Newtonian Relativity: Galilean Relativity & Beyond

[harrylin]

The following discussion emerged under the topic "at rest" in Einsteinian relativity, and while out of place there it may be worth a little elaboration:

Originally Posted by harrylin

As Newton's mechanics uses Galilean relativity, your claim implies that he should have found an experimental violation of his theory of mechanics to justify his absolute space postulate

Originally Posted by DaleSpam

Yes, exactly.

Newton argued that we mere mortals cannot sense absolute time or absolute space. For the most part all we can sense are relative time, relative distance, relative motion. However, Newton also argued that we can catch a glimpse of this absolute time and space in the concave surface of a rotating bucket of water and in the equatorial bulge of a rotating planet.

Yes indeed. Newton developed a mechanics that uses Galilean relativity as a logical consequence of his model of the world that was based on such observations.

Thus, to demand Newton to disprove Galilean relativity in order to support his model is a demand for self contradiction. Isn't that obvious?

 

[Dale]

Yes. He should contradict/correct himself.

Scientific assumptions should either be empirically justified or logically required from things that are empirically justified. The assumption of absolute time and space is neither, so it should be removed. That was Galileo's (correct) point, and would require that Newton contradict himself.

Alternatively, he should find experimental evidence supporting the idea. Such evidence would necessarily refute his 3 laws, and would again require that he correct himself.

 

[harrylin]

Yes. He should contradict/correct himself.

Scientific assumptions should either be empirically justified or logically required from things that are empirically justified. The assumption of absolute time and space is neither, so it should be removed. That was Galileo's (correct) point, and would require that Newton contradict himself.
[..]

I don't recall to have ever seen anyone claim that Newton's theory is self contradictory. I think that it's generally accepted that the theory is self consistent, and to me it always looked very logical, based on observations - even critics such as Mach did not state otherwise. Please present the apparent contradiction.

 

[harrylin]

Interestingly in the thread on Einsteinian relativity now another comment was added that to me sounds like an attack on Newton:

[..] None of our experiences mandate the existence of an absolute reference frame, so I have trouble even understanding where the default assumption of an absolute reference frame would come from. Perhaps it comes from the thought of a fish-tank universe with God looking through the glass. Perhaps he's there, but whether he is or not, there is no basis for assuming he is nor any value in making the assumption. If one acknowledges that he and his frame are completely undetectable, then speculation about his existence is of no value in a scientific setting. It is purely a religious belief. [..]

Newton's scientific argument can be found here:
http://gravitee.tripod.com/definitions.htm
Press "cancel" and scroll to halfway in his Scholium.

 

[Dale]

He should contradict/correct himself.

Newton's theory is self contradictory

That is an excellent straw-man.

Why don't you start with my premise, that scientific assumptions should be experimentally justified or logically implied, and attack my actual argument.

 

[harrylin]

That is an excellent straw-man.
Why don't you start with my premise, that scientific assumptions should be experimentally justified or logically implied, and attack my actual argument.

I commented on your claim that Newton should have found an experimental violation of his theory of mechanics to justify his absolute space postulate. Perhaps my reply wasn't clear or incomplete; or perhaps we misunderstood each other. I'll try again. As his theory of mechanics is based on his postulates and relies on them, your demand for Newton to contradict himself doesn't make any sense to me. It suggests that Newton's theory as he developed it is illogical, inconsistent or not based on experiments.

D_H and I referred earlier to Newton's explanation of his logic as based on experimental evidence, and I next provided a link to that section in which he set out the experimental basis for his mechanics, in disagreement with Leibniz. The therefrom following theory of mechanics is presented on the following pages. It establishes what we nowadays call Galilean relativity. In order to judge the argument that you have against this logical presentation, you should first present it.

 

[Dale]

As his theory of mechanics is based on his postulates and relies on them, your demand for Newton to contradict himself doesn't make any sense to me.

The point is that the absolute velocity postulate is superfluous, and it is not correct to say that his theory of mechanics relies on the idea of absolute velocity. It is a part of the theory that is unnecessary, as pointed out by Galileo and recognized by most everyone from Galileo on.

Do you agree with my premise?
(P) Scientific assumptions should be experimentally justified or logically implied

Then my argument is as follows:
(1) Absolute velocity is not experimentally justified
(2) Absolute velocity is not logically implied
(3) Therefore, absolute velocity should not be a scientific assumption

(3) follows logically from (1) and (2) given (P). So if you disagree with (3) then please identify what you disagree with: (P), (1), or (2).

 

[harrylin]

The point is that the absolute velocity postulate is superfluous, and it is not correct to say that his theory of mechanics relies on the idea of absolute velocity. It is a part of the theory that is unnecessary, as pointed out by Galileo and recognized by most everyone from Galileo on.

The issue was between the model of Leibniz and the model of Newton, as elaborated for example here:
http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Newton_bucket.html

Do you agree with my premise?
(P) Scientific assumptions should be experimentally justified or logically implied

Quite, but not in absolute way: postulates and models should be allowed as basis of a theory. Else it's not really a theory - and it's just not how science works. Instead, one invents physical or mathematical models that could explain observations, preferably in a simple way. And if one has two models with different predictions, then if one of the two fits the observations, that's what one uses for the further theoretical development.

Then my argument is as follows:
(1) Absolute velocity is not experimentally justified
(2) Absolute velocity is not logically implied
(3) Therefore, absolute velocity should not be a scientific assumption

(3) follows logically from (1) and (2) given (P). So if you disagree with (3) then please identify what you disagree with: (P), (1), or (2).

The only alternative model of the time was the relative velocity model of Leibniz - and it didn't work. Newton's absolute velocity model did work, just as he explained. That is sufficient experimental justification for any theory of physics.

 

[russ_watters]

I'm not sure I need/want to participate in this thread since Dale is doing great as always, but since my post was copied into it (which is fine), I'll give a quick $.02:

1. I'm a big fan of Newton. Inventing calculus as a tool to help him figure out gravity is a genius two-fer. Einstein may have had 3 ideas worthy of Nobel prizes, but they were all basically separate. Newton, on the other hand, created one masterpiece as a mere stepping stone to a second. He may have been the all-time champ.

2. I didn't intentionally challenge him with that post, but after reading the descriptions of Newton's position on the issue, it does indeed read like a direct challenge.

3. The history is interesting to me too and it is now my understanding (just from reading here) that Newton's contemporaries noticed the superfluous nature of the assumption and pointed it out at the time, resulting in some controversy. That's fascinating to me.

4. Learning about this mistake of his way invalidates #1 for me: Invention/discovery is an inherrently error-prone process.

5. This is a little more than just an error due to insufficient information and incomplete development (as opposed to, say, Newton's gravity's conflict with GR). I agree with Dale that this error was Newton not adhering to the scientific method/process/way of thinking. But I'll cut him some slack on that: That had just been invented too!

6. Though I just gave a genius a pass for an error I considered unforgivable by laypeople in another thread, there is no contradiction in my position there: The difference is 500 years, during which time the scientific process proved its mettle and the knowledge that was originally only accessable to all-time giants came down into high schools. But to clarify just a little:

7. I'm fine with people being religious (if that's the origin of this error). But people should be self-aware enough to recognize when they are making a conscious choice to accept a non-scientific belief. But that isn't happening in the other thread. We're still discussing the issue precisely because one user refuses to accept that the error is, in fact, an error -- at least in a scientific context. Once again, Newton may have been guilty of the same thing (not being self-aware about his belief), since his statement about the rotating bucket implies to me that he believed the PoR wasn't really valid and that absolute time and space did exist and was identifiable experimentally. But also again, he didn't have anything anywhere close to the mountain of evidence and theoretical backing to climb out of in order to maintain that belief that today's crackpot does.

 

[russ_watters]

Also, in reading the link, it appears to me that he recognized the contradiction and was looking for a way out, possibly involving rotation. He says at the end, essentially, that if rotation is absolute, then a rotating or orbiting object must be in absolute motion. It just seems like he doesn't get that that doesn't privide the bridge he is looking for.

 

[D H]

Do you agree with my premise?
(P) Scientific assumptions should be experimentally justified or logically implied

No. Change the "or logically implied" to "and logically consistent" and I agree. To me, an axiom that is not testable is metaphysics, religion, or flubnubitz.


Newton needed time to be absolute for religious rather than physical reasons. His absolute state and time are not testable; they are not a good starting point from the point of view of physics. His bucket argument does not require velocity to be absolute. What Newtonian mechanics does require is that rotation and acceleration are absolute, and that displacement and duration are invariant.

 

[harrylin]

Actually I agree with much of what you say; and as usual, I'll merely comment on where we strongly disagree:

[..]
5. This is a little more than just an error due to insufficient information and incomplete development (as opposed to, say, Newton's gravity's conflict with GR). I agree with Dale that this error was Newton not adhering to the scientific method/process/way of thinking. But I'll cut him some slack on that: That had just been invented too! [..]

It's unclear to me if we completely disagree about the scientific method, or if you agree with me on the scientific method but, for some reason that escapes me, you think that Newton did not follow it.Harald

 

[harrylin]

No. Change the "or logically implied" to "and logically consistent" and I agree. To me, an axiom that is not testable is metaphysics, religion, or flubnubitz. [..]

What do you mean with "testable"? For example, quarks and EM fields can not directly be tested; instead we measure effects that fit with the models. And do you disagree with the scientific method of model testing?

 

[harrylin]

Also, in reading the link, it appears to me that he recognized the contradiction and was looking for a way out, possibly involving rotation. He says at the end, essentially, that if rotation is absolute, then a rotating or orbiting object must be in absolute motion. It just seems like he doesn't get that that doesn't privide the bridge he is looking for.

I have the impression that this again questions the scientific method... Leibniz had a model of relative motion and Newton showed that it didn't work; while his model based on absolute motion did work. That's how model testing is done in physics. The resulting theory was a big success and it survived so long as no clear deviations were observed.

 

[russ_watters]

I believe Newton did not follow the scientific method.

 

[Dale]

Quite, but not in absolute way: ...

Since you don't completely agree with the premise of my argument then there is no point in proceeding until we have resolved that. However, it sounds like my premise is not too far from something you would agree to completely, so perhaps I can agree to your version instead. Please write a premise that you would agree with "in absolute way" of the form:

Scientific assumptions should ...

 

[russ_watters]

What do you mean with "testable"? For example, quarks and EM fields can not directly be tested; instead we measure effects that fit with the models. And do you disagree with the scientific method of model testing?

There is no "directly" here. Quarks and em fields are testable.

You are about to fall into the "true nature" trap. That is the philosophical belief that there is a "true nature" to things independent of our scientific models. This enables a non-religious justification of the absolute reference frame issue, for example. That is completely unscientific. In science, a phenomena or object is nothing more or less than the sum of its properties and behaviors. Quarks have testable properties and those properties is what they is.

 

[Dale]

I'm a big fan of Newton. ... He may have been the all-time champ.
...
this error was Newton not adhering to the scientific method/process/way of thinking. But I'll cut him some slack on that: That had just been invented too!

I agree 100%.

 

[A.T.]

Newton showed that it didn't work; while his model based on absolute motion did work.

In what sense was Newton's model "based on" absolute motion? Is absolute (linear) motion a requirement for his model to work (give correct quantitative predictions)? Or is it just an irrelevant assumption that doesn't change the quantitative predictions of his model?

 

[rbj]

No. Change the "or logically implied" to "and logically consistent" and I agree. To me, an axiom that is not testable is metaphysics, religion, or flubnubitz.

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

Newton needed time to be absolute for religious rather than physical reasons.

for (relative) speeds that are slow (w.r.t. c), isn't absolute time a reasonable axiom to draw from everyday experience? since Newton was a few centuries before Einstein or even Maxwell, he might consider a particle property of light traveling at a finite speed, but since this speed was sooo far faster than anything else he witnesses, i can totally understand why the absoluteness of time would be taken as axiomatic for that time. in fact, it continues to work for 99% of the mechanics we do today, including that of planetary and spacecraft motion.

so i don't get either yours or Dale's critique of Newton's axiomatic insights of the day. they sure seem reasonable to me, but given them we would expect an absolute frame of reference for Maxwell's equations and we always seemed to put that in our own frames, as observers. eventually physicists started to think about testable consequences of that notion and hence the Michaelson-Morley experiment was conceived. even though Einstein must have known about M-M, he did not use it in his SR thought experiment. it was more of this insight that, if all constant-velocity observers have equal claim to being "at rest" (and they are at rest from the POV of their own frame-of-reference), then their laws of nature must be equal and they both should measure and observe c to be the same. that is sort of a logical consequence of Galilean relativity, but it's subtle, at least for the 17th century. he came to that insight without drawing explicitly on the negative result of M-M, but i imagine that he used that to reinforce his thinking.

i wonder what Einstein would have done if there was some systemic mistake made in M-M and repeated experiments that caused them to conclude we were moving through the aether. he might have ignored it as non-sensical and proceeded with his development of SR.

still, i don't see how Newton would have been expected to use any other axiom for time than he did, given the physical world he observed. and this lesson should apply to us today regarding SR and GR, QM, Standard Model, ΛCDM, etc. what we take now as axioms might be refuted by our descendants. for instance, the accelerating expansion of the universe surely left me slack-jawed in the 90s. i did not believe it at first, but unlike superluminal neutrinos (which i also didn't believe), the accelerated expansion of the universe is an observation that is standing the test of time and repeatability.

 

[D H]

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.

for (relative) speeds that are slow (w.r.t. c), isn't absolute time a reasonable axiom to draw from everyday experience? since Newton was a few centuries before Einstein or even Maxwell, he might consider a particle property of light traveling at a finite speed, but since this speed was sooo far faster than anything else he witnesses, i can totally understand why the absoluteness of time would be taken as axiomatic for that time. in fact, it continues to work for 99% of the mechanics we do today, including that of planetary and spacecraft motion.

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.

 

[harrylin]

I believe Newton did not follow the scientific method.

Evidently we disagree, as my summary description of what Newton did is IMHO a good example of the scientific method. Perhaps there are different opinions about what the scientific method is; and we should not deviate too much from the topic (or start it in a separate thread). However, the first description that I found as it is linked from Wikipedia, is the following:

http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html

At first sight my opinion is consistent with that description of the scientific method; and it would be helpful if you can elaborate, consistent with that description, why you believe that Newton did something quite different.

 

[harrylin]

In what sense was Newton's model "based on" absolute motion? Is absolute (linear) motion a requirement for his model to work (give correct quantitative predictions)? Or is it just an irrelevant assumption that doesn't change the quantitative predictions of his model?

As always with such things (never sure to call them postulates, axioms, hypotheses or whatever) one can certainly replace one hypothesis by another one; but I suppose that you do not ask that. Merely deleting that hypothesis from his presentation results in lack of definition of such things as rotation and linear acceleration; and as you can verify for yourself, already his first law becomes then undefined so that it cannot predict anything. He assumed (don't forget when he lived and what he could know!) that the stars are fixed in space; a practical application of this was to measure absolute rotation as relative to those "fixed stars". You can also be in relative rotation without being in absolute rotation, and vice versa.

 

[harrylin]

There is no "directly" here. Quarks and em fields are testable.

You are about to fall into the "true nature" trap. That is the philosophical belief that there is a "true nature" to things independent of our scientific models. This enables a non-religious justification of the absolute reference frame issue, for example. That is completely unscientific. In science, a phenomena or object is nothing more or less than the sum of its properties and behaviors. Quarks have testable properties and those properties is what they is.

That sounds like positivistic philosophy to me (or, to use your phrasing, the "positivistic philosophy trap"); using the word "unscientific" isn't helpful and on that issue I side with Popper - which is again another topic...

PS. thanks to this discussion I took Popper from the shelve, and I agree with Einstein's remark there, in agreement with Popper and against positivism:
"theory cannot be fabricated out of the results of observation, but it can only be invented".

 

[harrylin]

[..] still, i don't see how Newton would have been expected to use any other axiom for time than he did, given the physical world he observed. and this lesson should apply to us today regarding SR and GR, QM, Standard Model, ΛCDM, etc. what we take now as axioms might be refuted by our descendants.[..]

Well seen; people often put extremely unreasonable/unfair demands on others in the past, and even pretend that those others used "wrong" (or illogical or whatever) thinking simply because these used hypotheses that they dislike or because they don't understand the logical development of thought, based on the knowledge and way of thinking of that person at that time.

 

[chrisbaird]

Newton developed a theory that matched and correctly predicted all experimental results within the level experimental accuracy available at the time. I don't see what the problem is. Universal time is very testable. Take two synchronized clocks and put one on the top of the mountain and the other deep in the ocean and let them run for awhile then bring them back and compare. Using the types of clocks available at the time of Newton, you would find them to match and therefore time is universal. Absolute time is also observable. There is an absolute t = 0 and it is the Big Bang. We cannot observe before the Big Bang, therefore time before then has no meaning. Newton was right on both counts (within the experimental accuracy of his time), so he does not need to correct anything. His theory is still right at low speeds and in small gravitational fields. To insist a dead theorist correct his theory because of experimental data that is only available hundreds of years later is absurd.

 

[harrylin]

Newton developed a theory that matched and correctly predicted all experimental results within the level experimental accuracy available at the time. I don't see what the problem is. [..] Using the types of clocks available at the time of Newton, you would find them to match and therefore time is universal. [..] Newton was right on both counts (within the experimental accuracy of his time), so he does not need to correct anything. His theory is still right at low speeds and in small gravitational fields. To insist a dead theorist correct his theory because of experimental data that is only available hundreds of years later is absurd.

While I don't share your view of calling not being measurably wrong the same as being right, the imagined problem isn't exactly that; instead it is alleged that Newton didn't follow the scientific method, or that his logic was illogical. However I have the impression that such allegations don't cut wood; as yet nobody showed the error that Newton supposedly made.

 

[A.T.]

In what sense was Newton's model "based on" absolute motion? Is absolute (linear) motion a requirement for his model to work (give correct quantitative predictions)? Or is it just an irrelevant assumption that doesn't change the quantitative predictions of his model?

Merely deleting that hypothesis from his presentation results in lack of definition of such things as rotation and linear acceleration; and as you can verify for yourself, already his first law becomes then undefined so that it cannot predict anything.

Sorry, I don't see your definition problems. Since Newton's laws work fine in all inertial frames, I don't see why the assumption of an absolute rest frame is necessary in his model.

 

[harrylin]

Since you don't completely agree with the premise of my argument then there is no point in proceeding until we have resolved that. However, it sounds like my premise is not too far from something you would agree to completely, so perhaps I can agree to your version instead. Please write a premise that you would agree with "in absolute way" of the form:

Scientific assumptions should ...

http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html sounds quite OK to me.
Thus, step 2:
Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.

 

[harrylin]

Sorry, I don't see your definition problems. Since Newton's laws work fine in all inertial frames, I don't see why the assumption of an absolute rest frame is necessary in his model.

You read Newton from the perspective of post-Newton models. Just read it again, and tell me what in his theory could be the basis for defining such items as "inertial frames" (and note that no such term appears in his theory). Interestingly, it seems that as recent as Einstein's first SR paper the term "inertial frame" wasn't in use, for there he defined the frames to which SR relates as those in which Newton's laws [supposedly] hold.

 

[Dale]

http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html sounds quite OK to me.
Thus, step 2:
Formulation of an hypothesis to explain the phenomena. In physics, the hypothesis often takes the form of a causal mechanism or a mathematical relation.

So you would agree in an absolute way with the premise "scientific assumptions should take the form of a causal mechanism or a mathematical relation". ?

 

[russ_watters]

Evidently we disagree, as my summary description of what Newton did is IMHO a good example of the scientific method. Perhaps there are different opinions about what the scientific method is; and we should not deviate too much from the topic (or start it in a separate thread). However, the first description that I found as it is linked from Wikipedia, is the following:

http://teacher.nsrl.rochester.edu/phy_labs/AppendixE/AppendixE.html

At first sight my opinion is consistent with that description of the scientific method; and it would be helpful if you can elaborate, consistent with that description, why you believe that Newton did something quite different.

I'm not sure how it could get any clearer, since we've been discussing the same point for the entire thread and in the other thread too! I'll do my best to state it as succinctly and clearly as possible:

Assume only that which is necessary.

That is an essential part of any activity [supposedly] grounded in logic. The danger in violating it is clear: if you throw in an irrelevant assumption, confirmation of your hypothesis' prediction will then erroneously appear to support that assumption. But fixing the problem is also simple: assume the opposite and see if the logic still works. If it does, then the assumption was unnecessary.

Merely deleting that hypothesis from his presentation results in lack of definition of such things as rotation and linear acceleration; and as you can verify for yourself, already his first law becomes then undefined so that it cannot predict anything. He assumed (don't forget when he lived and what he could know!) that the stars are fixed in space; a practical application of this was to measure absolute rotation as relative to those "fixed stars". You can also be in relative rotation without being in absolute rotation, and vice versa.

That is not true now nor was it true then. As already stated, Newton's contemporaries even pointed that out to him. Rotation is not inertial motion, so showing that rotation and acceleration are absolute does not tell you anything useful about whether inertial motion is absolute. Newton knew the difference. From your link:

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.

Notice: "absolute motion" in this context refers only to translational motion, not rotational motion.

And so, instead of absolute places and motions, we use relative ones; and that without any inconvenience in common affairs; but in philosophical disquisitions, we ought to abstract from our senses, and consider things themselves, distinct from what are only sensible measures of them. For it may be that there is no body really at rest, to which the places and motions of others may be referred.

There he says that the use of relative motion only is "without any inconvenience" and that the assumption of absolute motion is "philosophical" only. In other words, he really should know that inserting the assumption adds no value to the theory.

And therefore this endeavour, does not depend upon any translation of the water in respect of the ambient bodies, nor can true circular motion be defined by such translation.

Here he shows that rotation is absolute, while stating that this does not change the fact that translation is not.

It is indeed a matter of great difficulty to discover, and effectually to distinguish, the true motion of particular bodies from the apparent; because the parts of that immovable space, in which those motions are performed, do by no means come under the observation of our senses.

Again he reiterates that absolute linear motion is undetectable.

 

[t_evans]

I'm aware that this is going off topic from the very meritable discussion on the scientific method, but it's one of my favorite points and relates to the initial question. [/ end off topic apology]

A really nice thing is to look at this whole exercise the other way around.

Normally, you'd think of Galilean relativity as a consequence of Newton's laws - i.e. it only contains second derivatives wrt to time, so you can add any first or zero order constants of integration you like, given you apply them correctly.

However, you can turn this argument beautifully on it's head - you can derive the classical action, and therefore all of classical mechanics, from assuming just assuming Galilean relativity. I would recommend reading Landau-Lifgarbagez Mechanics I to anyone who hasn't yet. Deriving Newton's laws in this way is pretty much the first thing done.

Thus you can think of relativity as the axiom and mechanics as the consequence, rather than the other way around.

 

[D H]

I'm not sure how it could get any clearer, since we've been discussing the same point for the entire thread and in the other thread too! I'll do my best to state it as succinctly and clearly as possible:

Assume only that which is necessary.

Drink that parsimonious wine!

(source: http://www.flickr.com/photos/shishberg/2213562731/)

Again he reiterates that absolute linear motion is undetectable.

And he does so even more clearly in Corollary V to his laws of motion:

The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards in a right line without any circular motion.

For the differences of the motions tending towards the same parts, and the sums of those that tend towards contrary parts, are, at first (by supposition), in both cases the same; and it is from those sums and differences that the collisions and impulses do arise with which the bodies mutually impinge one upon another. Wherefore (by Law II), the effects of those collisions will be equal in both cases; and therefore the mutual motions of the bodies among themselves in the one case will remain equal to the mutual motions of the bodies among themselves in the other. A clear proof of which we have from the experiment of a ship; where all motions happen after the same manner, whether the ship is at rest, or is carried uniformly forwards in a right line.​

Galilean relativity, right down to the ships.

 

[harrylin]

[..] Galilean relativity, right down to the ships.

That would be right if in Galilean relativity the motion of the ships was defined as in Newtonian relativity, but almost certainly that is not true - and that subtle difference seems to be the focus of the discussion. Does anyone here know Galileo's reference for the motion of the ships in his illustration, in particular Galileo's definition of "right line" motion?