George Jones

But, its finite extent notwithstanding, a 3-sphere has the same cardinality as the real line, and thus has same "fault" as a model of positions in space as (any segment of) the real line ...

In the city in which I used to live, I attended very lively astronomy club meetings. Unfortunately, I moved away from this city eight years ago, and, as I now am an astronomy "lone wolf", I can only a somewhat off-topic comment. I work as an instructor, and I prefer to look at it as follows (which I call Jones's theory of relativity): every year the first-year students get a year younger.

I can remember four episodes in (the original) Star Trek that involved travel into the past, three into Earth's past, and one into the past of another planet.

General relativity does not seem to prohibit time-loops (called closed timelike curves by physicists), but quantum theory might prohibit these, This is what Stephen Hawking thought. Stephen Hawking: "It seems that there is a Chronology Protection Agency which prevents the appearance of closed timelike curves and so makes the universe safe for historians." This roughly states that near the boundary in spacetime where time-loops form, the energy for quantum fields blow up (e.g., infinite blueshift), thus preventing (by wall-of-fire barriers) physical objects from crossing into the region where there are time-loops. There seems to be some semi-classical (part classical, part quantum) evidence for this conjecture, but a more refined analysis by Kay, Radzikowski, and Wald muddies the picture a bit. Their analysis shows that the energy is ill-defined, but not necessarily infinite, at such a boundary. This may be just an indication that the semi-classical theory breaks down at chronology horizons, and that full quantum gravity is needed for definitive predictions.

Yikes! I am enough of a Geek that I recognize the equation to which Cox points. It comes from Feynman's path integral formulation of quantum theory.

I have not forgotten about this thread. I had intended to make a longer post on the weekend, but I go a bit snowed under by family life, including loads of ice skating with my 12-year-old daughter. Now I have stuff to do at work, but I hope soon to make a longer post. I would like to say, though, that I most certainly have not used any particular interpretation of quantum theory in my above post on the uncertainty principle. I have used a particular interpretation of probability (independent of quantum theory), the frequentist interpretation.

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.