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Space and time are still smooth in QM. They take derivatives, compute integrals. That implicitly assumes a smooth manifold. The problem is the stuff that fills space and time, not space and time themselves. Vacuums are no longer vacuums if you look at them very closely. Virtual particles pop in and out of existence. The closer one looks the frothier things get. You get infinities in quantum mechanics, too. Things such as 1+2+4+8+... keep popping up. Physicists found that giving meaning to divergent series such as this had attracted the best minds in mathematics for over a century. That the answer to this apparently meaningless series is the even more meaningless -1/12 was a viewed as a bit of a problem. Physicists don't just do math and develop theories. They experiment. Experimental results showed that this apparently nonsense answer to this apparently nonsense series was -1/12. That led to investigations into what is now called the renormalization group. This work let those mid 20th century physicists get past the infinities that plagued their work on quantum electrodynamics and quantum field theory. One of the problems between GR and QM is that the renormalization tricks that worked so nicely in quantum field theory just don't work. The infinities won't budge. An even bigger problem is that melding GR and QM represents two big huge steps taken at once. The first step is a Grand Unification Theory that somehow will show that the electroweak and strong interactions are different aspects of the same interaction. The next step is a Theory of Everything that somehow will show that this unified electromagnetic/weak/strong interaction and gravitation are different aspects of the same interaction. It took a lot of work to develop electroweak theory. Taking two big huge steps at once is perhaps overreaching. An even bigger problem yet is experimental validation of a GUT or even worse, a TOE. The energy scales are absolutely phenomenal. Even if someone comes up with a mathematically sound theory, testing that this is what describes the universe is going to be a huge, huge challenge.

That's a number of non sequiturs and a huge boatload of chipped and fractured ceramics, David. That's three non sequiturs. They do not prove your conjecture. The Moon is receding from the Earth due to tidal interactions. You cannot use the Moon's recession as your proof because the galactic gravity gradient across the span of the entire solar system is exceedingly small. Besides, what tidal interactions do you propose that would cause this very tiny recession? Mars had liquid water in the past because it had not yet lost its atmosphere and because it was still warm from its formation. The loss of the atmosphere was very significant. Negligible atmosphere = negligible greenhouse effect. The presence of liquid water on Mars does not prove that it was closer to the Sun, and even if it was, it doesn't prove that stars recede from the galactic center. The Earth is drifting from the Sun, and by an anomalously large amount. The predicted rate based on all known phenomenon yield a recession rate of 1.5 cm/year. The observed rate is 15 cm/year. This is an interesting open issue. The most likely explanation is that astronomers are doing something wrong in their measurements, their data analyses, or both. This is the explanation astronomers themselves invoke. The problem is that nobody can see what's being done wrong. The known phenomenon don't apply to stars orbiting a galaxy. The unknown explanation doesn't either for the simple fact that it's unknown. Gas flowing inward toward the galactic center. Google and Google scholar are your friends. You should them it before making wild conjectures. No. This is nonsense. No. This is even more nonsense.

David, You need to be much more specific about your complaint. I don't know what it is you are going on about. Let me try a second guess: Do you think the stars are spiraling in toward the center of the galaxy along the spiral arms? If that's what your objection to spiral galaxies is, you're right. That is not what is happening. We are currently about 27,000 light years from the center of the galaxy. That was also more or less the distance to the galactic core when the Sun formed, about 4.6 billion years ago. Our solar system has orbited the galaxy about 18 times since it formed, and it has done so without spiraling in toward the galactic core.

You are thinking that all of BC looks like Victoria and Vancouver. It doesn't. BC is big and mountainous. Those coast mountains on the west suck all the moisture out of the atmosphere. In addition to being home to the wettest cities and towns in all of Canada, British Columbia is also home to the driest cities and towns in all of Canada except the high arctic. Ashcroft BC gets about 8 inches of rain per year.

That was long and rambling, and perhaps dissembling. If you are asking why it's wintertime in the Southern hemisphere when it's summertime in the Northern hemisphere, and vice versa, the answer is simple. It has nothing to do with gravity, nothing to do with the speed of light. The Earth's rotation axis and the Earth's orbital axis don't point in the same direction. The angle between those two directions 23.4 degrees. This axial tilt, or obliquity, is what drives the seasons. Right now it's summertime in the Northern hemisphere because the rotation axis is pointing somewhat toward the Sun. This makes the Northern hemisphere receive more sunlight than average. At the same time it makes the Southern hemisphere receive less sunlight than average. That's why it's wintertime right now in the Southern hemisphere. The situation will be reversed six months from now. Then it will be winter in the Northern hemisphere, summertime in the Southern. If you're asking something else, be clear with regard to what you are asking. If this is a setup for some personal theory, my advice is to not do that.

David, After re-reading what you've written, it appears that this "angular momentum Theory" you dislike so much is the law of conservation of angular momentum. Please tell me that 'm mistaken.

There's no problem between quantum mechanics and special relativity. That is what quantum electrodynamics (QED) is all about. Feynman was awarded the Nobel Prize in physics for his work on QED. The problem is between quantum mechanics and general relativity. They aren't in conflict with one another. It truly is a matter of incompatibility. So far, that is.

What is this "angular momentum Theory" about which you are writing? I haven't the foggiest idea what you are going on about here. Please cite a reference of some sort: A web page, an article, a book, something.

That's not right, ACG. Reducing the Moon's velocity by a factor of 10 would put the Moon in a highly elliptical orbit with the apogee at the Moon's current orbital radius and perigee well inside the Earth. Perigee inside the Earth means it would collide with the Earth. However, this 90% reduction represents a huge change in velocity, and since kinetic energy is proportional to the square of velocity, it is an even larger percentage reduction in kinetic energy. David Levy cherry-picked an extreme example as if it somehow validates his claim of a "very critical balance between the gravity force and the rotation [sic] velocity." He also claimed that "assuming that the moon will slow down It's quite clear that the gravity will force it to come closer and eventually it will collide with Earth." That's false in general. It's true for very large change, but he did not quantify his statement. Since it's false for anything but a very large change (more than an 84% reduction), his claim is false.

Mike, I'm not the one who gave you the downvote, but please, stop. Stop with the silly cartoons. Start using math. This isn't even nonsense.

Come off it. A 99% reduction in the Moon's kinetic energy is not representative of your "very critical balance between the gravity force and the rotation velocity." That energy change, by the way, would take humanity about 69 million years to accomplish if every single joule of our current energy consumption was applied to making that change. What outcome would you expect if the Moon's orbital velocity suddenly decreased to 200 meters/second? That's still a 96% reduction in kinetic energy. 150 meters/second? What exactly constitutes a critical balance in your mind?

Learn to use the quote button, and sans that learn to use my correct user name. Okay. I'll be more specific. Nonsense. Nonsense. Nonsense. Huh? That probably wasn't specific enough for you. I'll be very specific. Suppose every last joule of energy consumed by humanity was somehow diverted to changing the Moon's velocity. How long would it take to: Change the Moon's average orbital velocity by 1%? Make the Moon collide with the Earth? Make the Moon escape Earth orbit?

You'll do much better if you work in the direction of not naming things after yourself. That is one of the key signs of a crackpot at work. Real scientists don't name things after themselves. They publish papers in refereed scientific journals that label their key expressions as something bland such as equation 42 or perhaps flashier but non-self referential such as the relativistic energy equation. Naming something after you is not your job. Not in the sciences. You'll do much better if you publish your work in a refereed scientific journal. Not on some website that cherishes crackpots, not in a self-published vanity press book. You'll do much better if you back off from the fancy diagrams and the elementary mathematics. You need solid math, and some ties to experiments. Just because you want the universe to behave according to ZHOU's equation does not mean that it does.

That wikipedia article that you referenced is exemplary of the problems with wikipedia. It is misleading at best. Right now, theory does not agree with reality. If spiral galaxies formed early but collisions led to elliptical galaxies we should see more spiral galaxies in the Hubble Deep Field than we see now. That's exactly the opposite of what we do see. Galaxy formation is still a challenge. That does not mean we should throw out everything for some nonsense non-theory that explains nothing. It means, hmmm, that's funny. Those two words are music to a scientist's ears. Go back to square one, David. What you wrote is completely wrong. You apparently don't even understand the two body problem, let alone galaxies.

I suspected a crackpot setup from the onset. Since he won't say what he's ranting about, this doesn't even belong in Speculations. This belongs in the Circular File forum.

It's best to ignore him, Ed. Zhou Jian is a write-only poster who has apparently selected this site as one of the places where he can drop his shards of broken ceramics.

Of course it did. Popular science shows oftentimes are bad science. It apparently has to be that way. Couple that people need to be entertained or they'll switch channels with the abysmally low knowledge of and interest in science in the general public and, well, this show is what you get. Bad as it was, the BBC did a good relatively good job here. At least they didn't have Brian Cox, Brian Greene, or Michio Kaku narrating. Or go to the equator and get pulled in by one of those water swirling down the drain hoaxes (the BBC fell for this hoax at least twice).

That is correct, but that isn't what the program is talking about. Keep in mind the target audience of the show. The gas cloud is falling toward the black hole, not into it. The closest approach to the black hole is predicted to be about 2000 times the event horizon radius. Fragments of the cloud might break off and add to the accretion disk.

That is not what I'm saying. Expand 1/(1+x) as a series. You'll get 1-x+x2-x3+... or [imath]\displaystyle{\sum_{n=0}^{\infty} (-1)^n x^n}[/imath]. Plug in x=1/2 and the series becomes 1+1/2+1/4+1/8+..., which is 2. The left hand side yields 1/(1-1/2), or 2. The series and the generating function agree for x=-1/2. This is true for all x between but not including -1 and 1. It's also true for all complex numbers with ||x||<1. This series has a radius of convergence of 1. Let's ignore this minor inconvenience and set x to 1. You'll get 1-1+1-1+... : Grandi's series. The generating function yields a value of 1/2. So in a sense, 1-1+1-1+... = 1/2. Setting x to -2 yields the series 1+2+4+8+... Here the generating function yields 1/(1-2)=-1. So in a sense, 1+2+4+8+... = -1. How valid is this? What you will be taught when you study series in high school, again in freshman calculus, and yet again in complex analysis says that what I just did is utter rubbish. There are however a number of reasons that say that this particular abuse is valid. The math that says this is valid is beyond what you'll learn when you're a sophomore or junior in college. This abuse of mathematics (or neat extension to mathematics) is critical in higher level quantum mechanics such as quantum field theory. The neat thing is that the experimental outcomes are consistent with what this renormalization nonsense says should be seen in those experiments.

Learn to use the quote button. Huh? That's a non sequitur. Nope. It's not even a non sequitur. Calling this a non sequitur would imply that you have some kind of logic, just badly done. You don't. It's not a sequitur at all. Astronomy is first and foremost an observational science. Astronomers classify galaxies as spiral, elliptical, or irregular based on what they observe. For any given galaxy they have but one observation of that galaxy, what they see now. Astronomers cannot see how or when a specific galaxy was created, nor can they see how it evolved. You appear to be under the assumption that a galaxy that is currently observed to be a spiral galaxy was always a spiral galaxy. That apparently is not the case. Over 2/3 of the close-by galaxies are spiral galaxies. Look further away (look further into the past) and the fraction of galaxies that are spiral galaxies drops. Look very far away, for example the Hubble deep field, and the fraction drops to less than 1/3. See R. Delgado-Serrano, et al, 2010, How was the Hubble Sequence, 6 Giga-years ago?, Astronomy & Astrophysics, 509, A78. Arxiv preprint: http://arxiv.org/abs/0906.2805. So how to explain this change? One simple solution is that spiral galaxies are the consequence of galactic mergers. See F. Hammer et al., 2009, The Hubble Sequence: just a vestige of merger events?, Astronomy & Astrophysics, 507, 1313. Arxiv preprint: http://arxiv.org/abs/0903.3962. That's another not even a non sequitur. I suggest you stop using your non-logic and start using mathematics. Another thing I suggest you stop doing is looking for root causes. There are two big unknowns in astronomy: Dark mass and dark energy. Dark energy isn't a big concern for galaxies; it rears it's ugly head only for very large scale structures. Dark mass is a huge concern with regard to galaxies. Scientists don't know what dark mass is. They don't even whether it truly exists; a small minority of scientists still advocate that some modification to how gravity works at galactic scale is the solution to the dark mass problem. Until the dark mass problem is resolved, it's a bit tough to develop models for how galaxies were created. There's nothing wrong in science with saying "we don't know". You appear to be of the mindset that "we don't know" means "wrong". That's wrong. "We don't know" means (1) scientists don't know (so stop asking), and (2) scientists would love to find out. Scientists love those "we don't know" problems. It's their bread and butter. Nonsense. The rotation of the central black hole is not responsible for the bar in barred spiral galaxies. You started with a falsehood, then made a conjecture that does not follow from that falsehood, and then compounded these errors by coming up with more nonsense. Here's some science on barred spiral galaxies: R. G. Abraham et al., 1999, The evolution of barred spiral galaxies in the Hubble Deep Fields North and South, MNRAS 308:2 569-576. Arxiv preprint: http://arxiv.org/abs/astro-ph/9811476. Nonsense. This is even more nonsense, and it is also a hijack of your own thread. Please post your nonsense in the appropriate forum.

There is a way around this problem (so long as you can get past the "SFN is offline briefly for an upgrade to the latest forum software and should be back online at around 10:20am GMT" problem). As you move your mouse from post description to post description in the new content view, you should see a gray circle that contains a small downarrow that moves up and down with your mouse. That circle is between the thread title and reply count fields. Move your mouse over that circle. The background should switch from gray to black. Click on it. This expands the description of the thread. You'll see a summary of the opening post, the first unread post, and the last post. Click on one of those and you'll be able to go to the selected post.

Planes don't fly at high altitudes because they can go faster at altitude. They do so because this lets them operate much more efficiently. Efficiency doesn't count for beans in air racing. Speed and maneuverability are all that count. Drag adversely affects speed, but only if the airplane doesn't have sufficient power to overcome that drag. Lack of power isn't a problem with the unlimited class of race planes. One of the key factors that limits the top speed of a prop-driven plane is the speed of sound. People have tried making supersonic propellers, but they never did work. The tips of the propellers need to be moving at less than the speed of sound lest all kinds of problems occur. In addition to prop issues, lift also becomes problematic as speeds approach mach 1. So why is this relevant? Mach 1, the speed of sound, is not an absolute. It varies with air makeup, but most importantly it varies with temperature. Since temperature normally drops with altitude, so does the speed of sound. This in turn means a prop-driven airplane will fly fastest at low altitude if atmosphere conditions are normal (positive lapse rate) and if the plane has sufficient power to deal with the increased drag.

Anywhere you look you'll see spiral galaxies. Lots and lots and lots of them. Therefore, the chance that your logic is correct is virtually zero!!! So let's look at this logic. 1. Astronomers and cosmologists don't know which came first, supermassive black holes, galaxies, or stars. A couple of things are certain. One is that those supermassive black holes were present very shortly after galaxies first started forming, and they might have been present before then. The other is that those supermassive black holes played a key role in the formation and evolution of galaxies. 2. Spinning - The fact that you are using "spinning" rather than orbiting is a dead giveaway that you don't know what you're talking about. You also apparently don't know what angular momentum is. 3. Escape - You apparently don't know what energy is, either. 4. What are you talking about? What scientists? Citation needed, please. 5. There is no glue between the stars? Really? Of course there is. It's called gravity.

All of these sums are examples of infinite whose partial sums don't converge to a single finite value. They are divergent series. In high school and lower level college math course you are taught that those divergent series don't have a value. They diverge, after all. That hasn't stopped mathematicians from trying to give meaning to divergent series. A number of different techniques have been developed. The averaging approach used by Grandi is one of the simpler techniques. This approach works nicely on series that are bounded but nonetheless fail to converge to a single value. Here the partial sums either alternate between a finite number of finite values or converge toward a set of alternating values. This averaging approach won't work on a series such as 1+2+4+8+... because the partial sums diverge rather than alternate. The way to assign a meaningful value to those divergent series that truly are divergent is via analytic continuation. The basic idea is to find an analytic function whose domain is larger than the series' radius of curvature and whose value is equal to that of the series over the series' radius of curvature. In a sense, that analytic function provides meaning to the series even outside the series radius of convergence.

Your argument is a cherry-pickin' lie. Why do the promulgators of that lie always cherry-pick 1998? Why not 2000, or 1996? Why not any year before 1996? Simple: 1997-1998 was a huge El Nino event. Year-to-year variations such as that El Nino need to be smoothed away to see what is happening on a decadal or longer time frame. Smooth out those variations, and yes, the global climate is still warming. Every single year from 2001 on has been hotter than 98 of the 100 years in the 20th century.