Sure. But the definitions you found agree with what I said. An acceleration is not a force. A force causes an acceleration. Kinematics does not describe forces at all. That is the subject of dynamics. Your own definitions say so: Displacements in no way "replace" force; the two concepts are completely different - they even have different units (dimensions). Similarly, acceleration is nothing like mass. In kinematic terms, simple harmonic motion is any motion in which the acceleration is always directly proportional to the displacement, but in the opposite direction. Note: no mention of forces or masses in this. In dynamical terms, simple harmonic motion is produced by a linear restoring force acting on an object with mass. There's no need to invoke Newton's laws to go from acceleration to velocity to displacement, or vice versa. You need to have a definition of velocity before you can do that. Either.
OK, try this: if "acceleration is nothing like mass", what accelerates in kinematic equations? If kinematics doesn't "describe forces at all" what equivalence does dynamics have with kinematics? They don't describe each other at all? Can displacements replace the idea of 'positions' 'velocities' and 'accelerations'? Can you substitute a displacement for a change in energy? Also, can you write any displacement in terms of space and time coordinate changes, i.e. arbitrary 'units' of length and duration? Does this mean any interaction is ultimately only observable in terms of (changes in) space and time?
Masses. But masses don't enter into kinematic equations. (The colour blue is nothing like the sky, so what colour is the sky?) None. They are not equivalent. I'm not sure what you mean by this. A displacement is simply the difference between two positions. No. They have different physical dimensions. Yes, by definition. I'm not sure what you mean by this.
I don't really follow this. The colour blue is a class of colour shades or hues. The sky is the colour: 'sky-blue' isn't it? Masses are 'independent' of kinematic equations, sure. Kinematics is the study of motion, so what moves? Masses do, but this has "nothing to do with the equations". This looks a bit shaky, to me, because an equation is independent of some quantity or property (like mass or force), if (and only if) that property is written or 'encoded' within some other property. Is this not true? If the displacements are of space or time, sure. If they're of something else then "different" may not be the case. However, we can only observe certain quantities (which ones)? The rest are a bunch of inventions - we induce them because we can see how they move, against a 'constant' time gradient, and a constantly expanding 'space gradient'. Some prof or other posed a question about all this, a simple enough looking query, that I suppose was designed to make students think about something(s). The question is: How equivalent are descriptions of kinematics and dynamics? You say there is none - these are 'independent of each other'...(?)
disease: The fundamental objects of "study" (if you even want to call it that) in kinematics are "trajectories" (vector functions of a real parameter called "time"), and literally all kinematics does is set up a few definitions (velocity is the time derivative of a trajectory, acceleration is its second derivative, speed is the norm of the acceleration, and so on), and evaluate these definitions in some specific cases (eg. rectilinear and circular motion). Automatically calling "mass" anything that has the property of "following a trajectory" is missing the point: dynamics is a branch of physics that attempts make specific (and falsifiable) predictions about how physical objects will behave when subjected to forces. Kinematics is just the natural language and mathematical setting of dynamics.
OK, you're saying kinematics is the 'code' we get, in terms of changes in space and time. Mass has to be something we perceive through this (space + time) code; in fact we need at least two things, in order to derive anything, including motion. When it comes to deriving 'observation', we have to look for 'observables' which are independent of each other. This connects nicely to the ideas in Information Theory, which says any code is ultimately just changes in position, and time. So we need a way to show that all the other 'dimensions' like mass and charge. and the constants like c and Avogadro's number, all the various ones in the QM 'algorithm', can be written in terms of space and time, and how that relates to spacetime, where space and time 'vanish'; the way as everyone should say, mass and force vanish from kinematics. So independence must explain something fundamental about observation. How independent is any one event from any other, in that case? We can talk about 'spatial independence' if an event is at a large distance from another similar one, or 'time independence' where events are separated by large intervals of time; then explain the mathematical nature of SHM as a simple 'observable' which relates periodicity - the 'exchange of energy' over time, either side of a central 'initial state' , with the environment around it, particularly if it's damped significantly, say by friction. Then make 'time' vanish from the scene and you're in the spatial domain, you explain SHM as observed 'points of return', or inflection. Two of these equal a 'return' to the same position so you divide the motion by two, and that's a 'period'. Independence is a kind of 'foreground/background' effect. We can switch these around to make 'time observations' into 'spatial observations'. Mass appears to come along for the ride. IOW, inertial SHM must explain the constant G as well, in fundamental terms.
Er, expanding on this, the answer to "what moves?" is: "something that doesn't (appear to) change", in SHM this is a "fixed" weight, which is also "fixed" or attached to a surface (which points in the direction of 'weight'); kinematics is valid for "fixed" inertial/gravitational fields. What the equations describe are geometric phases; we then derive 'mass' and other "fixed potentials" by observing their motion (motion encodes something). What 'independence' means then, is how 'motions' appear to be 'disconnected', and 'connected' in spatial and temporal ways. Synchronous kinds of 'motion' are all we have to compare this to. Going back to the example of a long elastic rod, or material cylinder - a 'solid' or fixed mass with certain dynamic 'potentials'. This rod can be fixed at one end (to a surface), and free at the other (to move 'transparently' through some medium), then the free end has some potential torsional motion which depends on the elastic constant of the material. If this torsional motion is periodic, there's a fixed elastic constant, if it 'rotates' continuously one way or the other, there's no elastic constant (no viscosity), the rod is infinitely plastic, at least to torsional motion. Wait long enough to see if the torsional motion slows and reverses, and you see an elastic constant. If the rod also extends and contracts lengthwise (axially), there's another 'independent' motion - a way to determine the dynamic property of this rod. So a potential is also a probability in the sense a material will have an elastic 'property', sufficient to cause periodic motion to emerge. Newton thought the stars were fixed points, and that visible light was like solid particles travelling along 'rays'. Today we know the stars are 'fixed' by gravity and the way it bends spacetime, that 'motion' is relative to observation (in space and time). So pick two independent observables, what would be two that are 'completely' independent? Say spectroscopic observations from across the sky, and spectra of different 'elemental' salts, something simple like flame photometry?
No. Er, you do realise The Matrix film trilogy was never intended as a physics documentary, right? :bugeye: Most of this doesn't make any sense (you seem to be taking a confused version of the "universe is like a computer simulation" analogy to the extreme) and is completely irrelevent to the topic of this thread, which is about the relationship between classical dynamics and kinematics. To answer the OP: they're not equivalent.
Ok then. I wonder if this question is worth posing in that case: are you saying we can see more than time and space 'out there', there are ways to measure more than changes in position and changes in 'time'? If you can answer this question, I'll be impressed given what seems like a dismissal of that very principle: i.e. that there is a code we get from the universe, which ultimately is simple changes in position, over time. But let's see a refutation that makes sense...? (If possible) That's nice and everything, but fails to answer the question: how equivalent are they? I think you may have missed something (but don't let me persuade you in the slightest, that kinematics and dynamics aren't totally independent, have no equivalence at all in any way shape or form). BTW, you're allowed to be as testy and irritable about this as you want. I don't actually give a monkey's. The fact remains, we have observables and we have 'independence'. So there should be a way to derive all the 'constants' we know about from observables - oh wait, we already did.
I'm not saying anything at all, whatsoever, about what we can see or measure. But since you ask: no, I don't know anything off the top of my head that doesn't boil down to measuring the position or motion of something (even if it's ultimately the oscillation of electrons in your eyes). If your whole thesis is just a fancy way of saying that physics is all about deducing the parameters and rules behind the evolution of positions we observe, then you're more or less correct, sort of, and I don't really see any point in arguing with you about the personal spin you're putting on things. Anyway, back to the thread topic: Not equivalent. They're related, but one can't be substituted for the other so "equivalent" simply doesn't apply to the relationship between the two. How you managed to deduce that I think kinematics and dynamics are completely unrelated from this: is a complete mystery to me.
Well, that's your answer, then. I would answer the question more like: "Kinematics describes motion, and dynamics describes certain 'fixed' properties of things that move. Dynamics encodes the intrinsic properties of 'matter' and kinematics encodes the extrinsic motion through space of matter, both assume a linear time 'clock'. Forces are where any equivalence can be made between the two models." Motion is the protocol that mass, charge, etc are encoded in.
