"Classical Physics Is Wrong" Fallacy - Comments

[Dale]

It is not part of the theory (as initially proposed by Newton) that the theory is only intended to apply up to a certain limit.

Of course not, the Newtonian limit is part of relativity and QM, not part of Newtonian mechanics. I have read the context and your statements repeatedly show this misunderstanding.

 

[JohnNemo]

Of course not, the Newtonian limit is part of relativity and QM, not part of Newtonian mechanics. I have read the context and your statements repeatedly show this misunderstanding.

Anyway. I am glad we are now agreed!

 

[Dale]

To say that Newton's laws are wrong, and then to turn around and use it, is an inconsistent act.

To say that it is accurate over a certain limit, and then to turn around and use it within those limits, is NOT an inconsistent act.

Particularly well said.

 

[bhobba]

But the curvature isn't "real" in some philosophical sense - there is an unobservable flat background.

This is bit off topic but I think it interesting enough to mention. That is Steve Carlip's view (look him up if you don't know him). I have been reacquainting myself with GR recently since I find as a mentor I answer more of these queries. Anyway if you don't know Lovelock's theorem you might find it sheds light on this.

Thanks
Bill

 

[PeterDonis]

That is Steve Carlip's view

Can you give a particular reference? I've read a fair number of Carlip's papers and I'm not sure I've seen him expound the "unobservable flat background" view.

 

[bhobba]

Can you give a particular reference? I've read a fair number of Carlip's papers and I'm not sure I've seen him expound the "unobservable flat background" view.

It was from when I posted a lot on sci.physics.relativity. He posted quite a bit until it became infested with too many cranks, but mentioned a few times it was an essentially undecidable philosophical question whether space-time was curved or was flat and simply acted like it was curved.

I must say that was at least 10 years ago so may have changed his mind. I do know he is a very approachable guy and I don't think he would mind anyone asking him what his current view is. Mine is he is correct - and until he mentioned it, it never even occurred to me - it was sort of a revelation..

Thanks
Bill

 

[PeterDonis]

He posted quite a bit until it became invested with too many cranks, but mentioned a few times it was a an essentially undecidable philosophical question whether space-time was curved or was flat and simply acted like it was curved.

Ah, ok. Yes, from a philosophical point of view, I agree the question is undecidable. The spacetime curvature interpretation of GR is, strictly speaking, an interpretation, not a claim about "how things really are". It just happens to be a very, very useful interpretation, so much so that physicists routinely talk about it as if it were a fact.

 

[Dale]

It just happens to be a very, very useful interpretation, so much so that physicists routinely talk about it as if it were a fact.

That is indeed a problem. In the Newtonian limit of GR, for example, the Christoffel symbols naturally become the force of gravity. So although we speak of gravity in GR as not being a force, in fact there is a mathematical quantity in GR that does serve that role and can be interpreted as a force. Choosing to not interpret that way is a matter of philosophy and can be discarded as needed. But that common (and useful) philosophical interpretation probably serves to exacerbate the “Newtonian physics is wrong” impression.

 

[bhobba]

Ah, ok. Yes, from a philosophical point of view, I agree the question is undecidable. The spacetime curvature interpretation of GR is, strictly speaking, an interpretation, not a claim about "how things really are". It just happens to be a very, very useful interpretation, so much so that physicists routinely talk about it as if it were a fact.

For what it's worth I am with Feynman who thinks the geometrical interpretation is marvelous - it's hard to think its not actually true - but strictly speaking like the difference between SR and LET you can't really prove it. I have read his lectures on gravitation and he starts with flat space-time and spin 2 particles. You still get the EFE's but if space-time actually curved is not so clear.

Later I discovered Lovelock's Theorem that put it more in context for me. Thinking of the metric as a field or it's natural geometrical interpretation doesn't make any difference - the theorem says you get the same result - but strangely only in 4 dimensions which is rather interesting.

Thabks
Bill

 

[PeterDonis]

You can make prediction of the consequences of a particular spacetime geometry and then measure those consequences

No, you can make a prediction of the consequences of particular solutions of particular equations, and then compare the predictions with measurement. But the equations don't have labels on them that say "these equations describe a spacetime geometry". Spacetime geometry, as I said in a previous post, is an interpretation of the equations. You don't need an interpretation to make predictions and compare them with measurements. Interpretation is a conceptual crutch for us humans, because we don't naturally think in equations, so we need some kind of story to tell about what the equations "mean". But the "spacetime geometry" story is not the only story you can tell about the equations of GR.

 

[Peter Morgan]

No-one responded to this comment on Facebook (https://www.facebook.com/groups/2204629320/permalink/10156235771439321/?comment_id=10156240941494321), so I'll make it here also and make a few additional comments to reflect the discussion above, "Not only is classical physics not wrong, it is more capable than generally understood. If we present classical mechanics as a commutative algebra of operators together with a noncommutative algebra of transformations constructed using the Poisson bracket, all acting on a Hilbert space in a Koopman-von Neumann formalism, a random field CM can even be equivalent to a QFT if there is a natural complex structure (which there is in the case of electromagnetism, provided by the Hodge dual)."

This obviously leads in a slightly different direction than either ZapperZ's article or the comments above. Seeing one concern expressed in the comments above, I'll also note that I take not only the Lagrangian and Hamiltonian formalisms to be part of "Newtonian physics", but also Liouvillean probability densities over phase space and the Koopman-von Neumann formalism, and the extensions into issues of analysis (random fields, say, citing my own preference because they they can be made to parallel quantum fields so closely, but there are other stochastic approaches) that are required to discuss probability densities in field theory cases.

A further comment, about special relativity: the wave equation, the Klein-Gordon equation, and any differential equation that is Lorentz invariant, fit into the Lagrangian, Hamiltonian, Liouvillean, and Koopman-von Neumann formalisms well enough, so there's not any necessity to consider a limit as the speed of light is much larger than characteristic velocities. Just solve the equations.

I should be open about this comment being part of an effort to get more good mathematical physicists to look at and send me comments on https://arxiv.org/abs/1709.06711. The math there has been stable for many months, but the abstract and introduction do not discuss the relationship between random fields and quantum fields as clearly as I would like (nor as clearly as those people who have looked at the paper would like). I am now very close to submitting to a journal, so if you decide to have a look please be quick! I will be happy to send a copy of the paper as I currently have it to anyone who expresses interest.

 

[GTrax]

Reading these posts makes me wonder how "wrong" some "outdated" approximation has to be, to cease to be useful.

I mean this not only in the day-to-day practical sense, but also in contributing to the wonderful human sense of pattern recognition and making those insight connections to come up with a whole new theory or concept that incrementally relegates the "old" into being an approximation. The new is built on the scaffold of the old - even if one ends up junking the entire scaffold!

Putting aside the Newtonian vs Einsteinian comparison, consider something older by Tycho Brahe. Apparently impressed by the mathematical benefits of a Copernican heliocentric system, but unable to imagine a "huge heavy sluggish Earth" moving at speed, he came up with a geoheliocentric model that was accurate. Tycho was obsessed with accuracy, and gathered the best measurements of the time.

Yes yes - we get it that Kepler, Newton, and others had a later different, and simpler, insight, and that they got there much on the back of Tycho's data, but Tycho could predict with the best of them! He could say when an eclipse would happen, or say when and where a planet would be would be when occulting a star. In his own mind, and among those who depended on his data, Tycho had a right to believe his model was the way celestial bodies really moved!

Take away Tycho, and his "wrong" model, and you take away one of the "shoulders" Newton and others would stand upon to see further.
Even now, however well we think we know where celestial bodies are, and how they move, they had better not be too far from where Tycho thought they should be! We now have a wonderful Quantum Mechanical description of the way things are, an absurdly abstract non-intuitive fairy story of the charmed and strange and sticky that agrees with experiment to enough decimal places to be impressively compelling.

Perhaps in the fine tradition of Maxwell (adding an unmeasured "displacement current" to make the equations come out right), because it seemed the right thing to do, the way things are need to be described with some sort of model that agrees with experiments. It is when we postulate mathematical fictions (however useful), we need to keep a watch on whether they are more than a calculation aid!

 

[ZapperZ]

But as I've said earlier, it is no longer that common that an older theory is discarded wholesale. This is because many of our older ideas are actually valid within the realm that they are applicable.

It was certainly more common with ideas from the 19th Century, where our methods of detection and awareness of our world are significantly less developed. The old idea of Caloric Theory is one clear example, where one of the first attempts at formalizing our understanding of thermodynamics has been basically discarded.

Interestingly enough, with QM and the idea of quantized lattice vibrations (phonons), the old concept of "corpuscular heat" of Caloric Theory is not totally crazy when applied to thermodynamics in solids.

Zz.

 

[GTrax]

Interestingly enough, with QM and the idea of quantized lattice vibrations (phonons), the old concept of "corpuscular heat" of Caloric Theory is not totally crazy when applied to thermodynamics in solids.

I love this! There was imagination to "Caloric".

Even so - I am cautious about taking this too far. The mental magic that allowed many to countenance a "negative weight" concept in the cause of "phlogiston" is one model where it's subsequent usefulness in practical calculation and prediction, is pretty much trashed by the manifest evidence of a new element, and a much more useful concept!

When I say "Classical Physics is not wrong", I do not mean any and every disproved notion. Within the accuracy by which we can usually verify our experiences, I mean the whole of classical physics "laws" that have never seen a single exception. It has to be an exception glaring and obvious, so that humans can recognize that it might belong in the same bin as phlogiston.

To know that something else might be going on, one needs to go to exceptional precision, and even then get used to the idea that there is a built-in uncertainty that messes with how well one can determine other values involved.

 

[Dr. Courtney]

I prefer to consider theories as "useful" or "not useful" for given applications rather than "right" (true) or "wrong". A theory is useful if it makes predictions that are sufficiently accurate for my purpose.

But the fact is, there were many occasions in my undergraduate (and graduate) education where the wrongness of the prevailing theory (inability to accurately predict an experimental result) was used to justify development of a new theory, and often classical physice was the prevailing theory portrayed as wrong in the circumstances described.

2. Classical physics has been shown to be derivable from SR and QM under special conditions that apply to our ordinary situation.

3. Any theory MUST have the ability to show that it merges to the classical description when applied to ordinary situation.

4. This can only be shown mathematically. It cannot be shown convincingly via hand-waving or qualitative arguments. It is the equivalent mathematical form that shows that one theory can derive the other.

The discussion leading to eqns 6 and 7 (and eqns 6 and 7 themselves) breaks down in the case of chaotic classical motion, and it is still something of a mystery how QM gives rise to chaotic classical motion in the limiting case. Some specific cases from atomic physics have received a lot of attention:

V = -1/r + B^2(x^2 + y^2)/8 (Model for hydrogen atom in a magnetic field)
V = -1/r + (Z - 1) exp(-ar) + Fz (Model for an alkali atom in an electric field)

I've published several papers studying the above two Hamiltonians, and I assure you there is no mathematical description showing how the classical solution of the Hamiltonian arises from the quantum solution in cases where the parameters give rise to strongly chaotic motion in the classical solution. Numerous other authors have reached the same conclusion in studying these problems.

I look at the epistemological question in physics analogous to the germ theory of disease in biology. Just as history gave rise to more and more diseases where the germ theory was not applicable, history gave rise to more and more cases where classical physics was not applicable. It is really a matter of definition whether one says "the germ theory of disease is wrong" or "here are the list of known cases where the germ theory of disease is known not to apply." Given that at one time, classical physics was throught to be universal, the position that it is wrong is defensible. But at some point the debate is silly, and it is more reasonable to address theories based on their usefulness rather than on their truth.

Euclidean geometry is similar. Before Einstein, it was widely held to be an exact and universal description of the physical world. Now we know that is not true. But it sure is useful and an exceedingly accurate approximation for most purposes.

 

[ZapperZ]

I prefer to consider theories as "useful" or "not useful" for given applications rather than "right" (true) or "wrong". A theory is useful if it makes predictions that are sufficiently accurate for my purpose.

You will notice that I tend to use the word "valid", rather than right, true, etc... But at some point, this becomes a matter of semantics, i.e. what exactly does one mean when one say "right" or "wrong". One doesn't usually use something, or do something, that is wrong. For classical mechanics, we use it a lot!

But the fact is, there were many occasions in my undergraduate (and graduate) education where the wrongness of the prevailing theory (inability to accurately predict an experimental result) was used to justify development of a new theory, and often classical physice was the prevailing theory portrayed as wrong in the circumstances described.

But are they "wrong" or simply not applicable or not accurate enough after a certain point? Your electronics use Ohm's Law, but I can show you a lot of circumstances where it doesn't work because the assumptions that Ohm's Law were derived from are no longer applicable. So is it wrong, or is it simply that it isn't meant to be used in that situation?

The discussion leading to eqns 6 and 7 (and eqns 6 and 7 themselves) breaks down in the case of chaotic classical motion, and it is still something of a mystery how QM gives rise to chaotic classical motion in the limiting case.

The article is not claiming that it has solved the classical-quantum boundaries. Far from it. Mesoscopic scale physics is still a very active area of research, and the classical-quantum "transition" (I'm using the pedestrian definition of this word) is still unknown. And I can go all day talking about emergent phenomena that can't be simply derived from all the basic interactions (superconductivity). However, there are still indication that one can get back the classical picture under certain circumstances. This is a piece of information that is not known by many members here who often made the claim that classical physics is wrong. Any physics student is aware of the derivation that I did in the article. It isn't news. It IS news to many who are not aware of such connection when they think that we shouldn't use classical physics anymore when it has been superseded by QM/SR/GR.

THAT is the main purpose of the article.

Zz.

 

[HAYAO]

In my view, I say that any major scientific development is a generalization procedure (in a very loose sense).

I don't know much instances where a theory was completely denied from the core. This is obvious because science is based on observation and experiment that is reproducible. Even geocentrism is not "wrong". Purely in terms of orbits, it is simply a matter of where the origin is defined to (the Earth or the Sun). Of course, we know that heliocentrism was right in light of new experimental evidence, but it still encompasses what was developed in geocentrism. If we understand heliocentrism (how the stars and planets move), then we can also understand geocentrism (how the sky looks like from a planet).

Similarly, classical physics is a specialized case/formulation of quantum mechanics. They are not "wrong". Non-relativistic quantum mechanics is a specialized case of QFT. They are not "wrong" (although I understand that QFT is still essentially QM and not precisely a good analogy).

If there is any new theory in physics, then they are going to encompass what has already been developed but more generalized, and can be used to explain more than we used to. It won't "deny" anything.Great article. I cannot agree more.

 

[diPoleMoment]

What difference does it make if you get the old theory from an upper limit or any other arbitrary direction? My point was that SR is considering space and time as completely different things comparing to old mechanics. This does not make any sense. If I say that the assumptions are: time is relative and space is Riemaniann and you say: time is absolute and space is euclidian, how can we be talking about the same theory?No, you are wrong. What I said was that the assumptions are different! If you look at how we treat all the experiments and particles / waves in quantum world, we see that space, time, energy and whatever are all different from what we knew from classical mechanics, which means, we cannot start to say that there exists a derivation from one to another, as they were talking, ever, about the same thing. Again, if you start with different assumptions how can you end up with theories converging at a limit that has been chosen to find a connection between them?

I am not saying that Newtonian Mechanics is wrong. this has nothing to do with being right or wrong. I'm talking about how do we explain an theory evolution without wanting to find convergencies that were created just to make understanding easier.

I agree with Orodruin with more knowledge, the parameters for the theory of Physics have changed. Now since Newtonian physics work and more detail is known, then retro fitting more defined parameters to the limited parameters makes sense to me. I would say doing this would ensure if the more defined parameters cannot be canceled out to fit within the limited parameters, then the new theory cannot really encompass the basics of physics. This theory then would mean it represents another reality. Which I know is all relative. However if elements on Earth can be found in space, then when chemistry is brought in the picture, physics in space have to relate to what happens on Earth. With that said, retrofitting quantum equations to fit Newtonian physics will ensure that with more parameters added that the idea has a sound basis to be built upon.

Now the theory of assumptions can be a matter of discussion, but I feel if quantum can explain mechanical in mathematical form then assumptions have to be reevaluated within the confines that mechanical theory works. So I love this article.

 

[Ziang]

I agree with the author. However, he wrote, "...if there are more general and more accurate theories beyond QM, SR/GR, ...".
Physicists say that SR expressions have been verified with accelerators. So, if there is any theory that gives a different expression, then it will not get along with results from the accelerators. This means that there is no way for a more accurate theory exists.

 

[ZapperZ]

I agree with the author. However, he wrote, "...if there are more general and more accurate theories beyond QM, SR/GR, ...".
Physicists say that SR expressions have been verified with accelerators. So, if there is any theory that gives a different expression, then it will not get along with results from the accelerators. This means that there is no way for a more accurate theory exists.

I think you missed the point, and you also seem to be unaware of the history of physics.

We ALWAYS come up with more comprehensive and more accurate theories. That has always been the pattern, and there's nothing to say that this will stop. The issue of unifying general relativity within the QM/QFT picture is one such problem we have right now. So if there is a more encompassing theory, then this new theory will have to have, at some limit, the SAME form as SR/GR, because of the successes of SR/GR already. It is why I showed the mathematical derivation and showed how the mathematical form matches classical description in some limit.

Please look again at the original post and the MAIN POINT of that post, because it appears that you didn't get that story.

Zz.

 

[Dale]

Physicists say that SR expressions have been verified with accelerators. So, if there is any theory that gives a different expression, then it will not get along with results from the accelerators. This means that there is no way for a more accurate theory exists.

A more accurate theory must reduce to the SR expressions under the conditions covered by the accelerator experiments. It may diverge from SR in other conditions.

 

[mfb]

I agree with the author. However, he wrote, "...if there are more general and more accurate theories beyond QM, SR/GR, ...".
Physicists say that SR expressions have been verified with accelerators. So, if there is any theory that gives a different expression, then it will not get along with results from the accelerators. This means that there is no way for a more accurate theory exists.

These theories give you answers to questions SR cannot answer.
SR cannot tell you what happens with gravity. GR can. In the absence of gravity, GR is identical to SR.
SR cannot tell you what happens if fields are quantized. QFT (quantum field theory) can. If the quantization is irrelevant, QFT is identical to SR.

 

[Ziang]

By working the math. A lot of things that we may verbally or philosophically consider different are mathematically equivalent. You may think that you are drawing an important distinction between Newtonian and Relativistic mechanics, but in the v<<c limit this distinction is only in your mind and does not appear in either the math or experiment.

The distinction does not appear in either the math or experiment may not be sufficient to conclude that they are the same theory or same fundamental concepts or same assumptions.

 

[ZapperZ]

The distinction does not appear in either the math or experiment may not be sufficient to conclude that they are the same theory or same fundamental concepts or same assumptions.

This is a very puzzling statement.

The argument isn't about "fundamental concepts" of "same assumptions". They are not! The postulates of SR is distinctively different than the classical Galilean transformation. That isn't the issue!

But when you have derived, under a certain limit, of the same mathematical form, then that theory can be logically shown to be able to reproduce all the results of that came out of the mathematical form!

I'm a bit surprised that this is even an issue. This is done in mathematics all the time! We manipulate our differential equations, for example, so that they can be in one of the known forms that results in one of the special functions. As soon as the mathematical form matches a known form, the work is done is showing what the solutions and the behavior of the solutions should be, because it has already been solved!

Zz.

 

[Dale]

The distinction does not appear in either the math or experiment may not be sufficient to conclude that they are the same theory or same fundamental concepts or same assumptions.

It is sufficient to conclude that the differences between the concepts and assumptions are scientifically, experimentally, and physically irrelevant. The remaining differences are only in our mind, not in nature, the assumptions do not matter to nature regardless of how important we perceive them to be. SR with v<<c is physically the same as classical physics in every way which can be tested.

This is related to the difference between a theory and an interpretation. If you have general questions about the difference between a theory and an interpretation, please start a new thread rather than detract too much from this thread.

 

[Hypercube]

Thank you for the Insight article.

I apologise to everyone if this is a dumb question, but would you say Newton's laws would further reduce to Kepler's laws under some limiting case?

 

[ZapperZ]

Thank you for the Insight article.

I apologise to everyone if this is a dumb question, but would you say Newton's laws would further reduce to Kepler's laws under some limiting case?

No. Kepler's law is an "application" of Newton's laws, the same way the kinematics of a mass sliding down an inclined plane is an application of Newton's laws.

Zz.

 

[Dr Whom]

Classical theory. Wrong but by so very, very little in everyday situations it is not worth the extra trouble using the correct theory.
And can we say the current theories are correct? As far as we know they are but as far as they knew at the end of the 19th century the classical theories were. Let us hope not, as where would be the fun in that?

 

[ZapperZ]

Classical theory. Wrong but by so very, very little in everyday situations it is not worth the extra trouble using the correct theory.
And can we say the current theories are correct? As far as we know they are but as far as they knew at the end of the 19th century the classical theories were. Let us hope not, as where would be the fun in that?

Since when is the limit of an approximation is considered to be "wrong" when it is used in that limit? That's like saying there is no point in even doing linear algebra or many-body physics, because these are all approximations (even valid approximations). If that's the case, then every single thing we use now is wrong, because I can guarantee you that no one has every managed to completely solve any of the many-body equations that described the behavior of your semiconductors, the behavior of current in a conductor, etc... etc.

The problem here is that among the general public, the word "wrong" has a very strong and distinct connotation. When something is wrong, you don't use it, or you don't do it. It is very black-and-white. Yet, this is not what is meant here, and in that sense, classical physics is definitely not wrong. So in that context, claiming that classical physics is wrong, is in fact, wrong!

Zz.

 

[Dr Whom]

Classical theories are approximations, not limits. Ergo, saying classical physics is wrong is wrong is wrong!

 

[Orodruin]

Classical theories are approximations, not limits.

If you have an "approximation", this suggest that it is an approximation of something. The aim of physical theories is to describe observations. If they do, they are good theories. In certain limits, classical theories work fine and they are good theories in those limits. What is meant by a theory being recovered as a limit of a different theory is that predictions agree to leading order as some model parameter is taken to zero. This is standard nomenclature. When the parameter is not exactly zero, but relatively close, yes you can use the classical theory as an approximation of the full theory, but this is conceptually different.

Ergo, saying classical physics is wrong is wrong is wrong!

This statement just makes it clear that you have missed the entire point of the discussion, which is that what laymen consider the word "wrong" to mean is fundamentally different.

 

[Dale]

Classical theories are approximations, not limits

Yes, they are. Did you not read the article?

Also, approximations are not inherently wrong in science.

 

[Dale]

Closed temporarily for moderation. Hope to reopen soon.

Edit: the thread is reopened after major cleanup. There will be no further discussion of flat Earth theory, which is a conspiracy theory not a scientific theory and thus forbidden by the rules. Everyone must find a different way of making their points than dragging this forum into a discussion of conspiracy theories. The scientific approximation of small sections of the Earth as flat was already addressed fully in post 2.

 

[Maximilian]

If you are traveling at 30mph down the road and a car passes you going 30mph faster, you can calculate its road speed using Newtonian or Einsteinian relativity. You will get the same answer to the precision you can plausibly measure. You need to take into account the velocity variation from flies crashing into the front of the car long before you need to care about Einstein. So simplifying the maths and using Newton isn't wrong.

Simplifying the math by using Newton is not wrong. But the justification you have given depends on Newton being wrong. Because you estimate the error you make by using Newton instead of Einstein. Without acknowledging that this is an error (and this can be an error only if Newton is wrong) you cannot estimate it, thus, it makes no sense to claim that it is small even compared with the flies.

Arguing that a given approximation is correct presupposes that one acknowledges it is only an approximation, and that there is something else which gives better results. And once another theory gives better results, it is clear that the approximation itself has to be wrong.

 

[Orodruin]

and that there is something else which gives better results.

This is a fallacy based on an idealisation. When the uncertainties in the incoming variables are much larger than any difference between the two theories, they are for all purposes equivalent in the given limit and there is no possibility to say that one is ”better” in that limit.

And once another theory gives better results, it is clear that the approximation itself has to be wrong.

This is also a bit naive and idealised. First of all, in the limiting case the other theory is not ”better”. Both theories agree perfectly up to experimentl precision. Second, if you are using ”wrong” in the global sense that is not what the article is about.

 

[Maximilian]

This is a fallacy based on an idealisation. When the uncertainties in the incoming variables are much larger than any difference between the two theories, they are for all purposes equivalent in the given limit and there is no possibility to say that one is ”better” in that limit.
This is also a bit naive and idealised. First of all, in the limiting case the other theory is not ”better”. Both theories agree perfectly up to experimentl precision. Second, if you are using ”wrong” in the global sense that is not what the article is about.

True and false, right and wrong are by their nature global. It is about the existence of an error, not about the size of the error.

And even if there is some equivalence in the limit, it does not change anything. We do not live in the limit, only quite close to this limit, and in every distance from the limit, however small, we can say which is better. Maybe we cannot measure the difference, but it exists, and we know, from regions far away from the limit, which theory is better.

One should not change the language without necessity. There are enough words to explain that in some circumstances an approximation is viable, appropriate, acceptable, accurate enough, and so on. To use, instead, words which have a different, global meaning, like true and false, right and wrong, distorts the language, makes it less precise.

Classical mechanics is wrong. It is falsified by a lot of observations and experiments. Point. That it remains nonetheless useful, as an approximation, is fine, but in no way changes the fact that it is wrong.

And it is the recognition that it is wrong which motivates scientists to find better theories, theories which will hopefully be closer to the truth. If we would not accept that not only classical mechanics, but even GR and QFT are wrong (which follows from the infinities and singularities they have), there would be no point searching for a theory of quantum gravity.

 

[Ibix]

Because you estimate the error you make by using Newton instead of Einstein.

Do it the other way round then. In either case the difference is one part in ten to the fifteen. At that level of precision the car isn't a rigid system with a single velocity. Ok, we could be talking about the velocity of the centre of mass of the car, but that is neither constant nor even a straight line. And it may or may not be the relevant velocity depending on why we want to know the relative velocity.

The whole conceptual basis of the question falls apart long, long before I need to worry about whether Einstein or Newton gives a more precise prediction. So both give the same answer to any precision it makes sense to ask. Because we are well within the domain of applicability of Newtonian theory.

 

[Maximilian]

Do it the other way round then. In either case the difference is one part in ten to the fifteen.

Yes, but this is not the question.

If I say that SR can be applied even to a car, given that the error we make by using SR would be only one part in ten to the fifteen, in comparison with classical mechanics, what would this be? Obviously nonsense.

The whole conceptual basis of the question falls apart long, long before I need to worry about whether Einstein or Newton gives a more precise prediction. So both give the same answer to any precision it makes sense to ask. Because we are well within the domain of applicability of Newtonian theory.

But you have no chance to find a domain of applicability of Newtonian theory, without acknowledging that Newtonian theory is wrong. Before 1905 where was no such animal as a domain of applicability of Newtonian theory, because it was not known that Newtonian theory is wrong. It appeared only after it was clarified that Newtonian theory is wrong, that means, that there exist regions outside the domain of applicability.

 

[PeterDonis]

Without acknowledging that this is an error (and this can be an error only if Newton is wrong)

The word "error" has a precise technical meaning when speaking of approximations. That meaning does not have the implications you are claiming here.

Arguing that a given approximation is correct

Nobody is arguing that the Newtonian approximation is "correct". Nor is anyone arguing that it is "wrong". The whole point is that "correct" and "wrong", binary categories, are not useful categories to use when talking about scientific theories and approximations. Much more useful are "less accurate" and "more accurate", which again have precise technical meanings in terms of how much error (using the technical meaning of that term, as above) there is in your predictions vs. the actual data.

If you have not read the Asimov essay that @Nugatory linked to in post #2, I strongly suggest that you do so, because it does a great job of discussing exactly this point and dispelling the kind of common confusion you are displaying here.

 

[PeterDonis]

Newtonian theory is wrong, that means, that there exist regions outside the domain of applicability.

If this is what you mean by "wrong", then you are using the word in a very different sense from its usual sense.

 

[Orodruin]

True and false, right and wrong are by their nature global. It is about the existence of an error, not about the size of the error.

No, this can only be correct in a philosophical sense and that has absolutely nothing to do with what is being discussed. Unless you are afraid that a bridge will break down because the engineers building it did not account for relativistic corrections you really have no case here because that is what the article is about. You are building a strawman argument. Empirical science is not about being right or wrong, it is about finding as good of a description of how nature behaves as possible.

If we would not accept that not only classical mechanics, but even GR and QFT are wrong (which follows from the infinities and singularities they have), there would be no point searching for a theory of quantum gravity.

This statement is just absurd. You are essentially saying that if wehad accepted Newtonian mechanics as false there would have been no point in developing relativity.

But you have no chance to find a domain of applicability of Newtonian theory, without acknowledging that Newtonian theory is wrong. Before 1905 where was no such animal as a domain of applicability of Newtonian theory, because it was not known that Newtonian theory is wrong. It appeared only after it was clarified that Newtonian theory is wrong, that means, that there exist regions outside the domain of applicability.

Again. Strawman and a failure to understand what the article is about.

 

[Maximilian]

If this is what you mean by "wrong", then you are using the word in a very different sense from its usual sense.

Given that I'm not a native speaker, this is imaginable. I know that there is also a moral meaning, right or wrong, which is not present for true and false, but in a physics discussion and in particular in the article this plays no role. The google translator gives "falsch" as the main translation, which backtranslates into "wrong, false, incorrect, counterfeit, mistaken, erroneous". This does not look like my use would be "a very different sense".

The word "error" has a precise technical meaning when speaking of approximations. That meaning does not have the implications you are claiming here.

Explain the difference. If I use an approximation instead of the correct theory, the consequence is a difference between my computation and the value the correct theory would give. This difference is part of the error I make, not? There are, of course, also other sources of error, but this error is the one relevant if one discusses an approximation.

Nobody is arguing that the Newtonian approximation is "correct". Nor is anyone arguing that it is "wrong". The whole point is that "correct" and "wrong", binary categories, are not useful categories to use when talking about scientific theories and approximations. Much more useful are "less accurate" and "more accurate", which again have precise technical meanings in terms of how much error (using the technical meaning of that term, as above) there is in your predictions vs. the actual data.

I disagree. I think these binary notions, which distinguish the theories as a whole, are very important.

If you have not read the Asimov essay that @Nugatory linked to in post #2, I strongly suggest that you do so, because it does a great job of discussing exactly this point and dispelling the kind of common confusion you are displaying here.

I have read it, and even quoted it in one of the many deleted postings.
To quote again: "John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together."

This statement is using "wrong" in the same sense I have used it. What I argue against is to name "When people thought the Earth was spherical, they were wrong" a fallacy.

No, this can only be correct in a philosophical sense and that has absolutely nothing to do with what is being discussed. Unless you are afraid that a bridge will break down because the engineers building it did not account for relativistic corrections you really have no case here because that is what the article is about. You are building a strawman argument. Empirical science is not about being right or wrong, it is about finding as good of a description of how nature behaves as possible.

First, I completely disagree philosophically. Science is about right and wrong (better true or false, to avoid the moral aspects which are not present). Empirically falsified theories are rejected because they are false. That they may be nonetheless used for approximate computations is fine and useful, but the scientific problem to find a theory which is not falsified remains.

This statement is just absurd. You are essentially saying that if we had accepted Newtonian mechanics as false there would have been no point in developing relativity.

What is absurd is your interpretation, because I'm saying exactly the opposite. If we had accepted Newtonian mechanics as true, and therefore ignored the open problems which had the potential to cause doubt (like MMX, Mercury perihelion) there would have been no point in developing relativity.

Again. Strawman and a failure to understand what the article is about.

No. The argument of the article simply fails to prove what is claimed to be proven, namely that "classical mechanics is wrong" is a fallacy.

All what it shows is that "There is somehow a notion that SR, GR, and QM have shown that classical physics is wrong, and so, it shouldn’t be used." But this is very different from "classical physics is wrong" being a fallacy. Classical physics is wrong, as any approximation, but it can be used as an approximation whenever the approximation error is sufficiently small.

 

[Dale]

it is clear that the approximation itself has to be wrong.

I disagree completely. What justification do you have for calling an approximation “wrong” when many experiments clearly show that the approximation is valid? You are not the judge of right and wrong in science: experiment is. In the domain where the approximation matches experiment it is scientifically validated. It is demonstrably not wrong.

 

[Ibix]

Classical physics is wrong, as any approximation, but it can be used as an approximation whenever the approximation error is sufficiently small.

Special relativity is only valid where gravitational effects are negligible. So it is wrong by your definition.

General relativity breaks down somewhere on the way to the inside of a black hole. So it is wrong by your definition.

Quantum theory breaks down somewhere on the way to cosmological scales because the cosmological constant is tiny. So it is wrong by your definition.

The same will be true of a successor theory. Either it will predict its own breakdown (like relativity) or it won't (like Newton). And there will always be a regime we've never tested it in. So it will be wrong by your definition. Or so we will have to suppose.

In fact, all of scientific theory is wrong by your definition. This does not seem like a helpful definition to me.

 

[Maximilian]

I disagree completely. What justification do you have for calling an approximation “wrong” when many experiments clearly show that the approximation is valid? You are not the judge of right and wrong in science: experiment is. In the domain where the approximation matches experiment it is scientifically validated. It is demonstrably not wrong.

It is demonstrably wrong, because else it would not be named an approximation but a viable physical theory. If it is not, but only useful as an approximation of some other viable physical theory, that means that it has been falsified by some empirical observation.
That it may be used, under some circumstances, as an approximation does not make a wrong theory true. And even in cases where the approximation is good as an approximation, one can compute (at least in principle) the difference between the approximation and the viable theory. This is, according to the viable theory, the error made by the approximation. It is non-zero, else it would not be named approximation, but exact solution. So we can be sure that we have a non-zero error.
We use the approximation because we know (or have estimated) that the error is below the accuracy we need in the application in question.
I judge the use of language. The words used have a meaning, and the meaning clearly gives some information about what experiments have told. Namely, that a theory which is used only as an approximation, and which is not named a viable theory, has been falsified by observation (or is not viable for other reasons, like internal inconsistency, as QFT on curved background, or because of infinities like GR.)

Special relativity is only valid where gravitational effects are negligible. So it is wrong by your definition.
General relativity breaks down somewhere on the way to the inside of a black hole. So it is wrong by your definition.

Correct.

Quantum theory breaks down somewhere on the way to cosmological scales because the cosmological constant is tiny. So it is wrong by your definition.

In my interpretation, it does not have to extend to cosmological scales, but breaks down for other reasons, but this is off-topic here, so correct too.

The same will be true of a successor theory. Either it will predict its own breakdown (like relativity) or it won't (like Newton). And there will always be a regime we've never tested it in. So it will be wrong by your definition. Or so we will have to suppose.

No. The existence of regimes not tested is irrelevant, because this does not make a theory wrong. Anyway we cannot prove by observation that it is true. But it is quite probable that theories like QG or TOE people think about developing now will be theories which can be easily seen to be false.

In fact, all of scientific theory is wrong by your definition. This does not seem like a helpful definition to me.

No. Only our actual scientific theories are wrong. That's why we have to search for better theories. Which is what many physicists are doing.

If one, instead, cares only about making sufficiently accurate predictions for observable things, there is certainly no need for quantum gravity or a GUT or TOE, and all that research is simply throwing away money.

 

[PeterDonis]

If I use an approximation instead of the correct theory, the consequence is a difference between my computation and the value the correct theory would give. This difference is part of the error I make, not?

No. You have two mathematical machines that generate predictions. You compare each prediction with the actual data. The difference between the prediction and the actual data is the error. That difference will never be zero; but if one theory is more accurate than another (such as General Relativity being more accurate than Newtonian gravity), then the more accurate theory will have a smaller error. No theory ever has a zero error.

these binary notions, which distinguish the theories as a whole

But they don't. No theory makes predictions which exactly match the data. So there is no way to sort them into binary categories. The best you can do is rank them along a continuum of how accurate their predictions are.

This statement is using "wrong" in the same sense I have used it

No, it isn't, because you are using "wrong" as a binary category. Asimov is using "wrong" as a continuum; he is saying some people are more wrong or less wrong than others. A binary category doesn't work like that; the only two possibilities are "wrong" and "not wrong". That's not what Asimov is describing.

Empirically falsified theories are rejected because they are false.

Some theories are rejected because all of their predictions are so different from the actual data that they are not useful at all. But Newtonian gravity and Newtonian mechanics are not like that. Once again, there is no sharp boundary where a theory becomes "false". There are no binary categories here.

If we had accepted Newtonian mechanics as true, and therefore ignored the open problems which had the potential to cause doubt (like MMX, Mercury perihelion) there would have been no point in developing relativity.

You are correct that Newtonian mechanics was not accepted as "true". But it also was not deemed "false" when relativity was discovered. You are mistakenly assuming that those are the only two possibilities. They're not.

else it would not be named an approximation but a viable physical theory

Then in your terminology, all theories are approximations. General Relativity is an approximation. Quantum field theory is an approximation. All of these theories make predictions which do not exactly match the data. They just make predictions which are closer to the data (smaller error). The only reason we don't commonly refer to GR and QFT as approximations is that we don't have any other theories that are more accurate than they are. But that is not expected to be true forever.

one can compute (at least in principle) the difference between the approximation and the viable theory. This is, according to the viable theory, the error made by the approximation.

No, it isn't; "error" means something else. See above.

 

[Maximilian]

No. You have two mathematical machines that generate predictions. You compare each prediction with the actual data. The difference between the prediction and the actual data is the error.

That means you use the word "error" simply for something very different and irrelevant here. This is what is done if we want to find out which theory is better. This has been (for the theories discussed here) long ago, during the last millennial. What is discussed here is the question if a theory which is known to be wrong in many different domains can be nonetheless used as an approximation in some other domains. To find out the answer it is reasonable to compare its predictions with those of a theory known to be better everywhere.

But they don't. No theory makes predictions which exactly match the data.

Of course, there is a measurement error. But you cannot use the measurement error to compute if a theory which is already falsified can be nonetheless used in some domain as an approximation. See the article itself. There was no list of experimental data. There was a computation of the error made by classical physics using not experiment, but SR.

So there is no way to sort them into binary categories. The best you can do is rank them along a continuum of how accurate their predictions are.

Sorry, you can. For the best theory, the one which is not yet falsified, you have no information about how accurate it is. All what you have is information about the accuracy of particular experiments, or particular measurement devices. But it is not yet falsified, that means it is as true as possible for a physical theory, which anyway remains hypothetical forever. An information how accurate the predictions of the theory are you have only for theories which have been already falsified. And then the accuracy of the theory is defined by comparison with a theory not yet falsified.

Ok, if you are not sure if certain experiments have falsified which theories, you can also assign degrees of plausibility to theories, using Bayesian probability. But these probabilities are also only probabilities if the theory is true or not. So, this gives only a continuous degree of our knowledge if the theory is true or not. The basic subdivision remains binary.

No, it isn't, because you are using "wrong" as a binary category. Asimov is using "wrong" as a continuum; he is saying some people are more wrong or less wrong than others. A binary category doesn't work like that; the only two possibilities are "wrong" and "not wrong". That's not what Asimov is describing.

But this is nice playing with words, which is what one can expect from a writer. So, I agree with the part where he uses "wrong". And the use of "wronger" is a nice word game, not more, but is about something different, namely the error made by the approximation. If there is an error, one is wrong. But of course it matters a lot how big this error is. And in this part I also agree with him.

Some theories are rejected because all of their predictions are so different from the actual data that they are not useful at all. But Newtonian gravity and Newtonian mechanics are not like that.

Indeed. You have to add to the reasons for rejection that using them instead of the true theory would not give any advance in computation. And this is, essentially, the main point the old theories are used yet - they define mathematically, computationally much simpler ways to compute the results.

You are correct that Newtonian mechanics was not accepted as "true". But it also was not deemed "false" when relativity was discovered. You are mistakenly assuming that those are the only two possibilities. They're not.

No. A theory is either true or false. It may be unknown if it is true, but usually it is known to be false. And if it is false, the question appears if it nonetheless useful for approximations. It is that simple.

Then in your terminology, all theories are approximations. General Relativity is an approximation. Quantum field theory is an approximation. All of these theories make predictions which do not exactly match the data. They just make predictions which are closer to the data (smaller error). The only reason we don't commonly refer to GR and QFT as approximations is that we don't have any other theories that are more accurate than they are. But that is not expected to be true forever.

Not all theories are approximations, but those we have today are. This is not expected to be true forever. There maybe, in principle, theories where we don't know that they are false. But I think the TOE - that hypothetical quantum theory which unifies GR and SM - will not yet be of this type. Simply because a continuous field theory has no chance. So, during the rest of my life it will remain so.

To find true theories is the aim of science.

 

[russ_watters]

Explain the difference. If I use an approximation instead of the correct theory, the consequence is a difference between my computation and the value the correct theory would give. This difference is part of the error I make, not? There are, of course, also other sources of error, but this error is the one relevant if one discusses an approximation.

I disagree. I think these binary notions, which distinguish the theories as a whole, are very important.

I don't understand how you can hold these two positions simultaneously. You seem to get that an error is quantifiable and "wrong" as you are using it is binary, so they can't be the same thing, can they? Unless your usage is that all non-zero "error" is "wrong", in which case the word "wrong" has no value because it is covered by the much more useful word "error".

I suppose definitions are conventions, so people can agree or agree to disagree. For all this arguing it is tough to see why this matters; why you couldn't just say "I understand how the words are being used but prefer a different way" and leave it at that?

Maybe your issue is a philosophical issue with the goal of science? The search for an ultimate Truth? [edit: per your previous post, it appears so] Perhaps what you may be missing is that even if scientists believe they are searching for an absolute Truth, that belief is of no relevance. Why? Because it is inherently impossible to know if they've found it. So it doesn't alter the practical assumption that all theories are wrong. Which - again - means you may as well use "wrong" in a relative sense so that the word is useful. Otherwise a statement like "that theory is wrong" is pointless/redundant.

 

[Dale]

It is demonstrably wrong, because else it would not be named an approximation

Nonsense. The naming convention doesn’t demonstrate anything. The experimental results are the relevant demonstration, and in the classical domain the approximation is experimentally valid. You can call it an approximation, a limit, or a flubnubitz, and what you call it does not change the experimental facts that validate it.

That it may be used, under some circumstances, as an approximation does not make a wrong theory true.

What makes a theory valid is whether or not it matches the result of experiments. Not whether or not it approximates some other theory.

And even in cases where the approximation is good as an approximation, one can compute (at least in principle) the difference between the approximation and the viable theory.

You have the purpose of this calculation backwards. The purpose of computing the difference between Newtonian mechanics and relativity in the classical domain is to establish the validity of relativity. Newtonian mechanics is already validated by experiments in that domain, and therefore relativity must show that any disagreements between it and Newtonian mechanics are less than the experimental precision.

 

[atyy]

Yes, they are. Did you not read the article?

Also, approximations are not inherently wrong in science.

If this is what you mean by "wrong", then you are using the word in a very different sense from its usual sense.

I disagree. And this is just a question of semantics. It is completely standard to say that Newtonian physics is demonstrably wrong.