Addressing the “Classical Physics Is Wrong” Fallacy
One of the common questions or comments we get on PF is the claim that classical physics or classical mechanics (i.e. Newton’s laws, etc.) is wrong because it has been superseded by Special Relativity (SR) and General Relativity (GR), and/or Quantum Mechanics (QM). Such claims are typically made by either a student who barely learned anything about physics or by someone who has not had a formal education in physics. There is somehow a notion that SR, GR, and QM have shown that classical physics is wrong, and so, it shouldn’t be used.
There is a need to debunk that idea, and it needs to be done in the clearest possible manner. This is because the misunderstanding that results in such an erroneous conclusion is not just simply due to a lack of knowledge of physics, but rather due to something more inherent in the difference between science and our everyday world/practices. It is rooted in how people accept certain things and not being able to see how certain ideas can merge into something else under different circumstances.
Before we deal with specific examples, let’s get one FACT to straighten out:
Classical physics is used in an overwhelming majority of situations in our lives. Your houses, buildings, bridges, airplanes, and physical structures were built using classical laws. The heat engines, motors, etc. were designed based on classical thermodynamics laws. And your radio reception, antennae, TV transmitters, wi-fi signals, etc. are all based on the classical electromagnetic description.
These are all FACTS, not a matter of opinion. You are welcome to check for yourself and see how many of these were done using SR, GR, or QM. Most, if not all, of these, would endanger your life and the lives of your loved ones if they were not designed or described accurately. So how can one claim that classical physics is wrong, or incorrect, if they work, and work so well in such situations?
What is true is that we discovered a more accurate, and more general description of our world. In this description, it turns out that classical physics appears as a “simplification” or “approximation” whereby it becomes more and more valid as various parameters approach the common, everyday, terrestrial values. This is an extremely important point to remember because, since classical physics works under our ordinary situation, any new theory or description must somehow converge and look like the classical physics description under such ordinary conditions. Otherwise, this new theory must show that it produces the same set of results as classical physics for all of our known phenomena that classical physics can already accurately describe.
So in this part of the article, I will show two specific examples where the more general theory of SR and QM merge smoothly into the classical physics form when one adopts the appropriate approximation. This means that at some limit, both SR and QM descriptions will be the same as the classical description.
Table of Contents
Example 1: Special Relativity Velocity Addition
The first example is from SR and deals with the velocity addition in different inertial reference frames. This is illustrated in the figure below:
The reference frame S’ is moving with velocity v concerning reference frame S. A vessel is moving with velocity v’ concerning S’ frame. What is u, the velocity of that vessel concerning frame S?
The “normal” way to find this velocity is using what is known as Galilean transformation. Here, since both v and v’ and in the same direction, the velocity of the vessel concerning the S frame is a simple addition, i.e.
u = v + v’ (1)
Keep that result in mind.
Now let’s look at how we do this in SR, which is the more general description of such kinematics. Here, we use what is known as the Lorentz transformation. Using the figure from above as before, the velocity u of the vessel in the S frame is:
(2)
where c is the speed of light in a vacuum.
Now, this looks different than the Galilean transformation that we are used to in Eq. 1. This works for reference frame S’ at any velocity v, even if it approaches c. At that value, Eq. 1 does not work, and the velocity addition that we are used to fails miserably.
However, what happens when v«c, i.e. when reference frame S’ moves much slower than the speed of light? This is what we normally encounter, i.e. someone moving in a vehicle or an airplane. For v«c, Eq. 2 simplifies quite a bit. Without having to do any kind of Taylor series expansion on the denominator of Eq. 2, we can already see that the ratio vv’/c^2 « 1, i.e. it is a very small fraction less than one (v’ cannot be greater than c). This means that, to a good approximation, the denominator of Eq. 2 is essentially just 1.
When that happens, Eq. 2 then simplifies to u = v + v’, which is exactly Eq. 1! We got back our familiar result when we applied the more general equation (Eq. 2) to our normal, terrestrial condition! This means that all of the velocity addition equations and concepts that we already know using Galilean transformation are derivable from the more general Lorentz transformation equations. The Lorentz transformation is the more accurate, more encompassing description of velocity addition, while the Galilean transformation, which is what we know and are familiar with, is simply a special case for when the other reference frame is moving much slower than the speed of light. Eq. 1 isn’t wrong. It has a limited range of situations when it is valid or accurate enough.
Example 2: Quantum Mechanics Rate of Change of Momentum
In classical Newtonian mechanics, for an object with mass m, we know about Newton’s Second Law that relates the force F and the resulting acceleration a, which is
F = ma
This familiar equation can be written in a more general form, which is in terms of the time rate of change of momentum p, i.e.
F = dp/dt (3)
We also know that force F can be related to the potential energy (V) gradient, i.e.
F = – dV/dx (in 1D) (4)
So that is from the classical mechanics’ side. Let’s look at what it says on the QM side. Here, we use the Ehrenfest theorem, which says:
(5)
Here, H is the Hamiltonian, Q is an operator representing any observable, the square bracket represents the commutator, and the angled bracket represents the average value. These are all the standard notations used in QM.
So what if we want to find the time rate of change of the momentum, p? In QM, p is an operator representing the observable momentum. Thus, Eq. 5 becomes
(6)
From here, it requires quite a bit of knowledge on how to perform the commutator and take the average. You may read the full derivation of it here. In the end, what you end up with is:
(7)
This says that the time rate of change of the average value of the momentum p is equal to the average of the gradient of the potential energy V. But this equation is equivalent to Eq. 3 and 4 from classical mechanics! They have identical forms!
It says that what we typically measure in our everyday lives are the “average” values of many, many, many values at the QM level. The QM description has made the connection to the classical description under the condition that the QM observables have been averaged. Again, as in the case of velocity addition, we get back the classical description from a more general starting point, in this case, a QM description, upon applying a particular condition to the QM picture. It shows that the classical picture is not wrong. It is the average over a large number of QM observables.
Moral of the Story
- Classical physics WORKS for our ordinary situation, so it HAS to be valid at some level.
- Classical physics is derivable from SR and QM under special conditions that apply to our ordinary situation.
- Any theory MUST have the ability to show that it merges with the classical description when applied to an ordinary situation.
- 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.
What this implies here is that, if there are more general and more accurate theories beyond QM, and SR/GR, then those theories must also show that they can be “simplified” into the mathematical forms of QM and SR/GR. Subsequent, more general theories must show that they can derive the mathematical forms of existing, already-working theories. The inability to do that will be a fatal flaw in any new theory.
I mentioned towards the beginning of this article that the inability to comprehend this concept of a more general idea merging and agreeing with something less general may have something to do with the differences between science and our everyday lives. It is unusual for many people to accept the possibility that a simplistic, less sophisticated, and different idea is a subset of a more general principle. The fact that one can actually start with a more general principle, apply certain criteria, and then get a seemingly different concept, is not something a lot of people are familiar with, or would even accept.
It is why for someone not trained in physics, the idea that classical mechanics can be derived from seemingly a different animal of QM or SR/GR would not even cross his/her mind. Yet, in science/physics, this is quite common. We always show how new ideas and theories will turn into the old, tested, and well-known ideas and theories under the appropriate parameters. It is very seldom that old theories are discarded wholesale.
PhD Physics
Accelerator physics, photocathodes, field-enhancement. tunneling spectroscopy, superconductivity
Applied to such situations, Newtonian mechanics is not just slightly wrong: it is totally wrongBut we are not talking about such situations. We are talking about classical situations where it is demonstrably not wrong.
That means you use the word "error" simply for something very different and irrelevant here.No, it's not irrelevant, since it's what everyone in this discussion except you is talking about.
Of course, there is a measurement error.Measurement error is not what I was talking about.
For the best theory, the one which is not yet falsified, you have no information about how accurate it is.I'm sorry, but you are not making sense. The difference between the theory's predictions and the actual data is information about how accurate the theory is.
this is nice playing with wordsNo, it isn't. Asimov wasn't playing with words. He meant exactly what he said. What he said is simply something that you are apparently unwilling to accept.
A theory is either true or falseBy your definition, all theories are false. Which makes your definition useless.
Not all theories are approximations, but those we have today are.Every theory we have ever had has been an approximation. On what basis would you expect some hypothetical future theory to not be?
This is not expected to be true forever.What basis do you have for any such expectation?
Was that directed at me? I'm not sure what the purpose of that is.Not specifically.
But it is quite different from the present situation when the motivation for new theories is driven by known deficiencies in currently accepted theories.Yes, I suppose if some scientists believe they have found the Absolute Truth, they might decide there is no need to keep looking. Others might decide to keep chasing that next order of magnitude of precision.
Here is an example from Rindler: https://www.amazon.com/Relativity-Special-Cosmological-Wolfgang-Rindler/dp/0198567324 (p108)
"Applied to such situations, Newtonian mechanics is not just slightly wrong: it is totally wrong."Was that directed at me? I'm not sure what the purpose of that is.
Other side of the coin: there is no way to know if it is Ultimate Truth or not, so scientists will assume it is not and keep looking.But it is quite different from the present situation when the motivation for new theories is driven by known deficiencies in currently accepted theories.
Here is an example from Rindler: https://www.amazon.com/Relativity-Special-Cosmological-Wolfgang-Rindler/dp/0198567324 (p108)
"Applied to such situations, Newtonian mechanics is not just slightly wrong: it is totally wrong."
So if one finds a conceptually complete and coherent theory in complete agreement with all experimental evidence, is it wrong? If you claim it is wrong, how can you prove that it is wrong?Other side of the coin: there is no way to know if it is Ultimate Truth or not, so scientists will assume it is not and keep looking.
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.So if one finds a conceptually complete and coherent theory in complete agreement with all experimental evidence, is it wrong? If you claim it is wrong, how can you prove that it is wrong?
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.
It is demonstrably wrong, because else it would not be named an approximationNonsense. 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.
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.
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.
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 wholeBut 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 itNo, 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 theoryThen 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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
If you are travelling 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.
Closed temporarily for moderation. Hope to reopen soon.
Edit: the thread is reopened. 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 conspiracy theories. The scientific approximation of small sections of the earth as flat was already addressed fully in post 2.
So, naming the "classical physics is wrong" a fallacy is wrong, not?It depends on what you mean by "classical physics". See below.
"Classical physics" is what the scientist have developed before they had QM and SR/GR.Not as that term is being used in the Insights article that this thread is about. In that article, "classical physics" means an approximation, which is recognized to be so.
at least many of them thought that Newtonian physics was exactly correctReally? Please provide your evidence for this claim.
Newton said things like "hypotheses non fingo" for a reason. I don't think he was trying to make the claim you are describing here.
Also, even if they did believe this, having that belief a couple of centuries before the discovery of GR and QM is very different from having it a century after the discovery of GR and QM. Discovering new theories changes the way we view older theories.
I'll assume your pulling my leg! You can't be serious.I'm not pulling your leg. I can't see how this doesnt follow logically/mathematically: the limit of the angle between the vectors approaches zero as the radius approaches infinity. when you drop the angle completely, you've used calculus on it to make it exactly zero.
Google searches on this issue produce a whole lot of noise, but I found one set of course notes and several papers that refer to this assumption as being a "flat earth" assumption. Example:
https://aapt.scitation.org/doi/10.1119/1.1866097
Then I will say that everything you are using is "wrong"! The semiconductor description in your electronics is wrong. Ohm's law is wrong. In fact, everything out of solid state physics/condensed matter is wrong. Anything that made use of series expansion is wrong. Statistics mechanics/thermodynamics is wrong. I will also claim that every single experimental measurement is an approximation, and thus, by your definition, is "wrong".Fine. What's the problem, if the error is small enough?
I have explained this before in an earlier post. The word "wrong" that is used in layman's term has a definite and distinct meaning. People do not use something that is wrong.No, they use it all the time. Those who don't have a problem – they think they make no errors, but in reality make them. If they are lucky, the error which in their opinion does not exist at all appears small enough and harmless.
Of course, most of the people have not even heard much about SR and QM, and all what they do could be described with sufficient accuracy with classical mechanics. But you can explain them that using a classical ruler to measure distances is inaccurate, given that the size of the rulers changes with temperature. Thus, to use such a ruler and to think that the result is accurate would be wrong. And give him an estimate of the error. Would he stop using rulers? Of course, not. He would reasonable and correctly think that the error is negligible and use it as before.
And if PeroK thinks differently this is not my problem. Every reasonable person knows that phrases like "every reasonable person thinks …" are simply rhetoric, and should be interpreted as something like "it is my personal opinion that a quite large number of reasonable persons think …".
So use your definition, and those anti-science faction will be jumping up and down with joy, because they now have a "proof" that science really is all wrong!
Congratulations!I have never had a problem acknowledging in communications with laymen that scientific predictions are not exact, but only approximations, and in this sense wrong. I also like to repeat to laymen, even freaks, that scientific theories are only hypotheses, which cannot be proven.
So how does the constant direction not incorporate a flat Earth? Earlier you said a "large" Earth and a "small" range: isnt the point of those assumptions that they make Earth flatter?I'll assume your pulling my leg! You can't be serious.
##g## is a assumed to be constant/approximately constant in magnitude and direction.So how does the constant direction not incorporate a flat Earth? Earlier you said a "large" Earth and a "small" range: isnt the point of those assumptions that they make Earth flatter?
Maybe I'm just misunderstanding what that entails; all equal magnitude and direction or just equal magnitude?##g## is a assumed to be constant/approximately constant in magnitude and direction. You need no further assumptions.
You can assume a uniform gravitational field without making any further assumptions. Even a flat Earth wouldn't produce a constant force of gravity with height.Maybe I'm just misunderstanding what that entails; all equal magnitude and direction or just equal magnitude?
I'm not quite following what points you are trying to make; physics classes do, in fact, teach that small ballistic trajectories are parabolas. Doesn't that require, among other assumptions, a flat Earth?You can assume a uniform gravitational field without making any further assumptions. Even a flat Earth wouldn't produce a constant force of gravity with height.
The subsidiary assumption is that the gravitational field around the Earth is approximated by the uniform field, over a small enough range.
There's no object that would produce a constant gravitational field in any case. You can't make any assumptions about the shape of the Earth that would lead to that.
What about air resistance? That the Earth is not a perfect sphere? The Coriolis force?
It's no more an ellipse than it is a parabola.
Introductory physics classes assume that the Earth is a large sphere, with an approximately uniform gravitational field in the neighbourhood of a local experiment.
They do not assume the Earth is globally flat, or anything like it.I'm not quite following what points you are trying to make; physics classes do, in fact, teach that small ballistic trajectories are parabolas. Doesn't that require, among other assumptions, a flat Earth?
edit: Moreover, I think it would be fairer to differentiate between multiple effects acting at once and approximations. Parabola vs ellipse is an approximation: ignoring the coriolis force is ignoring an additional contributing factor.
Very simple – they are good approximations. But every approximation is, certainly, wrong – and reasonable laymen, as well as scientists, know very well that the approximations are wrong.You really shouldn't attribute your opinions to other people. You hold extreme opinions on this matter, which obviously you don't recognise as extreme and you then assume wrongly that the average scientist shares these opinions.
You have no evidence that "reasonable laymen, as well as scientists" share your opinion. I, for one, don't share your opinion.
Very simple – they are good approximations. But every approximation is, certainly, wrong – and reasonable laymen, as well as scientists, know very well that the approximations are wrong. They use the approximations for very simple reasons: Because compute the exact, true results is either (most of the time) simply impossible, or one would need much more to compute them. More time for computation using more complex mathematics, more investment in measurements.But, while I think almost everybody agrees, after learning SR/GR/QM, that classical mechanics is wrong, I have not seen yet a single person arguing that therefore classical mechanics should not be used. So, the "should not be used" sounds like a strawman.Then I will say that everything you are using is "wrong"! The semiconductor description in your electronics is wrong. Ohm's law is wrong. In fact, everything out of solid state physics/condensed matter is wrong. Anything that made use of series expansion is wrong. Statistics mechanics/thermodynamics is wrong. I will also claim that every single experimental measurement is an approximation, and thus, by your definition, is "wrong".
I have explained this before in an earlier post. The word "wrong" that is used in layman's term has a definite and distinct meaning. People do not use something that is wrong. It is why this question crops up on this forum. It wasn't asked by another physicist. So use your definition, and those anti-science faction will be jumping up and down with joy, because they now have a "proof" that science really is all wrong!
Congratulations!
Zz.
So how can one claim that classical physics is wrong, or incorrect, if they work, and work so well in such situations?
Reference https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/Very simple – they are good approximations. But every approximation is, certainly, wrong – and reasonable laymen, as well as scientists, know very well that the approximations are wrong. They use the approximations for very simple reasons: Because compute the exact, true results is either (most of the time) simply impossible, or one would need much more to compute them. More time for computation using more complex mathematics, more investment in measurements.
So, what reasonable people do is to recognize that they make errors, and not to minimize these errors at all costs, but to estimate the size of the error, and to use the wrong result once the error is small enough.
If I, instead, think that classical physics is true/correct/valid/whatever, but not wrong, then I have no base to estimate the error which I make by using classical mechanics. Using a correct theory is not an error at all, and once I make no error using it, I cannot estimate the error, the error is zero.
Ok, if I'm not completely stupid, there will be some other errors which I can estimate nonetheless. Like the measurement errors and so on. But the error of using classical mechanics instead of GR/SM would be nothing I could estimate and consider as part of the error I make. So, my error estimate would distorted, wrong, in the same sense as classical mechanics is wrong.
2. Classical physics has been shown to be derivable from SR and QM under special conditions that apply to our ordinary situation.
Reference https://www.physicsforums.com/insights/classical-physics-is-wrong-fallacy/No. It is derived only as an approximation. And therefore remains wrong. Because even if we are in an ordinary situation, a difference remains. And, with sufficiently accurate measurement instruments, the difference can be measured. The clocks on the top and the bottom of a house go differently, contrary to Newtonian theory, and we can measure it, and falsify Newtonian theory even if the situation itself is ordinary.
It is, in fact, other people who seriously claimed that classical mechanics is wrong and should not be used, at all, something that I find absurd.It would be absurd. But, while I think almost everybody agrees, after learning SR/GR/QM, that classical mechanics is wrong, I have not seen yet a single person arguing that therefore classical mechanics should not be used. So, the "should not be used" sounds like a strawman.
In introductory physics classes, they often teach that trajectory of a thrown ball traces a parabola. This is an approximation resulting directly from assuming that the Earth is flat. If you take into account that the Earth is spherical, the ball instead traces an ellipse.What about air resistance? That the Earth is not a perfect sphere? The Coriolis force?
It's no more an ellipse than it is a parabola.
Introductory physics classes assume that the Earth is a large sphere, with an approximately uniform gravitational field in the neighbourhood of a local experiment.
They do not assume the Earth is globally flat, or anything like it.
the term "Flat Earth Theory" has a meaning that is not the one you are implicitly giving it here. To see that meaning, Google "flat earth society"To put this in a way that correctly captures the analogy with classical physics, suppose there were a group of people, with a website and a formal organization and all, who claimed that Newtonian physics was exactly correct and that all of this stuff about general relativity and quantum mechanics being the correct theories was a conspiracy of scientists to hide the truth. And suppose they called their claimed exact theory "Classical Physics" and called their formal organization the "Classical Physics Society".
Those people would be wrong, in the same way that the Flat Earth Society is wrong. And that would not in the least change the fact that classical physics is a valid approximation in a particular domain.
This is not a fair comment. Maximilian was not claiming that flat earth theories are a "valid subject". That is not what he was saying. He was saying something different. Maximilian was making a "reductio ad absurdum" argument against Greg Bernhardt's article.
You can think of the purpose of physics as either devising a method of solving problems that produces answers consistent with experimental results within experimental error so you can use those methods in practical applications, or you can think of the purpose of physics to actually try to understand the real Universe, the best that we can, and to try to continuously improve our understanding, not for any application, other than our own innate curiosity, and desire to understand. According to the first definition, for most practical purposes in daily life, classical mechanics is just as good as relativity or quantum mechanics because it gives the answers, within the margin or error, as you would also get if you took into account relativity and quantum mechanics. However, according to the second definition, quantum mechanics and relativity is undeniably better than classical mechanics, since it is more true, proven by the fact that it has a wider range of applicability. Therefore, if your goal is to actually understand the truth about the Universe, you would obviously say that relativity and quantum mechanics are better than classical mechanics since they are more true than classical mechanics. That does not mean that you don't continue to use classical mechanics when it is a good approximation.
In introductory physics classes, they often teach that trajectory of a thrown ball traces a parabola. This is an approximation resulting directly from assuming that the Earth is flat. If you take into account that the Earth is spherical, the ball instead traces an ellipse. That does not mean that physics classes should not teach physics students that a thrown ball traces a parabola, since that is a good approximation, even through, in that case, they are actually using Flat Earth Theory, since in that case, it is a good approximation. According to the first definition of physics, in the case of tracing the trajectory of a thrown ball, Flat Earth Theory and Round Earth Theory give the same answer, within the margin of error, so they are equally good. According to the second definition of physics, to try to get closer to the actual truth of understanding the Universe, Round Earth Theory is better than Flat Earth Theory, because it is more true, proven by the fact that it has a wider range of applicability. Of course we know that the Earth is not really flat, in the same way, we know that the classical mechanics is not really true. We use classical mechanics all the time, even though we know it's not really true, because it's a good approximation, same as in physics classes, we teach the students that a thrown ball follows a parabolic trajectory, which assumes that the Earth is flat, because it's a good approximation.
In a introductory physics class, they tell the students a thrown ball follows a parabolic trajectory, which is an example of Flat Earth Theory being taught in a physics class. If you wanted to make your result more accurate, you could switch from Flat Earth Theory to Round Earth Theory, and get the result that a thrown ball traces an ellipse instead of a parabola. If you wanted to make it even more accurate, you could switch from classical mechanics to special relativity. If you wanted to make it even more accurate, you could switch from special relativity to general relativity. If you wanted to make it even more accurate, you could take into account quantum mechanics. You would probably not do that because classical mechanics is a good enough approximation for describing a thrown ball just as Flat Earth Theory is a good enough approximation for describing a thrown ball. Of course, if your goal is not to get an answer to the specific problem of describing a thrown ball, but instead to understand the Universe, you would say that Round Earth Theory is more true that Flat Earth Theory, special relativity is more true than classical mechanics, general relativity is more true than special relativity, quantum mechanics is more true than classical mechanics, etc.
No one would say Flat Earth Theory was true just as no one would say classical mechanics was true, despite the fact that we use Flat Earth Theory when calculating the trajectory of a thrown ball just as we use classical mechanics when calculating the trajectory of a thrown ball.
The moderator I quoted could just have easily written the following.
"Classical mechanical is neither a valid subject on PF nor does it belong here. This threads is basically about the limits of validity of physical theories, not about premature nonsense like classical mechanics."There continue to be a severe misunderstanding of what I had written and the purpose of it.
First of all, that was my article, not Greg's.
Secondly, you used the word "true" repeatedly. You'll notice that I never used such claim with respect to classical mechanics, SR, and QM. What I used was the word "valid", and I often paired that with the degree of accuracy and applicability of the theory and its usage.
The article was written to counter posts from people that are often ignorant of your first definition, that there is nothing wrong with the validity of classical mechanics when it is used within known limits. The two examples were presented to clarify this claim, that the more complete (notice I did not say "more true") theories can, in fact, match the classical description under certain parameters or range. I make NO claims of one being true while the other being false. It is, in fact, other people who seriously claimed that classical mechanics is wrong and should not be used, at all, something that I find absurd.
Zz.
I would suggest to write another article, reformulating this one in a quite straightforward way, against the
"Flat Earth Theory Is Wrong" Fallacy.
It works, indeed, nicely on the soccer field near my home, and gives accurate predictions for trajectories of the ball.The problem with this is that the term "Flat Earth Theory" has a meaning that is not the one you are implicitly giving it here. To see that meaning, Google "flat earth society". The Flat Earth Society meaning of "Flat Earth Theory" is the one that is not a suitable subject for discussion here, and which @fresh_42 was referring to in his response to you.
Your point about what I'll call the "flat Earth approximation" is well taken, and, as @Nugatory has pointed out, was already made in post #2 of this thread.
Maximilian was not claiming that flat earth theories are a "valid subject". That is not what he was saying. He was saying something different. Maximilian was making a "reductio ad absurdum" argument against Greg Bernhardt's article.And the problem with that argument is that the term "Flat Earth Theory" doesn't mean what he was implicitly assuming it means. See above.
All of the rest of your post is perfectly valid, and makes the same points that Asimov's article, linked to in post #2 of this thread, makes. Nobody here is arguing against any of that.
Flat earth is neither a valid subject on PF nor does it belong here. This threads is basically about the limits of validity of physical theories, not about premature nonsense like flat earth.
Please remain on topic. Thank you.This is not a fair comment. Maximilian was not claiming that flat earth theories are a "valid subject". That is not what he was saying. He was saying something different. Maximilian was making a "reductio ad absurdum" argument against Greg Bernhardt's article.
You can think of the purpose of physics as either devising a method of solving problems that produces answers consistent with experimental results within experimental error so you can use those methods in practical applications, or you can think of the purpose of physics to actually try to understand the real Universe, the best that we can, and to try to continuously improve our understanding, not for any application, other than our own innate curiosity, and desire to understand. According to the first definition, for most practical purposes in daily life, classical mechanics is just as good as relativity or quantum mechanics because it gives the answers, within the margin or error, as you would also get if you took into account relativity and quantum mechanics. However, according to the second definition, quantum mechanics and relativity is undeniably better than classical mechanics, since it is more true, proven by the fact that it has a wider range of applicability. Therefore, if your goal is to actually understand the truth about the Universe, you would obviously say that relativity and quantum mechanics are better than classical mechanics since they are more true than classical mechanics. That does not mean that you don't continue to use classical mechanics when it is a good approximation.
In introductory physics classes, they often teach that trajectory of a thrown ball traces a parabola. This is an approximation resulting directly from assuming that the Earth is flat. If you take into account that the Earth is spherical, the ball instead traces an ellipse. That does not mean that physics classes should not teach physics students that a thrown ball traces a parabola, since that is a good approximation, even through, in that case, they are actually using Flat Earth Theory, since in that case, it is a good approximation. According to the first definition of physics, in the case of tracing the trajectory of a thrown ball, Flat Earth Theory and Round Earth Theory give the same answer, within the margin of error, so they are equally good. According to the second definition of physics, to try to get closer to the actual truth of understanding the Universe, Round Earth Theory is better than Flat Earth Theory, because it is more true, proven by the fact that it has a wider range of applicability. Of course we know that the Earth is not really flat, in the same way, we know that the classical mechanics is not really true. We use classical mechanics all the time, even though we know it's not really true, because it's a good approximation, same as in physics classes, we teach the students that a thrown ball follows a parabolic trajectory, which assumes that the Earth is flat, because it's a good approximation.
In a introductory physics class, they tell the students a thrown ball follows a parabolic trajectory, which is an example of Flat Earth Theory being taught in a physics class. If you wanted to make your result more accurate, you could switch from Flat Earth Theory to Round Earth Theory, and get the result that a thrown ball traces an ellipse instead of a parabola. If you wanted to make it even more accurate, you could switch from classical mechanics to special relativity. If you wanted to make it even more accurate, you could switch from special relativity to general relativity. If you wanted to make it even more accurate, you could take into account quantum mechanics. You would probably not do that because classical mechanics is a good enough approximation for describing a thrown ball just as Flat Earth Theory is a good enough approximation for describing a thrown ball. Of course, if your goal is not to get an answer to the specific problem of describing a thrown ball, but instead to understand the Universe, you would say that Round Earth Theory is more true that Flat Earth Theory, special relativity is more true than classical mechanics, general relativity is more true than special relativity, quantum mechanics is more true than classical mechanics, etc.
No one would say Flat Earth Theory was true just as no one would say classical mechanics was true, despite the fact that we use Flat Earth Theory when calculating the trajectory of a thrown ball just as we use classical mechanics when calculating the trajectory of a thrown ball.
The moderator I quoted could just have easily written the following.
"Classical mechanical is neither a valid subject on PF nor does it belong here. This threads is basically about the limits of validity of physical theories, not about premature nonsense like classical mechanics."
I would suggest to write another article, reformulating this one in a quite straightforward way, against the
"Flat Earth Theory Is Wrong" Fallacy.
It works, indeed, nicely on the soccer field near my home, and gives accurate predictions for trajectories of the ball.This particular line of argument, and indeed this exact example, is covered n post #2 of this thread.
Repeating the link from that post: http://chem.tufts.edu/answersinscience/relativityofwrong.htm
It appears as if my request to remain on topic has been in vain. Again: We do not discuss Flat Earth anymore. Look up the existing threads. Flat earth is not part of this discussion, as chem trails aren't. It is about the validity of classical physics, not the validity of nonsense.
Thread closed for moderation.
Feel free to ignore my arguments, once you don't like the consequences, but my argument is on-topic, about your thread. It shows that applying your reasoning leads to absurd results. I'm not at all interested discussing flat Earth theory itself, but used it simply as an example of an obviously wrong theory.Just because you tell me it is on topic, doesn't mean it is. This is not a political discourse where it is a fact simply because someone stated it.
Your argument is nothing more than saying that the local solution is simply part of a more general solution. The "flat earth" approximation is nothing more than a simplification of a more general solution when solved very near the surface. I can solve for ONE general equation, get the solution, and then simplified it for the near-suface case.
This is NOT what I've argued here, because both classical mechanics and QM/SR are very different theories conceptually. The starting points are different and it isn't just a matter of simplification (i.e. averaging isn't a simplification).
And per your "advice", you are also free to ignore this thread if you "don't like the consequences".
Zz.
It is on-topic because the obvious aim is to prove that the argument is absurd, because it leads, applied to a different, nonsensical theory, to absurd consequences, namely that "flat Earth theory is wrong" is a fallacy.
This is an elementary, valid, and reasonable strategy of showing an argument is wrong: To apply it to something different, to show that it would be applicable, and to show that the result is absurd.
First, it is not a problem of my logic, but a problem with naming classical physics (or flat Earth theory) not wrong.
In my logic, the situation is quite simple, much simpler than your list. Flat Earth theory, as well as classical mechanics, are nice and useful as approximations in a certain domain of applicability. This does not change the fact that both are wrong. Simply because if a theory is true, it can be applied everywhere, and the result predicted by this theory would be accurate, with arbitrary high accuracy. This is the normal, layman version of the meaning of truth, and it is also the scientific, educated meaning of truth, as, for example, used by Popper.
Instead, in your logic, important parts of fundamental physics are completely useless. As long as there is no experimental evidence in the domain of quantum gravity, the search for theories of quantum gravity is nonsense, we have already the True Theory GR, as well as the True Theory of the SM on a curved background. They are incompatible and even internally inconsistent? So what? They are True because they give accurate predictions for everything, at least if applied with a little bit common sense to circumvent the internal inconsistencies.
Common sense, and Popper's scientific method, work differently. They accept theories as possibly true only as long as there is not even a single falsification, and theories with internal inconsistencies (like QFT on curved background) or singularities (like GR) cannot even pretend to be true, they are known to be wrong even without a single problem with observation.
No, it is not. The Earth is flat on my soccer field. This is the region where Flat Earth theory appears applicable and well-tested. Maybe those who have initially proposed flat Earth theory meant it differently? Quite probable, but it does not matter. But, sorry, those who have developed classical mechanics have also thought differently about its applicability, nobody has said, say, around 1850 or so that it will become inapplicable for large velocities (>c) or small actions (<hbar).Unfortunately, if by your logic you are unable to distinguish between classical physics and flat-Earth theory, then you have made yourself unable to study science.
No, it is not on topic.
The thread is to show that Classical Physics that is being used is not wrong based on the misunderstanding that it has been superseded by QM and SR. Your premise is that some application of classical physics is not wrong because it is a simplification of ANOTHER application of classical physics. It is not relevant here, and I wish you'd start your own thread and not hijack someone else's.
In fact, there is already an existing thread that discussed possible experiments to disprove flat-earth scenario. Why not join the fun there?Feel free to ignore my arguments, once you don't like the consequences, but my argument is on-topic, about your thread. It shows that applying your reasoning leads to absurd results. I'm not at all interested discussing flat Earth theory itself, but used it simply as an example of an obviously wrong theory.
It is on-topic because the obvious aim is to prove that the argument is absurd, because it leads, applied to a different, nonsensical theory, to absurd consequences, namely that "flat Earth theory is wrong" is a fallacy.
This is an elementary, valid, and reasonable strategy of showing an argument is wrong: To apply it to something different, to show that it would be applicable, and to show that the result is absurd.No, it is not on topic.
The thread is to show that Classical Physics that is being used is not wrong based on the misunderstanding that it has been superseded by QM and SR. Your premise is that some application of classical physics is not wrong because it is a simplification of ANOTHER application of classical physics. It is not relevant here, and I wish you'd start your own thread and not hijack someone else's.
In fact, there is already an existing thread that discussed possible experiments to disprove flat-earth scenario. Why not join the fun there?
Zz.
Flat earth is neither a valid subject on PF nor does it belong here. This threads is basically about the limits of validity of physical theories, not about premature nonsense like flat earth.
Please remain on topic. Thank you.It is on-topic because the obvious aim is to prove that the argument is absurd, because it leads, applied to a different, nonsensical theory, to absurd consequences, namely that "flat Earth theory is wrong" is a fallacy.
This is an elementary, valid, and reasonable strategy of showing an argument is wrong: To apply it to something different, to show that it would be applicable, and to show that the result is absurd.
The problem with your logic is as follows:
a) If you use classical physics where it applies (e.g. to build an aircraft), then classical physics is not wrong in that sense.
b) If, however, you declare that classical physics applies everywhere and that relativity and quantum mechanics must be wrong, then that is not right.
c) If you know that your soccer field is flat and work to that you are correct. Although, in fact, the Earth locally is highly variable with flat regions, high mountains and deep valleys and everything in between.
d) If, however, you declare the Earth to be flat globally (which is the flat-Earth theory), then you'd be wrong.First, it is not a problem of my logic, but a problem with naming classical physics (or flat Earth theory) not wrong.
In my logic, the situation is quite simple, much simpler than your list. Flat Earth theory, as well as classical mechanics, are nice and useful as approximations in a certain domain of applicability. This does not change the fact that both are wrong. Simply because if a theory is true, it can be applied everywhere, and the result predicted by this theory would be accurate, with arbitrary high accuracy. This is the normal, layman version of the meaning of truth, and it is also the scientific, educated meaning of truth, as, for example, used by Popper.
Instead, in your logic, important parts of fundamental physics are completely useless. As long as there is no experimental evidence in the domain of quantum gravity, the search for theories of quantum gravity is nonsense, we have already the True Theory GR, as well as the True Theory of the SM on a curved background. They are incompatible and even internally inconsistent? So what? They are True because they give accurate predictions for everything, at least if applied with a little bit common sense to circumvent the internal inconsistencies.
Common sense, and Popper's scientific method, work differently. They accept theories as possibly true only as long as there is not even a single falsification, and theories with internal inconsistencies (like QFT on curved background) or singularities (like GR) cannot even pretend to be true, they are known to be wrong even without a single problem with observation.
d) If, however, you declare the Earth to be flat globally (which is the flat-Earth theory), then you'd be wrong.No, it is not. The Earth is flat on my soccer field. This is the region where Flat Earth theory appears applicable and well-tested. Maybe those who have initially proposed flat Earth theory meant it differently? Quite probable, but it does not matter. But, sorry, those who have developed classical mechanics have also thought differently about its applicability, nobody has said, say, around 1850 or so that it will become inapplicable for large velocities ##>c## or small actions ##<hbar##.
I would suggest to write another article, reformulating this one in a quite straightforward way, against the
"Flat Earth Theory Is Wrong" Fallacy.
It works, indeed, nicely on the soccer field near my home, and gives accurate predictions for trajectories of the ball.This is a nice analogy. As long as you use it in its domain of applicability, treating the earth as flat is fine. No one corrects for the sphericity of the Earth when tiling their kitchen floor, and no one would regard that as wrong. It all falls apart when you try to map the Americas on a flat piece of paper, however.
As PeroK notes, the problem is that "flat earth" is often used to mean that the Earth is globally flat, which is wrong. A walk around the coast of Australia will be a very different proposition to what a flat-earth planning session would suggest. But then, applying Newtonian physics to something doing 0.999c gives grossly incorrect predictions too.
Edit: oops – just saw @fresh_42's post. Will shut up here and leave it up to him if he wants to delete.
Flat earth is neither a valid subject on PF nor does it belong here. This threads is basically about the limits of validity of physical theories, not about premature nonsense like flat earth.
Please remain on topic. Thank you.
I would suggest to write another article, reformulating this one in a quite straightforward way, against the
"Flat Earth Theory Is Wrong" Fallacy.
It works, indeed, nicely on the soccer field near my home, and gives accurate predictions for trajectories of the ball.The problem with your logic is as follows:
a) If you use classical physics where it applies (e.g. to build an aircraft), then classical physics is not wrong in that sense.
b) If, however, you declare that classical physics applies everywhere and that relativity and quantum mechanics must be wrong, then that is not right.
c) If you know that your soccer field is flat and work to that you are correct. Although, in fact, the Earth locally is highly variable with flat regions, high mountains and deep valleys and everything in between.
d) If, however, you declare the Earth to be flat globally (which is the flat-Earth theory), then you'd be wrong.
I would suggest to write another article, reformulating this one in a quite straightforward way, against the
"Flat Earth Theory Is Wrong" Fallacy.
It works, indeed, nicely on the soccer field near my home, and gives accurate predictions for trajectories of the ball.
Classical theories are approximations, not limitsYes, they are. Did you not read the article?
Also, approximations are not inherently wrong
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.
Classical theories are approximations, not limits. Ergo, saying classical physics is wrong is wrong is wrong!
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.
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?
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.
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?
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.The scientific method cannot distinguish between two models which make the same experimental predictions, even if they have different assumptions. Scientifically they are identical. As a result usually they are considered to be different interpretations of the same theory, particularly in Quantum Mechanics where this occurs frequently. They are not considered different theories, despite the different assumptions.
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.
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.
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.
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.
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.
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.
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 completly 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.
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.
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.
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.
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.
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.
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!
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.
You can make prediction of the consequences of a particular spacetime geometry and then measure those consequencesNo, 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.