But you're right that "transparent" is more suggestive of what it is. There's a tradition in the wording of physics. It's more like book-keeping than concept-suggesting.

Very nice. Thank you. +1

You're going a bit blurry here, in spite of my efforts to be concrete. Does philosophy make you uncomfortable? I sympathize (if not necessarily agree), but I can't do what you do. Philosophy always distracts me. +1. @Sensei is Boolean in nature.

Your point is well taken. By "philosophies" (countable English noun) I mean each and every particular philosophical theory, irrespective of their merits, whatever criterion we use to measure those. By "philosophy" (uncountable English noun) I mean the activity itself, which more or less can be associated with the grouping together of all philosophical theories. The activity itself. I suppose you can do that without losing much specificity. It's true, e.g., that some people reject philosophy flat-out. Those would be the ones that subscribe to option 0. On the one hand, it's possible that they have considered each and every philosophical theory there is and reject them all but keep "hoping for the right one" (in that sense, they would reject all philosophies so far but wouldn't have given up yet on philosophy altogether). On the other hand, there's the possibility that these people, at some point, grow tired of looking for philosophical arguments and finally decide to give up on philosophy altogether. That goes to show that you're right in that a finer distinction could be made, so I admit that I'm simplifying a little bit. But I don't think that I'm overlooking any big demographics here by identifying all philosophies with philosophy in general. I'm subsuming people who don't like any philosophical theory at all into the group of people who just don't think philosophy should be paid much attention. Would it be good because it might be right or might it be right because it would be good? "Bad" or "good" are defined in a particular sense in the options for the poll. They are not described "for themselves". Good: useless/too arbitrary/self-serving... Bad: has something useful (interesting points to consider)

I've missed that point. +1 I was so distracted with the equation itself, and then the OP completely changed the subject to gravity. It threw me off...

I'm testing my first poll today. I've scanned for similar topics but wasn't able to find collocations "good philosophy" or "bad philosophy". Especially if your option is the third one, I'm very interested in your criteria, exceptions, and so on. Thank you very much.

No can do. God may play dice, but that's too much of a stretch. Another brilliant logical point. +1