Newtonian Relativity: Galilean Relativity & Beyond

[russ_watters]

The scientific method judges theories by their results; other criteria are a matter of philosophy and taste. It doesn't matter here: surely the only alternative hypothesis in Newton's time was the one which he proved to be wrong.

Considering that this issue of "philosophy and taste" (or as I called it, "logic") is the entire issue being discussed, I'd say it matters quite a lot. Again, it is your thread/question: if you didn't want to discuss it, you shouldn't have.

The scientific method requires more than just a positive result to an experiment. How you get from point a to point b matters, as does interpretation of the result beyond the equation. That should be obvious: if it didn't matter, there'd be no reason to write a paper about it!

 

[Dale]

You put words in my mouth with which I strongly disagree - please don't!

Which words am I putting in your mouth? I went to great effort to get you to express your opinion in your own words and to verify that I was correctly understanding you and not putting words in your mouth.

I am only showing you the logical consequences of your own words. Intelligent design assumes that there is an intelligence which caused the biological life we see on earth. Since that is a causal mechanism it qualifies as a scientific assumption under your stated criterion: "Scientific assumptions should take the form of a causal mechanism or a mathematical relation".

Would you like to revise your criterion? (I would recommend it)

 

[russ_watters]

I agree with Russ that this is getting tedious: several people continue to make the empty claim that Newton could have omitted one of his postulates without consequence for his theory, without actually even trying to show it. Please, stop with arguing on the side and try to show that this can be done without introducing a different hypothesis instead of the one that he chose, or admit that you were mistaken.

Sorry, harry, it doesn't work that way. I gave you one example but what you are saying requires proving the negative in every part of Newton's theory. That is not a reasonable bar. In fact, 'i'm right unless you prove me wrong' is crackpot logic.

Since you claim the assumption has utility, it should be fairly easy to provide one example demonstrating it.

 

[russ_watters]

Also, regarding the scientific method: it is a free internet, so you can choose whatever formulation of the scientific method as your personal preference. But you can't cange reality or history with opinion. The reality is that the vast majority of professional scientists require the use of logic and the history is that even Newton's contemporaries agreed. So you can choose to believe in unicorns if you wish, but that choice has no value outside your head.

 

[rbj]

regarding String Theory or M-Theory, are they metaphysics, religion, or flubnubitz? is it experimentally testable (i think the right word might be "falsifiable")?

That's a different topic.

so was it a different topic when you said

To me, an axiom that is not testable is metaphysics, religion, or flubnubitz.

?

You misunderstand the concept of absolute time and space. You are thinking of time duration as being invariant. One second on the Earth = one second at Pluto's orbit = one second on a spacecraft going at 100c (there is no speed of light limit in Newtonian mechanics). That is not absolute time. Absolute time has duration as an invariant plus a fixed point in time, presumably the moment God began creation, designated as T=0. Absolute space similarly has deeply religious undertones. Per Newton, both absolute time and absolute space are for the most part hidden from us mortals. And yes, Newton did think that way. He was deeply, deeply religious, even by the standards of his time. In a sense, Newton wasn't the first scientist; he was the last magician.

i don't see the difference between absoluteness regarding time intervals (for every observer in every reference frame) and simply following those ticks back in time to some time defined as the origin. who defines the origin and where it is defined is immaterial to Newtonian mechanics (only time differences exist in Newtonian mechanics). but the (ostensible) fact that all of our clocks tick at the same rate, independent of the frame of reference is not immaterial, and, as humans found out a century ago, was a mistaken notion.

the fact that Newton was religious (or an alchemist) is non sequitur. what i thought was the topic was how could have Newton been so "unscientific" to take as an axiom that your clock ticks the same as mine (from my POV) independent of the motion of your clock relative to me. it's mistaken (as we know now), an invalid axiom, but it came from observation of reality in a world where nothing of substance (that people could watch and draw inference from) moved, relative to anything else, at anything close to relativistic speeds.

it would be, as best as i can tell, a perfectly reasonable axiom for Newton and his contemporaries to make. after Michaelson, then it becomes a little more questionable as an axiom. and for Einstein to understand it as he had, purely from thought experiment, does not reflect poorly on Newton's scientific method but only on Einstein's singular genius.

 

[Dale]

harrylin, I did notice earlier that you seem to like Popper for your philosophy of science. As you say, it is a matter of taste and philosophy, but you may want to look into his concept of falsifiability. His statements may be something we can both agree on as a premise. One commonality with intelligent design, undetectable unicorns, Lorentz's aether, and Newton's absolute frame is that none of them are falsifiable.

 

[harrylin]

Considering that this issue of "philosophy and taste" (or as I called it, "logic") is the entire issue being discussed, I'd say it matters quite a lot. Again, it is your thread/question: if you didn't want to discuss it, you shouldn't have.

The scientific method requires more than just a positive result to an experiment. How you get from point a to point b matters, as does interpretation of the result beyond the equation. That should be obvious: if it didn't matter, there'd be no reason to write a paper about it!

Negative experimental results matter just as much; thanks to this discussion which is on another topic, I took Popper out of the book shelve. Anyway, in view of your reaction I won't even mention topics to you that differ from the discussion topic.

 

[harrylin]

harrylin, I did notice earlier that you seem to like Popper for your philosophy of science. As you say, it is a matter of taste and philosophy, but you may want to look into his concept of falsifiability. His statements may be something we can both agree on as a premise. One commonality with intelligent design, undetectable unicorns, Lorentz's aether, and Newton's absolute frame is that none of them are falsifiable.

Sorry Dalespam, but that's wrong again: we are not concerned with an illusionary "absolute truth" of models, instead we are concerned with testing one hypothesis against another; and we already discussed in this thread how this was applied by Newton. If one hypothesis or model predicts observation A and another one predicts observation B, then commonly it's accepted that these hypotheses are falsifiable and can be tested against each other. However, you already disagree on that fundamental point.

 

[Dale]

Sorry Dalespam, but that's wrong again: we are not concerned with an illusionary "absolute truth" of models, instead we are concerned with testing one hypothesis against another; and we already discussed in this thread how this was applied by Newton. If one hypothesis or model predicts observation A and another one predicts observation B, then commonly it's accepted that these hypotheses are falsifiable and can be tested against each other. However, you already disagree on that fundamental point.

Huh?!? I think we must be talking past each other.

I don't disagree with anything you said, except that Newton's ideas of absolute velocity and position do NOT predict any different observations. Newton was clearly aware of that in his writings, particularly in the Scholium that you cited. That is why those ideas are non-scientific, per my criteria and per Popper's falsifiability criterion.

 

[harrylin]

Also, regarding the scientific method: it is a free internet, so you can choose whatever formulation of the scientific method as your personal preference.

I already clarified that I did not do that; I will thus take it that you talk about yourself.

But you can't cange reality or history with opinion. The reality is that the vast majority of professional scientists require the use of logic and the history is that even Newton's contemporaries agreed. So you can choose to believe in unicorns if you wish, but that choice has no value outside your head.

Nobody here suggest that science is illogical - and I can't help it if you believe in unicorns either! For a last time: please make your case - not just loose remarks - to show that Newton's theoretical development is "illogical". Then your argument can be discussed, just as we discuss the arguments from people who pretend that Einstein's theoretical development is illogical.

 

[harrylin]

Huh?!? I think we must be talking past each other.

I don't disagree with anything you said, except that Newton's ideas of absolute velocity and position do NOT predict any different observations. Newton was clearly aware of that in his writings, particularly in the Scholium that you cited. That is why those ideas are non-scientific, per my criteria and per Popper's falsifiability criterion.

I have noticed that in many discussions with others I just do not have enough patience or long-windedness (or perhaps just really not enough time!) to clarify things to the point that people finally "get" it, and in such cases it's often you (or ghwellsjr) who, with three times as much posts of double the length, finally manage to make things sufficiently clear to those people. Regretfully you cannot take up that role here, as you are on the other side of the discussion. So, I must simply ask you, what was not clear in my posts #4 and #6? For there I really thought to have:
1. provided the link to Newton's falsification of the model of Galileo-Leibniz, and which he replaced with his own model.
2. pointed out that he thus compared two models, one of which was falsified in favour of the other.
Surely I don't have to explain to you that if Galileo was right, such experiments and many others would falsify Newton's model?

 

[Dale]

I really thought to have:
1. provided the link to Newton's falsification of the model of Galileo-Leibniz, and which he replaced with his own model.
2. pointed out that he thus compared two models, one of which was falsified in favour of the other.
Surely I don't have to explain to you that if Galileo was right, such experiments and many others would falsify Newton's model?

But neither of those are relevant to the falsifiability of Newtons absolute position and absolute velocity concepts. Falsifiability is intrinsic to a theory and has nothing to do with comparing one theory to another. The fact that Galileo-Leibniz had a theory which was falsified is irrelevant to the question of the falsifiability of Newtons assumption.

Newtons assumption of absolute velocity and absolute position is non falsifiable in it's own right because there is no observation which could disprove it. Therefore it is non scientific according to Poppers criterion. The rest is irrelevant.

 

[Ken G]

I'm a bit unclear on exactly what claims are being discussed here. Surely Newton's postulate of absolute time and space were perfectly scientific concepts, and they did indeed turn out to be falsifiable. What's more, it is arguable that they also satisfied Occam's Razor (never perfectly clear, but arguable what that entails), because they were consistent with known observations and explained the shape of water in a spinning bucket in a way that was simpler than other ways (like Mach's principle applied to general relativity). Were there not observational evidence in favor of GR, no one would adopt the latter approach (the approach that spacetime does not have a global a priori geometry, but rather a local geometry that can be expressed in any global coordinate system that expresses the correct local curvature and which responds to the history of the situation rather than being a priori). To me, the real crux of the question of absolute space and time is whether space and time are global or local concepts, and making them global would always seem to be an advantage if it was possible. Newton had only data that suggested it was possible-- we know today it isn't. Locally, the geometry of spacetime is determined by the inertial paths, and that is as close to anything "absolute" as we can get, but it's not particularly clear that being able to identify inertial paths requires that anything be absolute, because there's nothing more absolute about an inertial path than a noninertial one-- you don't know what either are until you have the global solution of the Einstein equations, so you need to know the mass distributions, boundary conditions, history, etc. But once you know all that, a spinning bucket is "absolutely" non-inertial, so I don't think we should say Newton was wrong, merely that his ideas were not sophisticated enough to treat the full situation. What else is new? That's typical of perfectly good science, it doesn't necessarily have anything to do with magic or religion.

 

[Dale]

Surely Newton's postulate of absolute time and space were perfectly scientific concepts, and they did indeed turn out to be falsifiable.

We have been discussing the concepts of absolute space and absolute velocity, but absolute time suffers the same non-falsifiability problem.

Consider two hypothetical universes in which Newton's laws hold. They are identical except that one is 10 m up, 3 m forward, 13 m left, and 5 s later wrt its absolute space and time than the other. What experiment could inhabitants of those universes do in order to determine which universe they were in?

Locally, the geometry of spacetime is determined by the inertial paths, and that is as close to anything "absolute" as we can get, but it's not particularly clear that being able to identify inertial paths requires that anything be absolute, because there's nothing more absolute about an inertial path than a noninertial one-- you don't know what either are until you have the global solution of the Einstein equations, so you need to know the mass distributions, boundary conditions, history, etc. But once you know all that, a spinning bucket is "absolutely" non-inertial

Agreed, but it is not relevant. We agree that there are a class of frames which share the same acceleration. These frames are called inertial frames, they are equivalent for the purposes of Newtonian physics, and they are related to one another via the Galilean transform. What is under dispute is whether or not selecting one of those frames and giving it preferred status in the theory is scientific given the fact that they are experimentally equivalent.

so I don't think we should say Newton was wrong, merely that his ideas were not sophisticated enough to treat the full situation. What else is new? That's typical of perfectly good science, it doesn't necessarily have anything to do with magic or religion.

The problem isn't being wrong. You can make a wrong hypothesis and still be doing completely good science. The problem is being unscientific. You may be right and still be unscientific. Newton's concepts of absolute space and absolute velocity are unfalsifiable and therefore unscientific.

This is not to demean Newton, science itself was brand new at the time and the scientific method hadn't been refined like it is today. But we need to recognize that even the greatest scientist of all time (IMO) was a fallible man and not some infallible prophet. He was limited not only by his data and experimental equipment, but also by his philosophical preconceptions. With the added benefit of his genius and several centuries of subsequent study, we should be able to recognize and accept those small limitations.

 

[harrylin]

Which words am I putting in your mouth?

OK then, since you insist to go on making an off-topic claim about my opinion which is the exact opposite of my opinion, I will clarify this in a new thread on your topic.

 

[harrylin]

[..] These frames are called inertial frames, they are equivalent for the purposes of Newtonian physics, and they are related to one another via the Galilean transform. [..]

I already remarked that, apparently, no hypothesis about such frames existed; that concept was developed based on Newton's theory. Nothing exists in the world that could have served him as logical basis for a physical model of "inertial frames".
And since you spoke of unicorns: here is a real unicorn that you try, after-the-fact, to impose on Newton: it would not make any sense to propose a space with respect to which one does not have velocity and position!

PS. "What is under dispute is whether or not selecting one of those frames and giving it preferred status in the theory is scientific".
Instead: we have not even discussed that point - and it is a misrepresentation of Newton's hypothesis, he did no such thing. Perhaps this whole discussion was due to a misunderstanding of what Newton was dealing with; but I thought to have clarified that in post no. #35 and, even more, #43

 

[harrylin]

[..] Newtons assumption of absolute velocity and absolute position is non falsifiable in it's own right because there is no observation which could disprove it. Therefore it is non scientific according to Poppers criterion. The rest is irrelevant.

It would certainly be unreasonable to demand that every logical consequence of a hypothesis should be falsifiable. And contrary to what you claim, Popper did not agree with your "positivist" thinking, as he called it. Here is how Popper formulated his criterion in chapter 6:

"It must be possible for an empirical scientific system to be refuted by experience".

That was certainly not a mistake of formulation, for earlier, in chapter 4, he elaborated as follows:

"it may be said [..] that I remove the barriers which separate science from metaphysical speculation.
[..]
The older positivists wished to admit, as scientific or legitimate, only those concepts [..] which were [..] 'derived from experience'; [..] that is, which they believed to be logically reducible to elements of sense-experience [...].
Modern positivists [...] wish to admit [..] only those statements which are reducible to elementary [..] statements of experience [..]. I must also reject all these attempts to solve the problem of demarcation. [...] positivists, in their anxiety to annihilate metaphysics, annihilate natural science along with it".

I thus found strong disagreement with your suggestion that since some but not all logical consequences of Newton's "absolute space" model can be verified in their own right, that therefore that model is non-scientific according to Popper's criterion.

 

[harrylin]

I'm a bit unclear on exactly what claims are being discussed here. Surely Newton's postulate of absolute time and space were perfectly scientific concepts, and they did indeed turn out to be falsifiable. What's more, it is arguable that they also satisfied Occam's Razor (never perfectly clear, but arguable what that entails), because they were consistent with known observations and explained the shape of water in a spinning bucket in a way that was simpler than other ways (like Mach's principle applied to general relativity). [..]

I agree; and I now came with suggestions for possible causes (positivistic philosophy or a misunderstanding of the status quo at the time of Newton) in the foregoing posts.

To me, the real crux of the question of absolute space and time is whether space and time are global or local concepts, and making them global would always seem to be an advantage if it was possible. Newton had only data that suggested it was possible-- we know today it isn't. [..]

Yes indeed, it seems to me that Newton made the simplest assumptions that he could think of and that were consistent with the data that he had.

But once you know all that, a spinning bucket is "absolutely" non-inertial, so I don't think we should say Newton was wrong, merely that his ideas were not sophisticated enough to treat the full situation. What else is new? That's typical of perfectly good science, it doesn't necessarily have anything to do with magic or religion.

Well, his way of thinking way was certainly affected by his religion, but not such that it made him illogical, as some people seem to think. And insofar as religion played a role in his creative thinking we should say happily so, as the result was a very useful theory that even today is still in use.

 

[Dale]

harrylin, I like and respect you, so I am going to drop out of the conversation at this point. I feel that it is getting emotional, which I don't usually mind when dealing with crackpots but I do mind here since here I am dealing with someone whom I respect and who is clearly not a crackpot.

You and I have a substantive disagreement about science and about Newton's absolute space concept, but frankly I don't think that the slim possibility of reaching agreement is worth the high possibility of damaging either of our experiences on PF.

 

[Russell E]

I agree with Russ that this is getting tedious: several people continue to make the empty claim that Newton could have omitted one of his postulates without consequence for his theory, without actually even trying to show it. Please, stop with arguing on the side and try to show that this can be done without introducing a different hypothesis instead of the one that he chose, or admit that you were mistaken.

None of Newton's definitions or postulates refer to absolute rest. To the contrary. He starts with 8 Definitions and 3 Laws. Definitions 3 and 4 and Law 1 refer to "rest", but in all three cases Newton qualifies it:

Definition 3: Inherent force of matter is the power of resisting by which every body, so far as it is able, peseveres in its state either of resting or of moving uniformly straight forward.

Definition 4: Impressed force is the action exerted on a body to change its state either of resting or of moving uniformly straight forward.

Law 1: Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.

These definitions and laws (along with the others, that don't mention "rest") are the basis of Newton's mechanics, and they very explicitly do NOT distinguish between rest and uniform motion in a straight line, so obviously Newton's mechanics is NOT based on the notion of absolute rest, as he explicitly re-affirmed many times.

His comments in the general Scholium about absolute space and time (as distinct from absolute rest or absolute motion) are not referred to in the rest of the Principia, until Book 3 (The System of the World), and they do not constitute postulates, and in any case they have a completely different meaning than what you seem to think. Essentially Newton was trying to identify the center of mass of the solar system (which he called the system of the world), about which not only the planets but also the Sun revolve. But he acknowledges that we can't even call the center of mass of the solar system absolutely at rest except by stipulation, since it could just as well be moving uniformly in a straight line. We simply hypothesize that it is at rest for talking purposes (but of course we now know that hypothesis is wrong - the center of mass of our solar system is not even perfectly inertial, and hardly anyone would claim it is absolutely at rest or the center of the universe, as it was thought to be in Newton's day). There's a discussion of Newton's ideas toward the end of this web page:
http://www.mathpages.com/rr/s4-01/4-01.htm

 

[harrylin]

harrylin, I like and respect you, so I am going to drop out of the conversation at this point. I feel that it is getting emotional, which I don't usually mind when dealing with crackpots but I do mind here since here I am dealing with someone whom I respect and who is clearly not a crackpot.

You and I have a substantive disagreement about science and about Newton's absolute space concept, but frankly I don't think that the slim possibility of reaching agreement is worth the high possibility of damaging either of our experiences on PF.

I agree as we seem to have reached a dead end, related to slightly different philosophies.

Meanwhile ZapperZ moved the discussion about the scientific method to the Social Sciences forum; I'm afraid that just like me, most physicists who think that it's an important topic for physics will never look for such a topic there!

 

[harrylin]

None of Newton's definitions or postulates refer to absolute rest.
To the contrary. He starts with 8 Definitions and 3 Laws. Definitions 3 and 4 and Law 1 refer to "rest", but in all three cases Newton qualifies it:

Definition 3: Inherent force of matter is the power of resisting by which every body, so far as it is able, peseveres in its state either of resting or of moving uniformly straight forward.

Definition 4: Impressed force is the action exerted on a body to change its state either of resting or of moving uniformly straight forward.

Law 1: Every body perseveres in its state of being at rest or of moving uniformly straight forward except insofar as it is compelled to change its state by forces impressed.

These definitions and laws (along with the others, that don't mention "rest") are the basis of Newton's mechanics, and they very explicitly do NOT distinguish between rest and uniform motion in a straight line, so obviously Newton's mechanics is NOT based on the notion of absolute rest, as he explicitly re-affirmed many times.

Russell thanks for joining in (I first thought that you were Russ, giving a more detailed comment!).

Perhaps you did not see my comments in posts #35 and #43. If you disagree, please clarify how you think "straight forward" is defined:
- in Galileo's model (if at all)
- in Newton's model.

His comments in the general Scholium about absolute space and time (as distinct from absolute rest or absolute motion) are not referred to in the rest of the Principia, until Book 3 (The System of the World), and they do not constitute postulates, and in any case they have a completely different meaning than what you seem to think.

Essentially Newton was trying to identify the center of mass of the solar system (which he called the system of the world), about which not only the planets but also the Sun revolve. But he acknowledges that we can't even call the center of mass of the solar system absolutely at rest except by stipulation, since it could just as well be moving uniformly in a straight line. We simply hypothesize that it is at rest for talking purposes (but of course we now know that hypothesis is wrong - the center of mass of our solar system is not even perfectly inertial, and hardly anyone would claim it is absolutely at rest or the center of the universe, as it was thought to be in Newton's day). There's a discussion of Newton's ideas toward the end of this web page:
http://www.mathpages.com/rr/s4-01/4-01.htm

Thanks for that link, it provides an interesting discussion! And that discussion is certainly useful as it cites some interesting passages. Even more, IMHO he gives the correct answer to the second question (with a suggested answer to the first one) that I just posed to you here above. In his words:

"It was essential for Newton to make sure his readers understood that "uniform motion" and "right lines" cannot generally be judged with reference to neighboring bodies (such as the Earth's spinning surface), because those bodies themselves are typically in non-uniform motion. Hence he needed to convey the fact that the seat of inertia is not the Earth's center, nor the Sun’s, nor any other material body, but is instead absolute space and time in precisely the same sense that spacetime is absolute in special relativity. "

I have the impression that most disagreement in the different discussions was strongly related to that point, on which I happen to agree with Kevin Brown. It appears that you disagree that it was essential and necessary to invent such a hypothesis, based on the experimental evidence.

PS. As a matter of fact, I had in mind to make the comparison with Minkowski's spacetime model; but now I don't need to, as it's already given in your reference.

 

[Russell E]

Perhaps you did not see my comments in posts #35 and #43. If you disagree, please clarify how you think "straight forward" is defined:
- in Galileo's model (if at all)
- in Newton's model.

If your interest is historical, it's well known that the historical Galileo was somewhat inconsistent in his articulation of the principle of inertia (i.e., the principle of relativity) that is commonly associated with his name. In particular, when discussing celestial motions he still sometimes said that motion in a circle could be "inertial", since a circle has a "perfect" form, and there would be no reason for an object to deviate from a circular path. It was only his immediate successors (especially Gassendi) who "interpreted and clarified" the meaning of Galileo's concepts and began to make consistent statements about uniform rectilinear motion. (And it wasn't until even later that people clarified the circular nature of such assertions, and how they serve as definitions as well as laws.) But Galileo certainly pointed the way clearly enough in most of his writings about sub-lunary phenomena to be credited with the principle of inertial relativity. It remained for Newton to show that this same principle also accounts for celestial motions (like the motion of the Moon), provided we introduce a new and very simple universal force - the very same force that causes an apple to fall from the tree, and let this force drop off as the inverse square of distance and extend all the way to the Moon. But that is historical. From the modern standpoint, what we call Galilean relativity (which Galileo DID articulate clearly enough for sub-lunary phenomena) based on the principle of inertia is the basis for Newtonian mechanics.

"It was essential for Newton to make sure his readers understood that "uniform motion" and "right lines" cannot generally be judged with reference to neighboring bodies (such as the Earth's spinning surface), because those bodies themselves are typically in non-uniform motion. Hence he needed to convey the fact that the seat of inertia is not the Earth's center, nor the Sun’s, nor any other material body, but is instead absolute space and time in precisely the same sense that spacetime is absolute in special relativity. [This is distinct from asserting an absolute state of rest, which Newton explicitly recognized as a matter of convention. [restored the crucial sentence in bold that was, inadvertently one assumes, omitted from the quote]"

I have the impression that most disagreement in the different discussions was strongly related to that point, on which I happen to agree with Kevin Brown. It appears that you disagree that it was essential and necessary to invent such a hypothesis, based on the experimental evidence.

I haven't seen a clear statement in this thread of what precise hypothesis you are arguing about (which may be why the argument goes on so long), but my impression is that you're conflating two very different sets of alternative hypotheses. One is the hypothesis of an absolute state of rest, and hence absolute motion. This is in opposition to the principle of relativity - both Galilean/Newtonian and Minkowskian, according to which there is no distinction between a state of rest and a state of uniform motion in a straight line (all defined based on the principle of inertia). Another hypothesis is relationism as advocated by Leibniz and Mach, which attempts to dispense with absolute inertia and attribute everything to the relations between substantial entities. This too is in opposition to the absolute space-time conception on which the principle of relativity - both Galilean/Newtonian and Minkowskian - is founded, which simply accept the existence and identifiability of inertial coordinate systems, without trying to attribute inertia to interactions between substantial entities. (The two could be reconciled without much trouble, though.)

If you asserted that the theory of relativity (both Galilean/Newtonian and Minkowskian) is founded on the principle of absolute space-time as opposed to the relationism of Leibniz and Mach, then you would be espousing a well known and uncontroversial fact, and probably wouldn't get into these arguments.

But at times you seem to be saying that the theory of relativity (at least the Newtonian variety) is founded on the concept of absolute MOTION, i.e., the existence of absolute rest (regardless of whether or not this can be detected). This is plainly wrong. No such concept is invoked in the development of Newtonian mechanics, as explained in the previous post. Newton explicitly and scrupulously ALWAYS follows the words "at rest" with the words "or moving uniformly in a straight line". His discussion of absolute space and time in the Principia, begun in the first Scholium, does not support (and was not intended to support) the claim that mechanics relies on the assumption of an absolute rest. It concludes in book 3, where it merely leads Newton to the conclusion that the center of mass of the solar system is at rest OR moves uniformly in a straight line. It could not do otherwise, because his definitions and postulates explicitly identify those states.

Then, since (Newton believed) the center of the solar system is the center of the cosmos, we could all agree (if we wish) to call it "at rest" - but this is no more than a linguistic convention (based on incorrect astronomical facts, by the way, since the COM of the solar system really isn't exactly inertial), of no significance for the development or functioning of Newtonian mechanics. It hardly even rises to the level of being metaphysical, because there is not even any conceptual commitment behind it. The important concept that Newton was trying to convey, as explained in the web page passage you quoted, is the concept of absolute space(time), i.e., the principle of inertia, not the concept of absolute rest. The latter has no meaning at all in the context of relationism, and at most only a metaphysical meaning in the context of relativity.

 

[Ken G]

Consider two hypothetical universes in which Newton's laws hold. They are identical except that one is 10 m up, 3 m forward, 13 m left, and 5 s later wrt its absolute space and time than the other. What experiment could inhabitants of those universes do in order to determine which universe they were in?

I don't believe that has much to do with the concepts of absolute time and space, that has to do with a distinguishable origin. Newton's absolute time and space could still be affine and the same issues would arise. I don't think Newton much cared if there was a spatial origin, nor does the spinning bucket have anything to do with that.

Newton's laws only work for inertial observers, so singling them out is the physical content of the concepts of absolute time and space. Einstein felt the principles of physics should apply for any observer, not just inertial ones, and that is the insight at the heart of general relativity. In Einstein's approach, noninertial motion is still distinguishable from inertial motion, but the laws of physics work fine for either type of observer, and what singles out inertial motion is a dynamic variable that depends on the history of the region, rather than being an a priori notion the way it is with absolute time and space. This is the key difference between Newton and Einstein, not the identification of an origin of the coordinates. It has to do with whether or not global coordinates are physically meaningful (as they are in an affine space, regardless of origin), or if only local coordinates correspond to the observables (as in spacetime with dynamical curvature)-- that's the essential issue of absolute spacetime. It's whether physics can be axiomatized globally or only locally.

Action at a distance has a similar flavor, and perhaps Newton's distaste for action at a distance should have led him to a similar distaste for absolute space, but the spinning bucket convinced him otherwise. Note that even today we often encounter theories that allow for absolute space (like aether theories)-- but not an absolute origin, the space is always affine.

What is under dispute is whether or not selecting one of those frames and giving it preferred status in the theory is scientific given the fact that they are experimentally equivalent.

But I don't believe Newton ever did any such thing. Where did Newton ever give preference to one inertial frame over another? Certainly none of his laws do. I believe what Newton meant by "absolute space" was simply an a priori and global determination of what constituted inertial motion, such that no equations of physics would ever be needed to establish inertial frames-- the inertial frames were the "background" of Newtonian physics. Liebnitz felt that all motion had to be relative, so whether an object was moving inertially or not could not have an absolute a priori meaning, it had to emerge from its motion relative to other things, i.e., it had to be a dynamical variable. That's essentially what Einstein did-- he made what constitutes inertial motion a dynamical variable, that's the alternative to absolute space.

Newton's concepts of absolute space and absolute velocity are unfalsifiable and therefore unscientific.

I don't think so. Are you saying that Newton's concepts of absolute space and absolute velocity have not been falsified, even today? I don't think that's what Newton meant by these concepts-- I think he meant global a priori established inertial motion, as opposed to the dynamical variable we have in general relativity. I think Newton's picture has indeed been falsified, so it could not have been unfalsifiable, so it could not have been unscientific.

This is not to demean Newton, science itself was brand new at the time and the scientific method hadn't been refined like it is today. But we need to recognize that even the greatest scientist of all time (IMO) was a fallible man and not some infallible prophet.

I agree. And it is well known that Newton had a strong mystic bent. So did Kepler and Faraday and many others, and perhaps one day Einstein will be counted a mystic for holding that God doesn't roll dice. Today's great scientist is tomorrow's mystic, I do see Newton as fallible but I don't see any of his physics ideas as unscientific. Perhaps there is some particular aspect of his writings on absolute space I am not aware of, I know more about his debates with Liebnitz on the subject, and of course the spinning bucket.

 

[harrylin]

If your interest is historical, it's well known that the historical Galileo was somewhat inconsistent in his articulation of the principle of inertia (i.e., the principle of relativity) that is commonly associated with his name.

Until this discussion I didn't know enough much about Galileo's model; and thanks for providing more background! This thread is a continuation of a discussion of historical criticism on Newton that was started in the relativity forum.

In particular, when discussing celestial motions he still sometimes said that motion in a circle could be "inertial", since a circle has a "perfect" form, and there would be no reason for an object to deviate from a circular path. It was only his immediate successors (especially Gassendi) who "interpreted and clarified" the meaning of Galileo's concepts and began to make consistent statements about uniform rectilinear motion. (And it wasn't until even later that people clarified the circular nature of such assertions, and how they serve as definitions as well as laws.) But Galileo certainly pointed the way clearly enough in most of his writings about sub-lunary phenomena to be credited with the principle of inertial relativity. It remained for Newton to show that this same principle also accounts for celestial motions (like the motion of the Moon), provided we introduce a new and very simple universal force - the very same force that causes an apple to fall from the tree, and let this force drop off as the inverse square of distance and extend all the way to the Moon. But that is historical. From the modern standpoint, what we call Galilean relativity (which Galileo DID articulate clearly enough for sub-lunary phenomena) based on the principle of inertia is the basis for Newtonian mechanics.

The disagreement that this thread started with was probably related to insufficient understanding of the fact that while Newtonian mechanics inherited a lot from Galilean mechanics, Galileo's relativity did not work well so that it could not serve as basis for Newton's relativity.

I haven't seen a clear statement in this thread of what precise hypothesis you are arguing about (which may be why the argument goes on so long), but my impression is that you're conflating two very different sets of alternative hypotheses.

In a nutshell: There was criticism on the logic of Newton's theoretical development of his theory. It was claimed that "Newton should have found an experimental violation of his theory of mechanics to justify his absolute space postulate", or that "there [was] no basis for assuming [this] nor any value in making the assumption" .

In contrast, I agree with Kevin Brown that Newton had to clarify that "uniform motion" and "right lines" cannot generally be judged with reference to neighboring bodies such as that of the Earth (or the rotating bucket).
Newton thus came up with a very abstract model that he called "absolute space"; I'm pretty sure that without a model for defining straight line motion, no construction of a physical theory of mechanics is possible. If you disagree, please show how this can be done.

One is the hypothesis of an absolute state of rest, and hence absolute motion. This is in opposition to the principle of relativity - both Galilean/Newtonian and Minkowskian, according to which there is no distinction between a state of rest and a state of uniform motion in a straight line (all defined based on the principle of inertia).

You seem to think that Newton contradicted himself in a rather silly way (and for centuries nobody noticed?). However, it is commonly thought that Newtonian relativity directly and logically follows from his hypotheses and laws. Perhaps you understand some of his definitions differently from me (and most others). To illustrate how I understand his definitions: Let's say for example that Atlantis exists somewhere under the ocean. Is it logical to make such a hypothesis without implying that, taking Atlantis as reference, one can be in a state of rest or motion?

On a side note, there have been similar discussions in the relativity forum concerning Lorentzian relativity, for example (from post 20):
- https://www.physicsforums.com/showthread.php?t=554741&highlight=absolute+frame&page=2
And a current one that is related to it (see my post number #34):
- https://www.physicsforums.com/showthread.php?t=595021&page=3

Another hypothesis is relationism as advocated by Leibniz and Mach, which attempts to dispense with absolute inertia and attribute everything to the relations between substantial entities. This too is in opposition to the absolute space-time conception on which the principle of relativity - both Galilean/Newtonian and Minkowskian - is founded, which simply accept the existence and identifiability of inertial coordinate systems, without trying to attribute inertia to interactions between substantial entities. (The two could be reconciled without much trouble, though.)

Thus you disagree even in principle with Einstein who at first thought that GR was consistent with Mach? Anyway, that is definitely off-topic here and we can't blame Newton for [STRIKE]choosing[/STRIKE] inventing a simpler model that matched experience.

If you asserted that the theory of relativity (both Galilean/Newtonian and Minkowskian) is founded on the principle of absolute space-time as opposed to the relationism of Leibniz and Mach, then you would be espousing a well known and uncontroversial fact, and probably wouldn't get into these arguments.

More or less so: obviously Newton's relativity is based on such a model. I do think that I as well as Kevin Brown expressed a well known and uncontroversial fact: for a theory of motion, one needs to define a reference - be it absolute space, absolute space-time, an infinite set of inertial frames, the Earth, a bucket, or whatever.

But at times you seem to be saying that the theory of relativity ([..] the Newtonian variety) is founded on the [..] existence of absolute rest (regardless of whether or not this can be detected). This is plainly wrong. [..] His discussion of absolute space and time in the Principia, begun in the first Scholium, does not support (and was not intended to support) the claim that mechanics relies on the assumption of an absolute rest.
[..]
The important concept that Newton was trying to convey, as explained in the web page passage you quoted, is the concept of absolute space(time), i.e., the principle of inertia, not the concept of absolute rest. The latter has no meaning at all in the context of relationism, and at most only a metaphysical meaning in the context of relativity.

As I now hope to have clarified, as I see it, Newton's concept of "absolute rest" is a logical consequence of his hypothesis of the existence of "absolute space". Thus in my eyes it's just a quarrel over words that you have with Newton, and I will not get into such arguments.

 

[Ken G]

I would say that I see no reason to think Newton believed in a concept of "absolute rest", nor is not notion required to have a concept of absolute space. (Note that Newton's explanation for the shape of the water in a spinning bucket works fine if the bucket has a constant velocity, for example.) Absolute space means that inertial paths are known by axiom-- in essence, space has an a priori global geometry that is not a dynamical variable, so precedes physics as a kind of geometrical background on which physics is defined, rather than being something that itself is described by physics. That is what Newton used the concept for, and motivates his laws (which only apply for inertial observers, a globally defined set of observers with no relative acceleration for whom Newton's laws hold good and who have no external forces on them). This was a scientific hypothesis which is falsified by the need for general relativity, in which inertial paths are a dynamical variable also and cannot be known a priori or absolutely, but instead result from the solution of local differential equations subject to boundary conditions that depend on the history of the region (i.e., on time as well as space).

This all comes down to the key question: how does a particle with no forces on it know how to move relative to an observer who also experiences no forces? Newton's first law answers this with a global axiom that does not arise from any of the other laws (it is often erroneously claimed that the first law is a subset of the second, missing the point of the first law). Einstein removes the first law, and includes it in the dynamics of the rest of the laws of motion. It is enforced by an arbitrary boundary condition, rather than by its own axiom. That is the difference between absolute space and a purely local version of the meaning of space.

 

[Russell E]

... while Newtonian mechanics inherited a lot from Galilean mechanics, Galileo's relativity did not work well so that it could not serve as basis for Newton's relativity.

Not true. Newtonian mechanics is based solidly on what is commonly called Galilean relativity (even though it wasn't entirely Galileo who formulated it). The problem here is that you've mis-interpreted the meaning and significance of "absolute space" in Newton's theory. It refers to the absoluteness of acceleration, not the absoluteness of either position or velocity.

In a nutshell: There was criticism on the logic of Newton's theoretical development of his theory. It was claimed that "Newton should have found an experimental violation of his theory of mechanics to justify his absolute space postulate"

That's just a mass of non-sequiturs. Again, the only sense of "absolute space" that Newton postulated was the sense of absolute acceleration, not absolute position or velocity. This is the foundation of his mechanics, and this is perfectly consistent with his discussion of "absolute space and time". I gave you Newton's definitions and postulates previously, and pointed out that they explicitly treat "rest" and "moving uniformly in a straight line" as equivalent. You seem to think that Newton's postulates for his mechanics include a postulate of the existence of absolute rest, but you are unable to point to any such postulate, whereas I have cited his actual postulates that say just the opposite of what you claim. I think that makes the matter fairly clear.

Newton had to clarify that "uniform motion" and "right lines" cannot generally be judged with reference to neighboring bodies such as that of the Earth (or the rotating bucket).

Right, and please note that deviations from "uniformity" (i.e., changes in speed) or "rightness" (i.e., changes in direction) are accelerations. They do not depend on any absolute position or velocity, which is why the absolute space (and time) of Newtonian mechanics does not include any concept of absolute position or velocity (except as we may agree by convention, e.g., to regard the center of mass of the solar system as the absolute resting center of the cosmos).

Newton thus came up with a very abstract model that he called "absolute space"; I'm pretty sure that without a model for defining straight line motion, no construction of a physical theory of mechanics is possible. If you disagree, please show how this can be done.

Again that's just a mass of non-sequiturs. The identification of uniform rectilinear motion self-evidently does not entail the identification of absolute position or absolute velocity. Newton's absolute space establishes absolute uniform rectilinear motion, meaning that it provides the basis for evaluating absolute acceleration, but it does not establish any basis for absolute position or absolute velocity. Newton says this himself many times, and it is explicit in his definitions and postulates.

You seem to think that Newton contradicted himself in a rather silly way...

No, I think Newton was admirably clear and self-consistent. I think you totally misunderstand and misrepresent him, claiming that he postulated absolute position and absolute velocity as the basis of his mechanics, when he clearly did no such thing. Please review the definitions and postulates at the beginning of Principia.

To illustrate how I understand his definitions: Let's say for example that Atlantis exists somewhere under the ocean. Is it logical to make such a hypothesis without implying that, taking Atlantis as reference, one can be in a state of rest or motion?

Forgive me, but I can't parse those words into anything that makes any kind of sense or has any relevance to the discussion. Am I to take those words as your attempt to show me that Newton postulated absolute position and absolute velocity in the Principia? It does not bear any resemblence to anything Newton said in the Principia (or anywhere else), nor does it imply or even suggest a postulate of absolute position or absolute velocity.

For a theory of motion, one needs to define a reference - be it absolute space, absolute space-time, an infinite set of inertial frames, the Earth, a bucket, or whatever.

Well, both Newtonian mechanics and special relativity are based on a sense of absolute space in which there is an equivalence class of inertia-based coordinate systems in terms of which all the laws of physics take their simplest (homogeneous and isotropic) form. In neither case does this entail absolute position or absolute velocity.

As I see it, Newton's concept of "absolute rest" is a logical consequence of his hypothesis of the existence of "absolute space".

Now you've reversed your position. Up until now you've been claiming that Newton postulated absolute rest, but now you're saying that YOU regard absolute rest as a logical consequence of Newton's theory (postulates). And you're attributing this inference to Newton as well. You're wrong on all counts, as has already been proven here. I gave you Newton's definitions and postulates, which explicitly exclude any distinction between rest and uniform motion in a straight line (which only specifies acceleration as absolute). And the only other mention of absolute position and velocity in the Principia comes in Book 3 where Newton described precisely what he means by "absolute rest" and absolute position, and reveals it to be a mere linguistic stipulation, to take the center of mass of the solar system as the resting center of the cosmos. But this verbal convention is given no justification - let alone a logical derivation. The only person who claims absolute rest is a logical consequence of Newton's theory is you, and yet you're strangely unable or unwilling to defend it by any rational argument. The closest you've come is some comments about Atlantis at the bottom of the ocean, which did not succeed in clarifying your reasoning.

In my eyes it's just a quarrel over words that you have with Newton, and I will not get into such arguments.

That's really an awful statement for you to make in this thread, that you yourself started. The whole point at issue is whether Newton's mechanics is based on, or logically implies, the existence of absolute position and absolute velocity. You've been shown that it does not, and that Newton never claimed it did. The argument here is not with Newton, it's with you, and it isn't over words, it is over the distinction between absolute acceleration versus absolute position and velocity.

 

[harrylin]

I would say that I see no reason to think Newton believed in a concept of "absolute rest", nor is not notion required to have a concept of absolute space.

That's surprising to me for two reasons:
1. He defined that term (and my following explanation is consistent with his definition);
2. He introduced a "space", the main purpose of which is to serve as reference for motion. If as you suggest, relative to it no rest (and thus no defined motion) is possible, then it looks much worse than proposing a unicorn: not only illogical but also useless. I gave a simple illustration with my Atlantis example of how I interpret it.

Absolute space means that inertial paths are known by axiom-- in essence, space has an a priori global geometry that is not a dynamical variable, so precedes physics as a kind of geometrical background on which physics is defined, rather than being something that itself is described by physics. [..]

I cannot find your model in Newton's description, so I fear that you are imagining things. The model that Newton invented was definitely much simpler, as you can read in the Principia (I provided a link).

 

[harrylin]

Not true. Newtonian mechanics is based solidly on what is commonly called Galilean relativity (even though it wasn't entirely Galileo who formulated it).

As I said: Galileo did not provide a correctly working reference.

The problem here is that you've mis-interpreted the meaning and significance of "absolute space" in Newton's theory. It refers to the absoluteness of acceleration, not the absoluteness of either position or velocity.

I'm afraid that I can't answer to such a misunderstanding about the meaning words... I already explained how illogical and inconsistent that is, but the following part of Newton's explanation could help, perhaps:

[..] You seem to think that Newton's postulates for his mechanics include a postulate of the existence of absolute rest, but you are unable to point to any such postulate, [..]

That's wrong, and from your assertions I thought that you knew his Scholium. I already explained why there was no need for him to "postulate the existence of absolute rest" and I have no doubt about the fact that he defined it, as follows:

"IV. Absolute motion is the translation of a body from one absolute place into another [..] and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore if the Earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth"

Forgive me, but I can't parse those words into anything that makes any kind of sense or has any relevance to the discussion. Am I to take those words as your attempt to show me that Newton postulated absolute position and absolute velocity in the Principia? It does not bear any resemblence to anything Newton said in the Principia (or anywhere else), nor does it imply or even suggest a postulate of absolute position or absolute velocity.

My illustration showed you exactly the contrary: if you would postulate the existence of Atlantis, it would be silly to ask you to postulate that someone can have a position or motion with respect to it; however you could of course define those things. If that is not clear, then I'm afraid that it would demand a philosophical discussion in another forum on such basic things as position and motion, postulates, definitions, or even existence.

[..] Now you've reversed your position. Up until now you've been claiming that Newton postulated absolute rest, but now you're saying that YOU regard absolute rest as a logical consequence of Newton's theory (postulates).

I could have imprecisely included "absolute rest" in a sentence about his postulates but I now checked and didn't find it; perhaps you confused me with dalespam who did make that claim in post #7.

[..] this thread, that you yourself started. [..]

Don't shoot the messenger: when others made off-topic claims about Newton's absolute space postulate (or hypothesis) being illogical or unscientific I started a new thread for them, so that their ideas could be properly discussed. Einstein's relativity isn't the proper thread for that discussion.

 

[harrylin]

Those who initiated this discussion seem to have left and the ones who still follow it seem to agree that Newton was logical and scientific; that kind of ends the original discussion.

However, as there is disagreement about what Newton actually wrote, in particular about "space", it will certainly be useful to present and discuss possible logical and consistent interpretations of those words. Here is a hopefully not too bad translation:

"Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

I. Absolute, true, and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration: relative, apparent, and common time, is some sensible and external (whether accurate or unequable) measure of duration by the means of motion, which is commonly used instead of true time; such as an hour, a day, a month, a year.

II. Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies; and which is vulgarly taken for immovable space; such is the dimension of a subterraneaneous, an æreal, or celestial space, determined by its position in respect of the earth. Absolute and relative space, are the same in figure and magnitude; but they do not remain always numerically the same. For if the earth, for instance, moves, a space of our air, which relatively and in respect of the Earth remains always the same, will at one time be one part of the absolute space into which the air passes; at another time it will be another part of the same, and so, absolutely understood, it will be perpetually mutable."

- http://gravitee.tripod.com/definitions.htm (click on "cancel")

 

[Ken G]

That's surprising to me for two reasons:
1. He defined that term (and my following explanation is consistent with his definition);

What was Newton's definition of absolute rest?

2. He introduced a "space", the main purpose of which is to serve as reference for motion. If as you suggest, relative to it no rest (and thus no defined motion) is possible, then it looks much worse than proposing a unicorn: not only illogical but also useless.

THe most immediate thing that emerges from Newton's first law is that any observer or object in constant rectilinear motion with respect to another observer or object that is inertial, will also be inertial. Nothing about that situation dictates a need for a frame of absolute rest, nor is there any reason to imagine that a frame in constant motion with respect to a frame of absolute rest would be inertial. In other words, the first law has no logical basis from which it stems, it is purely a postulate, and it doesn't say anything more than it says, Note in particular that there is no law like "let there be a frame of absolute rest" in Newton's laws, because a law like that would have no use (in particular, it wouldn't explain the first law, so could not replace it). However, Newton did believe in "absolute space", but its only relevant meaning, in the context of his actual laws (which define his mechanics), is that inertial frames of reference are determined a priori by some logical necessity that rectilinear motion be inertial (that's the first law). Hence I equated the dynamically relevant notion of "absolute space" with "a global geometric constraint on what type of motion will make observers be able to use the laws of physics", i.e., it makes the attributes of space an axiom in the laws of physics, such that the laws may only be used by observers who have the particular relation of being in mutual rectilinear motion. Go back to his resolution of the spinning bucket-- there is no reference to an absolute frame of rest, there is only to a frame of absolute non-rotation (which is not at all the same thing, as it does refer to the first law, and a frame of absolute rest does not).

I cannot find your model in Newton's description, so I fear that you are imagining things.

I cite his First Law. That is what matters, not the picture he had in his head as he applied that law. A theory of physics is how it works, not how it is interpreted (witness quantum mechanics). Newton never put a frame of absolute rest into his laws, that much is clear enough.

 

[Ken G]

Those who initiated this discussion seem to have left and the ones who still follow it seem to agree that Newton was logical and scientific; that kind of ends the original discussion.

Yes, I agree that Newton's first law is completely scientific. However, the first law is not a claim on a frame of absolute rest. From your quote, it does appear that Newton chose to imagine an absolute frame of rest, perhaps similar to the aether of Lorentz, but he did not put it in his laws. That means he understood it was not necessary for his mechanics, and as I said, it did not explain the first law either. It was how Newton pictured the situation, but the simple fact that he did not place it among his laws makes it clear he knew that it was a dynamically sterile concept in the context of his own mechanics. The dynamically active concept, expressed in the first law, is the global inertial geometry that singles out rectilinear motion, borrowing from how Euclidean geometry axiomatizes straight lines. Thus what is "absolute" in Newton's actual laws is just the Euclidean geometry, which has no origin and no direction in spacetime that is singled out as a frame of absolute rest.

 

[Russell E]

As I said: Galileo did not provide a correctly working reference.

What do you think was Galileo's "reference", and what do you think was "incorrect" about it?

It's true that the Galilean transformation between inertial coordinate systems turned out to be wrong (inertial coordinate systems in which the laws of mechanics hold good in their isotropic and homogeneous form are actually related by Lorentz transformations), but Newton never realized this and certainly never corrected it. Also it has no bearing on whether Newtonian mechanics is based on or implies absolute rest, because both the Lorentz transformation and the Galilean transformation are equally relativistic.

Russell e wrote: "Newton's theory refers to the absoluteness of acceleration, not the absoluteness of either position or velocity."

I'm afraid that I can't answer to such a misunderstanding about the meaning words... I already explained how illogical and inconsistent that is...

I haven't seen your explanation, and frankly can't even imagine what such an explanation could consist of, unless you are making the truly silly mistake of thinking that absolute acceleration cannot have meaning in the absence of absolute position and absolute velocity.

Look, take Newton's second law as an example: F = ma. The "a" in that expression stands for acceleration. There is no x and no v in that expression, so it is manifestly indifferent to any absolute position and any absolute velocity. The same applies to each of Newton's definitions and laws, and Newton himself pointed this out. So it's beyond question that Newtonian mechanics is neither based on nor implies any physically meaningful notion of absolute position or absolute rest. If you agree with this, it would help the discussion immensely if you would say so. And if you disagree with it, it would help if you could bring yourself to articulate why you disagree.

the following part of Newton's explanation could help, perhaps...

Newton's comments in the first Scholium don't support your position, as has already been explained. He does indeed refer to absolute places, absolute rest, absolute motion, etc., first relative to the ship, but then noting that the ship could be moving (accelerating) relative to the Earth, and then noting that the Earth could actually be moving (accelerating) relative to the Sun, and then later (in Book 3) he notes that the Sun is moving (accelerating) relative to the center of mass of the solar system, and then he says [please pay attention to this:] "The center of mass of the solar system, by corollary 4 of the Laws, either will be at rest or will move uniformly straight forward." He says this because he regarded the solar system as isolated, so its center of mass couldn't be accelerating. So even at this stage he is explicitly acknowledging that his laws of mechanics don't distinguish between rest or uniform motion in a straight line.

Then he says that IF we hypothesize that the center of the solar system is at absolute rest, then it follows that the center of the solar system is at absolute rest (ta da!), and thereby we have finally fulfilled our promise in the first Scholium to explain how we can find the true motions of bodies.

So what are we to make of this? Obviously he has not identified absolute rest, either as a logical consequence of his mechanics or based on observations of phenomena (quite the contrary)... but he HAS explained (as well as anyone could have explained in 1687) what he meant by absolute motions and an absolute reference frame. He meant that a true absolute frame suitable for applying the laws of mechanics is an unaccelerated frame. This is exactly what we teach freshman physics students today. To apply Newton's laws in their bare form (with no fictitious forces), motions must be described in terms of a true inertial coordinate system, and the COM frame of the solar system is as close as Newton could come to such a system, given the astronomical knowledge of that time.

My illustration showed you exactly the contrary: if you would postulate the existence of Atlantis, it would be silly to ask you to postulate that someone can have a position or motion with respect to it...

You're being intentionally obtuse. You are trying to smuggle in the "postulate of the existence of Atlantis", and then pretend that the argument is just about whether we would then need an additional postulate about the existence of motion relative to Atlantis. But you must know your argumentation is false, because there is no postulate of Atlantis. In your very next comment you deny ever saying that Newton postulated "absolute rest", which may or may not be what "Atlantis" is supposed to represent in your little obfuscatious word game. (It would really help if you just said what you mean, in terms relevant to the discussion, rather than devising allegories whose connection to the real discussion can only be guessed.)

The point is that the defintions and postulates on which Newton based his mechanics do NOT include any postulate or definition of absolute rest (in fact, they carefully exclude it), nor is absolute rest a logical consequence of Newton's mechanics. If you agree with this, then we are in agreement. If you disagree, then you really ought to either find absolute rest in one of Newton's laws, postulates or defintions, or you ought to explain how absolute rest is a logical consequence of his laws, postulates, and definitions. We both know that you can't do either one.

Your entire basis of belief seems to be "If there is absolute acceleration, then it follows logically that there is absolute position and absolute velocity." But that does not follow logically at all.

 

[harrylin]

What was Newton's definition of absolute rest?

Cited in post #79

THe most immediate thing that emerges from Newton's first law is that any observer or object in constant rectilinear motion with respect to another observer or object that is inertial, will also be inertial. [..]

Where did you read "inertial", in which text? And how did Newton define "inertial" in your text? It sounds as if you consulted a different (and strongly differing!) text or translation than the one to which I referred. Of course it's normal to disagree if we base ourselves on disagreeing translations.

In other words, the first law has no logical basis from which it stems, it is purely a postulate

Surely you agree that he should have defined somewhere what he means with motion, relative to what. Did you find that definition?

[..] Hence I equated the dynamically relevant notion of "absolute space" with "a global geometric constraint on what type of motion will make observers be able to use the laws of physics", i.e., it makes the attributes of space an axiom in the laws of physics, such that the laws may only be used by observers who have the particular relation of being in mutual rectilinear motion.

Yes, taking in account that you based yourself on a faulty translation ("**** happens!"), I can finally understand your reasoning. Never mind, thanks to this thread I discovered something about Galileo's theory, and perhaps you will similarly benefit concerning Newton's theory.

[..] I cite his First Law. That is what matters, not the picture he had in his head as he applied that law. A theory of physics is how it works, not how it is interpreted (witness quantum mechanics). Newton never put a frame of absolute rest into his laws, that much is clear enough.

Sorry where did you cite his first law? I did not see it. A theory of physics can only be correctly applied if its parameters are properly defined, and Newton actually did so on the preceding pages, of which I cited a part in post #80.

Yes, I agree that Newton's first law is completely scientific. However, the first law is not a claim on a frame of absolute rest.

I would like to continue the discussion of this thread starting from Newton's text as cited in post #80, as it enables a logical and straightforward discussion. Discussing a law before first checking out the intended meaning of terms is not useful.

 

[Ken G]

Where did you read "inertial", in which text?

"inertial" is a modern word that simply means "Newton's laws hold good." It doesn't need to be in any text, it is obvious.

And how did Newton define "inertial" in your text?

See above. Newton didn't define it, I did, using the common meaning that I thought you understood.

Surely you agree that he should have defined somewhere what he means with motion, relative to what. Did you find that definition?

In physics, motion is an observable. Hence it is always defined with respect to an observer. This is how all theories of physics are checked, so no other definition is even possible within physics, lest is be untestable (and therefore not physics).

Never mind, thanks to this thread I discovered something about Galileo's theory, and perhaps you will similarly benefit concerning Newton's theory.

It was interesting to see that Newton did clearly picture an absolute frame of rest, but I still see it significant that he steadfastly avoided including any such proposition in his laws of mechanics. He must have been puzzled about why the need for absolute rest seemed intuitive to him, yet never appeared anywhere in his theory of mechanics.

Sorry where did you cite his first law?

I believe we can take as given the first law. Do you think I have some incorrect interpretation of it? It seems pretty clear to me-- bodies with no forces on them will follow rectilinear motion in spacetime as perceived by observers who have no forces on them (and whom the laws are claimed to hold good). This is the routine interpretation of the first law, perhaps in clarifying language that makes the law more useful and accessible (and clearer why it is so different from the second law).

I would like to continue the discussion of this thread starting from Newton's text as cited in post #80, as it enables a logical and straightforward discussion.

The problem with that is that the text in post #80 is quite irrelevant to Newton's mechanics, it is only of historical interest to show us how Newton pictured and interpreted his own theory. It is clear from the above discussion, I think, that none of that is required for Newton's theory, nor appears anywhere in Newton's theory, so it is only of historical interest that he held to a picture that was never necessary anywhere in his actual theory. Personally, I think the "Newton's bucket" thought experiment is much more revealing-- it shows that Newton's laws require for inertial motion to be absolutely specified a priori as being rectilinear, so it requires that the concept of rectlinear motion (in spacetime, to be fully clear) be establishable by axiom. This is the heart of "absolute space", it is the only aspect of it that matters in Newtonian mechanics, and relaxing it is the key to the innovation of general relativity.

 

[harrylin]

[...] In physics, motion is an observable. Hence it is always defined with respect to an observer. [..]

Not in Newton's mechanics; you can find his definition and further explanations in the link in post #80. No serious discussion of the meaning of a physics equation is possible without verifying the meaning of the terms according to the author.

It was interesting to see that Newton did clearly picture an absolute frame of rest, but I still see it significant that he steadfastly avoided including any such proposition in his laws of mechanics. He must have been puzzled about why the need for absolute rest seemed intuitive to him, yet never appeared anywhere in his theory of mechanics.

I see it as significant that he included it in the definitions of the terms with which he formulated those laws, in such a way that a competing definition would have resulted in a different theory.

I believe we can take as given the first law. Do you think I have some incorrect interpretation of it? [..]

Yes indeed - see next.

It seems pretty clear to me-- bodies with no forces on them will follow rectilinear motion in spacetime as perceived by observers who have no forces on them (and whom the laws are claimed to hold good).

Sorry, in Newton's theory, motion is in space - not spacetime, a concept that didn't exist!
I interpret it just as Kevin Brown put it (see post #72): absolute space defines "rectilinear motion".

the text in post #80 is quite irrelevant to Newton's mechanics, it is only of historical interest to show us how Newton pictured and interpreted his own theory. [..] Personally, I think the "Newton's bucket" thought experiment is much more revealing [..].

Regretfully, as the text there plus the definitions that it refers to disprove your assumptions, it is useless to continue our discussion if you refuse to scrutinise Newton's explanations. But that's up to you; and Newton's bucket is part of that same chapter, it hangs all together.

 

[Russell E]

"I see it as significant that he included it in the definitions of the terms with which he formulated those laws, in such a way that a competing definition would have resulted in a different theory.

I think you're mis-informed. Newton's defintions are easy to find in the Principia... they are the statements labeled "Definitions". Likewise his postulates ("laws") and corollaries, are carefully labeled and enumerated, so they can be used and cross-referenced in the development of his axiomatic structure. As has been clearly explained here, Newton's mechanics consisting of this axiomatic theoretical structure contain no notion of absolute position or absolute rest. In fact, they specifically exclude it. That's why at the end of the Principia Newton finds that, by corollary 4 of the Laws, he can only conclude that the center of the Universe is either at rest or in uniform straight motion. There simply is nothing in Newton's mechanics to give any meaning to that distinction.

What you keep quoting is not part of the axiomatic structure of Newton's theory proper, it is a Scholium, which is intended as verbiage to hopefully help people grasp the new concepts, but such popularizations, no matter how well written, are always prone to misunderstanding, for the simple reason that they are verbal and therefore necessarily contain all the imprecisions and ambiguities of everyday language applied to rigorous scientific concepts. (Newton originally drafted some much more prosaic wording for that Scholium, with images of horses pulling on carts, etc., but then thought better of it.) It's the same with people trying to learn modern physics by reading popular verbal accounts of it, rather than actually studying and understanding the actual axiomatic conceptual structure. When reading the first Scholium you need to actually think clearly about what is being said, about what is actually shown by the spinning pail example - Does it distinguish absolute position or velocity from relative position and velocity? Of course not. Does Newton claim that it does? No, he does not. He REFERS to something called absolute rest, but by the end of the Scholium all he has done is explained why nothing he has said so far enables him to distinguish it from uniform straight motion. So he concludes the Scholium by promising to explain in the rest of the book. But you will seek in vain for any further mention of the subject in Books 1 or 2, in which his mechanics is fully developed. And when he finally does return to the subject, in Book 3, he STILL says we can't distinguish - based on the laws of physics - between absolute rest and uniform motion in a straight line, even for the putative "center of the universe". So there is simply no basis for your claim that Newton's physics was based on or implies any meaningful notion of absolute rest, nor even for your claim that Newton believed it did.

I interpret it just as Kevin Brown put it (see post #72): absolute space defines "rectilinear motion".

But in that same post it was noted that you had misrepresented your source, by omitting the crucial sentence "This is distinct from asserting an absolute state of rest, which Newton explicitly recognized as a matter of convention." I think both Ken G and I are in agreement that Newton's "absolute space" serves to establish uniform rectilinear motion (which is Newton's term for what we call inertial motion). Since you agree as well, it seems we are all in agreement. The only difference is that, for reasons which you steadfastly refuse to explain, you believe this implies some meaningfully significant sense of absolute rest, whereas I deny that implication. In other words, you think (or at least you think Newton thought) the existence of absolute acceleration implies the existence of absolute position and absolute velocity. The Principia itself refutes your beliefs.

 

[Ken G]

Not in Newton's mechanics; you can find his definition and further explanations in the link in post #80. No serious discussion of the meaning of a physics equation is possible without verifying the meaning of the terms according to the author.

No. A physics theory is not defined by the terms according to its author, it is defined by the predictions it makes. It is perfectly standard to recast all physics theories in modern terms, this happens all the time (pick any theory you like). Newton came relatively early in the scientific revolution, and he did not recognize the need to cast physical theories in terms of observables. Hence it makes no difference how Newton defined motion-- Newton's theory is a physics theory, so must satisfy the requirements of a physics theory.

One such requirement is that everything that the theory predicts must be cast in terms of observables, or else it isn't science at all. Of course, many scientific theories invoke interpretational steps that are not observables (such as quantum mechanical wave functions), but these are always open to multiple interpretations, and are never part of the actual theory. That is quite important-- it is the reason we have only one Newton's mechanics, and one quantum mechanics, rather than multiple versions for every possible intepretation one might care to invoke. Again, it makes no difference at all what interpretation Newton invoked for his mechanics-- it is purely of historical interest, the theory of mechanics known as Newton's laws stand squarely on its observable predictions, and that is fortunate-- for there is no debate about what those are, nor any debate about how accurate they are.

I see it as significant that he included it in the definitions of the terms with which he formulated those laws, in such a way that a competing definition would have resulted in a different theory.

That is precisely what is not true. For example, the definitions I give are the modern ones used in concert with Newton's laws, and they spawn exactly the same theory as Newton's (by virtue of invoking the same mathematics for calculating the same observable predictions), which is why it is called Newtonian mechanics. There are even alternate approaches that get called Lagrangian mechanics and Hamiltonian mechanics, which can be viewed as different yet equivalent versions of the same theory because they use different mathematics to arrive at the exact same observable predictions.

Sorry, in Newton's theory, motion is in space - not spacetime, a concept that didn't exist!

Obviously, and that is quite irrelevant. There is no such thing as "motion" in Newton's theory, there is what predictions you can test-- and that is x(t), position as a function of time. I can place those predictions into any mathematical milieu I desire, if I find it pedagogically illuminating. That is called understanding a theory-- it does not in any way imply or require a new theory. Embedding x(t) into an x-t space is quite an illuminating step that does not in the slightest bit alter Newton's theory.

I think the problem here is in the understanding of what a physics theory is-- versus the more cultish approach of imagining that theories are whatever their inventors cast them as. Physics theories are quite clearly not that, much to their advantage, as opposed to, for example, interpretations of religious texts. This I believe is also what Russell E is saying-- there is an important difference between Newton's theory of mechanics and whatever pictures he invoked in his own mind as he exercised that theory. The former is the same today as it was when it was created, the latter always varies with time and from person to person, as it has for every physics theory for time immemorial. Not making that distinction is a large part of the source of miscommunication in this thread.

I interpret it just as Kevin Brown put it (see post #72): absolute space defines "rectilinear motion".

As do I. But now simply place that rectilinear motion where it belongs-- in spacetime. Poof, gone is any need to even think about a frame of absolute rest! That's exactly why this is such a powerful way to envisage Newton's theory, and had he done it himself, he could have avoided the need to mention frames of rest altogether.

Regretfully, as the text there plus the definitions that it refers to disprove your assumptions, it is useless to continue our discussion if you refuse to scrutinise Newton's explanations. But that's up to you; and Newton's bucket is part of that same chapter, it hangs all together.

What is useless is trying to understand what a physics theory is if you think it depends on some religious text. Newton's bucket can be completely analyzed without ever mentioning a frame of absolute rest, which is why Newton's explanation has stood the test of time, even if some of his language has not.

 

[harrylin]

What do you think was Galileo's "reference", and what do you think was "incorrect" about it? [..]

Here are the links again:
http://galileoandeinstein.physics.vi...aft/index.html
http://galileoandeinstein.physics.vi..._153to160.html

Based on a quick read of those, it looks to me that internet commentaries are correct in suggesting that Galileo took material bodies such as the Earth as physical reference for motion. If someone could either confirm that conclusion or show it wrong by means of an unambiguous citation of Galileo's writings, that would be very useful of course.

[..] Look, take Newton's second law as an example: F = ma. The "a" in that expression stands for acceleration. [...]

Sorry, I am only interested in a serious discussion here. As I did not copy-paste the definitions to which Newton refers in my post #80, it may be useful to take the one that defines the meaning of the term "motion" (not "acceleration") as used in his second law:

The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

His definition of "motion" as used for his second law:

The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.

Next he stresses that further explanation is required for a correct understanding of the meaning of those words, and he provides that as follows:

"Hitherto I have laid down the definitions of such words as are less known, and explained the sense in which I would have them to be understood in the following discourse. I do not define time, space, place and motion, as being well known to all. Only I must observe, that the vulgar conceive those quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into absolute and relative, true and apparent, mathematical and common.

[... note: I already cited I. and II. in post 80]

III. Place is a part of space which a body takes up, and is according to the space, either absolute or relative. I say, a part of space; not the situation nor the external surface of the body. For the places of equal solids are always equal; but their superfices, by reason of their dissimilar figures, are often unequal. Positions properly have no quantity, nor are they so much the places themselves, as the properties of places. The motion of the whole is the same thing with the sum of the motions of the parts; that is, the translation of the whole, out of its place, is the same thing with the sum of the translations of the parts out of their places; and therefore the place of the whole is the same thing with the sum of the places of the parts, and for that reason, it is internal, and in the whole body.

IV. Absolute motion is the translation of a body from one absolute place into another; and relative motion, the translation from one relative place into another. Thus in a ship under sail, the relative place of a body is that part of the ship which the body possesses; or that part of its cavity which the body fills, and which therefore moves together with the ship: and relative rest is the continuance of the body in the same part of the ship, or of its cavity. But real, absolute rest, is the continuance of the body in the same part of that immovable space, in which the ship itself, its cavity, and all that it contains, is moved. Wherefore if the Earth is really at rest, the body, which relatively rests in the ship, will really and absolutely move with the same velocity which the ship has on the earth. But if the Earth also moves, the true and absolute motion of the body will arise, partly from the true motion of the earth, in immovable space; partly from the relative motion of the ship on the earth; and if the body moves also relatively in the ship; its true motion will arise, partly from the true motion of the earth, in immovable space, and partly from the relative motions as well of the ship on the earth, as of the body in the ship; and from these relative motions will arise the relative motion of the body on the earth. As if that part of the earth, where the ship is, was truly moved toward the east, with a velocity of 10010 parts; while the ship itself, with fresh gale, and full sails, is carried towards the west, with a velocity expressed by 10 of those parts; but a sailor walks in the ship towards the east, with 1 part of the said velocity; then the sailor will be moved truly in immovable space towards the east, with a velocity of 10001 parts, and relatively on the Earth towards the west, with a velocity of 9 of those parts."

He does indeed refer to absolute places, absolute rest, absolute motion, etc., first relative to the ship, but then noting that the ship could be moving (accelerating) relative to the Earth, and then noting that the Earth could actually be moving (accelerating) relative to the Sun, [..] He meant that a true absolute frame suitable for applying the laws of mechanics is an unaccelerated frame. [..]

Instead, I see here that he defined of "motion" as the translation from one place to another, and he found it important to distinguish "absolute" from "relative" motion.

[..] If you disagree, then you really ought to either find absolute rest in one of Newton's laws, postulates or defintions, or you ought to explain how absolute rest is a logical consequence of his laws, postulates, and definitions. We both know that you can't do either one. [..]

You can find Newton's definition of the same cited here above.

I think you're mis-informed. Newton's defintions are easy to find in the Principia... they are the statements labeled "Definitions".

Well seen

[...] What you keep quoting is not part of the axiomatic structure of Newton's theory proper, it is a Scholium, which is intended as verbiage to hopefully help people grasp the new concepts but such popularizations, no matter how well written, are always prone to misunderstanding, for the simple reason that they are verbal and therefore necessarily contain all the imprecisions and ambiguities of everyday language applied to rigorous scientific concepts. [...]

Sorry, I'm not buying that - playing down Newton's attempt to remove prejudices only serves to promote such prejudices. Any physics model is prone to misunderstanding, and the purpose of this thread is to diminish that. As a matter of fact, you are here referring to his explanation of the sense in which the terms of his equations must be understood.

But in that same post it was noted that you had misrepresented your source, by omitting the crucial sentence "This is distinct from asserting an absolute state of rest, which Newton explicitly recognized as a matter of convention."

Instead, the point of discussion was:

I think both Ken G and I are in agreement that Newton's "absolute space" serves to establish uniform rectilinear motion (which is Newton's term for what we call inertial motion). Since you agree as well, it seems we are all in agreement.
[..] The Principia itself refutes your beliefs.

Your beliefs as well as mine are completely irrelevant for physicsforums.

A physics theory is not defined by the terms according to its author, it is defined by the predictions it makes.

Again: I present the theory according to which a=b*c. How can you test my predictions if you refuse to check out my definitions of a, b and c?

[..] Newton came relatively early in the scientific revolution, and he did not recognize the need to cast physical theories in terms of observables. Hence it makes no difference how Newton defined motion-- Newton's theory is a physics theory, so must satisfy the requirements of a physics theory.

This thread started with a similar but contrary allegation that Newton's theoretical development was unscientific and/or illogical. You seem to say that by ignoring his theoretical development and assuming that it is scientific, it is perfectly scientific. Sorry, that's really besides the point.

Since my post #80 I am trying to turn this thread into a constructive fact-finding conversation about Newton's theory on his own merit - not to be confounded with the theories of some unknown later writers or second-hand explanations by others. I have no doubt that such is much more useful and instructive for eventual onlookers than quibbling about perceived disagreements; most reasonable disagreements will automatically disappear by just presenting the facts. If someone is interested in that, I will continue to give my input here.

Note: The issue about what is "scientific" was already discussed in this thread, for example in posts #58, #67 and you can give further comments in the thread on that topic which was moved to:
https://www.physicsforums.com/showthread.php?t=598724

 

[Russell E]

Based on a quick read of those, it looks to me that internet commentaries are correct in suggesting that Galileo took material bodies such as the Earth as physical reference for motion. If someone could either confirm that conclusion or show it wrong by means of an unambiguous citation of Galileo's writings, that would be very useful of course.

"Eppur si muove"

See "Dialogue on the Two Chief World Systems", and "Two New Sciences". I would seriously urge you to study both of those carefully. It might also help to read some commentaries on them, written by people who actually have a grasp of the concepts Galileo discussed. You'll learn that one of Galileo's (several) claims to fame is that he was one of the originators of the principle of inertia (with the caveats mentioned previously), and the great champion of the relativity of motion (which, please note, is quite different from relationism!), in support of the Copernican model of the solar system. He developed his dynamics (not just kinematics) to explain why all physical phenomena proceed just as if the Earth was at rest even though it is rotating and orbiting the Sun, in so far as a point on the Earth's surface is moving approximately uniformly in a straight line over a sufficiently short interval of time.

Sorry, I am only interested in a serious discussion here. As I did not copy-paste the definitions to which Newton refers in my post #80, it may be useful to take the one that defines the meaning of the term "motion" (not "acceleration") as used in his second law: "The alteration of motion is ever proportional to the motive force impressed..."

I think your comment shows that you are NOT interested in a serious discussion. You inform us that Newton's 2nd law refers to motion rather than acceleration, and yet when you quote the law, it refers only to "alteration of motion", which of course is nothing but acceleration. That's the whole point: Do Newton's laws refer to the absolute quantity of motion, or do they refer only to "alterations of motion", i.e., acceleration? The answer is obviously the latter, which is why Newton's mechanics is totally relativistic. Do you honestly deny this? Posting quotes over and over again, without understanding them, is not really useful.

Likewise your quotations from the first Scholium do nothing at all to support your position. As everyone knows, Newton was arguing there against relationism (cf Leibniz), NOT against relativity (cf Galileo). The spinning pail and the revolving globes both are arguments for the need for absolute acceleration, which refutes relationism, but does not conflict with relativity at all; in fact it is BASED on relativity, which is synonymous with the principle of inertia. Again, posting quotes over and over again, without understanding them, is not really useful.

Now, it is true that Newton had a religiously motivated metaphysical preference for imagining that one particular state of motion was true rest (similar to Lorentz's concept), which he identified in the General Scholium at the end of the Principia as the "sensorium of God" (just as Lorentz did in a letter to Einstein), because he thought to do otherwise would encourage atheism, but these metaphysical notions have no bearing on Newtonian mechanics as a scientific theory. No one (certainly not Newton) disputes that Newtonain mechanics is perfectly relativistic, in the sense that it is invariant under Galilean transformations, meaning that it is indifferent to the choice of inertial reference frame. In fact, this is the content of Proposition V (from memory) of the Principia.

Playing down Newton's attempt to remove prejudices only serves to promote such prejudices. Any physics model is prone to misunderstanding, and the purpose of this thread is to diminish that. As a matter of fact, you are here referring to his explanation of the sense in which the terms of his equations must be understood.

I'm not playing down Newton's writing, I'm explaining it to you. He was arguing for the need for absolute space as opposed to RELATIONISM in order to give an intelligible account of phenomena, because relationism cannot account for inertial phenomena. That's why he based his mechanics on Galileo's principle of inertia (now known as the principle of relativity), which he acquired by way of Gassendi and Descartes. The prejudice he was trying to dispel was the idea that we can base everything on the relations between material bodies, without reference to any underlying properties of space (and time). It is a very important point, and forms the basis of Newtonian mechanics.

In modern times people sometimes try to use the first Scholium in an entirely different debate, the one between relativity and etherism (in the tradition of regarding "ether" as signifying an embodiment of absolute rest in space), but in the 17th century that debate was conceived in terms of the plenum (etherism) and the void or vacuum (relativity). On that debate Newton was, for most of his life, a proponent of the vacuum, i.e., he was an anti-etherist, although in his late 70's and 80's he did add some queries to the Opticks musing about a possible etherial substance, but he was equivocal on the subject. In any case, it was and is unrelated to his mechanics.

Your beliefs as well as mine are completely irrelevant for physicsforums.

I don't believe that's necessarily true. It depends on what kind of beliefs we're talking about. For example, you have a metaphysical belief in absolute position and absolute velocity, and I might agree that this forum isn't really a suitable place for you to promote that kind of blatantly metaphysical belief. On the other hand, you also seem to have a belief that Newtonian mechanics is not invariant under Galilean transformations, and I would say that such a belief actually is a fit subject for discussion in this forum, because one of the main purposes of this forum is to help people learn about things like that.

Since my post #80 I am trying to turn this thread into a constructive fact-finding conversation about Newton's theory on his own merit - not to be confounded with the theories of some unknown later writers or second-hand explanations by others. I have no doubt that such is much more useful and instructive for eventual onlookers than quibbling about perceived disagreements; most reasonable disagreements will automatically disappear by just presenting the facts.

I don't think that will be useful or instructive. The way you repetitively post quotes, that you thoroughly mis-understand, and none of which support your position, reminds me of certain other individuals who post to various science-related forums. Ever heard of Pentcho Valev? Your messages are beginning to resemble his more and more. In case you've never seen them, let me just say they are neither useful nor instructive.

If you want to discuss Newton's religion, psychological motivations, metaphysical preferences and prejudices (which of course shifted over the course of his life) for historical reasons or whatever, that's fine, but since this is a PHYSICS forum, I don't think you should be surprised to find people actually discussing Newtonian mechanics as a theory of physics, and making distinctions between the actual content of the theory described in Principia versus Newton's metaphysical and religious comments in the Scholium about how God constitutes space and duration.

 

[Ken G]

Again: I present the theory according to which a=b*c. How can you test my predictions if you refuse to check out my definitions of a, b and c?

You are missing the point-- that theory predicts a via the formula a=b*c, hence by the data that is inserted into the equation, not what you picture in your head when you write it down. The definitions of b and c can change, and indeed almost always do, in every physics theory. But a does not change, and the theory does not change, expressly because it predicts precisely the same outcome as did the original version. So it is with Newton's laws (have you ever seen the form of calculus that Newton used? That's a perfect example of how definitions change but the theory is still the same).

You seem to say that by ignoring his theoretical development and assuming that it is scientific, it is perfectly scientific.

Why on Earth would I say such a foolish thing? Why do you think I said any such thing? What I actually said is that Newton's path to his theory is of historical interest only-- what matters is the theory, which is defined by the mathematics it uses to make its testable predictions. Like all physics theories, that's what a physics theory is. Definitions almost always change along the way as they get cleaned up and clarified. Haven't you noticed this? It happens with all theories, yet does not spawn any new theories, it merely changes how we regard what we are doing when we do the mathematics that results from the theory. What changes is the interpretation, not the theory.

Since my post #80 I am trying to turn this thread into a constructive fact-finding conversation about Newton's theory on his own merit - not to be confounded with the theories of some unknown later writers or second-hand explanations by others.

Again you are badly misusing the meaning of the term "theory." Newton's "theory" is exactly the same today as when he formulated it, as I have explained, yet no physics book today that explains Newton's theory will look anything like a similar book from 1800. Does that mean the theory has changed in the interim? No it does not. This is just how physics is, it's perfectly routine. Why do you think no one teaches Newtonian mechanics from the Principia, or relativity from Einstein's papers? Are we all teaching different theories if we choose a different textbook that interprets the meaning of the terms in ways that seem more pedagogically effective?

So what you need to do is, decide if you want a fact-finding conversation of historical interest about what was going on in Newton's head, or if you want a fact-finding conversation about what the theory of Newtonian mechanics actually asserts. Those are quite different things, as I have stressed because it is the main source of inconsistency in the discussion. The bottom line is, a frame of absolute rest has nothing whatever to do with Newtonian mechanics, even though Newton himself did seem to believe in it. Read that as many times as it takes.

 

[harrylin]

"Eppur si muove"
See "Dialogue on the Two Chief World Systems", and "Two New Sciences". I would seriously urge you to study both of those carefully. [...]

I gave you a link to the one to read; it would be useful if you give a link to the other Dialogue as well.

[..] No one (certainly not Newton) disputes that Newtonain mechanics is perfectly relativistic, in the sense that it is invariant under Galilean transformations, meaning that it is indifferent to the choice of inertial reference frame. In fact, this is the content of Proposition V (from memory) of the Principia. [..] He was arguing for the need for absolute space as opposed to RELATIONISM in order to give an intelligible account of phenomena, because relationism cannot account for inertial phenomena. That's why he based his mechanics on Galileo's principle of inertia (now known as the principle of relativity), which he acquired by way of Gassendi and Descartes. The prejudice he was trying to dispel was the idea that we can base everything on the relations between material bodies, without reference to any underlying properties of space (and time). It is a very important point, and forms the basis of Newtonian mechanics.

That's what I meant with fact finding instead of quibbling: it's good to see that we actually agree on the basics! However, you disagree with actually trying that:

I don't think that will be useful or instructive. The way you repetitively post quotes, that you thoroughly mis-understand, and none of which support your position [...]

That's exactly what I think of you, such as by your claim that the ship's motion means acceleration; and so you may be right that such would not be fruitful in practice.

You are missing the point-- that theory predicts a via the formula a=b*c, hence by the data that is inserted into the equation, not what you picture in your head when you write it down.

Well, it happens to be me who made that point: without knowing the meaning of "a", "b" and "c", you cannot test anything at all. For example the Lorentz transformation formula can also be used in acoustics, but there both the meaning of the symbols and their application are completely different - same equation but nothing to do with relativity theory.

Definitions almost always change along the way as they get cleaned up and clarified. Haven't you noticed this? It happens with all theories, yet does not spawn any new theories, it merely changes how we regard what we are doing when we do the mathematics that results from the theory. What changes is the interpretation, not the theory.

Certainly I noticed those things, but to what extend that has happened only became clear to me many years after I finished my study. With an eye on the topic: Suppose some famous vacuum cleaner producer, let's call him Mr. Hoover, sells vacuum cleaners to you for distribution. You think that the motor is no good and replace it by a better one from China, selling the vacuum cleaners with the label "Hoover". Perhaps your customers are perfectly happy. Still there is a tiny risk that one day the police knocks on your door. But as we know, the standards are different in teaching (as well as in religion): many teachers consider such cheating not a crime but a virtue. Note the subtle but important difference with accreditation: it's the subtle difference between selling it as a Hoover, or selling it as "Hoover with China motor".

[..] Why do you think no one teaches [..] relativity from Einstein's papers?

I have news for you: in the relativity forum several of us are quite successful explaining relativity to newbees with help of Einstein's papers and books.

[..] decide if you want a fact-finding conversation of historical interest about what was going on in Newton's head, [..] The bottom line is, a frame of absolute rest has nothing whatever to do with Newtonian mechanics, even though Newton himself did seem to believe in it. [..].

As there is no common interest on anything to discuss (except perhaps the two of you), I now also leave this thread. Harald

 

[Russell E]

I gave you a link to the one to read; it would be useful if you give a link to the other Dialogue as well.

The links didn't work in my browser, but it doesn't matter because I have paper copies of the books. Like you, I wouldn't dream of making pronouncements on the subject if I hadn't already studied both of them thoroughly, along with the vast secondary literature. If I was only now just becoming acquainted with these works, I would be in the mode of asking questions and learning, not trying to explain things to people much more knowledgeable than myself.

That's exactly what I think of you, such as by your claim that the ship's motion means acceleration...

But our situation isn't symmetrical, is it?

Obviously there are relative positions and velocities between the ship and the earth, etc., but Newton's laws are indifferent to position and velocity, they recognize only alterations in motion, i.e., acceleration. If the ship was moving uniformly in a straight line, then Newton's laws would be fully satisfied by referring all positions and velocities and accelerations to the rest frame of the ship. The same applies to the Earth and to the Sun. Finally Newton arrives at the center of mass of the solar system, and since he regards this as the entire cosmos, he declares (by mere convention) THIS is the absolutely resting center of space (which of course it isn't). This just illustrates the fact that Newton's laws give no warrant for selecting any particular frame as absolute rest, other than that it be perfectly unaccelerated. So that's why I highlighted the acceleration aspect of the ship/earth/sun discussion, to help you understand how Newton's discussion in the Scholium relates to the physical theory that he describes in the Principia.

I am trying to turn this thread into a constructive fact-finding conversation about Newton's theory on his own merit - not to be confounded with the theories of some unknown later writers or second-hand explanations by others... Certainly I noticed those things, but to what extent that has happened only became clear to me many years after I finished my study... Suppose some famous vacuum cleaner producer, let's call him Mr. Hoover, sells vacuum cleaners to you for distribution... or selling it as "Hoover with China motor".

Okay, so your interest is not physics, per se, but the historical thoughts and beliefs of one specific individual (Isaac Newton), and you regard as untrustworthy the views of any scholars who have studied Newton and his works and might try to explain them to you. And you feel you've been swindled by unknown writers (shiver!) who expressed things differently than Newton did, and who you suspect of bastardizing Newton's actual theory.

That's kind of a weird form of obsessive conspiratorial paranoia, but to each his own. The real problem with what you said is the phrase "fact-finding". That's not a cut-and-dried process. For example, the second law refers only to acceleration, but when you scanned the text you saw the phrase "altered motion", so you gleaned the "fact" that Newton's second law refers to motion, not acceleration. The problem is that the phrase "altered motion" means acceleration. So the "fact" you found was not a fact at all.

You can spend the rest of your life gathering "facts" like that, but you still won't understand anything, because you aren't thinking about what the words mean. Newton certainly thought about and understood what his words meant, so if you really want to understand his thinking, you need to understand what he wrote, not just scan the text for individual words that superficially conform to your pre-conceptions and prejudices. And you simply must learn to distinguish between physical and metaphysical concepts.

 

[Ken G]

Suppose some famous vacuum cleaner producer, let's call him Mr. Hoover, sells vacuum cleaners to you for distribution. You think that the motor is no good and replace it by a better one from China, selling the vacuum cleaners with the label "Hoover".

The analogy has nothing to do with how physics works, so is irrelevant. Don't reason by analogy-- physics theories are the observables they predict, period. Do you think otherwise?

I have news for you: in the relativity forum several of us are quite successful explaining relativity to newbees with help of Einstein's papers and books.

I have news for you-- no one teaches physics that way in classrooms. Now why do you think that is?

 

[harrylin]

[...]you gleaned the "fact" that Newton's second law refers to motion, not acceleration. The problem is that the phrase "altered motion" means acceleration. So the "fact" you found was not a fact at all. [..]

Just a final clarification for any potential onlooker: As is easy to check, in post #89 I tried to explain to Russell that the term in the second law to verify with Newton's definition is not, as he claimed, "acceleration" but "alteration of motion"; and that, consistent with that fact, the "relative motion of the ship" does not mean, as Russell pretended, "the ship could be moving (accelerating) relative to the Earth" but, according to Newton's definitions, motion is a translation from one place to the other.

Obviously no reasonable conversation is possible and I will next unsubscribe from this thread to prevent myself from looking at more of such distortions and verbal abuse.

 

[harrylin]

The analogy has nothing to do with how physics works, so is irrelevant. Don't reason by analogy-- physics theories are the observables they predict, period. Do you think otherwise?
I have news for you-- no one teaches physics that way in classrooms. Now why do you think that is?

Ken, how physics works relates to the topic of scientific method on which I started a thread, and I think that I already answered your question there:
https://www.physicsforums.com/showthread.php?t=598724

And why no one uses any original papers in the classrooms (which I doubt) is again a totally different topic... if you start a thread on that (which will likely end go to "Social Sciences"!) I will be happy to participate.

 

[Russell E]

Just a final clarification for any potential onlooker: I tried to explain to Russell that the term in the second law to verify with Newton's definition is not, as he claimed, "acceleration" but "alteration of motion"...

But "alteration of motion" IS acceleration. That's the whole point. The second law is completely indifferent to absolute position or absolute velocity - it depends only on absolute acceleration, which Newton referred to as "alteration of motion". This is why the absolute value of motion itself is of no significance in Newtonian mechanics, as Newton himself says many times. The same for absolute positions. This is because Newton bases his theory (in the Principia) on definitions, postulates, and laws that refer only to accelerations, and they explicitly equate "rest" with "uniform motion in a straight line". Hence it was inevitable that Newtonian mechanics does not distinguish between these.

In addition to the numbered axioms, definitions, propositions, and laws that constitute the development and structure of Newton's presentation of his theory, he also interspersed several Scholia, providing somewhat informal commentary on the theory. In the first Scholium he admits that he hasn't actually defined space, time, velocity, etc., but he realizes that some guidance is needed, because his propositions clearly don't apply to arbitrary systems of reference. In light of what we said above, the necessary and sufficient condition is that we be able to identify true uniform straightness, because all the definitions and laws are expressed in terms of deviations from uniform straightness. So he needs to identify the class of inertial coordinate systems, which he does in a physically meaningful way by noting that forces causing acceleration, so we need freedom from external forces to be unaccelerated. Fine. This is the operational basis of the theory.

Now, he also includes in the Scholium some additional statements - the ones that have confused you - declaring the existence not only of absolute acceleration (which is all that is relevant to his theory of mechanics as he has described it), but of absolute velocity and absolute position as well. However, regarding these unsupported declarations, he also admits that they "by no means fall under our senses", and he admits that he is unable to give them any operational meaning, and he does not give any indication of how they might be determined or what they signify. Hence these are self-admittedly metaphysical notions. It's true that nothing in the theory of mechanics described in the Principia forbids us from asserting that one particular inertial frame is the "true" one, but it's also true that nothing in theory requires it or makes any use of it. It is a purely metaphysical and superfluous conception.

According to Newton's definitions, motion is a translation from one place to the other.

No, Newton's definition of the quantity of motion is the product of velocity and mass (so it is what we call momentum), but of course he doesn't define velocity. In the Scholium he admits that he hasn't formally defined the basic terms, but he gives an informal discussion, necessary to establish the physically meaningful concept of an inertial reference frame. Interspersed with this discussion he refers to "absolute places", but he does not define them, and indeed admits that they have no operational meaning, so his theory is not based on them. (It is fortunate that those things are irrelevant to his actual theory, because if mechanics depended on "absolute place" or "absolute velocity" it would be worthless.)

Obviously no reasonable conversation is possible and I will next unsubscribe from this thread to prevent myself from looking at more of such distortions and verbal abuse.

None of the comments that you regard as "distortions and verbal abuse" are anything of the kind. They probably seem that way to you only because you are unable to grasp the concept of indefinite integrals. Acceleration has absolute significance, so you think the integral of acceleration (i.e., velocity) must also have absolute significance, and the integral of velocity (i.e., position) must also have absolute significance. One could continue defining more variables by taking successive integrations, but you have not articulated any justification for assigning absolute values to them. Newton gave his reason: Space is the sensorium of God, and it would be absurd to think that the sensorium of God moves. But that is not part of his theory of mechanics, it is just a metaphysical belief.

 

[D H]

But "alteration of motion" IS acceleration.

Yes and no.

Newton intentionally did not use his calculus in his Principia. It was too new, potentially too controversial; Newton didn't want to pile one new thing atop another. He wanted his Principia to stand on its own. This is also why he barely used algebra in the Principia. His weapon of choice was instead geometrical reasoning. For the next fifty years or so following Newton's death mathematicians and physicists undertook rewriting Newton's concepts in terms of calculus and algebra.

There is no doubt that F=ma (better: F=kma; the idea of consistent units for force, mass, length, and time was a hundred years after Newton's death) is Newton's second law. It just isn't how Newton wrote it. Without words, Newton's second law as written by Newton is
\Delta \vec p \propto \int_0^{\Delta t} \vec F\,dt
In words, "The alteration of motion is ever proportional to the motive force impressed, and is made in the direction of the right line in which the force is impressed."

Since "quality of motion" is mass times velocity, another way to express Newton's second as expressed by Newton is
m\Delta \vec v \propto \int_0^{\Delta t} \vec F\,dt
There's no need for absolute velocity here. Just change in velocity.

Getting from the above to the F=ma that we use now is a trivial application of calculus, plus a not so trivial effort to turn that proportionality into an equality.

 

[Ken G]

And why no one uses any original papers in the classrooms (which I doubt) is again a totally different topic... if you start a thread on that (which will likely end go to "Social Sciences"!) I will be happy to participate.

Actually, it's completely relevant, and has a very simple answer. As you have chosen to duck it, I will give it to you: original papers are not used to teach physics because invariaby the exact same theory described in those papers is better understood in modern terms that have emerged later than the original papers. The reason this is clearly relevant is that you insist on equating the theory of Newtonian mechanics with Newton's mental pictures about frames of absolute rest, but the two are not at all the same-- the former being explained in very different terms in classrooms today, yet still being exactly the same theory. If you don't see that, then you do not understand what scientific pedagogy is (a rather separate topic from the scientific method, by the way).

 

[Ken G]

There's no need for absolute velocity here. Just change in velocity.

Exactly. Newtonian mechanics, as described by Newton and still applied today, requires no reference to any concept of absolute rest, nor is any such concept ever invoked in the teaching of Newtonian mechanics. Yet, it is clear that Newton himself felt that there was an essentially philosophical need for such a frame. So we can clearly differentiate the theory itself from Newton's own opinions about its interpretation. That also answers earlier objections about whether or not Newton was being scientific-- to the extent that he was creating a testable theory, he was certainly being scientific, and to the extent that he was choosing a mental picture to interpret his theory, he was under no responsibility to be scientific, because the rules of science become quite fuzzy in the realm of interpretations, and that is just as it should be-- science and philosophy as non-overlapping magisteria that nevertheless interact closely.