geordief Posted October 8, 2016 Posted October 8, 2016 here is the classical version of the principle of least action. In simplistic form the principle of least action can be expressed as. [latex]Action=S=\int_{t_0}^{t_1}[\frac{1}{2}m (\frac{dx}{dt})^2+-mgx]dt [/latex] Between events t_0 and T_1 there is millions of possible paths. Starting and ending at those points. The correct path is the one where the sum of kinetic energy (LHS of the + sign) and potential energy (rhs of the + sign) is lowest. the lowest action path between potential energy and the objects kinetic energy determines the path Does the principle of least action also apply at relativistic speeds? Or does it perhaps apply but not in an obvious way? (apologies in advance for display of ignorance or simplicity ) Has anyone attempted to explain the principle of least action or is it just one of those things that is "obvious" once it is noticed and accepted as presenting no possible anomalies?
studiot Posted October 8, 2016 Posted October 8, 2016 Does the principle of least action also apply at relativistic speeds? Or does it perhaps apply but not in an obvious way? (apologies in advance for display of ignorance or simplicity ) Has anyone attempted to explain the principle of least action or is it just one of those things that is "obvious" once it is noticed and accepted as presenting no possible anomalies? Yes it is one route to general relativity. https://en.wikipedia.org/wiki/Einstein%E2%80%93Hilbert_action
Mordred Posted October 8, 2016 Posted October 8, 2016 (edited) still applies just a different formula to incorperate relativity. The principle of least action is a key for freefall geodesics in relativity. cross posted with Studiot. If you think about fields and potential energy. You can see that even if the field has zero charge (vector direction) the field still has potential energy until it interacts with the particles being measured. Thats when it equates to a charge towards center of mass. Edited October 8, 2016 by Mordred
Strange Posted October 8, 2016 Posted October 8, 2016 Has anyone attempted to explain the principle of least action or is it just one of those things that is "obvious" once it is noticed and accepted as presenting no possible anomalies? It is a generalisation of the fact that systems try to reach the lowest energy state. This is, for example, why bubbles and planets are (roughly) spherical, for example. And why apples fall on heads. I don't know if that needs explaining at some deeper level, or if it is just the way the universe is, or if it is "obvious" and couldn't be any other way.
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 OK, well I've just read through the first lesson from a series at Cambridge University (get me!!) on concepts of theoretical physics, and been introduced to POLA. Can't seem to post a link, but it's by a Daniel D. Baumann, and it's really well written - my how things have changed since my undergraduate days (maths)! I think I will attempt to work my way through all the chapters as a project. But anyway, the first one deals with POLA. I can see the relevance to motion, and certainly it's very interesting and would seem necessary to a proper grasp of modern physics. In terms of my query - which perhaps can be better phrased as essentially "what IS motion?" - there is still a lot of room for ruminating (including philosophizing on POLA of course ,as alluded to by Strange). But I still want to get my head around motion as a "property" ... objects seem to possess it yet they don't in isolation, because it requires time to be expressed. Contrast this with the property of mass - which you can deduce by isolating and totting up the mass of the constituent particles say. I hope you can see where I can coming from, even if you don't think it is very interesting. P.S. Am I a troll? Well I enjoy a good game of one-upmanship if that's what's on offer. And I do have a thick hide . But no I am not a troll.
Strange Posted October 9, 2016 Posted October 9, 2016 But I still want to get my head around motion as a "property" ... objects seem to possess it yet they don't in isolation, because it requires time to be expressed. Absolutely not. The motion of an object is not a property of the object. Motion, and related properties such as kinetic energy, are observer dependent. So one observer may say that X is moving east at 10km/s (with a corresponding kinetic energy) while another observer will say it is stationary with zero kinetic energy. Contrast this with the property of mass Which is in inherent property of the object. All observers will agree on the mass. (Assuming we are talking about rest mass, which is what "mass" should mean). which you can deduce by isolating and totting up the mass of the constituent particles Plus the energy holding it all together.
studiot Posted October 9, 2016 Posted October 9, 2016 Rasher Null If your interest is genuine, why do you not answer comments directly affecting your original post and keep introducing extraneous material? Both of these practices are against forum rules. The question What is motion ? is a much better question than your original one.
geordief Posted October 9, 2016 Posted October 9, 2016 . The question What is motion ? Yes ,"what is motion?". Is relative motion so different from non-inertial motion that the description "motion" (as applied to either ) is misleading as the two phenomena are perhaps unrelated?
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 (edited) Absolutely not. The motion of an object is not a property of the object. Motion, and related properties such as kinetic energy, are observer dependent. Sure. Motion is not wholly a property of the object and depends on the observer. But it is partially a "property" in the sense that 2 objects generally present different motions to the observer. If your interest is genuine, why do you not answer comments directly affecting your original post and keep introducing extraneous material? Both of these practices are against forum rules. The question What is motion ? is a much better question than your original one. One has to make a value judgement as to how "directly affecting" a post is. It is my experience from other fora that science topics contain certain technical terms or words that trigger a strong desire on the part of many posters to rattle off knowledge relating to the word without really having read and comprehended a post properly. This is human nature, I spose. (As is some impatience on my part, perhaps). Also, if one is "leading" a thread - even if one is the least knowledgeable - it is not practical to reply to every branching issue . I am probably guilty of having a poor thread title that maybe didn't help the thread get off to a good start .... Yes ,"what is motion?". Is relative motion so different from non-inertial motion that the description "motion" (as applied to either ) is misleading as the two phenomena are perhaps unrelated? Seems like a good question! Relative motion is observed, while non-inertial motion is experienced.... maybe?? Edited October 9, 2016 by Rasher Null
Strange Posted October 9, 2016 Posted October 9, 2016 (edited) Sure. Motion is not wholly a property of the object and depends on the observer. But it is partially a "property" in the sense that 2 objects generally present different motions to the observer. Of course. That is why we have theories of relativity (whether Galilean, special or general). Yes ,"what is motion?". Change in (relative) position over time. Is relative motion so different from non-inertial motion that the description "motion" (as applied to either ) is misleading as the two phenomena are perhaps unrelated? They are both relative. The reason that special relativity specifies non-inertial frames of reference is because external forces (especially gravity) complicate things. Hence general relativity, which relaxes that restriction. Edited October 9, 2016 by Strange
geordief Posted October 9, 2016 Posted October 9, 2016 They are both relative. The reason that special relativity specifies non-inertial frames of reference is because external forces (especially gravity) complicate things. Hence general relativity, which relaxes that restriction. Is the motion caused by rocket propulsion different to the other two motions (which you are perhaps saying are the same in GR)? Is that motion "un-relative" in that an observer in the FoR does know it is in absolute motion(if I am right) ?
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 Change in (relative) position over time. That's obv a good and proper start, though I am hoping to delve deeper into the matter So some follow up questions 1) Is there such a thing as a "position" which is not "relative"? 2)In terms of a minimal definition, is not "Change in (relative) position" sufficient ... is the "time" bit necessary?
Strange Posted October 9, 2016 Posted October 9, 2016 (edited) Is that motion "un-relative" in that an observer in the FoR does know it is in absolute motion(if I am right) ? Velocity is relative, acceleration is absolute (because you can measure it from within the accelerated frame of reference). 1) Is there such a thing as a "position" which is not "relative"? No. 2)In terms of a minimal definition, is not "Change in (relative) position" sufficient ... is the "time" bit necessary? As it can't occur in zero time, yes. And because velocity is the differential of position wrt time. And because we are dealing with 4 dimensional space-time. Edited October 9, 2016 by Strange
geordief Posted October 9, 2016 Posted October 9, 2016 (edited) Velocity is relative, acceleration is absolute (because you can measure it from within the accelerated frame of reference). Are there such things as units of acceleration (not connected to gravity) ? Is there a maximum theoretical acceleration rate similar to the way there is a maximum speed ( c ) ? Edited October 9, 2016 by geordief
Strange Posted October 9, 2016 Posted October 9, 2016 Are there such things as units of acceleration (not connected to gravity) ? It is usually expressed as distance/second2 (the second derivative of position wrt time). But if you are measuring it from within a frame of reference (with no reference to anything external) then you would measure force as a proxy. Is there a maximum theoretical acceleration rate similar to the way there is a maximum speed ( c ) ? I don't believe so.
geordief Posted October 9, 2016 Posted October 9, 2016 It is usually expressed as distance/second2 (the second derivative of position wrt time). But if you are measuring it from within a frame of reference (with no reference to anything external) then you would measure force as a proxy. I don't understand. You mean indirectly?
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 (edited) no [there is no such thing as a position which is not relative]. As it can't occur in zero time, yes ["time" is necessary to include in the definition]. What I write below is not to be argumentative for the sake of it or to try and "win" something. I guess I am taking a philosophical approach and all that and trying to get to the bottom of things, think things out slowly and thouroughly and all that... I'm declaring this as I am aware I have not come across well previously... hmmm, well it would seem to me then, that the most minimal definition of motion would therefore be either "change in position over time", or even "change in position". The latter definition is the more contentious one with you, given that you say that time is necessary for positions to change. But what is time if not defined by change? So is not the use of "time" introducing circularity into the definition? Edited October 9, 2016 by Rasher Null
geordief Posted October 9, 2016 Posted October 9, 2016 I don't believe so. So a bit similar to the way there is no maximum frequency?
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 I've never thought about there being no maximum acceleration or frequency! If there's no maximum frequency, one could imagine certain state flipping changes being permissible without consideration of time??
Strange Posted October 9, 2016 Posted October 9, 2016 I don't understand. You mean indirectly? Yes, that's the word I was looking for! But what is time if not defined by change? That is not how time is defined (although it seems to be an incredibly common idea). Time is a dimension, equivalent to the real spatial ones. That is why you need to specify 4 numbers if you want to meet someone. If there's no maximum frequency, one could imagine certain state flipping changes being permissible without consideration of time?? I'm not sure why.
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 (edited) OK, special relativity insists on time being a fourth dimension. So motion can be defined as "change of position over time". Position of what though? Is it only "objects" that can change position over time? Objects presumably come in two flavours - classical and quantum? Edited October 9, 2016 by Rasher Null
Strange Posted October 9, 2016 Posted October 9, 2016 (edited) OK, special relativity insists on time being a fourth dimension. So motion can be defined as "change of position over time". Position of what though? Is it only "objects" that can change position over time? It depends on what you mean by "object". Does that include neutrinos? Or photons? Things get more complex at the quantum level (as swansont has already noted) as we can't say anything about what happens to a photon, for example, between it being created at A and detected at B. We can assume it travels in a straight line, but that conflicts with things like the double slit experiment. Edited October 9, 2016 by Strange
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 Would it make sense to define an object , for now, as anything that has the property of occupying a position? (Objects might possibly then be subdivided into "classical" and "quantum")
Strange Posted October 9, 2016 Posted October 9, 2016 That pretty much rules out quantum-scale things.
Rasher Null Posted October 9, 2016 Author Posted October 9, 2016 (edited) Well leaving out quantum scale things (for now at least), shall we say that an "object" is something that has a position? We could call it an "aardkarv" even - but some name would be useful if the definition of motion is based on a "change of position", because presumably that means a change of position of something and it would be convenient to have a name... FANFARE!! I may be in a position to resolve one aspect of "motion" that is bugging me - about being able to "freeze" a moving object and being able to discern its velocity. ... Can this not be done - by an external observer at least - by looking for relativistic length contraction? Edited October 9, 2016 by Rasher Null
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