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22

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 ...


19

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 ...


12

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), ...


6

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). ...


5

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 ...


5

I was taught that the Standard Model was a misnomer; that it ought to be called the Standard Theory. I'm inclined to agree, though theories and models are both indispensable in science. Ultimately, the purpose of a model is provide local understanding of a particular phenomena. A model: Typically considers only fields, objects or quantities relevant to a ...


5

A theory is a set of statements that is developed through a process of continued abstractions. A theory is aimed at a generalized statement aimed at explaining a phenomenon. A model, on the other hand, is a purposeful representation of reality. As you can see, both share common elements in their definitions. What differs one from the other (in my opinion) ...


3

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 ...


2

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 ...


1

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 ...


1

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 ...


1

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 ...


1

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 ...


1

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 ...


1

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 ...


1

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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