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On 27 Sep 2018 at 22:35:00 user 'Jcobban' wrote: Issues in Quantum Mechanics and General Relativity

Part of the problem with any short discussion of anything to do with quantum mechanics or general relativity, and black holes are one of the intersections between those two mathematical models, is that they have to skip the math.  But these are mathematical models which have both been tested thousands of times over the century since they were proposed.  Those tests are not conceptual tests, they are hard experiments in which the predictions have been verified to the limits of the experimental design, in some cases to 11 digits of accuracy!  To understand why these models make the predictions they make you have to do the math.  Unfortunately math education is seriously deficient, as demonstrated by the notorious grade 6 EQAO results.  So even in High School physics the discussion breaks down to a lot of handwaving, and almost nothing discovered since 1850 is included in the curriculum, because the students, and frequently the teachers, do not have the mathematical background to understand.  
I studied both quantum mechanics and general relativity in university.  Each required a full semester, and even then the quantum mechanics course only got as far as concepts proposed in 1936.  That is the basic model of the behavior of electrons within the electric field of an atom, which explains the chemical behavior of the elements and why they can be arranged in the familiar periodic table that is posted in most science classrooms.  There wasn't time to understand the Dirac theory which requires the existence of anti-matter, or Bose-Einstein vs Fermi-Dirac statistics, or Electroweak theory, or the standard model of fundamental particles, the differences between the Copenhagen model and the many worlds model for interpreting the results of quantum mechanical experiments, quantum-chromodynamics which explains the strong force as an exchange of gluons between quarks, the Higgs field and its associated boson which explains the origin of intertia, or any of the GUTs.
The current consensus model does make nonsensical predictions below the Planck length but there are several proposals that address those predictions such as Supersymmetry, loop quantum gravity, and String Theory, and it is quite possible that the various ways of resolving the problems will turn out to be just different ways of describing the same thing.
And of course there is the really big problem: constructing a theory which combines quantum mechanics with general relativity, which is critical to understanding what happened in the first nano-second of the existence of the Universe, but is difficult because at the energy levels we can attain with our existing particle accelerators quantum mechanics only manifests at very short distances while general relativity is only distinguishable from Newtonian gravity at very large distances.  Which brings us back to black holes, because observable quantum mechanical events occur at the event horizon of a black hole.

On 19 Oct 2018 at 22:11:46 user 'jcobban' wrote: Understanding General Relativity

Because of the weak mathematical foundation that most students have most of the description of Physics that is presented in high-school science classes is sloppy and employs a lot of handwaving arguments.

In particular there is an enormous flaw in Newtonian Mechanics that is completely ignored until students are years into their University education.  Newton's Laws of Motion only apply in an "inertial frame of reference". That is in a frame of reference which is not being accelerated by any force external to the frame of reference.  But it is trivially obvious that there is no such animal!  Every point in the Universe is subject to many external forces.  The classroom in which Newtonian Mechanics is taught is sitting on top of a planet whose gravity pulls on every object in the classroom.  The classroom is spining around with the rotation of the Earth. The Earth is following a roughly elliptical path around the Sun at about 30km/s while also being tugged at by the gravity of the Moon and all of the planets, while the entire Solar System is following a very complex path around the Milky Way Galaxy subject to the collective gravitation of over a hundred billion stars, black holes, gaseous nebulae, and being pushed and pulled by whatever is represented by Dark Energy and Dark Matter! It is no surprise that two millenia of philosophers prior to Galileo never recognized that there was a simple set of Laws of Motion.  In any real-world experiment all of the non-inertial forces: gravity, electro-static charge, magnetism, and friction, were enormously greater than the effects that Galileo and Newton descibed.

So what typically happens in a high school physics lab is that every reasonable effort is made to minimize the influence of external forces on the experiment, and then poorly explained concepts such as "friction" are used to explain why the experiments only demonstrate Newton's Laws of Motion approximately.  For example an air table may be used to create a 2-dimensional almost frictionless environment within which objects can interact with each other in a way that approximates an "inertial frame of reference".

Every physics experiment and theoretical explanation of the behavior of the Universe prior to 1917 just glossed over this issue.  There is a game played by first year university physics students to make up "thought experiments", to use Einstein's phrase, in which you get mutually contradictory results in Special Relativity depending upon the frame of reference.  For example: Imagine you have a pole-vaulter carrying a 5m long pole and running at 75% of the speed of light.  From the point of view of a "stationary" observer the pole is only  3.3m long.  The pole-valuter runs through the open door of a building which is 4m deep, and you slam the door shut behind him. However from the point of view of the pole-vaulter the building is only 2.5m deep and the pole doesn't fit!

Three centuries of western physicists just ignored the fact that the "inertial frame of reference" which they required for their results did not exist in the real world, because everything actually did work in the real world to the limit of every experiment.    In particular the great mathematicians such as Carl Friedrich Gauss had demonstrated that you could explain the motions of all of the objects in the Universe to any desired degree of accuracy by applying Newton's Laws of Motion.  That is everything except a microscopic deficiency in the motion of Mercury, which most assumed would be accounted for by a previously undiscovered planet orbiting closer to the Sun.

But there was one man who wasn't satisfied.  He observed that Newton's Laws of Motion appeared to work even in accelerated frames of reference as long as the acceleration was constant over the period of observation and was due only to gravity.  So he hypothesized that in fact no experiment could be performed in a constantly accelerating frame of reference that would give different results depending upon the cause of the acceleration.  That is Newton's Laws of Motion, along with all other laws of science, are true not only in the fictional "inertial frame of reference" but in constantly accelerating frames of reference as well.  The constant acceleration of the frame of reference is called gravity when it is observed in a physics classroom on the surface of the Earth.

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