joigus

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!

And it does. Welcome to our world (the real one.) Radiation pressure is proportional to the number of photons per unit time that hit the mirror and the average energy of the photons, which is, \[\hbar\omega\] which is affected by frame-dependence. Inverse time transforms exactly like frequency. In GR is a bit more complicated, but it can be locally understood in terms of inertial frames. So it's not an invariant (or your cryptic "absolute" word.) Radiation pressure is a frame-dependent object as well. I rest my case. This is about the first time that you've asked a question. I think you can learn some relativity in a reasonable time (compared to Eddington's years) today thanks to the fact that you've got lots of material, in the form of online courses. Many people here can help you. There are wonderful free e-books out there. You're not dumb, you're just sticking to your guns to the point of nonsense. You can teach yourself relativity by reading good books and following excellent courses, but you've wandered alone for too long. Neither Einstein nor Eddington were lone wanderers. Every (static) exact solution in GR carries with it what you call an acceleration field. What the meaning of it is is far less clear to me. What's sure is that changing coordinates to locally flat (inertial) takes you to what the free-falling observer sees. But the starting point from the exact solution is far less clear in my opinion. I'm looking forward to what the experts in this community have to say. Mercury's precession is already a solved problem to 43'' of arc per century. Bettering that is a pretty tall order. I would start with vector calculus and a relatively simple model of field theory, like Maxwell's equations. When Einstein postulated his equations, he took Maxwell's as a model.

So if I understand you correctly, and I think I do, you're proposing to go after a galaxy that's receding from us at close to the speed of light (because of the universe's expansion) by going after it at close to the speed of light, and then, you will: 1) Catch up with it after having given the galaxy a head start of 14 billion-odd years 2) When you do, you will be there seeing it at rest from your spaceship Do you see where the problem is? Or maybe it's nearby, in which case it's not receding very fast from us (Hubble's law,) but a really considerably head start is still there, and if you want to catch up with it, you will have to squeeze the brake! Out of the box is OK with me. What you're proposing is not out of the box. You can't even see the box right now. And, believe me, I applaud your enthusiasm and share that longing with you of embracing the stars.

Some musings from reading you, brethren in curiosity. If I understand Taeto and Studiot correctly, yeah, dropping properties that seem but commonsense to physicists, chemists and engineers, and delving into more abstract mathematics is a healthy thing to do for someone at some point. Science needs some valiant people to go down those dark alleyways. Drop basic assumptions about compactness, drop space-time itself, what have you. Easier said than done, though. It's really dark down those alleyways. We've lost too many brave ones to the depths of maths, whence they never came back. Another thought I'm pondering is that physics has always taken a quantum leap when very deep mathematics has percolated to the more 'math-dummies' like me, at least next-door, which is theoretical physics AFAIK. But the possibility that it's some kind of dice throwing game doesn't bear thinking. I like to think there's going to be another Planck, some day. Then the Paulis, Diracs, and Heisenbergs will appear who clarify the mathematical rules of the game. I first heard of Napoleon's theorem from a friend mathematician. I'm not sure anybody has used it in physics.

Missed this. This really says it all. A viewing angel is telling me from nth layer that you're mistaken. Cheers

Hello, Trestone. Special Relativity is not an observer-dependent theory. All observers sharing the same reference frame agree on their observations. A very common misconception of relativity is that it's about subjectivity. Quite the contrary. It's about carefully distinguishing which observations are frame-dependent and which are not (invariants.) Once the matter is settled, SR goes on to work on non-frame dependent quantities in order to assure that the physics is not ill-defined. Working out for yourself some dynamical problems of decay, collision, etc. is very illuminating in this respect. Experiment has always supported the theory, which is the most important point. Thereby my point. If you don't know what qualifies as observer, how can you tell with any degree of confidence what you must include in your picture of the multi-observer, multi-universe framing of the physical world? I have nothing against your theory, and far less against you. I'm just calling you to task. If what you want to do is set forth a new scientific theory, I think you must work on those details. So far, and I don't think I'm alone in this, I don't think you have proposed a scientific theory. And thank you for your sportsmanship and good manners. Not everybody one disagrees with is like that. If you have to go to a different logic to disprove Cantor's diagonal argument, that kind of says it all.

Just to correct myself, at the risk of going further off-topic, energy determination is limited by Heisenberg's uncertainty principle.

What the mathematics of physical theories suggest is: If time were infinite and the universe were a closed dynamical system, then it would follow that anything that has happened is bound to (approximately) happen again given enough time. The name for that statement is Poincaré recurrence theorem. It is by no means clear that the universe as a whole can be treated as an closed system. Besides there are enough cosmological features further complicating this question for anybody to be able to say anything to any degree of accuracy. The statement "anything that can happen will happen" is, rather, physicists' vernacular for QM's feature that "anything that is dynamically possible is somehow present in the evolution of one single instantiation of a dynamically evolving state." (That's my attempt at re-phrasing.) The motto is due to Murray Gell-Mann. But it's nothing to do with finiteness of time. Rather, with multi-branching of the wave function in the Feynman path integral. There's another funny version: Anything bad that can happen, will happen. That's Murphy's law.

Larry Tesler, inventor of the cut, copy, and paste commands, dies at 74. Larry Tesler, inventor of the cut, copy, and paste commands, dies at 74. Larry Tesler, inventor of the cut, copy, and paste commands, dies at 74. Larry Tesler, inventor of the cut, copy, and paste commands, dies at 74. Larry Tesler, inventor of the cut, copy, and paste commands, dies at 74. The man who controlled x, controlled c, and controlled v. My humble homage from here.

Well, it would depend on what you mean by 'substance,' but considering what most people mean when they say that word, I agree 100 % with Swansont. Energy is not a substance for many different reasons. AAMOF, the concept of 'substance' in physics is long gone. Particles appear and disappear. Energy is not conserved in cosmology. On the other hand, energy conservation is limited by Heisenberg's uncertainty principle. Besides, energy is only conserved when there is time translation (Noether's theorem.) As most cosmological models are time-dependent (galaxy-co-moving universal time,) energy is not conserved in cosmology. And to wrap it up, vacuum energy, calculated with QFT, gives a value 10120 times larger than it should from cosmological observation (problem of the dark energy.) What kind of a substance is that? I'd say that, at the very least, considering it a substance is very iffy. Think otherwise. Matter-antimatter has to do with gauge charge. Electric charge (and all other gauge charges too) has nothing to do with distortions of space. Gravitation does. Electric charge requires an 'internal space' or additional direction to space with very different translation rules (gauge connection,) not related to a metric. It is in that spirit that Einstein took Kaluza-Klein theory as a way to attempt to formulate a unified field theory. Both Einstein and Schrödinger tried to work out a geometric theory of the electromagnetic field. At about the time that Yang and Mills formulated a generalization of the electromagnetic field that could work for elementary particles, people started to give up on the attempt to formulate gauge fields as space-time distorsions. That's not correct. The numeric value of energy means nothing outside of the particular parametrization you're using to solve your problem, except in gravity, where it must be zero when summing up geometric and material terms, vacuum energy, if it means anything at all. It's spatial gradients or spatial variations of energy which imply force in general, not value of energy. In classical gravity it also makes sense to define an 'absolute' value of energy, as your potential must go to zero at infinity. Sorry, this went quite a way off topic.

Aaaaw. Exactly what I was thinking. Now I know you're a senior member.

Wow! You must be really good at music. Let's burn the ship and jump on a piece of flotsam. Good idea.

I can't say I do, I'm sorry. I'm thinking of taking a back sit on this one. I'm not ready for this discussion... just yet. I want to read more arguments. Yes, I did. I had nothing to add to that one. Yes and no just doesn't do it for me. It's just that I want to take a break from fundamentals of QM for a while. I've had so much arguing for years with my friends from university... There's been so much nonsense said and written about it through decades that I feel overwhelmed. It is entirely possible that I misinterpreted. Occasionally I need to take a step back and let everything sink in.

Try to say that when they stop you for speeding.

So you do dimensional analysis... I'm impressed!

Studiot, could you elaborate on this, please? Chicken and egg seems to imply indefinite causation, a 'what comes first' kind of question. In case anybody is interested, I am too, and I do think this topic is worth discussing. Any insight would be welcome. I'm in doubt, to tell you the truth. Your points are well taken, but emergent properties (pressure, temperature,...) always go from small to big, not the other way around. I would be more convinced is there were a single argument that the mass of the Higgs (or any other one of the free parameters of the Standard Model, mixing angles, etc.) came from some kind of cosmological average, boundary conditions... I don't know what to think about this one, to be honest. I do think the OP has a point.

Fortunately, that excludes me.