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Everything posted by joigus

  1. I recognize no truth, but degrees of certainty.
  2. What external forces do you wish to consider? So far it's the first time you mention any external forces. If you consider external forces, the problem changes completely and it's the first case I've discussed which applies. Make up your mind, please. The rest of your points only show you should study classical mechanics thoroughly before you make such assertions. I have a busy afternoon. Maybe later.
  3. If you had an external field that acted on the COM coordinates, then you would have a potential energy depending on such coordinates. The Lagrangian is, \[L=T-V\] with T the kinetic energy and V the potential energy. The generalized momentum for the COM coordinates is, \[\boldsymbol{P}_{\textrm{cm}}=\frac{\partial L}{\partial\dot{X}_{\textrm{cm}}}\] and the evolution equation for X_cm is, \[\frac{d}{dt}\left(\frac{\partial L}{\partial\dot{X}_{\textrm{cm}}}\right)=\dot{P}_{\textrm{cm}}=\frac{\partial L}{\partial X_{\textrm{cm}}}=-\frac{\partial V}{\partial X_{\textrm{cm}}}\] Instead, you have, \[-\frac{\partial V}{\partial X_{\textrm{cm}}}=0\] So the equation of motion for the COM coordinates is, \[\dot{P}_{\textrm{cm}}=\frac{d}{dt}\left(\frac{\partial L}{\partial\dot{X}_{\textrm{cm}}}\right)=0\Rightarrow P_{\textrm{cm}}=\textrm{const.}\] Doesn't depend on internal details. You could have a whole civilization of tiny beings living inside. It's not gonna change anything. I'm sorry.
  4. My opinion is that you cannot seriously believe in god if you've studied science in any length. Specially biology. But many scientists believe in believing in god. That is, they decide that it's a good social deal to keep saying they believe in god and, if pressed, talk about an abstract god, as in "god is the order in the cosmos" or something like that. Just to escape hostility from believers. Scientists discuss science even when the gathering has finished and the discussions keep going while they go back home, or to their respective hotel rooms. But I've never seen anybody discuss theology when they go back home from the church, the synagogue or the mosque. Religious people will leave you alone if you just say you're a believer. For all they care your "god" could be a telepathic giant cat living in another planet and handling the universe from there. As long as you say "I believe."
  5. I have overlooked nothing that is relevant. Ficticious forces inside the ship can never result in acceleration of the COM. No one can write equations for variables that haven't been specified. What are the degrees of freedom of the system? Your new dynamical system looks very different now. It reminds me of a conveyor belt now.
  6. I couldn't have put it more clearly. This big picture Ghideon is talking about saves you a lot of needless work. And believe you me, when you're working on difficult problems you need to have these tools handy, so you can save yourself a lot of workload. My background is that of a theorist. In theoretical physics you want to use powerful mathematical tools that allow you to treat problems that otherwise would be intractable. When you go back to simpler problems, like this, it feels as if you had X-rays to see the physics in them. Your system won't move.
  7. Yes, your analysis is correct. The Hamiltonian formalism is not so efficient for this discussion, however. Noether's theorem is relevant in the Lagrangian formalism. The Lagrangian can be written in terms of the COM coordinates plus a couple of angle variables. There are obvious constraints between the axial rotation angle of what I've called the "nut" and the axial rotation angle of what I've called the "bolt" and the linear motion of both moving pieces, but there's no potential energy involving the COM coordinates (actually, no potential energy at all), so the problem is a one-liner in the Lagrangian formalism: \[\dot{P}_{\textrm{cm}}=\frac{d}{dt}\left(\frac{\partial L}{\partial\dot{X}_{\textrm{cm}}}\right)=0\Rightarrow P_{\textrm{cm}}=\textrm{const.}\] End of story. The beauty of the Lagrangian formalism is that you don't have to think about forces ever again, if your professional situation allows for that. Engineering works do require the Newtonian analysis very often, though. Whenever you have a constraint, you include it in a very straightforward way without thinking about forces. Internal forces "vanish" into constraints. Fictitious forces can also be dealt with very easily. They are relevant when there are external fields. They are all summarized in the constraints and they just don't appear in the formulation (they have to do with the use of curvilinear coordinates), if what you want to describe is the COM motion, which I think is the OP's primary interest.
  8. And Feynman improved upon it: "Science is imagination in a straight jacket."
  9. It's not that we can't see what you see. It's rather that you're the only one here who can't see what everybody else can. Anybody who knows anything about physics has spent some time in their youth trying to make a toy model like the one you're proposing in their mind. It's a rite of passage. You must do all these checks in your mind if you want to understand better why you can't violate the momentum and angular momentum conservation laws. And then you must learn to unlearn them when you're studying general relativity. Because they don't always apply there. Do you know that there is a weak and a strong formulation of Newton's 3rd law concerning mutual directions? You seem not to be aware of it. It is the isotropy of space that forbids that action-reaction forces be in any other direction than the relative position vector for any two parts of the system. That's the basis for the strong statement of Newton's third law: Mutual forces are equal in magnitude and opposite in direction, and their direction coincides with the relative position vector. So that, \[\left(\boldsymbol{r}_{i}-\boldsymbol{r}_{j}\right)\wedge\boldsymbol{F}_{ij}=0\] for every pair, i, j. Otherwise, empty space would be anisotropic.
  10. I know what you're trying to get at, and I'm trying to tell you it won't work and why. You can't transform internal angular momentum into COM momentum. You're trying to obtain translation from rotation. I know that from the very beginning. It won't work. I can invest a certain amount of time in telling you why in more detail, but I must assess carefully how much it's going to be worth it* in terms of a useful (hopefully for both of us and other interested users) dialogue in terms of elucidating meaningful physical concepts. The patronizing treatment ("well done!," "congratulations!," as if they were the advanced students that "understand better" what you're trying to do won't sell your idea any better. *Edit: Also, other users are handling this very well, so my help here is not much needed.
  11. I think everybody has noticed that. You can argue that most everything has some kind of inner structure. They can't and they never do. They can decelerate, though, by means of radiation reaction. But it's the radiation field that pulls the electron almost to a standstill. Electrons, of course, are decelerated by their own radiation field, not by means of internal forces. You can argue that the electron "ejects" something (radiates photons). Nothing can either brake or accelerate itself without ejecting or absorbing something or having an external field producing these effects. It's a property of space-time (symmetries) not a property of any particular system you come up with. Your system looks very much to me like a frictionless nut turning around in a bolt. No new physics there that I can intuit. Transfer of mass doesn't apply to the system that you seem to be representing in your drawing --as noted by Swansont. Rockets obtain momentum by liberating exhaust mass to space. That's what makes the dm/dt term relevant. Your equations for force and torque do not apply to a system where there is mass transfer. Mass transfer does not apply to solid systems. The mass "stays there." Please, consider this possibility: What if you're about to embark on an ill-conceived project that will make you waste a number of years in something that can't work just because you won't listen to criticism? Your enthusiasm is praiseworthy, but you seem to be applying physical principles incorrectly.
  12. Swansont's point is well taken. And it is, of course, pertinent. If you don't specify your variables on a diagram it's impossible to point out where the mistake is. What is possible to declare beyond any doubt is that there must be a mistake in your analysis, (Ghideon has pointed that out too) unless empty space be inhomogeneous or anysotropic at small scales. And the reason is the part of my analysis that you seem to have chosen not to address. Namely, Linear momentum appearing from nowhere requires space not to be symmetric. That's why I know it cannot be correct. If you were as kind as to provide more detail about the position of what exactly is it that r_A and r_R represent, maybe someone could, upon reflection, tell you were the mistake is.
  13. What you've got at the end is a rocket equation, in contradiction with your opening statement that it's reactionless. The force, \[\frac{d\boldsymbol{p}}{dt}=-n_{r}\boldsymbol{u}_{\textrm{rel}}\frac{dm}{dt}\] Is the reaction force (with mass transfer) of the fuel against a rocket. How did this reaction term come about from an allegedly reactionless mechanism? As pointed out above, also, you can't have self-propulsion from internal forces in outer space, because that would imply momentum is not conserved for a system of particles. This, in turn, would imply that empty space is inhomogeneous at small scales. There can be no exception. I could explain in further detail, but you must have either all three Newton's laws or none. They are not really independent. Otherwise you may have a system satisfying Newton's laws but it would be completely impossible to consider it made up of smaller parts that also satisfy Newton's laws. You can't just cross out the third law without giving up Newtonian mechanics altogether. Newton's third law, \[\boldsymbol{F}_{ij}=-\boldsymbol{F}_{ji}\] Is really a statement already implied by Newton's 1st and 2nd laws for binary partitions of a system into two subsystems exerting mutual forces (internal). These must cancel in pairs, \[\boldsymbol{F}_{ij}+\boldsymbol{F}_{ji}=0\] Otherwise the composite system in the absence of external forces (free) would be subject to accelerations. It would contradict Newton's laws for the COM (all of them, in particular F=ma for the COM and the corolary, the 1st law too).
  14. I think your argument is quite correct. If you pressed the theory too much, you would need a working approximation of special relativity for the case when instantaneous forces act on bodies, either to stop them suddenly or to set them in motion instantly. In the case that a rigid ruler stops, by an instantaneous impulsive force applied when its tip reaches Earth, applied at that point, a wave would have to propagate carrying both the momentum of the impulsive "braking" and a Lorentz contraction factor, if I'm thinking correctly. In fact, you have pointed to a well-known logical consequence of special relativity: Namely: That no perfectly-rigid bodies can exist, for the simple reason that they would contradict relativistic causality. The reason being that one tip of the ruler would have to stop instantly and it would take some time for the local perturbation to reach the other end. This is in close analogy to the Doppler effect, in which a kinematic factor (length contraction/time dilation) travels along with a propagation effect by the receding speed that would be present even if Galilean relativity were exact. That's why in the last analysis you need waves (fields) to implement special relativity in an absolutely watertight manner. Rigid bodies can't play the part of physical objects. Point-like particles can do the job, but at the price of introducing densities, which are far removed from direct intuition and have nontrivial transformation properties. This is an extremely clever point. But I don't think @michel123456's arguments have to do with it.
  15. I think it's in the eyes of the beholder. Or, in this case, in the ears of the listener. Rudeness is relative, because language is relative. The ultimate reason being that language's main purpose is to relate. And it is no coincidence that "to relate" means both "to interact" and "to tell."
  16. I think this is a great question, and I would like to see it asked (as well as read proposals to answer it) in a more general context.
  17. Have you completely missed @Ghideon's point, or have you completely missed Ghideon's post? Geometric patterns in Nature tell you nothing about conscience. Complexity is not the equivalent of conscience, nor have you shown that to be the case. If you think that to be the case, it is for you to come up with a clinching argument that proves you right. Then propose an experiment. You are conscious because you have sensory organs and a centralized processing organ for all the stimuli, not because your eyes are approximately spherical, or elliptical, or whatever shape. I would demand as much for a planet.
  18. You're very, very likely right, @Bufofrog. For me it's a last-ditch attempt. After this I think I'm done. But I'll still keep an eye on the thread, only to read alternative complementary explanations, for my toolkit.
  19. I'm not 100 % sure this is at the root of @michel123456's problem, but I have a feeling that it may be. Please, pay utmost attention to this: (Emphasis mine.) I think this observation by Janus is absolutely essential. Here's something you said a while ago, that I think is very significant and, to me at least, betrays that you haven't understood what Janus was trying to say: The length and time that undergo dilation and contraction in relativity are not the naive "as seen" lengths and times that one intuitively gets from common experience, the projections on your retina, so to speak, and on your inner clock. Your use of "see" and "measure" as interchangeable has set off my alarms. In relativity you must be careful about what you mean by position and time (and thereby by length and duration) from the get go. So much so that I think you're not there yet. Coordinatizing events is the groundwork for everything else you do in special relativity. When objects are distant from you, you must establish some kind of measurement standards to guarantee that you know what you're talking about when you say "it is at x at time t." This is at the core of what Janus meant by "see" and "say" in my previous quotation of him. Distinction, this one, that becomes absolutely crucial when discussing the relativistic Doppler effect, because there is a mixture there of both aspects. But it is very important in general. The standard observer in SR is not one that simply believes what she sees. She sets up measuring devices so as to be able to say where and when something distant happened, knowing full well that the more distant something is, the later it gets to her. Einstein pictured a frame of reference as an infinite set of observers relatively at rest with respect to each other, and with clocks that have been sync'd at t=0. That's not necessary. You can set, as @md65536 said before, one reliable clock and get any timing from light signals back and forth from it. The standard observer in SR already knows objects are expected to be "seen" different from what they "are." Please, take a good look at Fig. 2.8 here (from https://www.academia.edu/39463786/R_dInverno_Introducing_Einsteins_relativity) by Ray D'Inverno: It is plain to see that, for any event, t2 is the time when you see it happen, but that's not the time when you infer (measure, in your wording) that it happened. The time when you infer (measure) it happened is, \[t=\frac{1}{2}\left(t_{1}+t_{2}\right)\] The difference between one and the other is source of much confusion for relativity students. When Janus says "see" he refers to t2 in Fig. 2.8 (or increments of it). When he says "say" he refers to coordinate time (or increments of it), which is different, and corresponds to t. The timing of events in relativity, the coordinate timing, is the time that you say (guess, if you know SOL), not the time that you see (paraphrasing Janus.) The times and lengths that you see are only too obviously deceiving you already, because the image of the head of the train, e.g., that's coming to you, obviously predates the image of the tail, as seen by you at the same "psychological" time. I really hope this helps. If it only adds confusion, feel free to ignore it. But in that case, I don't know what it is you don't know.
  20. That seems right. But that's a sufficient condition. Suppose the 20 aminoacids were the same, and all the molecules had the same handedness. How would we know which forms of life came first? Maybe we would have to go to genetic trees, as @Endy0816 suggests...
  21. I think that's a very sharp observation. I'm in two minds about that, to be honest, and ultimately I can't give you an answer. But that shift seems to be going on. For one thing I rather like geometrical theories. They are mathematically complicated, but very beautiful and simple to formulate in principle. But for the other, principles of negative content, the "don't go there" kind or principles, like thermodynamics' laws; IOW, the "impossibility to tell this from that", kind of principles, tend to be very stable, very robust. They may be signaling that new variables, or that a new creative splitting of the significant variables must be proposed. Maybe the distinction between source and interaction field cannot be assumed to be always valid. Or maybe, as Nima Arkani-Hamed says, "space-time is doomed." I wish I knew the answer to that. Edit: I'm not even sure I'm addressing your question properly.
  22. He means low-energy experiments have been used to study the properties of elementary particles from the very beginning of the subject. Meanwhile, in Saint Petersburg... Attempts to study deviations from the standard model with simple spectrometers https://www.natureindex.com/institution-outputs/russia/peter-the-great-st-petersburg-polytechnic-university-spbpu/5139070b34d6b65e6a001c3a?utm_source=facebook&utm_medium=social&utm_campaign=nindx-Sep20RH&utm_content=SPU&fbclid=IwAR0vPuvAw1jImwSoe-Hk07f5e6xyCe9qDK_xQLm-pmizjpq6nOKk14uMXLU#highlight Just in case it is significant. High-energy experiments are important, and they probably will always be. But they're not the only game in town. Edit: The reason why high-energy experiments are so important in studying small things lies in Heisenberg's uncertainty principle. Probing small distances generally requires using very high energies.
  23. I address what may be the origin of your confusion in this thread:
  24. Conscience in other planets is an idea about aliens. Conscious planets is an alien idea altogether.
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