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In quantum field theory bosonic fields $\varphi_\alpha\left(x\right)$ satisfy $\left[\varphi_\alpha\left(x\right),\,\varphi_\beta\left(y\right)\right]=0$, unless noncommutative geometry is incorporated in which case we achieve the moral general case in the first equation you've asked about. This is analogous to the fact that discrete quantum mechanics ...

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If I compare your case (which is similar to mine) I will graduate when I'm 27 and then I can start a phd so i will be 31 years young :) If you love what you do, just do it ! eventually it will be worth it !

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Definitely not too late! I've known graduate students in physics entering anywhere between 20 and 30, and I know there are even older and younger out there. Even better, it's not like information technology is a completely irrelevant- in physics (particularly high energy physics) we routinely deal with big data and I'm sure you could apply some of what you ...

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Think of it in terms of percentage error. If a reading is $100 \pm 2$ metres this is $100 \pm 2\%$. Now divide the 100 metres by 5 to give 20 metres. The percentage error does not change so the value is $20 \pm 2\% = 20.0 \pm 0.4$ metres. If you are not given a percentage error then you would have to judge it from the given value. 110 might have the ...

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Forget all ideas about vectors and velocity and relate it to a car which is travelling at a speed of 70 mph slowing down to a speed of 50 mph. So the idea is negative means slowing down and positive means speeding up. This would be a reasonable start and all the subtleties can come later.

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I would explain that we can feel acceleration in a car. As our speed increases we are pushed back into the car seats. This is positive acceleration. As we slow down we are pulled back by the edge of the seat/seat bell. If the child is happy that acceleration is a change of speed then they should be able to tell with their eyes closed if the ...

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Reusing your car example: use the fact that acceleration is "change in velocity". This can be positive (acceleration in the usual/common sense), but everyone knows that velocity can also be decreasing. This is what phsicists call negative acceleration.

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Positive means speeding up, negative means slowing down. Now this is assuming you are traveling in the positive direction but through an axial change you could always guarantee this. I think this would be a good starting point for a child.

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It depends on the type of number. If the dimensionless number arises from pure math or counting, then it essentially has infinite precision and doesn't limit the number of digits you report. This is the case for the $2$ relating radius and diameter, or the $1/2$ in the kinetic energy formula, or the $N!$ you often see in statistical mechanics. $\pi$ is the ...

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Even in the old quantum theory, prior to 1925, to transition to the classical limit, known as the Bohr Correspondence principle, one doesn't let h -->0, but instead n --> Infinity.

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The term "dequantization" is used in other domains, and apparently in this context (e.g. in the preface to Quantum-Classical Correspondence: Dynamical Quantization and the Classical Limit, Bolivar, 2004, or in Variational approach to dequantization, Mosna et al., 2006). I do believe the question might deserve more context, in other words is the question ...

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Yes. Assuming that you have two independent and uncorrelated sound sources, then the intensity observed will be the sum of the intensity of the two sources. Whether they were summed electronically before being turned into sound, or whether they were generated as separate sound waves that are summed when they reach your ear, is irrelevant. Whether that ...

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The uses of this two theories are completely different. Statistical Mechanics is used to see how by modelling the behavior of microscopic constituents you can predict the macroscopic phenomenas that you observe. On the other hand Many Body Theory uses first principle techniques to see what happens microscopically when you have large no of particles in your ...

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You may want to refer to Jackson's 'Classical Electrodynamics' for several examples of solutions using Green functions. I also found chapter 7 of 'Mathematics for classical and quantum physics' by Byron and Fuller quite helpful. Its title itself is 'Green functions'.

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As somebody who works in the field of chaos theory (for whatever that’s worth), I confirm Dmckee’s assessment: There is no reasonable relation to any concepts from chaos theory. There is, however, an attempt in your quote to relate this to the phenomenon of criticality – which is not chaos theory, but like chaos theory is related to the field of complex ...

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I am recent graduated physicist. Assuming that you are looking for rigorous learning instead of just popular science, I would like to recommend a few books to get started in this amazing field of knowledge. Before you learn some hard Calculus, you can read this books: Physics for Scientist and Engineers. Tipler & Mosca. This books are the easiest ...

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As someone who did a degree in physics before moving into electronics and s/w R&D, my experience would suggest "yes". Over the years I have been involved in a number of projects that could be classified as experimental physics, and in all cases knowledge of electronics was a vital part. At the very least a physicist should be able to read a circuit ...

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Axiomatic theories started with geometry, back at the time of Pythagoras. At that time mathematicians and philosophers were one and the same thing. There is a rumour that even Homer was a mathematician. Education was a one throw business at that time. How did geometry start? It started in the flat spaces of Egypt and Mesopotamia where it was necessary to ...

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I don't think there is a universally agreed phrase to describe this, but I think the closest is the principle of geometrical reversibility.

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can we get a false positive of a theory being right just because the instruments doing the measuring have that theory built in? This sounds dangerously close to a contradiction-in-terms, so let me carefully read you as saying that the instruments doing the measuring "are interpreted according to that theory," possibly by calculations that sit between ...

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Can we tell when an established theory is wrong? Not always. And not everybody. Sometimes one or more people can, and they explain why. But other people won't entertain it, then the "established theory" gets even more established. I was reading the following answer from this question: In physics, you cannot ask / answer why without ambiguity. ...

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You have to give a concrete example. Experiments are designed so as not to depend on what they are trying to measure. Your speed of light example is not good. Was not the whole scientific community in a dither because superluminal neutrinos were supposed to have been measured? Until it was found that there was a malfunction in an instrument? In any case ...

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It is pretty much simply a short way to notate both vector field operations by looking at $\nabla$ as a vector operator by writing $$\nabla=\left(\frac{\partial}{\partial x},\frac{\partial}{\partial y},\frac{\partial}{\partial z}\right)$$ in $\mathbb{R}^3$, or equivalently \nabla=\frac{\partial}{\partial ...

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There are definite advantages of differential forms, geometric calculus, and four vectors over 3d Gibbs vector algebra and vector calculus. Specifically you can solve for the electromagnetic field first ... and then let someone break it into electric and magnetic parts later if they feel like it (if at all). For instance the field due to a non accelerating ...

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Here's a paper for you to ponder on: Teaching electromagnetic field theory using differential forms Excerpt from the abstract: computational simplifications result from the use of forms: derivatives are easier to employ in curvilinear coordinates, integration becomes more straightforward, and families of vector identities are replaced by ...

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This is, as you stated in the title of the question, a problem of definition. In order to be useful for Physics (and most Science), there is a key characteristic of the properties we use: they have to be objectively measurable. As dmckee stated in a comment to the question, the property does not only need to be able to be put in scale (as you said, you ...

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If you are interested in references you might also have a look at Scientillion. It is a search engine, mainly for physics publications and shows the references for many articles like Sample Article which saves you the time looking them up in the PDF.

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