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George Jones

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Everything posted by George Jones

  1. Last scattering occurs, roughly, when the early universe is no longer hot enough to ionize matter (more accurately, last scattering occurs slightly later than this). Our baryon-antibaryon imbalanced universe is about 13.7 billion years old, and last scattering happened about 0.0004 billion years after the Big Bang. I do not know when last scattering occurs in a baryon-antibaryon universe.
  2. Thanks. Yes. After collisions stopped (and assuming that there are not any physical processes that change the number of baryons) there would be a fixed "number" of baryons, but the density of baryons still decreases because the universe continues to expand.
  3. I am a little curious about this. Ironically, earlier today I was reading about exactly this. Consider a more a general situation. Let X be a type of particle an X be the corresponding anti-particle. (Dear algebra, Stop asking me to find your X. She/He is not coming back.) Suppose the universe is symmetric in X and X. In the small, early universe Xs and Xs would be in close proximity, and would be continually annihilating with each other. As the universe expands, eventually the Xs and Xs will thin out to the point that they will no longer be able to find orther, and thus they no longer be able to annihilate with each other. This is called freeze-out. After freeze-out, there will be residual equal numbers of X and X left over. Expansion of the universe from the freeze-out time to the present time will further thin out the Xs and Xs. When freeze-out occurs depends on the mass of X. Taking X to be protons and neutrons (with an equal number of anti-protons and anti-neutrons), and running the number gives that the present density of baryons would be a billion times smaller than the density that is actually measured.
  4. My guess is that something like standard deviation or variance rather than mean is used as a measure of dispersion.
  5. Welcome from Prince George. When my wife, daughter and I went to see the eclipse last August, we crossed the border at Abbotsford. My father moved from Britain to Canada when he was fourteen, but I have never been to Britain. Maybe someday.
  6. From a modern text on quantum field theory, "Quantum Field Theory in a Nutshell", by Anthony Zee:
  7. I haven't looked at the book, but I think that this is the way Greene expresses in words the fact that the 4-velocity (or proper velocity) of any massive particle has frame-invariant "length"^2 = c^2.
  8. In addition to the good points that Andrew has made, there are other lines of evidence for dark matter. First, a digression that does not involve dark matter. Consider gas infalling on a star, neutron star, or black hole. As it spirals in, the gas heats up why? Friction caused by electric/electromagnetic forces. Now consider the hot, dense soup of stuff in the very early universe. Some parts of this primordial soup are slightly more/less dense than other parts. These inhomogeneities set up gravity/pressure oscillations. In an overdensity, the region collapses because of gravity. As collapse proceeds, matter heats up until pressure becomes large to counteract gravity, after which the regions starts to expands. as it expands, it cools, pressures drops, gravity wins, and the region starts to collapse. And so on. Both normal matter and dark matter contribute to the gravity part, but only normal matter contributes to the pressure part, since dark matter is electromagnetically inert. The effects of these oscillations are imprinted on the the observed Cosmic Microwave Background radiation as very small temperature variations. Different amounts of the various components of the universe will affect these oscillations. Statistical analysis of the observed angular size of these temperature variations in the CMB give 68% dark energy, 26% normal matter, and 5% normal matter. Note that this argument is independent of the amount of normal matter that remains unseen by our present instruments.
  9. Baez's paper is very nice. I am not sure about physics programmes in the UK, but, in North America, I think that students find quantum theory easier than GR because they spend more time studying quantum theory. A longer more personal version of this comment: https://www.physicsforums.com/threads/is-gr-harder-than-qm.607638/#post-3925089
  10. Quantum theory is much harder, both conceptually and technically, than general relativity.
  11. Yes, it is absolutely true that the visual speed of a watched moving clock depends on velocity, not just speed. What is not really true? I use a mish-mash of the Doppler effect, Lorentz contaction, and time dilation in https://www.physicsforums.com/threads/basic-problem.177939/#post-1384776 to do the calculation.
  12. The statement "A moving runs slow." needs to be unpacked carefully, as time dilation is not something that is seen visually, at least not directly. This depends on what is meant. Suppose that the train is moving towards the platform, that Ted is on the platform, and that Alice is on the train. If Ted keeps one eye on his watch and his other eye on Alice's watch, then Ted sees Alice's second hand spinning faster than his second hand. Alice, however, sees Ted's second hand spinning faster. Now suppose hat the train is moving away from the platform. If Ted keeps one eye on his watch and his other eye on Alice's watch, then Ted sees Alice's second spinning slower than his second hand. Alice, however, sees Ted's second hand spinning slower. So the direction of the train does matter for visual effects. Neither of the above scenarios, however, involves the standard mathematical expression for time dilation. I am going to attempt to explain the difference between the above visual effects and time dilation. Unfortunately, my explanation is going to be somewhat complicated, as I will use four clocks, the watches of Ted and Alice, and clocks A and B that are stationary with respect to Ted, and that are directly between Ted and Alice. Suppose that 1) Alice initially is more than 20 light-years away from Ted (according to Ted) 2) Alice moves directly towards Ted at 80% of the speed of light 3) clock A is 4 light-years from Ted 4) clock B is 20 light-years from Ted. As Alice moves towards Ted, she first encounters clock B and then clock A. Ted watches all this with his telescope. I want to consider three time intervals. 1) T1 = 20 years is the difference in readings on clock A when Alice encounters A and clock B when Alice encounters B. 2) T2 = 12 years is the difference in readings on Alice's watch between when she encounters A and B. 3) T3 = 4 years is the time that elapses on Ted's watch between when Ted, with his telescope, sees Alice encounter clocks A and B. T1 in Ted's frame is greater than T2 in Alice's frame. This is what is meant by "Moving clocks run slow.", and is given by the time dilation expression. Notice that two different clocks in Ted's fame are used to measure T1. T3 in Ted's frame is less than T2 in Alice's frame, because, visually, Ted sees Alice's second hand spinning faster than his second hand. This is given by the relativistic Doppler effect, because the Doppler effect applies to all periods, including the periods of second hands. I hope I haven't screwed up my calculations.
  13. As Andrew said, the worldlines, and the experiences on the worldlines, are very different. In order to compare clocks, one observer has to "turn around" and come back. You might argue that each observer sees the other observer turn around and come back, so the situation is symmetrical. Only one observer, however, experiences acceleration during the turn around. To see this asymmetry, consider the following. Give each observer an accelerometer. Each accelerometer consists of two main parts - a hollow sphere like a basketball inside of which is a slightly smaller sphere. Initially, the centres of the spheres coincide, so that there is a small, uniform gap between the spheres. If an observer is accelerating, the gap will be closed, and contact between the spheres will be made. An alarm that indicates accelerated motion will sound. If the observer is not accelerating, no alarm will sound, and constant speed, straight line motion is indicated. Only one observer hears the alarm sound.
  14. Since we are talking about relativity, i would argue that the term "popular" is relative. The number of people that like popular science is small when compared to the number of people that like popular music, but, in both cases, the number is large relative to the number of people that actually practice the thing, scientists and musicians.
  15. Actually, topology alone gives us no information about the curvature of space or spacetime. In order to talk about curavture, we need more structure, like a metric, which is a way of making local measurements of space and time. With topology alone, we can talk about whether a universe is spatially finite or infinite. If space is compact, it is finite; if space is not compact it is infinite. "Compact" is a technical maths term within the subject of topology, but it has somewhat of the flavour of its use in everyday English. Sorry if I have been too technical, but my wife (a high school maths and science teacher) is auditing (for fun) a uni math course that includes an introduction to topology, so I have brushing up on this stuff.
  16. Sometimes experiment is ahead of theory, e.g., perihelion shift in Mercury's orbit was observed before it was explained by the theory of general relativity, and spectral lines were observed before they were explained by quantum theory. Sometimes theory is ahead of experiment, e.g., Peter Higgs published his theory in 1964 and Steven Weinberg and Abdus Salam (using Higg's result) published electroweak theory in 1967, and it was years before these theories received any experimental backing. When a theory has no experimental backing, it is difficult to know if this is because experiment has not caught up with theory, or if it is because the theory is not Nature's way. I like Steven Weinberg's description of the scientific method: " scientific research is more honestly reported as a tangle of deduction, induction, and guesswork "
  17. You most surely are bashing science. It is hard not to take this personally, as I put bread on the table by teaching physics. Yesterday, I got up at 4:30 am so I could finish marking assignments and preparing material on introductory quantum theory for a 10 am lecture. Last week, I taught material not in the text on Hawking radiation. It seems that I made this effort with some nefarious purpose in mind.
  18. No, when relativity is taken into account, simple arithmetic addition of speeds is not valid. The correct way to combine speeds u and v is (u+v)/(1 + u*v/c^2), where c is the speed of light. if one of the speeds is the speed of light, e.g., take u = c, this result gives (c+v)/( 1 + c*v/c^2) = c(1 + v/c)/(1 + v/c) = c, and all is well. Logic alone is not sufficient to do science.
  19. Actually, these results say nothing about dark matter. Dark matter ("weird" stuff; not protons and neutrons, which are baryons) makes up 25.8% of the mass/energy density budget of the universe, and baryonic normal matter ("normal" stuff; protons and neutrons) makes up 4.8%. The 4.8% normal matter component is inferred from things like patterns in the the Cosmic Microwave Background (CMB), i.e., it does not come from direct astronomical observation. Prior to the results published in the papers referenced in this thread, only about half of the 4.8% of the normal matter component had been observed "directly". The results in the papers account for more of the 4.8% normal matter component (without increasing the number 4.8), and say naught about the 25.8% non-baryonic dark matter component.
  20. Welcome to SGL. I live just "up the road" 325 kilometres, in Prince George. We just drove through 100 Mile House on the way to/from a viewing in Oregon of the total solar eclipse.
  21. My wife, daughter, and I are traveling, as the crow flies, about 1000 kilometres (620 miles) to see the eclipse. We will leave from north central British Columbia, Canada on Saturday morning, drive about ten hours to Seattle, Washington, and then stay Saturday night at our friends' house. On Sunday, we drive to a campsite (already booked by our friends) about 100 km (62 miles) from the centre of the eclipse zone. The highway that we hopefully will take just reopened after being closed quite some time because of the forest fires. If it closes again (a definite possibility), the trip to Seattle will be more like eleven or twelve hours.
  22. I collect books, and I just bought a couple of books by Valerio Faraoni, one of the coauthors of this paper. Another paper, at a lower and more pedagogical level (but still at the upper-level undergraduate physics level), is https://arxiv.org/abs/gr-qc/0508052 This paper examines whether cosmological expansion affects a "classical" atom.
  23. If a galaxy is "moving" exactly with the expansion of the universe, the galaxy is said to be comoving. Just as gas molecules have random motions, galaxies have random motions with respect to the expansion of the universe. A galaxy's motion relative to comoving with the expansion is called a peculiar velocity. On small cosmological scales, expansion speeds are small, and peculiar velocities can dominate. On large cosmological scales, expansion speeds are much larger than peculiar velocities, so peculiar velocities are not noticeable. On a small cosmological scale, when, by chance, a galaxy's peculiar velocity is towards us and larger than the expansion speed, then the galaxy moves towards us, and we its light blueshifted.
  24. Should I post a short demonstration that uses introductory calculus?
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