George Jones

I think that you mean something like https://www.sheffield.ac.uk/polopoly_fs/1.162375!/file/topic5.pptx I am going to try (might not be successful) to expand on the material in (but using electrons) https://pubs.acs.org/doi/abs/10.1021/ed082p1210 http://iopscience.iop.org/article/10.1088/0143-0807/32/2/018/meta and in some notes that I wrote 13 years ago for the double slit set-up. I am not sure if these are behind paywalls, but a version of the first in pre-journal format is at http://www.users.csbsju.edu/~frioux/diffraction/N-single-slit.pdf

I think that some of the main quantum field misconceptions about Neumaier has written first make their appearance in the simpler context of the uncertainty principle in standard quantum mechanics. Many quantum mechanics texts and courses give incomplete and/or incorrect presentations of the uncertainty principle. At the undergraduate level, "Introduction to Quantum Mechanics" by David Griffiths, and at the (extreme) graduate level, "Lectures on Quantum Mechanics" by Steven Weinberg, give nice presentations. Two of the main competitors to Griffiths do not give presentations that are as nice. Arnold Neumaier: "According to the Born rule, the distribution of a quantum observable gives the probabilities for measuring values for the observable in independent, identical preparations of the system in identical states. ... Thus it is misleading to interpret vacuum fluctuations as fluctuations in the common sense of the word, which is the traditional name for random changes in space and time. The vacuum is isotropic (i.e., uniform) in space and time and does not change at all. The particle number does not fluctuate in the vacuum state; it is exactly zero since the vacuum state is an eigenstate of the number operator and its local projections in space-time, with eigenvalue zero. Thus there is no time or place where the vacuum can contain a particle. In particular, in a vacuum particles are nowhere created or destroyed, not even in the tiniest time interval." Weinberg: "It should be emphasized that Δx is the spread in values found for the position if we make a large number of highly accurate measurements of position, always starting with the same state with the same wave function ψ, and likewise for Δp. The uncertainties depend on the state, not on the method of measurement." Note that Weinberg did not write "... depend on uncertainty in the state ..." Consider an uncertainty principle example from the first-year text used at my school: "The speed of an electron is measured to be 5.00×10^3 m/s to an accuracy of 0.000300%. Find the minimum uncertainty in determining the position of this electron." As the Weinberg quote shows, this is rubbish. For concreteness, I am going to consider the position-momentum uncertainty principle ΔxΔp≥ℏ/2 applied to the (quantum mechanical) harmonic oscillator. Typical woolly statements about why the lowest (ground state) energy of a quantum oscillator is not zero go something like "According to the uncertainty principle, the quantum oscillator has to jiggle a bit." This evokes the image of an oscillator whose state changes in time, but the ground state of oscillator does not change with time. More about this below. Consider a very large number N of identical harmonic oscillators all prepared in the identical states, which I will take to be the lowest energy (eigen)state, i.e, the ground state. Very accurately measure the position for half, N/2, of the systems; Very accurately measure the momentum for the other half, N/2, of the systems. Each of the N measurements is on a different oscillator, i.e., on different but identical copies of the system and state. Calculate the statistical standard deviation for the the N/2 position measurements; call this Δx. Calculate the statistical standard deviation for the the N/2 momentum measurements; call this Δp. When N is very large, Δx and Δp will satisfy ΔxΔp≥ℏ/2. This is the uncertainty principle in quantum mechanics. Note that position and momentum are never measured on the same oscillator copy. Note also that Δx and Δp have nothing to do with an intrinsic limitation on the accuracy with which individual measurement are made. Finally, note that nothing was said bout the time at which the measurements were made. All the measurement could be made at the same time, or they could be made spaced by random time intervals. For very large N, the same statistical distributions of measurement vales will result, so the spread in values is not due to oscillators "jiggling" with time. (Since the ground state is an eigenstate of the Hamiltonian, and the Hamiltonian governs time evolution, each oscillator stays in the ground state until a measurement is made, independent of when in time the measurements are made.)

You still haven't referenced an actual argument. This attempt at a simile is completely irrelevant.

While I certainly do use links found by Google, I also like to make extensive use of my own personal library of university-level (and beyond) physics and math books (more than 500). in this case, my plan (which may change) is to learn the material in the first two sections of chapter 7 "Scalar Fields and the vacuum fluctuation" from the book "Cosmological Inflation and Large-Scale Structure" by Liddle and Lyth. Largely the same argument. A quote by David Griffiths, whose books are used ubiquitously to teach physics courses (we use two of them): "In general, when you hear a physicist invoke the uncertainty principle, keep a hand on your wallet." I think that you need to take some care, as you seem to have shouted this from on high without referencing any actual arguments. No one is arguing that the Planck length does not exist as a mathematical quantity (i.e., there is a combination of c, G, and h that has units of length). Physicists eventually need more than mathematical evidence. Over the last twenty-five years, I have worked with many physicists at several universities. Most professional physicists have never worked through a Planck scale argument, so they don't "believe" anything one way of the other; they are agnostic. High energy physicists constitute a (vocal) minority of professional physicists. I have taught university lecture courses in quantum theory dozens of times (most recently, a first introduction to quantum theory in Sept. - Dec. 2017, and a course in advanced quantum mechanics for physics Master's students in Jan. - April 2018), and while I find Planck scale arguments to be interesting, I do not find them to be compelling. Now to start reading.

I think that there is a hand-waving argument for this, and the argument does involve non-commuting operators. Annihilating the vacuum and then trying to produce a quantum particle is different than creating a quantum particle from the vacuum and then annihilating that particle. Tentatively, my project for tomorrow morning is to see whether I can make heads or tails of this argument. Time for a groan. Q: Why don't matrices live in the suburbs? A: They don't commute.

Because of the heads-up by @Owmuchonomy (thanks!) in starting this thread, I received my copy about six weeks ago. Fascinating! I was nine for Apollo 13, and I remember my mother telling me that there was a problem in space.

Also here a Reddit thread about the group and its director of research (read comments at bottom): https://www.reddit.com/r/Physics/comments/7kbmdg/whats_the_story_behind_quantum_gravity_research/

If I remember correctly, the author has a bit of a reputation for being a cosmology crackpot who advocates a special relativistic kinematical explanation for the cosmological redshift. Also the paper does not appear to have been published, i.e., it does not seem to have been peer-reviewed by cosmologists. The info page for the paper, where this is usually listed, is https://arxiv.org/abs/physics/0407077

For an observer who freely falls from rest from a great distance, light received from a star that is directly overhead is redshifted, not blueshifted. At the event horizon, the redshift factor is 2, and as the singularity is approached, the redshift factor approaches infinity. Roughly, Doppler redshift between source (star) and receiver trumps gravitational blueshift.

My wife is a high school maths and science teacher, and I sometimes look at the maths texts. Even though I have decades of experience in advanced university maths, it can require substantial effort for me to figure out what the current Canadian high school maths texts are on about. To see where you stand, it my might be a good idea to get a hold of a copy of any edition the book "Engineering Mathematics" by K. A. Stroud (not to be confused with "Advanced Engineering Mathematics" by the same author), either from a library, or by purchasing a relatively inexpensive used copy. The first few hundred pages of this massive tome review GCSE mathematics, followed by treatment of more advanced mathematics. Use the Amazon "Look Inside" feature to look at the detailed table of contents, https://www.amazon.co.uk/Engineering-Mathematics-K-Stroud/dp/1137031204/ref=pd_bxgy_14_img_2?_encoding=UTF8&pd_rd_i=1137031204&pd_rd_r=54ea6fbd-b5dd-11e8-9ef1-419f427e8ea3&pd_rd_w=zAcKA&pd_rd_wg=mgyOi&pf_rd_i=desktop-dp-sims&pf_rd_m=A3P5ROKL5A1OLE&pf_rd_p=9eec4bbd-c065-4a4d-b0d1-92d63ee9e53b&pf_rd_r=S5JMZQVEZZYM236VS3RH&pf_rd_s=desktop-dp-sims&pf_rd_t=40701&psc=1&refRID=S5JMZQVEZZYM236VS3RH

Science is not in the business of proving theories. As an example, consider Newton's theory of gravity. Given the masses of any two objects and the distance that separates the objects, Newtonian gravity gives a maths expression for the gravitational force between the objects. To prove that Newtonian gravity is true, we would have to verify experimentally the maths expression for gravitational force for all possible masses and all possible separation distances. It is impossible, even in principle, to verify this infinite set of possibilities. Even if we verify it a zillion times, tomorrow we could make a measurement that we can't square with its force expression. It only takes one (set of) measurement(s) to prove it wrong. A good scientific theory is consistent with known observational evidence, but being consistent with known observations does not constitute a proof of a theory.

???? The vast majority of folks who as trained (to the Ph. D. level) as theoretical physics do not work in physics at all, i.e., if they are wealthy it is they work in areas like commercial data mining or finance.

Welcome from British Columbia. As others have said, you should get as big a scope a possible, subject to two criteria: 1) you are willing to pay for it; 2) the size of the scope will not physically limit its use (if you consider big, think hard and realistically about this) I am thinking about getting a larger scope subject to 2) and a modifified 1') the Commander-In-Chief is willing to let me pay for it. I have made the trip between Ontario and New Brunswick many times. This summer, on the way to New Brunswick, my wife, daughter, and I stayed one night in Levis, and, on the way back to Toronto, we stayed two nights in Quebec (City), and one night in Trois-Rivieres. My daughter, who is in French immersion at school, has gone shopping for French novels at malls in Levi and Drummondville. Also, 20 years ago, I lived for 18 months in Lennoxville (Sherbrooke).

I like what Robert Geroch wrote (in his non-technical book "General Relativity from A to B about physics theories and "proofs" of theories: Geroch was a very deep thinking, very good, professor in the departments of mathematics and physics at the University of Chicago.

Because of spacetime curvature between "over there" and "over here", it is difficult to define the speed of an object "over there" with respect to us "over here" in a way that respects all of our everyday experiences with speed. This leads to a first explanation for the possibility of recessional speeds greater than the speed of light. Special relativity prohibits speeds greater than the speed of light. Cosmology, however, is governed by the curved spacetime of general relativity, to which special relativity is a good *local* approximation. Consequently, we will never see anything moving faster than the speed of light in our local neighbourhood, where special relativity is a good approximation. Stuff at the edge of the universe is not in our local neighbourhood, and thus is not governed by the laws of special relativity. Alternate (more technical) explanation for recessional speeds greater than the speed of light. speed = distance/time, so if different definitions of distance and time are available, we can have have differing definitions of speed. The definitons of distance and time used in cosmology lead to cosmological recessional velocities that correspond not to velocity in special relativity, but to something different called rapidity (sometimes called the "velocity parameter"). In special relativity, there is a relationship between velocity and rapidity, which, for some reason is not used in cosmology. If this relationship were uswed in cosmology than a recession rapidy of 3.4 corresponds to a recessional speed of 0.998 times the speed of light.