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1

Newton described his theories with maths, and they worked great, until Einstein came along and found that as objects approached the speed of light, Newwton's maths broke down. Empirical evidences trumps theory.


2

Good question. When we build a theory we start from a couple of assumptions that we BELIEVE that are valid, i.e. in the everyday life, and/or in previous experiments, they were confirmed. From this point we use mathematics and obtain other results. As long as we need our new results for proving even more theorems, things may be fine. But a physical theory is ...


1

Your toy theory is i) local and ii) sounds like it's counter-factual definite, that is, every measurement that could be or could have been performed would result in a single, definite outcome (roughly speaking, an object's properties are pre-existing or real). You want to know whether you can evade Bell's inequalities [that permit i) or ii) but not both], ...


0

Richard Feynman has nice words about science. It is not bad to read chapter 3 of "Feynman Lectures on Physics". The main point of his lecture is that "there is no strict boundary between different fields of science", "nature doesn't concern what we call its parts!" So, we can't look for a line that divides celestial works into astronomical or astrophysical ...


0

Astronomy talks about celestial objects (such as stars, galaxies, nebulae etc) and celestial phenomena (such as gamma ray bursts etc), their position, motion, evolution, chemistry, physics. Astrophysics is a sub-branch of astronomy to deal with physics of celestial objects and phenomena. The first encounter: A guy put microscope in front of rainbow spectrum ...


1

A few off the top of my head: Double pendulum is a nice example of chaotic motion and quite simple to model. Ising model of a magnet can provide a good introduction to modelling quasi-random processes. Solving the heat equation with various combinations of sinks/sources. Lots you could do with optics from very simple to very complex. Also lots you could do ...


3

An ADS search for "star formation" turns up about 142,000 articles with "star formation" in the title or abstract. The first article is a 43 page review paper of Star Formation in Galaxies in the Hubble Sequence, written by Robert Kennicutt, Jr, one of the leaders of the field. He never defines anything else to mean star formation and one of the "key words" ...


0

Consider an UHECR neutron approaching a magnetar. The Lorentz force acting on the quarks will soon exceed the QCD string tension, at that point quark anti-quark pairs get created giving rise to pions. These pions in turn get polarized and you get more pions. So, you basically get a chain reaction yielding more and more pions until the speed of the pions ...


1

I join the comments of Julian Fernandez. Just some hints for some of your ideas: Spacetime is relative i.e. observer-depending. It seems that behind relative spacetime there is a system of absolute time (= proper time) and absolute space (=space without considering time dilation and length contraction which are relative) where spacetime is "mixing up" ...


1

First, caveat -- I am still in the learning phases of QFT. Math skills used and needed: Linear Algebra, vectors in Hilbert Space, Hamiltonians, Lagrangians (just like regular QM). Tensor notation, 4-vectors, special relativity, metric tensors at times. Feynman Path Integrals. Calculus of Variations. Fourier Analysis. And, certainly this list is not ...


1

I believe that particle physics is a field where to be able to contribute to the field you must have the mathematics. Without them your understanding will be severely limited and in many cases not even wrong. On the other hand it is possible to contribute to physics to in general with no more math than you get in junior high. This is because physics is the ...


4

Personally, I think the primary reason for thinking about interpretations is that they can lead to new predictions. They generally don't do this directly - almost by definition, an interpretation makes no new predictions by itself - but by changing the landscape within which new theories can be proposed. The best example I know of is the Lorentz equations ...


0

The "authority" that decides the answer to your question is the WAVE-FUNCTION. So, it can create different situations: 1) If the wave-function is a given eigenfunction of the observable that you measure, the answer is deterministic and equal to the eigenvalue corresponding to that eigenfunction. 2) If the wave-function is not as in the case 1, then the ...


1

Ok, let me state, that both are correct. And i explain why: Determinism is either total or there is no determinism. Determinism means that one can determine everything that one wishes with any accuracy desired. This is a by definition a total statement. As such determinism is total. Partial determinism is just another name for in-determinism. Exactly ...


2

Richard Fitzpatrick's free e-book A Modern Almagest: An Updated Version of Ptolemy’s Model of the Solar System presents a modernized version of Ptolemy's Almagest. (I mention it here.)


0

Simple and to the point (some people might refer to this as KISS principle). Assuming that theory refers to a mathematical theory, then the interpretation is that thing that tells when and where to apply the theory Simple as that, no more no less. UPDATE (after comment and downvote): "In a more general context, that would be a reasonable way to define ...


1

The intensity that you talk about can be represented bt the Poynting vector. $$ {\bf N} = {\bf E} \times {\bf H}$$ The units are Watts per square metre. The power produced by an oscillating electric dipole can be derived by integrating an expression for the Poynting vector over a surface area enclosing the dipole. $$ P = \oint {\bf N} \cdot d{\bf S}.$$ ...


2

The energy required to accelerate a massive object from below the speed of light to the speed of light (or beyond it) would be infinite, so it's not thought to be possible at all. This can be derived from the fact that the momentum $p$ of an object with nonzero rest mass $m$ and velocity $v$ is given by $p = mv / \sqrt{1 - v^2/c^2}$, which approaches ...


6

In the sense of "Copenhagen Interpretation", what exactly is an interpretation? What purpose does an interpretation serve? I would describe interpretations of quantum mechanics as part of the philosophy of physics. Here is a well-known quote by Bertrand Russell: "As soon as definite knowledge concerning any subject becomes possible, this subject ceases ...


2

I think the opportunities for "amateurs" are quite extensive these days. There is an increasing move towards open-access publishing, which means that in many fields you can keep bang up to date without having to have deep pockets or access to a university library. In addition, the computing resources that are available (and the open source software ...


26

You can check this yourself using this very long link which will give you a list of Hawking's work that has been published in refereed journals, ordered by the number of times they have been cited in other papers (a measure of how influential they are on other scientists). This is a way of providing at least some non-opinion based answer to this question. ...


26

The two largest contributions that come to mind are both in the realm of general relativity. The first is his contribution to the singularity theorems. These are purely general relativistic results (i.e. no quantum mechanics involved), and they mathematically prove that generically one expects to find singularities in spacetime. That is, except in somewhat ...


-2

Rather, I pronounced it like $A$ bar dot $B$ bar. Or $A$ bar cross $B$ bar


5

The first bullet would be read "$A$ dot $B$" or "The dot product of $A$ and $B$" The second bullet would be read "$A$ cross $B$" or "The cross product of $A$ and $B$"



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