joigus

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.

I forgot this. Your theory must be falsifiable.

There goes your theory. Ockam's razor. A universe for every observer is inordinately uneconomic. We have enough universes, thank you very much. Observer-dependent is a bad, bad thing. I think there are unsolved problems in QM --other people disagree--, but this in not one of them. How many 'observers' are there in the union of all universes? Are there observers without universe? And universes without observers? How do different observers relate to each other and correlate their observations? Is there a meta-universe where they all correlate? Do different universes correlate in the first place? How do you define a universe? And an observer? What is an observation? Is a rock an observer? And a cat? If I see an amoeba and you see an amoeba, how do our universes agree on the 'amoeba' aspects of our observations? From what I can understand in what you say, your ideas go against the grain of what science is about. Objectivity is far more important than reality. How could that be? Prime factorization depends on the properties of the integers. What does 'layer-dependent' mean? What does 'layer' mean? What do you mean by 'could be'? You don't know?

Yes, that sounds totally right. I should have written it down. My bad. But just for calculations, it's simpler to assume radial escape, right? Correcting myself. Radial trajectory most efficient for calculations, as escape velocity doesn't depend on angle. Efficiency is a different matter completely. Thanks a lot, Janus.

Elephants are everywhere. That must mean something. Nice topic. I think it's to do with the arrow of time. When you try to solve the wave equation in spherical coordinates, there are solutions that go inwards that must be discarded just because you know that there is an arrow of time, as the inward-going solutions can be obtained by taking the negative radius. Waves only propagate outwards; never inwards. That's very mysterious. A definite direction of time is closely related with a definite orientation inside-outside. But I'm just guessing. I think it's an interesting question.

"Jeez, Bots. Do you mind if I unplug you for a while?, I must vacuum now. But you're my friend, and I'll remember you while I'm vacuuming. So don't worry, I will plug you back in a couple of minutes. Even if I evolve into the Dark Knight, I'll still be nice to you." Wink. Nice topic.

Blimey! 7 years! No wonder he's experiencing time dilation. Thanks a lot, Studiot.

Thank you, Markus. Although you've shot too far ahead for him. I can't +1-you because I've run out of points.

'Absorption and instantaneous re-emission' was a colloquial way of saying 'radiation pressure' of the photons on the cavity where you're confining them to make the clock. I said that to have you picture in your mind that the photons are interacting within the clock by means of non-gravitational forces. Then I rephrased it as 'radiation pressure,' just to see whether you understood it better: Then, on your linked Caltech article (https://www.caltech.edu/about/news/caltech-scientists-create-tiny-photon-clock-1029😞 Lo and behold, your Caltech publication confirms my diagnostic. What was I telling you? Radiation pressure. You've missed the point completely. That's what makes your clock be affected by time dilation (never mind it's made of photons.) And I, and everybody here, is tired of repeating to you, but there it goes once more: Time dilation is a frame-dependent effect. As I spent many hours, c. 1990, thinking about toy models for massive elementary particles made up of bouncing photons (massless) and had to rule them out because I wasn't able to postulate the self-interaction, I know what I'm talking about. IOW, I had the same idea (just the non-crazy snippet) than you 30 years ago and it took me less than 24 hours to throw it in the garbage can. I didn't in my wildest dreams try to model gravity with that, though. And please, don't try to smother me with big names like Eddington or Feynman to try and push ahead a crazy idea. We're all grown-ups here, or are we?

Clue: angular velocity for the first at fixed r (which gives you equality between centrifugal energy and grav. potential energy) and radial velocity for the second one (most efficient escape orbit.)