# Tag Info

121

"Physics breaks down" is a bad way of saying what people are trying to say. It's the sort of thing that sounds cool at first, but then it starts misleading people. What scientists mean is "our best theory produces non-sensical or contradictory results in this situation, so we know the theory doesn't make good predictions there." They do ...

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Here is a mathematical theorem: the internal angles of a triangle add up to 180 degrees (i.e. half a complete rotation). To be a little more thorough, let's define a triangle: it is a closed figure consisting of three straight lines, and a straight line is the line of shortest distance between two points. Ok so we have a nice mathematical theorem. Now we go ...

101

My question would be, what happens in the scientific community if one experiment proves it wrong We have already seen what happens in this circumstance by looking at what happened to Newtonian gravity. First, well before the development of general relativity there were observations that did not fit with Newtonian gravity. For example, Uranus’ orbit did not ...

86

Ever since the time of Newton physics is about observing nature, quantifying observations with measurements and finding a mathematical model that not only describes/maps the measurements but, most important, it is predictive. To attain this, physics uses a rigorous self-consistent mathematical model, imposing extra postulates as axioms to relate the ...

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Exact (non-)solvability is an issue that pops up in every area of physics. The fact that this is surprising is, I believe, a failure of the didactics of mathematics and science. Why? Consider the following: You solve a simple physical problem and the answer is $\sqrt{2}$ meters. So what is the answer? How many meters? Have you solved the problem? If I do not ...

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I think this question makes hidden, inarticulated assumptions about reality. In physics, we make observations and then try to find models that match them. The models, though, belong only to us and exist in our heads and textbooks. We perform the calculations required to make our predictions in our models. We cannot say whether nature makes similar ...

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Let me give an example of a very, very mild case of 'theory breaks down'. Boyle's law is stated as follows: $$P_1V_1 = P_2V_2$$ Expressing that for a given quantity of gas the pressure and volume are inversely proportional to each other. At low pressures Boyle's law holds good. The reason that it holds good is that at low pressure the gas molecules take up ...

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"Falsified" is more philosophical than scientific distinction. Newton laws have been falsified somehow, but we still use them, since usually they are a good approximation, and are easier to use than relativity or quantum mechanics. The "action at distance" of Newton potentials has been falsified (finite speed of light...) but again, we use it every day. So,...

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@annav's answer already describes well how physical theories work and how they require self-consistency. I'd like to add some comments from a different perspective to that. TL;DR Physical theories have to be self-consistent AND consistent with observation. Mathematical self-consistency Firstly if we treat a physical theory as a mathematical axiom system (...

39

Just an example. There were times when physicists tried to explain electromagnetic forces using mechanics. Something like "there is some media which fills the space, in presence of electric charges this media can be stretched or compressed hence we have some forces". It was a common belief that true explanation of various phenomena must be mechanical, like ...

39

There's no rule against infinity, only a rule against being empirically wrong. Historically, the infinite has hinted we're missing something, but so have plenty of other things too. Let's discuss some historical examples. The ultraviolet catastrophe and its resolution respectively come down to physical reasons to care about $\int_0^\infty x^2dx=\infty$ and $\... 37 Words like "proven" and "wrong" have to be used carefully in this context. It is more meaningful to talk about "accuracy" and "limits". If an experiment was conducted tomorrow that contradicted general relativity it would by no means make general relativity a useless theory, nor would we get rid of it. The purpose of ... 32 None of the interesting equations in physics can be derived from simpler principles, because if they could they wouldn't give any new information. That is, those simpler principles would already fully describe the system. Any new equation, whether it's the Navier-Stokes equations, Einstein's equations, the Schrodinger equation, or whatever, must be ... 31 This is a very broad subject, but as a rule of thumb, highly non-linear means that the non-linearities cannot be treated with perturbation theory, as these are not negligible as compared to the linear part of the equations (and, in general, they not only are non-negligible, but actually dominate the dynamics). As an example of a non-linear theory which can ... 31 Newtonian Physics is accurate in the specific domain it was designed for Physics is not about identifying the "truth" of the world around us. It's about creating mathematical models that allow us to accurately predict the behavior of the world. Nobody is trying to create a perfect model, because the complexity of such a model would be infinite. Instead, ... 27 You lack complete knowledge of the system you're asking about. You only know about the jar. And if the complete system is the jar then yes, it has always been empty because there's nothing to interact with it. But if you suppose there are things which may have been in the jar, now those are added to the system. That puddle of water on the floor, was it ... 27 The Banach-Tarski paradox seems like an obvious candidate. It's possible to cut a sphere up into finitely-many pieces, then glue it back together into two spheres each identical to the original The math is correct, but this is obviously not possible in the real world, so what's going on? Every mathematical proof is based on some set of "axioms", or ... 25 There's a difference between the "laws of physics" which are our current best model for how the universe works, and the true laws of physics, the underlying behaviour and nature of the universe. We could quite easily encounter a situation that defies the former - we already know that our two best models, for astronomical and microscopic scales, don'... 24 They are derivable from classical mechanics using either the continuum or molecular points of view. Starting with a continuum view, one applies conservation of mass, momentum, and energy to a control volume and the result is the Navier Stokes equations. The Navier Stokes equations, in the usual form, apply to Newtonian fluids, that is fluids whose stress ... 23 Roughly speaking, one law is more fundamental than another if it explains it. (There's no guarantee any law is "fundamental", in the sense of there being nothing even more fundamental; maybe all laws have a deeper explanation, but at any given time our knowledge is finite.) The most obvious guess at what it means for$A$to explain$B$is that$B$is ... 22 "Physics breaks down" sounds good, but it is confusing. A better phrasing would be "known physics breaks down." Physics attempts to model reality using mathematics. In this sense, physics has no "laws." In the famous words of Captain Barbossa, "They're more like guidelines." However, we have many of these ... 22 Infinity is a shorthand for unbounded. When we say that$\frac 1 x$goes to infinity as$x$approaches$0$, what we really mean is that we can make$\frac 1 x$as large as we like by using a value of$x$that is sufficiently close to$0$. The actual value of$\frac 1 x$when$x=0$is undefined. If we restrict ourselves to real numbers then there is no such ... 20 There is a great paper from the group of Howard Stone on this subject: Wetting of flexible fibre arrays (freely available here) They specifically study when 2 closely positioned parallel fibers (i.e. hairs) clump together due to the water droplets on the fibers. They quantatively determine when the volume of liquid is sufficiently small to cause ... 20 I once asked Putterman after a similar colloquium what he meant by this statement, and his answer was "long time tails". Long time tails are fractional powers that appear in the long time behavior of correlation functions, see, for example, here and here. These fractional powers are seen in molecular dynamics (they are more difficult to see experimentally), ... 20 I think the answers above are excellent, but I'd like to point out a related issue. During the early 20th century we developed two entirely new types of physics, GR and QM. Its difficult to imagine two theories that were more different from each other. GR is essentially classical mechanics in a non-Euclidean geometry, QM is, well, still being debated. So ... 19 here's an answer from Dr.Richard Feynman http://www.feynmanlectures.caltech.edu/II_01.html#Ch1-S1 You know, of course, that atoms are made with positive protons in the nucleus and with electrons outside. You may ask: “If this electrical force is so terrific, why don’t the protons and electrons just get on top of each other? If they want to be in an ... 18 Accuracy can mean different things. While the question asks about the statistical accuracy, what immediately comes when talking about the Newton's laws is that they are non-relativistic, i.e., they are valid up to small corrections of order$v/c\$. Physics laws are based on empirical observations, the symmetries of the universe, and approximations appropriate ...

17

If the only mathematical statements admitted in a physical theory were those having immediate empirical content (i.e. they can be tested by an unambiguous experiment), then you would have a very good case to make. Why? Because the consistency of the world of experience would guarantee the consistency of the mathematical formalism. End of story. In reality, ...

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