Newtonian Relativity: Galilean Relativity & Beyond

[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?

 

[harrylin]

[..] 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.

I think that you hit the nail on the head, but perhaps not in the way you meant: From the discussions I get the impression that most people look at Newton's theory with a modern notion of "Galilean relativity", instead of trying to judge his theory based on his knowledge and logical reasoning.

 

[harrylin]

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". ?

While that sounds quite OK to me, I don't think that any of us has the right to define how scientists should work "in an absolute way", so as to limit scientific endeavor. The scientific method consists of providing new hypotheses that could better explain certain observations than old ones, and then testing the theory that is based those hypotheses. If the resulting theory has more predictive power or is more accurate than the foregoing, then it is considered to be a better theory. Providing such new hypotheses is a creative process - as I noted, Einstein stressed that theory cannot be fabricated out of the results of observation. Perhaps you have a contrary opinion.

 

[A.T.]

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.

Galileo lived before Newton.

Just read it again, and tell me what in his theory could be the basis for defining such items as "inertial frames"

From: http://en.wikipedia.org/wiki/Galilean_invariance#Formulation

Among the axioms from Newton's theory are:
There exists an absolute space, in which Newton's laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.

If the laws are the same in all inertial frames, there is no scientific justification to call one of them "absolute".

 

[harrylin]

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 requirement is not contained, as far as I can see, in common descriptions of the scientific method like the one to which I provided the link; it seems to be an auxiliary, philosophical demand by a certain group of people. Thus we obviously disagree on the scientific method, and with that the basis of the discussion is more or less gone. However, I see that next you talk of "irrelevant assumptions" which may relate to a misunderstanding of Newton's logical development:

[..] 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. 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. [..]

Sorry, I'm afraid that your vocabulary doesn't correspond to Newton's definitions of words; in which case no meaningful discussion is possible!

However, this can be easily fixed as follows:
- please adhere to Newton's definitions of terms, so that your criticism matches the text that you criticize;
- omit any assumption that you claim to be irrelevant, and show that it has no effect on the theory building.

In that case you will still not have shown that Newton made an error, but you will have shown that he could have simplified his theory more, just as some people claim about Einstein's development of special relativity.

Thanks,
Harald

 

[harrylin]

[..]If the laws are the same in all inertial frames, there is no scientific justification to call one of them "absolute".

Again: that term apparently emerged centuries later, based on Newton's theory; just repeating that term is as helpful as asking why Newton didn't use GPS.

 

[A.T.]

Assume only that which is necessary.

That requirement is not contained, as far as I can see, in common descriptions of the scientific method

In that case, why not add little undetectable fairies which live on the equally undetectable planet Absolutus which is at absolute rest and defines absolute space?

Sorry, I'm afraid that your vocabulary doesn't correspond to Newton's definitions of words; in which case no meaningful discussion is possible

So if Newton had been a Chinese guy, you could discuss his model only in Mandarin?

 

[harrylin]

I will still seriously reply the following questions, but as it starts to sound like trolling, I won't continue the conversation if it proceeds like this:

In that case, why not add little undetectable fairies which live on the equally undetectable planet Absolutus which is at absolute rest and defines absolute space?

If such a postulate would induce a theory of physics with more accuracy or more predictive power (a possibility which I deem much less likely than the explosion of a nuclear reactor), then that's what we should prefer, based on the scientific method.

So if Newton had been a Chinese guy, you could discuss his model only in Mandarin?

If his model would not be translated in a language that I can understand, then I would not pretend to be able to discuss it. However, we are lucky to have his model in English, complete with his definitions of his terms.

 

[harrylin]

Everyone here thanks for this interesting discussion, as it led me to discover a related issue that is new to me: according to several comments that I found on internet, the relativity that Newton disproved was the one of Galileo. IOW, Leibniz simply expressed the erroneous view of Galileo's relativity. If true, then criticism on Newton's theoretical development should take that fact in account.

PS I now finally found a seemingly good and easy to read text online:
http://galileoandeinstein.physics.virginia.edu/tns_draft/index.html
http://galileoandeinstein.physics.virginia.edu/tns_draft/tns_153to160.html

 

[Dale]

that sounds quite OK to me

Well, then I am afraid we have a substantive disagreement. To me, that seems like a really bad criterion for judging scientific assumptions. It allows one to arbitrarily assume undetectable unicorns doing anything as long as it is expressed as a causal mechanism or mathematically. Intelligent design and aether are current examples of such assumptions.

I don't think that any of us has the right to define how scientists should work "in an absolute way", so as to limit scientific endeavor.

This feels like just an attempt to avoid the discussion.

Professional organizations do this kind of thing all the time, and we can always judge what we think is good science and what we think is bad science. Just because someone slaps the label "scientist" on themselves doesn't make them immune from judgement or scrutiny.

Don't try to avoid the discussion, either conceed the point or take a stand.

The scientific method consists of providing new hypotheses that could better explain certain observations than old ones, and then testing the theory that is based those hypotheses. If the resulting theory has more predictive power or is more accurate than the foregoing, then it is considered to be a better theory. Providing such new hypotheses is a creative process

I agree. But no creative process uniformly produces good results. So how are we to judge good ones from bad ones? Particularly in the case where two different ones produce the same experimental predictions.

Please don't try to avoid this. Put some real mental effort into articulating what you think makes good science. "Scientific assumptions should ..." If you think the above criteria are good, then defend them, because I think they are not. If you agree that they are not good, then propose some other criteria and let's see.

Einstein stressed that theory cannot be fabricated out of the results of observation. Perhaps you have a contrary opinion.

Nope, I agree. That is not at all inconsistent with my criteria that scientific assumptions should either be empirically justified or logically required from things that are empirically justified. In fact, Einstein's postulates and the Lorentz transform are prime examples, the postulates are empirically justified and the Lorentz transform logically follows from them.

 

[russ_watters]

That requirement is not contained, as far as I can see, in common descriptions of the scientific method like the one to which I provided the link...

True. That link presupposes one already has an understanding of how to use logic. Try this one:
http://grockit.com/blog/lsat/2010/08/05/applying-%E2%80%9Cnecessary%E2%80%9D-and-%E2%80%9Csufficient%E2%80%9D-to-assumption-questions/

Sorry, I'm afraid that your vocabulary doesn't correspond to Newton's definitions of words; in which case no meaningful discussion is possible!

However, this can be easily fixed as follows:
- please adhere to Newton's definitions of terms, so that your criticism matches the text that you criticize;

If you'd tell me where I erred, I'd appreciate it.

- omit any assumption that you claim to be irrelevant, and show that it has no effect on the theory building.

This is getting tedius. You know which assumption we are discussing. This is your thread!

Furthermore, I simply can't accept that you need a proof that the assumption is unnecessary. If asking Newton wasn't enough, a quick look at any equation coming from Newton's theories will show you that they none require an absolute reference frame (for example, the "r" in the gravitational force equation explicitly referrs to a relative distance). But more to the point, this issue is one that has been vetted by 500 years of physics. It does not need to be proven here and your insistence that it must is starting to appear to be feigned ignorance.

In that case you will still not have shown that Newton made an error, but you will have shown that he could have simplified his theory more, just as some people claim about Einstein's development of special relativity.

I'm sorry, but you're basically dismissing the issue of the logical error, which is the entire point that you are getting wrong. So before we proceed further, you'll need to learn how the logic works. Please read the link I provided.

 

[A.T.]

In that case, why not add little undetectable fairies which live on the equally undetectable planet Absolutus which is at absolute rest and defines absolute space?

If such a postulate would induce a theory of physics with more accuracy or more predictive power...

It doesn't. And that is the point. It has no impact on the quantitative predictions, just like the assumption of absolute space.

 

[harrylin]

[..] Professional organizations do this kind of thing all the time, and we can always judge what we think is good science and what we think is bad science. Just because someone slaps the label "scientist" on themselves doesn't make them immune from judgement or scrutiny.
Don't try to avoid the discussion, either conceed the point or take a stand.

I already took my stand: I agreed with the first university summary that I clicked on and now it's clear that you don't. As there is no "universal truth" on the philosophy of science, we evidently simply have to acknowledge in this thread about Newtonian relativity that we disagree on the topic of scientific method.

I agree. But no creative process uniformly produces good results. So how are we to judge good ones from bad ones? Particularly in the case where two different ones produce the same experimental predictions.

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.

 

[harrylin]

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.

 

[Dale]

we disagree on the topic of scientific method

That is fine. As I showed, your approach declares undetectable unicorns, intelligent design, and all sorts of other theories as equally valid to SR and QED, but as you mention it is a matter of taste and philosophy. Personally, I find it very distasteful to call intelligent design a scientific theory.

 

[harrylin]

That is fine. As I showed, your approach declares undetectable unicorns, intelligent design, and all sorts of other theories as equally valid to SR and QED, but as you mention it is a matter of taste and philosophy. Personally, I find it very distasteful to call intelligent design a scientific theory.

You put words in my mouth with which I strongly disagree - please don't! Regretfully for religious people, comparing the predictive power of intelligent design vs. that of evolution theory hasn't been rewarding for intelligent design, especially in recent years. If you disagree, we should start a topic on that!

 

[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.