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71

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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@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 ...


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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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If theories were only used to describe what we already know and observe, maybe they would not need to be self-consistent; they could even just degenerate into big lists of observed phenomena. This is what science looked like in Sumer, 5000 years ago. If we want physical theories to be predictive, they have to be self-consistent in the sense that they have to ...


7

Physical theories are not a collection of mathematical axioms, they are attempts at describing nature. Not only that. Physical theories are also supposed to make predictions. This is part of the Scientific Method. One does not expect to predict new phenomena - that can later be veryfied - using a non self-consistent theory. We cannot cheat. Following ...


7

Mathematical theories which are not consistent prove contradictory things (this is just a statement about mathematics and what it means to be inconsistent, not to do with physics in particular). We do not want theories of physics that predict contradictory things. Ideally we don't want theories that make any wrong predictions, but if our theory makes two or ...


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Physics is the art of compressing our knowledge of the universe. As it happens, whenever we stick two massive bodies near each other (or notice them near each other), they seem to move towards each other. Now, we could simply record the fact that every massive body (individually) is moving towards every other massive body (individually). This is a large ...


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Yes. Ordinary quantum field theory is as wrong as Newtonian gravity for not including GR effects. That is to say, it is a perfectly fine theory inside its domain of validity, which in this case means pretty much everything below the Planck scale, just as Newtonian mechanics is valid for speed much less than the relativistic scale (the speed of light). ...


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This actually extends beyond just computational approaches and applies to experimental approaches also. And it's not at all a trivial problem to address. Generally speaking, we construct a model of some physical system -- either computationally or experimentally -- and we make certain assumptions to simplify the problem. In your circuit example, maybe we ...


3

Theoretical physics is the attempt to describe a system (a subset of nature) using mathematics, making certain assumptions and idealizations if necessary. Put another way, the language of theoretical physics is mathematics. Roughly speaking, you need an axiomatization of the notion of states, observables and a dynamical law. Most physical theories have more ...


3

A physical theory uses mathematical objects to model physical systems. In broad strokes, the theory consists of (a) rules for how to relate these objects to the initial conditions of an experiment, (b) mathematical claims about properties that the model must have, and (c) a description of how mathematical characteristics of the model lead to testable ...


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To put it in a short way: Self-consistency is required because we expect nature to stick to laws that can be described mathematically. Mathematical descriptions by definition have to be self-consistent.


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Good question. Is the many-world interpretation with its insistence on self-consistency and conclusions like that gravity must be quantized really preferable to the Copenhagen interpretation, which just stays agnostic on those matters? One advantage of the insistence on self-consistency is that the theory becomes more falsifiable, because it is sufficient to ...


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In the standard model of particle physics which fits the data up to now elementary particles entering the lagrangian are point particles with mass. The electron, for example is one of the elementary particles, and it does have a mass and the fit gives it 0 volume. There are experiments which try to set limits to how small the volume of the electron is. ...


3

Your question states that We think we know that matter is anything having mass and that it occupies space but in fact, we know better than that. We have good reason to believe that fundamental particles are point-like. In other words, they have no internal structure, size, or volume. And they indeed have mass. We have a theoretical understanding (in ...


3

I don't think we should think about this in terms of definitions, and of a particular model being or not being a toy model, but rather it is a matter of the spirit with which a model is considered. A model usually qualifies as a toy model when it is considered mainly not as a (however rough) description of reality, but as a simplified version of a more ...


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A toy model is simply a very simple model which nevertheless is able to explain qualitatively a certain phenomenon. A model should be able to explain natural phenomena in a quantitative way. Also, a toy model can be fundamentally flawed, mathematically or physically, or totally unrealistic. A model instead should be mathematically consistent and not ...


1

From a lightcurve all you can get is a temperature ratio. The relative contribution to the light curves are $R_{1}^2 T_{1}^4/R_{2}^2 T_{2}^4$. The relative surface brightnesses are $(T_1/T_2)^4$. At primary eclipse minimum, some area of the primary is eclipsed by the secondary. At secondary minimum, the same area of the secondary is eclipsed by the primary....


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A "theory" is nothing more than a recipe to describe a natural phenomenon. There can be many theories to describe the same thing, just as I can use different words to describe the same object. Theories can be very different from one another for several reasons. They can describe the same exact phenomenology with different formalism (different words for the ...


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The model is good as a probability model for quantum mechanics, up to the "superposition", where you say: Nobody knows where is the red and the black card, so each card is red or black with the 50% of probability. In other words each card is red and black at the same time (superposition). No , just the state of the card is unknown, it is not half ...


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I would say there are two essential distinctions. 1) A toy model is based on assumptions that we KNOW TO BE FALSE. And not just for the sake of simplification in the sense of "point masses" and "frictionless planes"... but assumptions that are more than idealizations for convenience, they are stripping the problem down to a cartoonified state that is not ...


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I'll address your question a little different, because talking about volumn and particles is problematic in many ways. Let's phrase your question "can there be two particles with mass be at the same place". The answer is yes. There are two types of particles:fermions and bosons. While fermions (electrons, protons) repel each other (not only because of the ...


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Many popular-science authors such as Stephen Hawking or Brian Greene would try to give you the impression that if M-theory passes all self-consistency checks, there will be one "Mathematically Inevitable Theory of Nature", M-theory. Not trying to diminish the immense proportion of the human achievement a "Theory of everything" would represent, the ...


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An equivalent Ohms law can be applied to gas flow and pressure drop, but only for particular mechanical flow restrictions and limited to a range of flow. But more generally for orifices and tubes the relationship between pressure and flow is quadratic, explained predominantly by the energy equation for flow, also known as Bernoulli's equation. In the ...


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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 ...



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