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That's off-topic, but when used without a qualifier, the word pound denotes either a unit of money or a unit of mass. Never force. The units of force in the customary system are the pound-force and poundal (which nobody uses). One issue here is that "directly" qualifier. That's why I used the bathroom scale as an example in my previous post. Hardly anything is "directly" observable. I think what you want is "somehow" observable. That's a good question. David Mermin asked that question in Is the moon there when nobody looks? Reality and the quantum theory, Physics Today, April 1985, http://www.iafe.uba.ar/e2e/phys230/history/moon.pdf. The thing that really throws a monkey wrench in the works is Bell's Theorem. It demands that you have to throw out something very dear. You either have to toss locality (what happens in Vegas stays in Vegas, at least for a little bit of time) or counterfactual definiteness ("realism") (the Moon is there even when we don't look at it). Pick your poison ...

Some questions for you, Rich. 1. Do you understand why that 0.1 mm/year figure is statistically insignificant in light of the ± 0.2 mm/year uncertainty, why one cannot reject the null hypothesis (that the Earth is not expanding) on the basis of that measurement, and why the null hypothesis is the best answer? (Do you even understand what the terms "statistically insignificant" and "reject the null hypothesis" mean?) 2. For the sake of argument, let's assume that that 0.1 mm/year radial expansion is correct. That means the Earth's circumference is expanding by 0.63 mm/year. I'll be generous and call it 1 mm/year. The question: How does your expanding earth model explain the observed fact that some parts of the Earth such as the north Tonga trench are moving 240 times faster than this 1 mm/year? 3. How does your expanding earth model explain convergent boundaries, which have been observed? 4. How does your expanding earth model explain subduction zones, which also have been observed? 5. How does your gas-filled Earth model explain the Earth's observed mean density of 5.52 grams/cubic centimeter, about twice the density of surface rock? 6. How does your gas-filled Earth model explain the over 100 years of seismic waves observations, which show that the Earth has a very dense liquid outer core and an even denser solid inner core?

There indeed are some. Phys. Rev. Lett. 82, 884–887 (1999), Phys. Rev. Lett. 87, 091301 (2001), MNRAS 327:4, 1208–1222 (2001), MNRAS 345:2, 609–638 (2003), ..., Phys. Rev. Lett. 107, 191101 (2011), MNRAS 422:4, 3370–3414 (2012) just to name a few. Fringy, definitely, but that those are definitely not crackpot journals. Aside: Never so fringy as to attribute the supposed variations to "vacuum quality difference in the space". The 2011 version caused quite a stir, but even it has pretty much been refuted in the eyes of most astrophysicists (e.g., A&A 540, L9 (2012)). That's quite the bold statement! There's a huge difference between physics and philosophy: Physicists need evidence of their bold statements. One job of experimental physicists is to come up with tests that either confirm or falsify the grandiose statements made by their theoretical brethren. So they test. And test. And test again. And again. It's important. The speed of light isn't of near the interest to physicists as are the dimensionless constants such as the fine structure constant. There are 25 or so of these in the standard model of physics. Change your units and you change the speed of light. Pick a convenient set of units and the speed of light, Newton's universal gravitation constant, the Planck constant, etc. all become one. That trick doesn't work for those dimensionless constants. They truly are supposed to be constant. That "supposed to be" is central to all of physics, so physicists test and test and test for variations in these fundamental constants. The consensus is that all variations seen to date are statistically consistent with the null hypothesis, which is of course that these fundamental constants are constant.

That depends very much on what you mean by "unobservable", and also by what interpretation of quantum mechanics you ascribe to. The kinds of observations physicists make are quite indirect. Take something as mundane as stepping on a bathroom scale to see how much you weigh. You aren't really observing your weight. You are observing the angular deflection of some pointing device. Yet you would never say "Wow! My diet is working! I only weight 37 degrees today!" For one thing, the scale isn't calibrated in degrees. For another, weight as angle doesn't make sense. That angular deflection is caused by a somewhat complex mechanism that converts the linear deflection of the scale's plate against a spring into that angular deflection. This linear deflection is no better than an angular deflection for representing weight. This linear deflection can be converted to force by assuming the spring in your scale obeys Hooke's law (which it doesn't). With this at hand, you could say "Wow! My diet is working! I only weigh 667 newtons today!" Physicists might think that is a good expression for weight, but colloquially and legally, weight means mass. One last thing needs to be done, which is to convert that 667 newton force value to a 68 kilogram mass value by assuming that this force results from a gravitational acceleration of 9.80665 m/s2 (which almost certainly isn't the acceleration due to gravity where you live). And that's just for stepping on the scale on the morning. The path gets very indirect when it comes to observing things like photons, electrons, neutrinos, and quarks. I would say that those photons and other things of interest to physicists are "observable" even though the observations are quite indirect. With this concept of observability, the Copenhagen interpretation, taken to its logical positivism extreme, pretty much says that that which is utterly unobservable doesn't exist. A slightly less extreme view that still falls under the Copenhagen interpretation umbrella is that the existence of something that is utterly unobservable is irrelevant to physics (except when it's a useful fiction, such as wave function collapse). There are other, more modern interpretations of quantum mechanics than the Copenhagen interpretation. Each has its weirdnesses. They pretty much have to; quantum mechanics is a bit (more than a bit) weird.

It's a boundary layer, and a somewhat arbitrary one. You aren't going to be able to find a spot above the Earth where 1 nanometer below you can say "that's the troposphere!" and one nanometer above, "that's the stratosphere!" (i.e., the tropopause). All of these -pauses are a bit fuzzy, a bit arbitrary, and shift with time. They are very useful concepts, but don't take them as gospel.

In order, nonsense, nonsense, more or less, no, no, silly question, nonsense, nonsense, and nonsense.

There is no reason why. That's why you are struggling. It's a good thing I wasn't drinking a soda when I read this. You would owe me a computer screen if I had been. This expanding earth nonsense is one of the silliest notions to come out of the crackpot community for quite some time. You would serve yourself much better if you learned some real science instead.

One of the key tests of general relativity was to observe stars during a solar eclipse, stars that nominally were close to being behind the sun. General relativity predicted that those stars should be visible because of the way gravitation affects light and because how the sun's mass curves space-time. The stars were visible, just as general relativity predicted. This experiment was first performed during the 1919 eclipse, and then again in 1922, and then again and again. Another place astronomers see how gravitation affects light is when a galaxy is directly behind another. Here's one such image: That bluish horseshoe-shaped object is a galaxy. The red object that it nearly surrounds is a another galaxy that is between us and that bluish one. The remote galaxy would be a little point of light were it not for gravitational lensing. So far I haven't mentioned the equivalence principle. While the equivalence principle was central to Einstein's development of general relativity, it is not a part of general relativity. The equivalence principle does not fully explain how light is affected by gravitation. Regarding those stars observed during solar eclipses: The equivalence principle only tells half the story. In other words, it yields the wrong predictions for the curvature of the light by the sun. General relativity predicts twice the curvature, and it is the value predicted by general relativity that has been observed.

Only if the giant comet was much larger than the Earth. A comet the size of the Earth is extremely dubious. A comet the size of Pluto would be a giant comet. A comet, even a giant one, would transit the GRB rather than eclipse it.

There's no need to invoke dark matter here. That last bit, " Since the momentum exchange is EM driven there would be no need for mass so long as enough energy is there" says it all. Light has energy, so it necessarily also has momentum. Mass is not needed. Light must necessarily transform momentum when it is absorbed or reflected because of conservation of momentum.

It's torture. One lesser reason not to use torture as a means of obtaining data from captured enemies (the moral reasons trump everything) is that torture doesn't work. When they are in pain, people will say anything to get the pain to stop. Most of the time, they will lie, make up anything to make you stop hurting them," he [Ali Soufan, a former FBI special agent] says. "That means the information you're getting is useless." (http://www.time.com/time/nation/article/0,8599,1893679,00.html?imw=Y) The exact same concept applies to numerology. It is a numerical torturing of data and text. Torture that data and text long enough / hard enough and it will tell you just about anything. The information you're getting is useless.

Exactly. We see stars.

Not a chance. That might have been ExoMars (http://en.wikipedia.org/wiki/ExoMars), but "Under the FY2013 Budget President Obama released on February 13, 2012, NASA terminated its participation in ExoMars due to budgetary cuts in order to pay for the cost overruns of the James Webb Space Telescope. With NASA's funding for this project completely cancelled, most of these plans had to be restructured." Now it's well over a decade away, mid 2020s.

Ahh. Future, not current. Unfortunately, also canceled about a year ago, http://www.spacenews.com/civil/110418-single-rover-mars-mission-2018.html. And it's not coming back until 2020 at the earliest, http://www.spacenews.com/civil/120508-figuera-rules-out-rover.html. The way over-budget Mars Science Lab and the way over-budget James Webb Space Telescope are killing NASA's science budget. Not to mention that the current economy is killing NASA's budget in general.

That sounds wrong, way wrong. Those numbers are way too close to circular for one thing. The along track error should be much bigger. Another problem is the use of "current" and "MER" in the same sentence. Are those your words, or theirs? This paper, http://web.mit.edu/larsb/Public/KnockeDispersionAIAA04.pdf, gives a 63 km x 9 km three sigma ellipse for the Mars Exploration Rovers. Your numbers are, I think, those for the Mars Science Lab (still in flight), see http://marsoweb.nas.nasa.gov/landingsites/msl/memoranda/MSL_Eng_User_Guide_v4.5.1.pdf. Note that those numbers were preliminary and did not include dispersions for winds during parachute descent. With winds, that 12 by 10 ellipse expands to 25 by 20. This site, http://www.planetary.org/blogs/emily-lakdawalla/2012/20120611-curiosity-landing-ellipse.html says that the ellipse has shrunk to 20 km x 7 km. Note this this is very current; it's from four days ago. In any case, all of those numbers are far too big for a human mission, particularly one in which multiple vehicles must land in more or less the same spot (e.g., this silly Mars One proposal). NASA thinks that a pinpoint landing capability of 100 meters CEP ("circle of equal probability") is needed for a human mission with multiple landers. That's about two orders of magnitude smaller (linear dimension) than current capabilities. Two order of magnitude improvements usually means uncharted territory.

Nobody ever said that papers in reputable journals are automatically legitimate. Getting a paper published is much closer to the starting point rather the ending point of the scientific process. On the other hand, there are journals and website that are so close to 100% crap that it is essentially pointless to look at them. Yep, someone might publish an absolute gem at vixra. The odds of that happening: Well there's a slim chance that I might win the lottery if I just played the stupid game. The odds are so low and the payoffs are so biased that it isn't worth it the time, effort, or money to do so.

Newtonian mechanics implies that massless objects can't have momentum. You are once again showing your Newtonian biases. You need to drop this. If you cannot do that you will not understand. The answer is simple: Massless objects can and do have momentum. Even though photons are massless, they do have momentum and energy. I. Give. Up.

Who decides? How do they decide? This list of yours would be elitism, no doubt, and who would make it? The publishers of the "good" journals? There are de-facto lists of what's good and what's bad, but it's generally word of mouth. Cha-ching! There's lots of money to be made by publishing hokey journals, particularly if you just pretend that you have a peer review process and don't have technical editors. Another problem is the publication industry, which far surpasses the oil industry in greedy capitalistic excess. There's a big push back nowadays against Elsevier et al, and one unintended consequence is a proliferation of some really crappy, so-called open journals. Yes and no. Impact factor is easily gamed by less than savory journals, particularly so in the physical sciences. Physicists and their kin tend not to use lots of references in their papers. The underlying idea is that a paper should stand on its own merits. Many papers have just a handful or so references. Some of the most influential papers have none. The editor of a disreputable journal can use this fact to bump that journal's impact factor relative to other journals in the same field. Simply ask authors to add references in the (supposed) peer review, maybe even suggesting one or two papers that just happen to be published in that same journal, and perhaps another paper in some crony journal that just happens to reference the suspect journal. And this is happening.

What question? I laid it all out. What part did you not understand? Alternative reality? The spaceship POV is just as real as the Earth-based POV, and it is part and parcel of the same reality. It just isn't your Newtonian reality, which you apparently just cannot give up. You don't even know that you are making assumptions of a Newtonian universe in every post you make. You say you accept the math, but it's obvious that deep down, you don't. You will not be able to understand these concepts until you can see that (1) you are assuming a Newtonian universe, and (2) you are willing to give up that point of view. It's not easy. Relativity is weird and can be very counterintuitive to our intuition. Our physical intuition is at best Newtonian, and more often than not its even more primitive than that. Our physical intuition is based on what we see around us. For example, the natural state of a rock is obviously at rest. A rock might roll down a hill if someone or something gives it a shove, but it inevitably comes to a stop. This makes it hard for many to accept Newtonian mechanics, let alone something as foreign as relativity.

So far so good. That some politicians know how to manage my life better than do I is a disease to which politicians of all ilk are susceptible. Not all Progressives suffer from this disease, and this disease is not limited to Progressives. All politicians are susceptible. This disease is at most epidemic in the Progressive movement in the US, but it is pandemic in the wacko religious right in the US. That's just wrong, at least in the US. Conservatives in the US tend not value privacy. Joseph McCarthy. Richard Nixon. All those dolts on the right who say "I'm a good Christian. I have nothing to hide." In the US, it has been primarily the left rather than the right who have supported privacy rights for a long, long time. It goes back to McCarthy, if not earlier.

The Cayley numbers are just another name for the octonions (to within an isomorphism). One shortcoming of the sedenions S is that the problem of zero divisors. There are non-zero sedenions whose product is zero. One consequence: [imath]|a|\,|b| = |ab|[/imath] is not necessarily true. Another consequence is that there's no way to define division. As I mentioned earlier, each step up the Cayley-Dickson hierarchy loses something. Tossing out the concept of division and tossing out the identity [imath]|a|\,|b| = |ab|[/imath] : You've lost a whole lot. This tosses a whole lot of mathematical structure out the door. The loss of that identity [imath]|a|\,|b| = |ab|[/imath] is quite deep. I think what you are talking about is Hurwitz' theorem, which says that the only finite dimensional normed division algebras over the reals are the reals themselves, the complex numbers, the quaternions, and the octonions (to within an isomorphism). This is in a sense an extension of the Frobenius theorem, which says that the only finite dimensional associative division algebras over the reals are the reals themselves, the complex numbers, and the quaternions (to within an isomorphism). Hurwitz' theorem is a bit different from Frobenius theorem, however. It talks about sums of squares. For example, if a,b,c,d are real, [math](a^2+b^2)(c^2+d^2) = (ac-bd)^2 + (ad+bc)^2[/math] Note that the left hand side is the product of a two sums of a pair squares, the right hand side is the sum of two squares. There are similar identities involving the product of two sums of four squares on the left and the sums of four squares on the right, and also for the product of two sums of eight squares on the left and the sums of eight squares on the right. The case n=1 is trivial. Are there any others besides 1, 2, 4, and 8? The answer is no. Hurwitz' theorem is also called the 1,2,4,8 theorem because of this. This can be brought back to the realm of algebras over a field by looking at the identity [imath]|a|\,|b| = |ab|[/imath]. Square both sides and you get [imath]|a|^2\,|b|^2 = |ab|^2[/imath]. Treat a and b as n-dimensional vectors with some kind of multiplication defined two vectors (i.e., an algebra over a field), expand out the terms and you get the product of two sums of n squares on the right, the sum of n squares on the left. Hurwitz' theorem says that the only n for which this holds are 1,2,4, and 8: The reals, the complex numbers, the quaternions, and the octonions. One final note: If you want to study this stuff in detail, I suggest you get a book (or take a course) on modern algebra or abstract algebra. Note well: I'm not talking kiddie algebra here. I'm talking about the algebra class (classes) that math majors take in college after they've taken multiple calculus courses and a class or two in analysis.

You are once again assuming that the universe is Newtonian is by thinking that time and distance are immutable. They are not. What you are missing is that time is subject to time dilation, length to length contraction. In the frame of the ship, those buoys are not 186,000 miles apart. They are only 161080.725 miles apart. At the time the ship emits the beam, the ships captain will compute that the beam will travel 4,832,421.75 miles. (Note well: It's not 60*161080.725 miles = 9,664,843.5 miles. It's half that. In the captain's frame, that last buoy is moving toward the captain at 1/2 c.) The clocks on the ship and the clocks in the space harbor master's frame (the frame in which the buoys are at rest) aren't running at the same rates, either. At the point that the ship has passed 30 buoys it's clock will not show 30 seconds. It will instead show 25.9807 seconds. From the captain's perspective, the beam of light is moving at 4,832,421.75 miles / 25.9807 seconds = 186,000 miles/second. (I've used your value for the speed of light here.)

What happens in a game of chess when someone moves a rook along a diagonal? To be a bit less flippant, there are two possible answers to your question. It can't happen, so stop asking. This is equivalent to asking what happens when a rook moves along a diagonal. It's an illegal move. It can't happen. There is however a problem with this answer: It assumes the laws of physics perfectly describe the universe. They don't. The rules of chess are made by humankind, so we know exactly what they are. The rules of the universe are fumblingly ferreted out by humankind. Our job in doing so isn't perfect or complete. Our laws of physics are best guesses based on evidence, logic, and math. Not perfect. So what if they're wrong? That leads to answer #2: We haven't the foggiest idea what would happen, so stop asking. Physicists have occasionally performed experiments where the outcome was "Whoa! That can't happen!" These experiments, if confirmed, have the effect of turning physics upside down. The Michelson-Morley experiment is one of the most famous of such experiments. Isaac Asimov: The most exciting phrase to hear in science, the one that heralds the most discoveries, is not "Eureka!" (I found it!) but "That's funny..." In the case of your mirror, we have very, very good reason to think that your question falls into category #1: "It can't happen, so stop asking." Suppose that it could happen. This means everything we know is wrong. Very, very wrong. This makes your question fall into category #2: "We haven't the foggiest idea what would happen, so stop asking."

You missed quite a few steps from naturals to the imaginary numbers. Natural numbers are 0,1,2,... (or 1,2,3,... depending on who you're reading). This has addition and multiplication as two base operations, and multiplication can be defined in terms of addition for the natural numbers. There's obviously an inverse to addition. 3+4=7, so define "-" such that 7-4=3, 7-3=4. But what's 3-4? Arithmetic completion leads to the integers, the first set you omitted. Doing the same with multiplication leads to division and the rationals, the second set you omitted. Cauchy sequences or Dedekind cuts lets to the reals the third (and arguably most important) set you omitted. The complex numbers add something very important to the reals: They are algebraically closed. All of the roots of any polynomial with complex coefficients are complex numbers. The complex numbers also remove something very important, which is the operation "<". Which is smaller, 1+i, or 1-i? The quaternions removes even more. Multiplication is not commutative: a*b is not necessarily equal to b*a. Each step up the Cayley–Dickson hierarchy adds a little, subtracts a little. The octonions aren't even commutative, but they are associative. The next step up, the sedenions, aren't even associative. You can go on forever creating new structures, but by the time you get to the octonions and beyond they aren't very useful.

Too cutesy!!! And not historically correct. Read "rumor has it" as "I just made this story up". What Einstein did do was try to envision what it would be like to "ride a beam of light" when he was 16. He didn't get all that far at this young age because he didn't have the necessary math or physics background. Ten years later he had the necessary tools and he had time to spare. He used this time to revisit his thoughts from a decade before. He found a novel and very simple way around one of the most vexing problems of the time, the inherent incompatibility of Newtonian mechanics and Maxwell's electrodynamics. Maxwell's equations strongly imply that the speed of light is the same to all observers. Most physicists were looking for ways around this implication (and around the conflict). Einstein simply took Maxwell's equations to heart. He accepted that the speed of light is the same to all observers and then determined the fall out from this assumption. This provided the answer to his thoughts from a decade before: You cannot ride a beam of light. That beam of light is speeding away from you at the speed of light. It doesn't matter how much faster you go. That beam of light is still going to go away from you at c. Always. An object with non-zero mass must always move at subluminal speeds. Your mirror cannot go at the speed of light.