joigus

Yes! The "it's complicated" one would have been my choice. Thank you for the article. I haven't been able to read it yet, though. Octonions are very promising. John Baez has a lot of stuff on octonions too. They relate topologically to the the spinors. They kind of split into spinors through a mapping that renders the algebra non-associative, as octonions are non-assoc. Thank you for the references. This topic is very interesting.

I meant to +1 Strange on the update to Couder. I remember back when I studied quantum mechanics, at some point we tackled the really hairy aspects of the mathematics. There were several attempts to formulate QM based on real numbers, quaternions and even octonions, if I remember correctly. The argument was that using a complex-number based mapping of the amplitudes seemed to be minimally essential to describing its properties satisfactorily. If that's true (I didn't completely understand the reason because it was not explained in detail,) it would be too much to expect that waves that are well-modeled by real functions would be able to reproduce all of QM. Especially fermions. Analogically mimicking photons would be a problem too, for obvious reasons. I'm confident that once we understand where the logical necessity of using complex numbers arises, we will understand the nature of a double solution better than De Broglie-Bohm. That's why I've voted for the 1st option. +1. Thank you. But those are pre-2015. Aren't they?

I know the answer to that one. Every time a newborn appears in this world after one's death, some form of auto-conscience appears again at some point in the future. The question is: Is that good enough for this form of auto-conscience that's asking the question?

That's only because I'm a remote object, and you're giving me the wrong coordinates. Apology accepted.

Boy, that's beautiful!

I meant "with weight equalling buoyancy." Yes, I have to teach chemistry sometimes, so have must think about those things. Although my chemistry laboratory practice seems very remote now.

Don't put words in my keyboard. The only one who believes in remote dilation as a frame-independent phenomenon here is you! That remote dilation is only in your mind. You don't even understand that, which says all about you as a "thinker." The fact of whether something suffers frame-dependent dilation or not does involve having things other than photons in it. In fact, in order to write down the geodesic equation for photons you must do an affine transformation, because their proper time is identically zero, so no common-sense clocking will help you describe their histories. But what am I telling you; you know next to nothing about relativity, that not being the worst. The worst being that you don't bother to examine your own assumptions, or anybody's criticism. Can you imagine Einstein telling Hilbert "please consider my silly mistake as a valid assumption"? Einstein quickly re-wrote his paper. Learnt much from Hilbert, and went on to publish one of the most important papers in the history of physics. I will pop up every now and then to see what experts and other serious thinkers have to say. Your post is only valuable in that sense. The only trouble is I will have to check for you twisting everything I or anybody else has said, just because you don't understand the first thing about relativity, you don't read what you write, let alone others, and you stubbornly stick to a bunch of silly pseudo-scientific propositions to no end.

Yes, I know, that's why I said "ditto." But then I realised there are even more reasons for confusion for physicists, so I just tried to throw them in, but there's always a risk that you're bringing more confusion. Totally, yes. We don't really know who is asking, though. Whether my explanation or yours have been helpful, we don't really know. I hope both have. I kind of have become a specialist in many common sources of confusion for the students. Believe it or not, sometimes it's in the language. Very recently I remember a problem on hydrostatics, and the source of the confusion came from how the statement had been worded. It said that the body was "floating," and it really meant that it had sunk in equilibrium with equilibrium equalling buoyancy. I don't know what word the person who wrote the problem would have used for floating like an iceberg. Maybe it would have been quasi-floating. That's a problem too. Oh, yes. You're right. I forgot. To me that would be negative. I also think considering it negative is quite standard, also in molecular biology. But it's not impossible that somebody somewhere could have a different criterion elsewhere. Is it different in any context that you know of in chemistry? It may well be. You're very interdisciplinary, and encyclopedic.

It is entirely possible that I'm overthinking it, in which case I apologize. But the way I see it, distinctions such as "work done on a system" and "work done by a system" are often confusing, especially when one is dealing with reversible work --in the physicist's sense--. Reversible work is of theoretical interest. And in order to define, e.g., variable pressure for reversible processes, you must make external pressure equilibrate internal pressure, so that the concept of "who" is doing the work becomes more confusing. I may have misinterpreted him, but Swansont's point that, Is of some importance here, I think. "Define your system," are key words for me in it. It's very easy to get lost in the different steps at which your definition might alter your formulae. For example, suppose somebody defined the different intensive thermodynamic parameters in different ways, while at the same time defined the criterion differently as to "who is doing the work." Example (homogeneous system with variable number of molecules): \[dU=\delta Q-PdV+\mu dN\] Maybe some "crazy author" decides to go one step further in an orgy of definitions and set the chemical potential as the negative of the usual one. One possible choice is (I think it's quite standard), \[P=-\left(\frac{\partial U}{\partial V}\right)_{S,N}\] \[\mu=\left(\frac{\partial U}{\partial N}\right)_{V,S}\] \[T=\left(\frac{\partial U}{\partial S}\right)_{V,N}\] But there could be others. The fact that pressure has a negative sign is just convention. No real meaning attached to that, I think. It's just a thermodynamic potential. And the real question is well away from any ambiguity when you express, \[dU=\left(\frac{\partial U}{\partial S}\right)_{V,N}dS+\left(\frac{\partial U}{\partial V}\right)_{S,N}dV+\left(\frac{\partial U}{\partial N}\right)_{V,S}dN\] Now, the signs there in the last eq. do not depend on any criterion. And I do confess I'm something of an unbearable stickler for sound definitions, axioms and language. Actually, I think the "usual" one is the opposite. That's kind of what I mean.

I'm kind of a stickler for language. I would say entropy is not experienced by systems. Entropy is a property of some systems about other systems they are measuring, observing or describing (if they are thinking systems.) So it's a correlative property (system A watches or describes system B.) Or a property of the description (system A describes system B.) In order to describe a system, you (another physical system) must produce in your brain an ordering, a structure that, as closely as possible, reproduces features of, or resembles, the described system. In order to do that, you unavoidably must ignore some variables of described system and probably own variables too. Thereby the necessity of an entropy. In the universe chances are that things won't repeat themselves because the universe is describing a sequence of more ordered states to less ordered states (IOW, the initial state was far more ordered than the later ones.) Also, the accelerated expansion may render complete thermalization impossible. Poincaré's recurrence theorem only works for closed systems after they completely thermalize, so that thermal fluctuations, given enough time, get you as close as you want to a previous condition or, AAMOF, to any particularly bizarre condition (Boltzmann's brains.) So, on second thought, the OP may be right in that "anything that may happen will happen" for thermal systems, given enough time. An example would be a thermally isolated gas in a box. Given enough time, some bizarre dynamical configurations might appear as a result of thermal fluctuations. They would last a gazillionth of a second, I surmise. The universe is not like that.

Everything else being equal, of course. So no heat exchange or other forms of work.

I see. Thank you +1. My memory was blurry. Germanium wouldn't work for polymer backbones, would it?

Just to give more examples and clarify more, if possible. The matter gets settled when you express your change in internal energy as, \[dU=\delta Q\pm\Sigma_{i}F_{i}dX_{i}\] The Fi quantities are intensive parameters (they are the same even if you re-scale the system), and the X are so-called control parameters and are extensive (they scale as the size of the system). The minus or plus sign is just a convention. What's not a convention is what it looks like when you express it in terms of the intensive and extensive parameters. For an ideal gas, e.g., the eq. \[dU=\delta Q-PdV\] does not depend on you criterion. If the gas expands, it looses energy, so, if you define, \[dU=\delta Q - \delta W\] then you must define \[\delta W = PdV\] but, if you define, \[\delta U = \delta Q + \delta W\] then you must define, \[\delta W = -PdV\] in such a way that, no matter how you define things, the gas loses energy when it expands, which is what really happens. As Swansont and Carrock suggest, you are on safer grounds if you think of your particular system in terms of energy being a constant and how the different parameters change your system's energy. I hope that was clear in case there were loose ends.

I'd say plastics and some waxes, but I'm not sure. Some waxes are produced by organisms, though. I don't consider too tight categorical thinking very useful. Some theories of how life evolved involve rocks. But I'd love to know what the experts have to say. I would say covalent bonds in the main chain is a must.

You're most welcome. It's such a pleasure to break the spell. Good luck to everybody else.

Ditto +1. Although I'm in a hurry. Just want to add that physicist's criterion kinda makes sense, because when the system does work, it loses energy. It happens to me all the time.

And I've I told you: MigL also told you: And, along the same lines, I said: IOW, it's not t2-t1 for the arrival times of the signals that mark up the ticking of the clock --the perceived time, which is the thing you seem to be thinking about, although nobody can be sure-- what determines the clock's ticking, it's the mean average of tout and tin. tout and tin being the delays in the forward and backward trip of your signals. The process repeated for 2 fiducial ticks of the remote clock, and then the calculation. The source of all your inconsistencies about "remote clocks" starts, I'm sure, from the very simple fact that you don't understand what it means to measure time in SR, let alone in GR, which is affected by second order derivatives. There are as many as 20 independent ones, that's known since the 19th Century. We could talk Einstein, we could talk Weyl if you want, but let's drop the tensors for a while, if you please. Please, tell me that you recognize something like what follows in terms of outgoing and ingoing signals in order to define coordinate time: \[t=\frac{1}{2}\left(t_{\textrm{out}}+t_{\textrm{in}}\right)\] where tout is the coordinate time of signal sending in your system, and tin is the coordinate time of signal receiving in your system. The coordinate time of distant events must be defined in terms of the times signals delay. k-calculus was developed by H. Bondi and is a very simple tool to understand this, and if you take my advise and read carefully chapter 1 of D'Inverno, which I recommended you, you will understand. IOW, you can keep your own close observations as your clock, so to speak, but for remote objects, you must send signals and, upon receiving them back, guess the coordinate time for the distant object. It's always like that in any relativity, S or G. Please, oh please, try to understand that and maybe we can talk about something meaningful and go on to tensors. Otherwise nothing we discuss is going to be meaningful. I think that's a preliminary requisite. I don't have much time, sorry if I mistyped or made another similar mistake.

Because I was the one to mention radiation pressure, and just to clarify, I never intended to argue that radiation pressure is a plausible point of departure to build the components of either the energy-momentum tensor, or the Einstein tensor, or anything else in GR. It was intended as a simple illustration that the slowing down of clocks (a frame-dependent effect, as I've repeated here to the OP till I got blue in the face) has nothing to do with the slowing down of photons. And it was in response to this rather bizarre statement by the OP: (my emphasis) And as photons do not slow down in any sense that I know of in a gravitational field, and please correct me if I'm wrong, I surmised that if a clock made of photons (and necessarily other things non-photonic) does slow down in a gravitational field, what other reason could it be attributed to but the fact that it's not made just out of photons, but also massive / charged matter interacting with them? IOW, the photons that are going back and forth inside the clock cannot be accountable for the slowing down of the clock, but the presence of the cavity, with which they interact. What the detailed analysis of this interaction would be is another matter, which I won't even try to analyze here or elsewhere. But there, that's how else you could explain it: because it's not 'just' photons falling! On the other hand, I totally agree with what the experts have said as far as I've been able to read and understand. And specifically concur totally with the point that considering space-time as a "medium" is completely the wrong way to try to approach it. My last point, and sorry for the lengthy argument. I'm not saying that GR is necessarily to stay with us forever, or that I'm 100 % sure of its total infallibility. But for anybody who claims to have come up with something new and/or better to supersede it or rival it, as Strange has been the most insistent to say on on this forum (from which the only thing of interest is the opinion of the learned people who have responded to the tsunami of nonsense) the minimum required is to reproduce its many impressive results. And sorry for the diacritics. They're just to emphasize what I consider the important points I want to make.

Exactly. This is the basis for the Elitzur-Vaidmann bomb tester. If you have a detector, even if the detector is unaffected, there is a measurement. It's also called "interaction-free measurement." P. G. Kwiat; H. Weinfurter; T. Herzog; A. Zeilinger; M. A. Kasevich (1995). "Interaction-free Measurement". Phys. Rev. Lett. 74 (24): 4763–4766. Bibcode:1995PhRvL..74.4763K ABSTRACT:

Only case in which I thought that could make any sense is about static solutions. But not even there. Thank you very much. +1 Eqs. rendered badly, prob. because insertion of HTLM tags. Dunno. Anyway, I meant, To be more precise. Einstein demanded, \[ \sqrt{-g}=1\] with, \[g=\textrm{det}g_{\mu\nu}\] which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory. His first version of field eqs. was, \[R_{\mu\nu}=\frac{8\pi G}{c^{4}} T_{\mu\nu}\] which doesn't covariantly conserve matter energy, his goal. As, \[D_{\mu}R^{\mu\nu}\neq0\] The moral of all this: Einstein was carefully scanning for mistakes in his proposal. You don't come across like you are, rjbeery.

To be more precise. Einstein demanded, \[\sqrt{-g}=1\] with, \[g=\textrm{det}g_{\mu\nu}\] which, as Hilbert pointed out, can't be in a diffeomorphism invariant theory. His first version of field eqs. was, \[R_{\mu\nu}=8\pi GT_{\mu\nu}\] which doesn't covariantly conserve matter energy, his goal. As, \[D_{\mu}R^{\mu\nu}\neq0\]

I don't know what this is in response to. Care to specify?

That's very interesting. Thank you. The concept of photons was Einstein's pride and joy, but it took decades for people to buy into it. It's not an easy concept and it remains so to this day. At the time when he published GR's founding papers, the concept hadn't still made it through the barrier of incredulity. Another thing is the concept of "invariance under general coordinate transformations," which to this day finds physicists discussing as to what it means exactly. In my opinion, it was a simplifying assumption that Einstein took, because he was in direct competition with David Hilbert to be the one to get first at the final form of the field equations. AAMOF, Einstein made a mistake on the first paper, including a condition that the determinant of minus the metric be 1, which is not an invariant constraint. Hilbert immediately noticed, and so told him. Einstein corrected it, and went on to learn about the Ricci tensor, which gave him the final form of the field equations. So did Hilbert too. Science historians admit today that Einstein got there first.

Right you are. It's absorbing photons. I hadn't noticed. Thank you. But as far as I've been able to read the photon clock made in Caltech does use radiation pressure. The point I was trying to make is that if you build a periodic system (clock) by having photons bounce back and forth, such photons aren't free-falling anymore; they are interacting by means of non-gravitational forces. What the OP was arguing, at the point that the question surfaced, was that free-falling photons must slow down. The reason being (as I understood the OP) that bouncing photons in a photon clock must slow down too to account for time dilation and length contraction. My argument, IOW: any such clock is not just made of photons bouncing in mid air, so to speak. It involves matter and interactions.

This is only valid for static solutions!