I would like to know how can you prove these laws, but not using devices that use the the same laws.
Every white swan you see is evidence that swans are white. However, this doesn't mean ALL swans are white. If the chornometer is following the Newton's laws then it must be white swan. Newton never saw a black swan.
Don't use a chronometer. Use a ruler, a watch, a spring, and a weight. Kids do this in early high school.
I think what he's trying to say is that argument is circular. Newton's laws proving Newton's laws.
If the instruments obey Newton then Newton would be one happy dude wouldn't he? I guess the OP wants to compare the situation to a court case where Newton is the client, the lawyer, the judge and the jury. Happy happy Newton!
I would like to know how can you prove these laws, but not using devices that use the the same laws.
You could never prove them. For one thing they're not "true," if by true you mean that the universe actually works that way. We know that for objects moving at very high speeds and/or objects with extremely large mass, Newton's laws are superseded by Einstein's; and that even for everyday object like bowling balls, Newton's laws are only an approximation.
Secondly, NO law of physics can ever be proved; because every law of physics is a historically contingent approximation, good to a few decimal places, to the results of the experiments we're capable of doing at any given level of technology. Our very best physical theory, quantum electrodynamics, gives the magnetic moment of the electron to "a few parts in [math]10^{13}[/math]. That's great by physics standards but there are a lot more decimal places out there and a lot of physics we still don't know.
No physical theory is true. Or rather, "true" is defined in physics as our best physical theory! So Newton's laws were true in 1687 with the publication of the Principia, and became false in 1915 with Einstein's publication of general relativity.
Pick your definition of true. The ultimate truth of the universe -- if there even is any such thing? Or just the latest widely agreed on theory from the physicists?
Let's not get too technical. The problem for the OP is how an instrument that is Newtonian can ever prove that some other event is NOT Newtonian in nature. If I only have red paint, whatever I paint will surely be red.
A better analogy is the biased judge adjudicating a case. The trial wouldn't be fair.
Let's not get too technical. The problem for the OP is how an instrument that is Newtonian can ever prove that some other event is NOT Newtonian in nature. If I only have red paint, whatever I paint will surely be red.
A better analogy is the biased judge adjudicating a case. The trial wouldn't be fair.
I responded primarily to the title of the OP without reading much of the post, and without reading the other responses in the thread. If I misconstrued the question, so be it. It's kind of a reflex on my part to point out that the laws of physics are historically contingent approximations; and that whether there are laws of the universe at all, let alone ones accessible to humans, is an open question. But if that wasn't the question, then ... well, what was the question. I didn't understand the bit about how Newtonian instruments could prove an event is not Newtonian. In fact perfectly conventional Newtonian telescopes were used to observe the solar eclipse in 1919 that confirmed Einstein's theory of relativity.
Note that by Newtonian telescope, I meant not only the OP's sense of a telescope operating by Newtonian physics; but also that the Newton invented the reflecting telescope! So there's a double meaning there.
Your post was great but I don't think it would've satisfied the OP who said:
I have already confessed to not reading the post and only lazily making one of my standard hobby horse points. Did you want me to confess again? Is there a particular punishment you have in mind? I watched the entire Democratic debate tonight, that was punishment enough!
As distinct from what? Instruments which don't follow Newtons laws? Like you have a choice? What are you talking about?
There's an even bigger point here which the OP is hinting at - that the theory of relativity which has supplanted Newton's was proven by instruments that had to follow Newton's laws.
I would like to know how can you prove these laws, but not using devices that use the the same laws.
If you've read my other posts then you know that the Theory of Relativity was derived from measurements from instruments that followed Newtonian laws. What do you have to say about that?
Every instance of the laws being verified is part of the proof isn't it?
The OP is not as concerned with the meaning of "proof" as he is concerned about the circularity of the proof. By "proof" he probably means the derivation process of the laws. It must have been that measurements were taken of mass, acceleration, and force to get to the equation F = ma, right? If each such measurement followed Newtonian mechanics then it, to the OP, looks like the laws proving themselves. This is what appears problematic to the OP (unfortunately he isn't here to confirm this) - that Newton's laws were/are used to prove Newton's laws.
Personally, I think if the instruments didn't follow Newtonian laws then that would be a problem because they would be the disconfirming exception, invalidating Newton's laws.
I mentioned the theory of relativity being proved by instruments that followed Newton's laws but what I forgot was that the theory of relativity is applicable at non-relativistic speeds too. The same can't be said of Newton's laws which are now like Aristotle's belief that objects naturally come to rest and that heavier objects fall faster than lighter ones.
Can you kindly clarify on the circularity which I mentioned above?
Is it a real/interesting question or is it a question borne out of ignorance? Or is it both?
Which areas of logic, science and math does such a question touch upon?
Get a narrow piece of plastic strip and bend into a u-shape measuring 5ft from end to end. Make sure that the plastic is lubricated so as to cut down on friction and wide enough for a ball-bearing. Place the ball-bearing at one end and let it drop (don't push or throw it). If the plastic track has minimal friction then the ball bearing should reach the same height, from whence you dropped it, at the end:
Repeat this for a plastic track measuring 10ft, then 15ft, then 20ft, then 25ft, and so on. If all plastic tracks and ball bearings have minimal friction then the ball bearing should again reach the same height at the end as the height at the beginning. From this we may inductively reason that if we don't allow the plastic track to bend back up at the end, then the ball-bearing could hypothetically go on forever at a constant velocity if no other net force is acted upon it, i.e. Newton's first law of motion.
Secondly, NO law of physics can ever be proved; because every law of physics is a historically contingent approximation, good to a few decimal places, to the results of the experiments we're capable of doing at any given level of technology.
While this isn't the only option, laws are basically a way of describing observations. Then you set up experiments to further test that the descriptions are on-target.
Unfortunately, you cannot prove anything about the real, physical world, simply, because its construction logic is unknown. The term "proving" means that you demonstrate that a theorem necessarily follows from the construction logic of its world.
Still, Newton's laws were really good at resisting falsification for a long while. Only by looking at quite unusual situations, they were falsified:
Experimentally, Newton's law of gravitation has been falsified due to for example the anomalous perihelion precession of Mercury, which matches instead with Einstein's theory of gravitation.
Still, Einstein's theory is rather used as a refinement and not as a replacement for Newton's laws.
alcontali:Unfortunately, you cannot prove anything about the real, physical world, simply, because its construction logic is unknown. The term "proving" means that you demonstrate that a theorem necessarily follows from the construction logic of its world.
Thank you all for your answers. They have somehow help me to think about the situation. Does someone just know what were the experiments Newton performed to prove his laws?
Sorry if I seem ignorant, but how can we know they are true then?
They seem to be true, but you can never be absolutely, 100% sure. Most people treat gravity and Newton's laws as true. It is practically very useful to think of them as true. But science is not capable of proving that they are true. Science has a lot of evidence that supports that Newton's laws are true, but science will never claim that Newton's laws are true.
So many respondents missing the point regarding "proof". He clarified that by "proof", he means showing to be true. This can be done through the relevant experiments. If you disagree, then you need to revise your conception of truth.
That circularity is gestured at as if it existed, but where and how exactly does it exist?
I'll offer an analogy. Imagine the color red = Newton's laws. The instruments used to "prove" Newton's laws can be considered as a pair of red-tinted glasses (obeying Newton's laws). Any and everything you see using these glasses will appear red i.e. obeying Newton's laws. This is what I think the OP is trying to say.
Newton's laws proving Newton's laws!
Now I think there's a distinction we have to make between a logical proof and a scientific proof. Circularity is a bad character in the former but is necessary in the latter.
For instance a classic case of circularity given in elementary logic books is the Bible proving God exists because it's the word of God. This is a vicious circularity and the argument is rejected.
In science the difference is laws discovered/proved are necessarily universal and must be obeyed by everything. So, the instruments, as of necessity, should obey the laws, in this case Newton's. I guess I'm saying in science there has to be circularity if unavoidable.
There's an even bigger point here which the OP is hinting at - that the theory of relativity which has supplanted Newton's was proven by instruments that had to follow Newton's laws.
Of course this is false. Newton looked through a telescope that he himself had made. He was a master lens grinder. That's peripheral to the discussion but just an interesting factoid. Now the point is that Feynman taught us exactly how light passes through lenses. The laws of optics were known to Newton or rather discovered by him. But optics are a quantum phenomenon and Feynman (and others) won the Nobel prize for elucidating this fact.
Everything in the world is a quantum phenomenon. A rock doesn't fly apart because of quantum theory. I think someone made this point earlier but it bears repeating. Newton didn't know his telescope worked on quantum principles, but eventually we discovered that it does.
If you've read my other posts then you know that the Theory of Relativity was derived from measurements from instruments that followed Newtonian laws. What do you have to say about that?
Me? Wasn't sure about the quoting. Newton's instruments only followed Newton's laws to a certain degree of approximation. They follow Feynman's laws -- quantum laws -- to a far greater degree of approximation. Newton didn't happen to know that, but it was true nevertheless. How is this point not perfectly obvious to everyone?
Every child who asks "Why?" sometimes gets caught in the whys and keeps asking long after the efficacy of the question has been exhausted.
Newton took a lot of flack at the time. His law of gravity told us what gravity does; but not what it is. He famously said that "I frame no hypotheses." Newton well understood that science is descriptive and not explanatory; a point that modern scientists and philosophers of science would do well to understand.
But at the time, Newton's contemporaries did NOT understand. Descartes had a theory of vortices that said what gravity WAS, not just how it acted. That was, by the scientific ethos of the time, better science than what Newton did. It took people a while to come around to Newton's point of view. We see this echoed today, when people want to "interpret" quantum mechanics rather than be satisfied that it describes what the universe does; and not necessarily why.
I would like to know how can you prove these laws, but not using devices that use the the same laws.
The basic hypothetico-deductive method works like this:
1. Assume that the system under consideration is described by some theory - in other words, it follows some laws, such as Newton's laws.
2. On the basis of this assumption, make predictions about the system's behavior under certain conditions.
3. Prepare the system and perform an experiment. If your observations are in line with your hypothesis, then your hypothesis, and by extension your theory, are confirmed, otherwise it is disconfirmed (falsified).
There are variations and elaborations of the above (with some, for example, prioritizing falsification over confirmation), but this is the basis of the so-called scientific method. For this method to work, you absolutely need your instruments to be predictable, i.e. to follow laws - including, yes, the laws that you are testing. You just need to consider the instruments as part of the system that you are testing and make your predictions based on that assumption. If the test fails, you could blame all or any part of the system for the failure, including your instruments. You could then try to isolate the problem by performing further tests. And if the test succeeds, and so do other tests, then you will have a high confidence that both the experimental system and your instruments act in accordance with the laws. There is no vicious circularity here.
Of course, in practice we often choose to simplify and neglect many things when modeling an experiment. Thus, we may leave the instruments and our own actions out of consideration. But these simplifications are not made willy-nilly: ideally, we make them only when our theory predicts that they will not have much impact on the result of the experiment. And when the experiment doesn't show what we expect, then one of the explanations that we have to consider is that our assumptions were overly simplistic. We may then have to go back and take into account factors that we thought we could neglect, such as the behavior of the instruments.
What are the experiments that Newton used to show their laws are true?
This question worries me a little. I hope that you are not under the impression that Newton's laws are accepted solely on the authority of Newton himself, much like a religious teaching is accepted on the authority of a prophet or a sacred text. How Newton convinced himself that his theory was correct is a question for a historian or a biographer, but it is quite irrelevant to a 21st century scientist. Newton's own thinking could be deeply flawed and his methods wholly inadequate, for all we care - his laws have been tested so thoroughly since then that it no longer matters.
Thank you for your answer. What are the experiments that Newton used to show their laws are true?
Newton did not arrive at his theory by empirical methods (experimenting) but by deductive methods, formulating mathematical equations that closely followed his observation of natural phenomena.
They appear to be true because when you plug in values into the equations they predict a result that resembles the equivalent event in real life. For instance his basic acceleration formula predicts that if you subject a mass to a force, it will accelerate. It just happens that if you actually take the mass and apply a force to it, it will accelerate as the formula predicts.
If you've read my other posts then you know that the Theory of Relativity was derived from measurements from instruments that followed Newtonian laws. What do you have to say about that?
Same with this, the theory of relativity was not developed empirically, it was completely formulated mathematically before physical evidence was observed. The predictions of the theory were so revolutionary that not even Einstein was convinced, until scientists were able to see the path of light bent by gravity, by measuring starlight distorting near the sun during a full eclipse.
I would like to know how can you prove these laws, but not using devices that use the the same laws.
If we know the devices (rulers, scales, telescope, etc) existed before Newton, and therefor before Newton's laws, what were the devices measuring? (so the device itself is not 'Newtonian', it existed before Newton!) Newton's laws described what the devices were measuring (predicted outcomes of measurements), more accurately than previous models.
I think you are putting the cart before the horse. Newton's laws are based on the measurements of those devices, not the other way around.
Also, Newton's Laws are not accepted as perfect in science. Relativity and Quantum Mechanics have introduced aspects to physics that are not in line with Newton's laws or pick up where Newton's laws stop working (as far as they can tell so far).
So many respondents missing the point regarding "proof". He clarified that by "proof", he means showing to be true.
All proofs mean that. Proofs in physics mean that. Except there are no proofs in the science of physics.
This is preposterous. Any one counter-example that does not obey the law destroys that law's usefulness. Newton's laws have not had examples in real life that would nullify his laws, but CONCEPTUALLY they may happen. Therefore a billion experiments and observations that are thought to be showing Newton's laws to be true by S and by Fernando Rios, can be shown to be false by just one experiment or one single observation.
This is philosophy of physics. If you want to see the LOGIC that lead Newton to arrive at pronouncing his laws, then that's a different matter. If you want to see the process in chronological order that were the steps of Newton's developing his insights that lead to the formulation of his laws, that can be done. But to see what makes his laws true, is not possible.
What do you make of the 1919 eclipse that confirmed Einstein and disproved Newton?
Newton's laws have been showed to work in special cases of the law that explained the 1918 experiment.
Newton's Laws were not refuted, but expanded with adding some special conditions under which N's laws were not useful.
Same thing as to say, (conceptual example follows) "Primes are consecutive non-zero positive integers", if you can only count to three. Once you learn about the numeral four, and the concept of four, you have to rework your claim, while your oginal claim is still true up to no. 3.
So your reworked claim will become, "All non-zero positive odd integers are prime", if you can only count to 8. Then you come to learn about "9", and you need to revise your claim again. Your third claim will not contradict your second claim if you only consider integers to 8.
Thank you everyone for your responses. I would only like to know how Newton knew his laws are true. What were the experiments he performed?
Newton didn’t do any experiments with regard to his laws of motion and gravity*. He believed that Kepler’s laws of a heliocentric model of the solar system, with its elliptical orbits, were true because of their predictive power and that they were formulated due to an analysis of Tycho Brahe’s comprehensive and accurate data of celestial observations. He also believed that Galileo was right about motion being relative and that objects fell at the same rate regardless of mass (overturning the contemporary prevalent view of Aristotelian motion).
With Kepler's planetary laws and his invention of differential calculus, Newton devised his universal law of gravity and with the experimental results of Galileo (my example prior being a modern interpretation of such an experiment) he devised his three laws of motion. Personally I don’t care whether Newton thought himself to be right, or Brahe, Kepler, and Galileo either. Because, as with most geniuses, they were insufferable arseholes who thought everything they did was true and correct. Honestly, each and every one of these people were know-it-all pricks who were about as welcome at parties as a fart in a crowded lift (elevator to my colonial cousins). But then again, I would’ve liked to party with Brahe as he seemed to be a larger-than-life character. He had a tin nose due to losing his own nose in a duel! He also made Kepler practically beg for his observational data (like I said, an arsehole!)
Why everyone else thought Newton’s Laws were true was because the laws themselves had great predictive power and his genius was (besides coming up with calculus) that his laws explained how the celestial and terrestrial bodies move all due to being bound by gravity. The idea that celestial and terrestrial movement were the same thing wasn’t even considered beforehand and the simplified elegance of this probably gave reason why Newton himself thought his laws true. Newton didn’t know why gravity (he didn’t even know precisely what the gravitational constant was) and so he credited God with this feat. It wasn’t until Einstein came along that a naturalistic account for gravity was given. Newton also admitted to a certain artifice to his calculations as he was acutely aware that messing about with numbers didn't prove anything empirical.
Incidentally due to Newton’s thin skin towards criticism and his dislike for other academics (especially Robert Hooke.Newton’s quote about standing on the shoulders of giants was a sarcastic dig at Hooke’s diminutive size) he sat on his calculations and it wasn’t until he was befriended by the astronomer Edmund Halley that he decided to tell of his findings. Even if Newton thought his laws were true, it seemed that he wasn’t that bothered if other people thought them true also.
*Newton was a theoretician about motion and gravity but it’s not to say he didn’t dabble with experiments himself. When formulating his theory of colour, he stuck a bodkin in his eye to see how this changed his perception of colour. Also in his later years, he dabbled in alchemy.
Newton's laws have not had examples in real life that would nullify his laws, but CONCEPTUALLY they may happen
It actually has happened. General Relativity shows that the force of gravity, as conceptualized by Newton's laws does not exist. That was one of the main issues that troubled Einstein: What is this "long invisible arm" that extends out of masses and reaches out to other masses?
Through the formulation off GR he showed that space and time are inseparable, that space-time curves around a mass, and that this curved space-time affects the movement of objects.
Newton would say the satellite orbiting earth is kept in orbit because the force of Earth's gravity is balanced by the satellite's centrifugal force.
Einstein would say the satellite is experiencing no force, it is simply moving through curved space-time.
Newton's laws are no laws at all. They are a mathematical representation of what Newton observed. Same with Einstein's theory of relativity. They are models approximating the real laws of the universe.
The actual, real laws of the universe are unknown to man, and although the perpetually evolving models and theories keep inching closer, there are still many important observations that can not be reconciliated with the latest theories.
to the OP, by asking the question of how can Newton's laws be proven to be true, there is an implication that they are true, and they are not. No present physics theory is true, and you can't prove the truth of something that is not true.
You can't. If by prove you mean the same sort of "proof" required in math. In sciences you try to see whether or not something is the case. In math where "proof" is generally used, you try to prove whether or not something MUST be the case. You can't prove whether or not Newton's laws must be the case but you can prove whether or not they are the case with good accuracy (through experiment)
Reply to khaled Didn't you read past the opening post? He clarified that by "prove", he means show to be the case. And we're obviously talking about science, not maths. This can and has been done with regards to Newton's three laws of motion, for example.
In summary, Newton's laws boil down to [I]f=ma[/I]. An enormous quantity of physical science has been developed by applying this simple mathematical law to different physical situations.
f = ma is essentially a definition. A very clarifying definition to be sure, but it's not a fact or a theorem. It's a definition. That is my understanding.
Thank you everyone for your responses. I would only like to know how Newton knew his laws are true. What were the experiments he performed?
Newton's laws of motion aren't true, they can't be proven logically or experimentally, they are a framework, useful to some extent.
Newton's 2nd law is a definition of the concept of Force. Newton defines Force as the product of mass and acceleration: if some object of mass m accelerates at the rate a, it is said by definition that there is a force F = m*a acting on it. It would be more accurate and less confusing to call it a definition rather than a 'law'.
From this definition it follows that if an object doesn't accelerate, that is if it is at rest or in uniform motion in a straight line, then there is no force acting on it: this is Newton's 1st 'law', merely a consequence of the above definition. Newton stated it first because he took it from Descartes:
Descartes’ first two laws of nature: the first states “that each thing, as far as is in its power, always remains in the same state; and that consequently, when it is once moved, it always continues to move”, while the second holds that “all movement is, of itself, along straight lines” (these two would later be incorporated into Newton’s first law of motion)
These two Descartes 'laws' were also a framework, not statements which could be proven logically or experimentally. It's not hard to imagine why he formulated these laws. Most things do not move along straight lines and do not always continue to move, but for instance when we let a solid ball roll on a flat surface it seems to keep moving in a straight line unless its course is stopped or changed by an obstacle or by the wind or by some other thing, so there is the desire to see uniform motion in a straight line as the state of natural motion, the simplicity and beauty of it is attractive. Descartes believed that the universe was created and preserved by God, so he looked at the universe through that lens.
It would be equally valid to come up with ugly 'laws' of nature instead, saying that the natural motion of things is chaotic, that things do not remain in the same state, and then only in rare circumstances do these chaotic motions combine to create a temporary uniform motion in a straight line. That's a different framework, a different way to look at the world, equally valid. But Descartes wanted to see simplicity and beauty as the basis of the universe, as signs of God's perfection, rather than chaos. Same goes with Newton.
Once Newton's 1st and second laws are taken as a basis, then by definition when an object stops moving uniformly in a straight line there is a force acting on it, of magnitude m*a. We can't know what force is acting on an object without measuring its acceleration, because Force is not defined independently from F = m*a, and that's precisely why F = m*a is the definition of Force in Newton's framework. When students are told to calculate the acceleration of an object knowing the force that is acting on it, this is stupid because in practice in order to calculate the magnitude of the force acting on it we had to measure its acceleration in the first place.
So what's the point of these two laws? Well we could do away with them, but here's an example to show how they can be a practical tool. Let's say you carry out a specific experiment on some object (let's call it object 1), and each time you repeat the experiment you measure that the object always accelerates at the same rate. Then you take some other object (object 2) and carry out the experiment on it, and you measure that it accelerates at half the rate of the other object, every time. Then you take a third object (object 3) and you measure that it accelerates 3 times faster than the first object, and 6 times faster than the second one.
One useful way to look at this is to say that there is a constant force applied on these objects, and that the different acceleration is due to the objects having a different resistance to acceleration. For instance you can say that object 2 resists acceleration twice more than object 1, and 6 times more than object 3. This resistance to acceleration is what is called 'mass'. If you define object 1 as the reference (mass m1 = 1), then you define object 2 as having mass m2 = 2, and object 3 as having mass m3 = 1/3.
And that's where F = m*a becomes useful, because as it turns out in many experiments these objects will have the same relative acceleration. For instance if you carry out another experiment with object 1 and measure its acceleration, you can predict how fast the other two objects will accelerate before carrying out the experiment with them, you can predict that object 2 will accelerate twice less and object 3 three times more. It doesn't work for all experiments, but it works often enough that Newton's framework is useful. Although in my view it would be less confusing to do away with Newton's laws completely, because you don't need the concept of force nor even of mass to make the same predictions.
Newton's 3rd 'law' can be seen as a definition of Mass. Mass is a relational quantity, to say that an object has mass m2 = 2kg is the same as saying that in many experiments it accelerates twice less than a reference object that is defined to have a mass m1 = 1kg. So the ratio of their masses is by definition the inverse ratio of their accelerations: m2/m1 = a1/a2, or m1*a1 = m2*a2. In experiments where they interact with one another (through an elastic collision for instance), they accelerate in opposite directions, so a1 and a2 have opposite signs, so m1*a1 = -m2*a2, which is Newton's 3rd 'law'.
Newton's laws are basically definitions of the concepts of force and mass. Mass is defined as relative resistance to acceleration, force is defined as mass times acceleration, and in that framework when objects don't move uniformly in straight lines we say a force is acting on them. The reason this framework works to some extent, is that in many different situations different objects have the same relative acceleration. Which leads to the concept of mass, which leads to the concept of force.
Examples of experiments that have led to this framework are observations of collisions, experiments with pendulums, with springs, observations of celestial bodies, more generally observations of motion, ...
Reply to SReply to S The OP was "I would like to know how you can prove these laws". I explained that the answer depended on what you mean by proof. No where was this: Quoting S
He clarified that by "prove", he means show to be the case.
Reply to khaled Thank you for confirming that you didn't get as far as even the fourth post from the opening post. There's only like five or so sentences between the opening post and his clarification.
Reply to S "show they are true" can also be interpreted both ways..... Either empirical or axiomatic proof. I was saying that you can't prove newton's laws axiomatically in the same way you can prove that the sum of angles in a triangle is always 180.
"show they are true" can also be interpreted both ways..... Either empirical or axiomatic proof. I was saying that you can't prove newton's laws axiomatically in the same way you can prove that the sum of angles in a triangle is always 180.
No, it can't really be interpreted both ways when the context is clearly science, not maths.
Comments (77)
Every white swan you see is evidence that swans are white. However, this doesn't mean ALL swans are white. If the chornometer is following the Newton's laws then it must be white swan. Newton never saw a black swan.
Quoting StreetlightX
I think what he's trying to say is that argument is circular. Newton's laws proving Newton's laws.
If the instruments obey Newton then Newton would be one happy dude wouldn't he? I guess the OP wants to compare the situation to a court case where Newton is the client, the lawyer, the judge and the jury. Happy happy Newton!
If the instruments didn't follow Newton's laws then they would disprove Newton.
It's necessary that the instruments too must obey the laws.
You could never prove them. For one thing they're not "true," if by true you mean that the universe actually works that way. We know that for objects moving at very high speeds and/or objects with extremely large mass, Newton's laws are superseded by Einstein's; and that even for everyday object like bowling balls, Newton's laws are only an approximation.
Secondly, NO law of physics can ever be proved; because every law of physics is a historically contingent approximation, good to a few decimal places, to the results of the experiments we're capable of doing at any given level of technology. Our very best physical theory, quantum electrodynamics, gives the magnetic moment of the electron to "a few parts in [math]10^{13}[/math]. That's great by physics standards but there are a lot more decimal places out there and a lot of physics we still don't know.
https://physics.stackexchange.com/questions/497087/what-is-the-most-precise-physical-measurement-ever-performed
No physical theory is true. Or rather, "true" is defined in physics as our best physical theory! So Newton's laws were true in 1687 with the publication of the Principia, and became false in 1915 with Einstein's publication of general relativity.
Pick your definition of true. The ultimate truth of the universe -- if there even is any such thing? Or just the latest widely agreed on theory from the physicists?
Let's not get too technical. The problem for the OP is how an instrument that is Newtonian can ever prove that some other event is NOT Newtonian in nature. If I only have red paint, whatever I paint will surely be red.
A better analogy is the biased judge adjudicating a case. The trial wouldn't be fair.
I responded primarily to the title of the OP without reading much of the post, and without reading the other responses in the thread. If I misconstrued the question, so be it. It's kind of a reflex on my part to point out that the laws of physics are historically contingent approximations; and that whether there are laws of the universe at all, let alone ones accessible to humans, is an open question. But if that wasn't the question, then ... well, what was the question. I didn't understand the bit about how Newtonian instruments could prove an event is not Newtonian. In fact perfectly conventional Newtonian telescopes were used to observe the solar eclipse in 1919 that confirmed Einstein's theory of relativity.
https://en.wikipedia.org/wiki/Solar_eclipse_of_May_29,_1919
Note that by Newtonian telescope, I meant not only the OP's sense of a telescope operating by Newtonian physics; but also that the Newton invented the reflecting telescope! So there's a double meaning there.
There are no 'instruments which are Newtonian'.
Actually I think your answer was the best by saying scientific claims are contingent.
I meant which follow Newton's laws
I have already confessed to not reading the post and only lazily making one of my standard hobby horse points. Did you want me to confess again? Is there a particular punishment you have in mind? I watched the entire Democratic debate tonight, that was punishment enough!
Quoting StreetlightX
There's an even bigger point here which the OP is hinting at - that the theory of relativity which has supplanted Newton's was proven by instruments that had to follow Newton's laws.
Kindly take one step back to the OP's question.
I wish you'd clarify our doubts because they probably reveal more ignorance than knowledge/understanding.
If you've read my other posts then you know that the Theory of Relativity was derived from measurements from instruments that followed Newtonian laws. What do you have to say about that?
Every instance of the laws being verified is part of the proof isn't it?
The OP is not as concerned with the meaning of "proof" as he is concerned about the circularity of the proof. By "proof" he probably means the derivation process of the laws. It must have been that measurements were taken of mass, acceleration, and force to get to the equation F = ma, right? If each such measurement followed Newtonian mechanics then it, to the OP, looks like the laws proving themselves. This is what appears problematic to the OP (unfortunately he isn't here to confirm this) - that Newton's laws were/are used to prove Newton's laws.
Personally, I think if the instruments didn't follow Newtonian laws then that would be a problem because they would be the disconfirming exception, invalidating Newton's laws.
I mentioned the theory of relativity being proved by instruments that followed Newton's laws but what I forgot was that the theory of relativity is applicable at non-relativistic speeds too. The same can't be said of Newton's laws which are now like Aristotle's belief that objects naturally come to rest and that heavier objects fall faster than lighter ones.
Can you kindly clarify on the circularity which I mentioned above?
Is it a real/interesting question or is it a question borne out of ignorance? Or is it both?
Which areas of logic, science and math does such a question touch upon?
Can you prove they are consequences of other math? Yes. I think you can get all the basic laws from Hamiltonian/Lagrangian mechanics.
What do you mean by that? Mathematical models proves that Newton's laws must be true?
How so?
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Newton's laws being theorems from other assumptions doesn't mean they describe reality.
Repeat this for a plastic track measuring 10ft, then 15ft, then 20ft, then 25ft, and so on. If all plastic tracks and ball bearings have minimal friction then the ball bearing should again reach the same height at the end as the height at the beginning. From this we may inductively reason that if we don't allow the plastic track to bend back up at the end, then the ball-bearing could hypothetically go on forever at a constant velocity if no other net force is acted upon it, i.e. Newton's first law of motion.
Well said!
Unfortunately, you cannot prove anything about the real, physical world, simply, because its construction logic is unknown. The term "proving" means that you demonstrate that a theorem necessarily follows from the construction logic of its world.
Still, Newton's laws were really good at resisting falsification for a long while. Only by looking at quite unusual situations, they were falsified:
Experimentally, Newton's law of gravitation has been falsified due to for example the anomalous perihelion precession of Mercury, which matches instead with Einstein's theory of gravitation.
Still, Einstein's theory is rather used as a refinement and not as a replacement for Newton's laws.
This is puzzling. Laws are descriptions of reality, right?
@alcontali read the underlined.
Physical laws can't be proven by science. All physical laws are subject to change, correction, or invalidation.
He did not prove his laws, so he performed no experiments to prove his laws.
This was the easiest question to answer so far on the forums.
They seem to be true, but you can never be absolutely, 100% sure. Most people treat gravity and Newton's laws as true. It is practically very useful to think of them as true. But science is not capable of proving that they are true. Science has a lot of evidence that supports that Newton's laws are true, but science will never claim that Newton's laws are true.
Sorry, this is how it is.
/thread
You've already been given examples, and you can look them up. So why ask me that?
You know that logo at the top, what does it say? It doesn't say, "The Science Forum", does it?
I'll offer an analogy. Imagine the color red = Newton's laws. The instruments used to "prove" Newton's laws can be considered as a pair of red-tinted glasses (obeying Newton's laws). Any and everything you see using these glasses will appear red i.e. obeying Newton's laws. This is what I think the OP is trying to say.
Newton's laws proving Newton's laws!
Now I think there's a distinction we have to make between a logical proof and a scientific proof. Circularity is a bad character in the former but is necessary in the latter.
For instance a classic case of circularity given in elementary logic books is the Bible proving God exists because it's the word of God. This is a vicious circularity and the argument is rejected.
In science the difference is laws discovered/proved are necessarily universal and must be obeyed by everything. So, the instruments, as of necessity, should obey the laws, in this case Newton's. I guess I'm saying in science there has to be circularity if unavoidable.
What say you?
Of course this is false. Newton looked through a telescope that he himself had made. He was a master lens grinder. That's peripheral to the discussion but just an interesting factoid. Now the point is that Feynman taught us exactly how light passes through lenses. The laws of optics were known to Newton or rather discovered by him. But optics are a quantum phenomenon and Feynman (and others) won the Nobel prize for elucidating this fact.
Everything in the world is a quantum phenomenon. A rock doesn't fly apart because of quantum theory. I think someone made this point earlier but it bears repeating. Newton didn't know his telescope worked on quantum principles, but eventually we discovered that it does.
Me? Wasn't sure about the quoting. Newton's instruments only followed Newton's laws to a certain degree of approximation. They follow Feynman's laws -- quantum laws -- to a far greater degree of approximation. Newton didn't happen to know that, but it was true nevertheless. How is this point not perfectly obvious to everyone?
What's wrong with you?
Newton took a lot of flack at the time. His law of gravity told us what gravity does; but not what it is. He famously said that "I frame no hypotheses." Newton well understood that science is descriptive and not explanatory; a point that modern scientists and philosophers of science would do well to understand.
But at the time, Newton's contemporaries did NOT understand. Descartes had a theory of vortices that said what gravity WAS, not just how it acted. That was, by the scientific ethos of the time, better science than what Newton did. It took people a while to come around to Newton's point of view. We see this echoed today, when people want to "interpret" quantum mechanics rather than be satisfied that it describes what the universe does; and not necessarily why.
https://en.wikipedia.org/wiki/Hypotheses_non_fingo
The basic hypothetico-deductive method works like this:
1. Assume that the system under consideration is described by some theory - in other words, it follows some laws, such as Newton's laws.
2. On the basis of this assumption, make predictions about the system's behavior under certain conditions.
3. Prepare the system and perform an experiment. If your observations are in line with your hypothesis, then your hypothesis, and by extension your theory, are confirmed, otherwise it is disconfirmed (falsified).
There are variations and elaborations of the above (with some, for example, prioritizing falsification over confirmation), but this is the basis of the so-called scientific method. For this method to work, you absolutely need your instruments to be predictable, i.e. to follow laws - including, yes, the laws that you are testing. You just need to consider the instruments as part of the system that you are testing and make your predictions based on that assumption. If the test fails, you could blame all or any part of the system for the failure, including your instruments. You could then try to isolate the problem by performing further tests. And if the test succeeds, and so do other tests, then you will have a high confidence that both the experimental system and your instruments act in accordance with the laws. There is no vicious circularity here.
Of course, in practice we often choose to simplify and neglect many things when modeling an experiment. Thus, we may leave the instruments and our own actions out of consideration. But these simplifications are not made willy-nilly: ideally, we make them only when our theory predicts that they will not have much impact on the result of the experiment. And when the experiment doesn't show what we expect, then one of the explanations that we have to consider is that our assumptions were overly simplistic. We may then have to go back and take into account factors that we thought we could neglect, such as the behavior of the instruments.
Quoting Fernando Rios
This question worries me a little. I hope that you are not under the impression that Newton's laws are accepted solely on the authority of Newton himself, much like a religious teaching is accepted on the authority of a prophet or a sacred text. How Newton convinced himself that his theory was correct is a question for a historian or a biographer, but it is quite irrelevant to a 21st century scientist. Newton's own thinking could be deeply flawed and his methods wholly inadequate, for all we care - his laws have been tested so thoroughly since then that it no longer matters.
Newton did not arrive at his theory by empirical methods (experimenting) but by deductive methods, formulating mathematical equations that closely followed his observation of natural phenomena.
They appear to be true because when you plug in values into the equations they predict a result that resembles the equivalent event in real life. For instance his basic acceleration formula predicts that if you subject a mass to a force, it will accelerate. It just happens that if you actually take the mass and apply a force to it, it will accelerate as the formula predicts.
Quoting TheMadFool
Same with this, the theory of relativity was not developed empirically, it was completely formulated mathematically before physical evidence was observed. The predictions of the theory were so revolutionary that not even Einstein was convinced, until scientists were able to see the path of light bent by gravity, by measuring starlight distorting near the sun during a full eclipse.
Quoting Fernando Rios
If we know the devices (rulers, scales, telescope, etc) existed before Newton, and therefor before Newton's laws, what were the devices measuring? (so the device itself is not 'Newtonian', it existed before Newton!) Newton's laws described what the devices were measuring (predicted outcomes of measurements), more accurately than previous models.
I think you are putting the cart before the horse. Newton's laws are based on the measurements of those devices, not the other way around.
Also, Newton's Laws are not accepted as perfect in science. Relativity and Quantum Mechanics have introduced aspects to physics that are not in line with Newton's laws or pick up where Newton's laws stop working (as far as they can tell so far).
Sorry, I missed a whole page of responses before posting above. Ignore my oversimplified summary if you have already received better answers.
All proofs mean that. Proofs in physics mean that. Except there are no proofs in the science of physics.
This is preposterous. Any one counter-example that does not obey the law destroys that law's usefulness. Newton's laws have not had examples in real life that would nullify his laws, but CONCEPTUALLY they may happen. Therefore a billion experiments and observations that are thought to be showing Newton's laws to be true by S and by Fernando Rios, can be shown to be false by just one experiment or one single observation.
This is philosophy of physics. If you want to see the LOGIC that lead Newton to arrive at pronouncing his laws, then that's a different matter. If you want to see the process in chronological order that were the steps of Newton's developing his insights that lead to the formulation of his laws, that can be done. But to see what makes his laws true, is not possible.
What do you make of the 1919 eclipse that confirmed Einstein and disproved Newton?
https://en.wikipedia.org/wiki/Eddington_experiment
Newton's laws have been showed to work in special cases of the law that explained the 1918 experiment.
Newton's Laws were not refuted, but expanded with adding some special conditions under which N's laws were not useful.
Same thing as to say, (conceptual example follows) "Primes are consecutive non-zero positive integers", if you can only count to three. Once you learn about the numeral four, and the concept of four, you have to rework your claim, while your oginal claim is still true up to no. 3.
So your reworked claim will become, "All non-zero positive odd integers are prime", if you can only count to 8. Then you come to learn about "9", and you need to revise your claim again. Your third claim will not contradict your second claim if you only consider integers to 8.
Newton didn’t do any experiments with regard to his laws of motion and gravity*. He believed that Kepler’s laws of a heliocentric model of the solar system, with its elliptical orbits, were true because of their predictive power and that they were formulated due to an analysis of Tycho Brahe’s comprehensive and accurate data of celestial observations. He also believed that Galileo was right about motion being relative and that objects fell at the same rate regardless of mass (overturning the contemporary prevalent view of Aristotelian motion).
With Kepler's planetary laws and his invention of differential calculus, Newton devised his universal law of gravity and with the experimental results of Galileo (my example prior being a modern interpretation of such an experiment) he devised his three laws of motion. Personally I don’t care whether Newton thought himself to be right, or Brahe, Kepler, and Galileo either. Because, as with most geniuses, they were insufferable arseholes who thought everything they did was true and correct. Honestly, each and every one of these people were know-it-all pricks who were about as welcome at parties as a fart in a crowded lift (elevator to my colonial cousins). But then again, I would’ve liked to party with Brahe as he seemed to be a larger-than-life character. He had a tin nose due to losing his own nose in a duel! He also made Kepler practically beg for his observational data (like I said, an arsehole!)
Why everyone else thought Newton’s Laws were true was because the laws themselves had great predictive power and his genius was (besides coming up with calculus) that his laws explained how the celestial and terrestrial bodies move all due to being bound by gravity. The idea that celestial and terrestrial movement were the same thing wasn’t even considered beforehand and the simplified elegance of this probably gave reason why Newton himself thought his laws true. Newton didn’t know why gravity (he didn’t even know precisely what the gravitational constant was) and so he credited God with this feat. It wasn’t until Einstein came along that a naturalistic account for gravity was given. Newton also admitted to a certain artifice to his calculations as he was acutely aware that messing about with numbers didn't prove anything empirical.
Incidentally due to Newton’s thin skin towards criticism and his dislike for other academics (especially Robert Hooke.Newton’s quote about standing on the shoulders of giants was a sarcastic dig at Hooke’s diminutive size) he sat on his calculations and it wasn’t until he was befriended by the astronomer Edmund Halley that he decided to tell of his findings. Even if Newton thought his laws were true, it seemed that he wasn’t that bothered if other people thought them true also.
*Newton was a theoretician about motion and gravity but it’s not to say he didn’t dabble with experiments himself. When formulating his theory of colour, he stuck a bodkin in his eye to see how this changed his perception of colour. Also in his later years, he dabbled in alchemy.
:kiss:
It actually has happened. General Relativity shows that the force of gravity, as conceptualized by Newton's laws does not exist. That was one of the main issues that troubled Einstein: What is this "long invisible arm" that extends out of masses and reaches out to other masses?
Through the formulation off GR he showed that space and time are inseparable, that space-time curves around a mass, and that this curved space-time affects the movement of objects.
Newton would say the satellite orbiting earth is kept in orbit because the force of Earth's gravity is balanced by the satellite's centrifugal force.
Einstein would say the satellite is experiencing no force, it is simply moving through curved space-time.
Newton's laws are no laws at all. They are a mathematical representation of what Newton observed. Same with Einstein's theory of relativity. They are models approximating the real laws of the universe.
The actual, real laws of the universe are unknown to man, and although the perpetually evolving models and theories keep inching closer, there are still many important observations that can not be reconciliated with the latest theories.
to the OP, by asking the question of how can Newton's laws be proven to be true, there is an implication that they are true, and they are not. No present physics theory is true, and you can't prove the truth of something that is not true.
You got me there.
Newton's Three Laws of Motion.
The correct answer isn't, "You can't". It's, "They have been".
f = ma is essentially a definition. A very clarifying definition to be sure, but it's not a fact or a theorem. It's a definition. That is my understanding.
Newton's laws of motion aren't true, they can't be proven logically or experimentally, they are a framework, useful to some extent.
Newton's 2nd law is a definition of the concept of Force. Newton defines Force as the product of mass and acceleration: if some object of mass m accelerates at the rate a, it is said by definition that there is a force F = m*a acting on it. It would be more accurate and less confusing to call it a definition rather than a 'law'.
From this definition it follows that if an object doesn't accelerate, that is if it is at rest or in uniform motion in a straight line, then there is no force acting on it: this is Newton's 1st 'law', merely a consequence of the above definition. Newton stated it first because he took it from Descartes:
These two Descartes 'laws' were also a framework, not statements which could be proven logically or experimentally. It's not hard to imagine why he formulated these laws. Most things do not move along straight lines and do not always continue to move, but for instance when we let a solid ball roll on a flat surface it seems to keep moving in a straight line unless its course is stopped or changed by an obstacle or by the wind or by some other thing, so there is the desire to see uniform motion in a straight line as the state of natural motion, the simplicity and beauty of it is attractive. Descartes believed that the universe was created and preserved by God, so he looked at the universe through that lens.
It would be equally valid to come up with ugly 'laws' of nature instead, saying that the natural motion of things is chaotic, that things do not remain in the same state, and then only in rare circumstances do these chaotic motions combine to create a temporary uniform motion in a straight line. That's a different framework, a different way to look at the world, equally valid. But Descartes wanted to see simplicity and beauty as the basis of the universe, as signs of God's perfection, rather than chaos. Same goes with Newton.
Once Newton's 1st and second laws are taken as a basis, then by definition when an object stops moving uniformly in a straight line there is a force acting on it, of magnitude m*a. We can't know what force is acting on an object without measuring its acceleration, because Force is not defined independently from F = m*a, and that's precisely why F = m*a is the definition of Force in Newton's framework. When students are told to calculate the acceleration of an object knowing the force that is acting on it, this is stupid because in practice in order to calculate the magnitude of the force acting on it we had to measure its acceleration in the first place.
So what's the point of these two laws? Well we could do away with them, but here's an example to show how they can be a practical tool. Let's say you carry out a specific experiment on some object (let's call it object 1), and each time you repeat the experiment you measure that the object always accelerates at the same rate. Then you take some other object (object 2) and carry out the experiment on it, and you measure that it accelerates at half the rate of the other object, every time. Then you take a third object (object 3) and you measure that it accelerates 3 times faster than the first object, and 6 times faster than the second one.
One useful way to look at this is to say that there is a constant force applied on these objects, and that the different acceleration is due to the objects having a different resistance to acceleration. For instance you can say that object 2 resists acceleration twice more than object 1, and 6 times more than object 3. This resistance to acceleration is what is called 'mass'. If you define object 1 as the reference (mass m1 = 1), then you define object 2 as having mass m2 = 2, and object 3 as having mass m3 = 1/3.
And that's where F = m*a becomes useful, because as it turns out in many experiments these objects will have the same relative acceleration. For instance if you carry out another experiment with object 1 and measure its acceleration, you can predict how fast the other two objects will accelerate before carrying out the experiment with them, you can predict that object 2 will accelerate twice less and object 3 three times more. It doesn't work for all experiments, but it works often enough that Newton's framework is useful. Although in my view it would be less confusing to do away with Newton's laws completely, because you don't need the concept of force nor even of mass to make the same predictions.
Newton's 3rd 'law' can be seen as a definition of Mass. Mass is a relational quantity, to say that an object has mass m2 = 2kg is the same as saying that in many experiments it accelerates twice less than a reference object that is defined to have a mass m1 = 1kg. So the ratio of their masses is by definition the inverse ratio of their accelerations: m2/m1 = a1/a2, or m1*a1 = m2*a2. In experiments where they interact with one another (through an elastic collision for instance), they accelerate in opposite directions, so a1 and a2 have opposite signs, so m1*a1 = -m2*a2, which is Newton's 3rd 'law'.
Newton's laws are basically definitions of the concepts of force and mass. Mass is defined as relative resistance to acceleration, force is defined as mass times acceleration, and in that framework when objects don't move uniformly in straight lines we say a force is acting on them. The reason this framework works to some extent, is that in many different situations different objects have the same relative acceleration. Which leads to the concept of mass, which leads to the concept of force.
Examples of experiments that have led to this framework are observations of collisions, experiments with pendulums, with springs, observations of celestial bodies, more generally observations of motion, ...
Quoting S
Said.
No, it can't really be interpreted both ways when the context is clearly science, not maths.