martillo Posted March 11, 2023 Posted March 11, 2023 1 hour ago, joigus said: I still think @MigL's example was brilliant. Why it --initially at least-- didn't have any effect on @martillo is beyond me. Force is something frame dependent. When I jump out of the plane I jump to a free falling frame (a switch of frame) where no force is perceived. I have no problem with that.
Genady Posted March 11, 2023 Posted March 11, 2023 17 minutes ago, martillo said: Force is something frame dependent. Are you sure? If you have a spring stretched between two walls, its force on the walls is frame dependent? 1
joigus Posted March 11, 2023 Posted March 11, 2023 As @Genady pointed out, force is frame-independent in classical mechanics --under the Galilean group. It's frame-nothing in GR, because force is not a thing in GR.
martillo Posted March 11, 2023 Posted March 11, 2023 1 hour ago, Genady said: Are you sure? If you have a spring stretched between two walls, its force on the walls is frame dependent? I'm talking about dynamics of moving objects where F = ma is valid. Not valid for "structural" forces. 1 hour ago, joigus said: As @Genady pointed out, force is frame-independent in classical mechanics --under the Galilean group. F = ma, a = dv/dt = d2x/dt2 . A force F is frame dependent as acceleration a is frame dependent. If the frame is the accelerated one on the free falling then F = a = 0. I think Galileans frames are those moving at constant velocities with no acceleration, am I wrong? 1 hour ago, joigus said: It's frame-nothing in GR, because force is not a thing in GR. @MigL presented an example about a gravitational force asking where it goes when jumping to a free fall. If gravitational force does not apply in GR then I assume he is not considering GR.
Genady Posted March 11, 2023 Posted March 11, 2023 17 minutes ago, martillo said: I'm talking about dynamics of moving objects where F = ma is valid. Not valid for "structural" forces. How about Coulomb force? Is it frame dependent?
joigus Posted March 11, 2023 Posted March 11, 2023 1 minute ago, martillo said: F = ma, a = dv/dt = d2x/dt2 . A force F is frame dependent as acceleration a is frame dependent. If the frame is the accelerated one on the free falling then F = a = 0. I think Galileans frames are those moving at constant velocities with no acceleration, am I wrong? As is well known, acceleration is not frame-dependent in Galilean physics. Classes of inertial reference systems are related by Galilean transformations, which in their most general form are, \[ \boldsymbol{x}'=R\boldsymbol{x}-\boldsymbol{v}t+\boldsymbol{a} \] \( \boldsymbol{x}' \) being the coordinates of certain point P in a new reference frame, \( \boldsymbol{x} \), such coordinates but in some old reference frame, \( \boldsymbol{v} \), \( t \) the time in both frames, and \( R \) a fixed rotation. So, as to acceleration, \[ \frac{d^{2}\boldsymbol{x}'}{dt^{2}}=R\frac{d^{2}\boldsymbol{x}}{dt^{2}} \] So if the vector of force on the, say, LHS of Newton's equation of motion is a vector under fixed rotations, the equations remain consistent. Only a fixed rotation is applied to them. That's why in engineering problems you can choose your axes at will. Otherwise usual engineering procedures wouldn't be consistent. Now, the force --in the last analysis-- always comes from a potential energy. It is the gradient of a potential. But that's not enough: It must depend on differences of the coordinates, and be a scalar under rotations. All known cases comply with this --gravity, electromagnetism. Nuclear forces are more complicated, but I think we should agree nuclear forces are best treated quantum mechanically, and under the Lorentz group, not the Galilean group. Under those assumptions, the potential \( V \) must have the dependence, \[ V\left(\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \right) \] so that, \[ \left\Vert \boldsymbol{x}'_{i}-\boldsymbol{x}'_{j}\right\Vert =\left\Vert R\boldsymbol{x}_{i}-R\boldsymbol{x}_{j}-\boldsymbol{v}t+\boldsymbol{v}t-\boldsymbol{a}+\boldsymbol{a}\right\Vert =\left\Vert R\left(\boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right)\right\Vert =\left\Vert \boldsymbol{x}_{i}-\boldsymbol{x}_{j}\right\Vert \] and so, as claimed, neither acceleration nor the law of force --in any fundamental case-- are frame-dependent. I forgot: \( \boldsymbol{v} \) is the velocity relating both inertial frames.
martillo Posted March 11, 2023 Posted March 11, 2023 8 minutes ago, Genady said: How about Coulomb force? Is it frame dependent? Any force when applied to moving objects is frame dependent while considering accelerated frames.
joigus Posted March 11, 2023 Posted March 11, 2023 The last part, that I leave as a simple exercise, is to prove that indeed \( \boldsymbol{F}=-\frac{\partial V}{\partial\boldsymbol{x}} \) is a vector under rotations. So no, neither forces, nor accelerations, are frame-dependent in Galilean physics.
Genady Posted March 11, 2023 Posted March 11, 2023 2 minutes ago, martillo said: Any force when applied to moving objects is frame dependent while considering accelerated frames. In which accelerated frame the Coulomb force between two charges becomes zero?
martillo Posted March 11, 2023 Posted March 11, 2023 (edited) 25 minutes ago, joigus said: As is well known, acceleration is not frame-dependent in Galilean physics. Classes of inertial reference systems are related by Galilean transformations, which in their most general form are, x′=Rx−vt+a As I already said very clearly, we are not dealing with Galilean transformations between inertial frames of references with relative constant velocities between them. We are considering an accelerated frame of reference. I can't believe we are discussing this... 18 minutes ago, Genady said: In which accelerated frame the Coulomb force between two charges becomes zero? I think we are going out of the scope of the thread... If the two charges move freely they both accelerate by attraction or repulsion depending on the type of the charges. In a frame attached to any of the charges the acceleration of its charge is zero. The charge is attached to the frame, it doesn't move in its own frame... Edited March 11, 2023 by martillo
joigus Posted March 11, 2023 Posted March 11, 2023 (edited) 15 minutes ago, martillo said: As I already said very clearly, we are not dealing with Galilean transformations between inertial frames of references with relative constant velocities between them. We are considering an accelerated frame of reference. I can't believe I'm discussing this... No. We are discussing physics and reality. You say forces are 'real' for some reason that's only clear to you. You want to discuss non-inertial frames? OK. But mind you, forces then become --if anything-- even less 'real' than you claim. In an inertial frame you have F=ma. Now you go to a non-inertial frame and you have F'=F, and obtain F'=ma'-mA, where A is the acceleration between frames. So, if you want to preserve Newton's laws at least formally, you must write F'+mA=ma'. Ficticious forces mA appear in the new system. https://en.wikipedia.org/wiki/Fictitious_force Fictitious, huh? 15 minutes ago, martillo said: I can't believe we are discussing this... Ditto. Edited March 11, 2023 by joigus minor correction
Genady Posted March 11, 2023 Posted March 11, 2023 12 minutes ago, martillo said: If the two charges move freely they both accelerate by acceleration or repulsion depending on the type of the charges. In a frame attached to any of the charges the acceleration of its charge is zero. The charge is attached to the frame, it doesn't move in its frame... I did not ask about acceleration. My question is about the force. The consideration was, is the force frame dependent? The charge is not attached to the frame. The frame is not a structure. You did not answer my question. But do not feel obligated.
martillo Posted March 11, 2023 Posted March 11, 2023 (edited) 12 minutes ago, joigus said: You want to discuss non-inertial frames? No I don't. Actually I think you are just not taking me seriously... 6 minutes ago, Genady said: I did not ask about acceleration. My question is about the force. The consideration was, is the force frame dependent? The charge is not attached to the frame. The frame is not a structure. You did not answer my question. But do not feel obligated. Same as for @joigus. You are just not taking me seriously... Actually I don't want to continue discussing this. You seem to not understand what I say. Edited March 11, 2023 by martillo
joigus Posted March 11, 2023 Posted March 11, 2023 (edited) 11 minutes ago, martillo said: No I don't. Actually I think you are just not taking me seriously... Actually, I am. That's what's painful. You say forces are real. MigL told you that in GR gravitational forces dissapear when you go to a locally inertial frame. After I understood you correctly --I hope-- I told you in Galilean physics forces that weren't there suddenly appear in a non-inertial frame --so-called fictitious forces. I repeat @MigL's question: 18 hours ago, MigL said: What happened to your force, Martillo ??? In the second case, where was the non-existent force? It's precisely because I'm taking you dead-seriously that I ask you these questions. Otherwise, I wouldn't entertain this conversation. Edited March 11, 2023 by joigus minor correction 1
martillo Posted March 11, 2023 Posted March 11, 2023 (edited) 16 minutes ago, joigus said: Actually, I am. That's what's painful. You say forces are real. MigL told you that in GR gravitational forces dissapear when you go to a locally inertial frame. After I understood you correctly --I hope-- I told you in Galilean physics forces that weren't there suddenly appear in a non-inertial frame --so-called fictitious forces. I repeat @MigL's question: I told you many times that in a free falling frame Galilean Physics does not apply as in the example. The frame is not moving at constant velocity, it is accelerating in relation to Earth. 16 minutes ago, joigus said: 18 hours ago, MigL said: What happened to your force, Martillo ??? In the second case, where was the non-existent force? It's precisely because I'm taking you dead-seriously that I ask you these questions. Otherwise, I wouldn't entertain this conversation. I already said that to get the complete picture we must consider the relative movement between me and Earth. If you put a frame on me on my free falling I don't move in that frame and is Earth that moves accelerated to me. There's a force acting on Earth now. Edited March 11, 2023 by martillo
joigus Posted March 11, 2023 Posted March 11, 2023 2 minutes ago, martillo said: I told you many times that a free falling frame is not an inertial one and that Galilean Physics does not apply in the example. A locally inertial frame in GR is not an inertial frame in SR. It is a non-inertial frame. Just a particularly convenient one. As to Newtonian physics, if fictitious forces appear in whatever non-inertial frame with respect to any inertial frame, we must admit a class of forces that merit the name fictitious. Why? Galilean physics is classical physics, which is Galilean physics, whether the frame of reference be inertial or non-inertial. It's called 'Galilean' only because it takes a particularly simple form in inertial frames, and Galilean transformations tell you how to correlate your observations between any two of these particularly convenient frames of reference.
martillo Posted March 11, 2023 Posted March 11, 2023 1 minute ago, joigus said: A locally inertial frame in GR is not an inertial frame in SR. It is a non-inertial frame. Just a particularly convenient one. Yes I got confused about that again. I was editing my post now to not mention "inertial frame"... 3 minutes ago, joigus said: Galilean physics is classical physics, which is Galilean physics, whether the frame of reference be inertial or non-inertial. It's called 'Galilean' only because it takes a particularly simple form in inertial frames, and Galilean transformations tell you how to correlate your observations between any two of these particularly convenient frames of reference. I consider a Galilean transformation as between frames moving at a constant velocity between themselves. Am I wrong in that?
TheVat Posted March 11, 2023 Posted March 11, 2023 12 hours ago, Genady said: I don't think it will. For a full and uncompressed description, you will have to simulate not only "every tree and animal and rock and chewing gum wrapper etc." but also every molecule, atom, electron, etc., IOW, to simulate complete quantum state of the system. But - here comes the punch line - no cloning theorem tells us that this is impossible. Thus, abstraction is inevitable. I think that "etc" in my comment was meant to convey that the simulation would involve all that and ergo be impossible. So, yes, compression and loss is inevitable. In fact, the perfect simulation of Idaho would have to occupy the same precise space as Idaho, and therefore would just be Idaho simulating itself. 😀 And, as @swansont noted, windshield bugs would be integral to any meaningful description. 11 hours ago, sethoflagos said: How's this for low-loss compression? Perfect. The line from your Coleridge clip, caverns measureless to man, seems an apt and fitting description of the epistemological boundaries.
joigus Posted March 11, 2023 Posted March 11, 2023 57 minutes ago, martillo said: I consider a Galilean transformation as between frames moving at a constant velocity between themselves. Am I wrong in that? Certainly not. But, as long as we're considering Newtonian physics, consider also this: To the extent that Newtonian physics is valid, inertial frames must exist within a reasonable degree of approximation. If they do, I can always go to an inertial frame where only those forces coming from fields and their identifiable sources are present. Now I go to a non-inertial frame of reference, and fictitious forces appear. That is, forces that in no manner can be identified with any physical sources by means of fields; forces that to all intents and purposes are kinematic in nature; ie, can be removed only with a reference re-labling. Now go to another non-inertial frame if you like. It's still incumbent upon you --the claimant that forces are real-- to explain why those forces are not present in an inertial frame, while they 'magically' seem to appear out of thin air in a non-inertial frame.
TheVat Posted March 11, 2023 Posted March 11, 2023 Side question - in a field theory of gravitation, it is also a fictitious force, isn't it? Akin to a Coriolis force. Mass is distorting spacetime and objects are just following their curved paths naturally (until electrostatic forces in, say, the ground, stop them from continuing.)
joigus Posted March 11, 2023 Posted March 11, 2023 1 minute ago, TheVat said: Side question - in a field theory of gravitation, it is also a fictitious force, isn't it? Akin to a Coriolis force. Mass is distorting spacetime and objects are just following their curved paths naturally (until electrostatic forces in, say, the ground, stop them from continuing.) In Newton's theory of gravitation, it is not. It is rather a field theory => gravitational field In Einstein's theory of gravitation, it is curvature of space-time. Although GR is peculiar, you still have sources (the momentum-energy density.) In pure geometry you don't have such a thing as "a source of geometry." People do call Einstein's famous G tensor "gravitational field," but its a peculiar geometric field.
MJ kihara Posted March 11, 2023 Posted March 11, 2023 Maybe we are synchronized, we humans we are just starting to scratch about quantum entanglement. I fear the extent to which AI is generating 'every thing' its high time we look for away to secure what is unique about ourselves.
martillo Posted March 11, 2023 Posted March 11, 2023 45 minutes ago, joigus said: Certainly not. But, as long as we're considering Newtonian physics, consider also this: To the extent that Newtonian physics is valid, inertial frames must exist within a reasonable degree of approximation. If they do, I can always go to an inertial frame where only those forces coming from fields and their identifiable sources are present. Now I go to a non-inertial frame of reference, and fictitious forces appear. That is, forces that in no manner can be identified with any physical sources by means of fields; forces that to all intents and purposes are kinematic in nature; ie, can be removed only with a reference re-labling. Now go to another non-inertial frame if you like. It's still incumbent upon you --the claimant that forces are real-- to explain why those forces are not present in an inertial frame, while they 'magically' seem to appear out of thin air in a non-inertial frame. I'm considering what you mention in deep also reading on your provided link about fictitious forces and also taking a look on the link about the equivalence principle. I don't know if I could reach to a good conclusion explaining my point of view. At a first look the consideration of the called "pseudo-forces" leaved Einstein to formulate his GR and I have no pretension at all to challenge that but seems this is involved someway and that's why you are following the conversation, isn't it? I mean, my statement that forces are real is challenging GR in its proper beginnings. I wasn't actually aware about that and it will take time for me to be able to defend my position if it was the case I could. As I said I'm not sure I could be able to do it. I will return if I find something good to present only.
MigL Posted March 11, 2023 Posted March 11, 2023 (edited) Wow. Go to work for a coupl of days and this thread has moved on quite a bit; and I hadn't even considered fictitious forces, Joigus. Point I was trying to make Martillo, is that you can't have a force in one frame, and not in another, and call that force 'real', as all frames are equally valid. And to be clear, both Newtonian and GR gravity are field theories, TheVat. If you consider the proper definition of a field, then geometry is the field in GR. ( quoting AJB ) On 3/10/2023 at 5:36 AM, Markus Hanke said: I don’t know if there are statistics about this, but I bet that, among people who have made important contributions in their fields - the arts, sciences, literature etc etc - a disproportionally large amount might be found to be on the spectrum, or at least have autism-like traits of some sort or another. I watched a movie with Ben Affleck, The Accountant, where he plays an autistic accountant to criminals and helps bring them to justice. As cover names he uses autistic mathematicians/authors/philosophers from the past, like Gauss, Carroll, Wolff, etc. Apparently they were all on the autism spectrum. Edited March 11, 2023 by MigL
sethoflagos Posted March 12, 2023 Posted March 12, 2023 17 hours ago, Genady said: How about Coulomb force? Is it frame dependent? How about Coulomb force? It is so similar in form to Newtonian gravitational force that one wonders whether it too is a fiction. Is spacetime possibly also configured to allow charge to propagate along some electromagetic geodesic as does momentum in a gravitational field? I'm sure this is an idiotic question in a sense, but I'm prepared to endure the humiliation of an informed response.
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