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That is a false comparison. A fair comparison is a meal at McDonalds versus a meal at some other restaurant, or a meal prepared at home using cheap, but admittedly not so healthy, ingredients versus your expensive fresh vegies and a small amount of meat (presumably not hamburger). The poor eat poorly because eating well is expensive. A meal at McDonalds is a luxury they can sometimes afford, just as is eating at a fancy restaurant is a sometimes affordable luxury to those of us who are better off. Get out bedroom, get out of my kitchen, get out of my house!

You've got that exactly backwards. Rather than doing this on your own, perhaps you should pick up a text on geodesy. You aren't going to find these derivations (written well) on the 'net. You can find some sites that do derive the nature of the bulge, but with more than a bit of hand waving. If you insist on doing this on your own, start with a uniform density object. You should find that the flattening is proportional to the square of the rotational rate and inversely proportional to density. I have. I suggest that you read a book.

The very first sentence of which is "This is the most important function in mathematics". The "this" to which Rudin is referring is the exponential function.

Nonsense. Cells cannot create matter. Now you're closer to the mark. Cells grow and divide only if they receive nutrients from outside. To reiterate, cells do not create matter.

It's called Kepler's constant, but only after the fact. Kepler did not find that r^3/t^2 is constant. That's an algebraic expression. He, like Newton, preferred to use geometry, where proportions (but not constants of proportionality) are the rule. Kepler said "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit." No mention of a constant. There is an implied constant in there, but that's because nowadays we prefer to use algebraic reasoning over geometric reasoning. Algebra was fairly new and somewhat suspect in Kepler's and Newton's time. Newton neither trusted nor liked it. Newton's Principia is almost entirely done using geometric reasoning. Very little algebra, and hardly any calculus. Saying that this is equal to force is the definition of force, rather than a derived result. It's how we define what force is: it's something which causes a change in momentum or an acceleration. I disagree with Cap'n Refsmmat's answer to this question. Saying that force is defined as the product of mass and acceleration means that Newton's second law is not truly a law of physics. It's merely a definition. IMO, Newton's second law of motion is a law of physics, not just a definition. Newton vaguely defined forces up front in his Principia in Definition IV: A force is an action on some body that changes the state of motion of the body. Newton's second law relates this already-defined concept of force to how force does change a body's state of motion. Note that F=ma^2 is in line with that vague definition of force. This equation certainly does mean that applying a force will change a body's state of motion. It is not in line with experimental evidence. Newton and his predecessors, particularly Galileo, did lots and lots of experiments that showed that for a given mass, acceleration was proportional to force and that for a given force, acceleration was inversely proportional to mass. So how to "prove" it? You can't. Scientific laws cannot be proven to be true. They can be proven to be false. All it takes is one experiment to blow away the lifetime's work of some theoretician. In fact, Newton's laws of motion is not universally true. Newton and his predecessors didn't have access to the particle accelerators. They worked in the regime of speeds that are very, very low compared to the speed of light. Particle accelerators are but one demonstration that Newton's laws are not correct at relativistic speeds. calculus Continuing my contrarian mode, I disagree with DrRocket's answer to this question. Newton proved his shell theorem in propositions 70 to 74 of book 1 of his Principia with not one smidgen of calculus. Instead he used geometrical reasoning, wall-of-text page upon wall-of-text page of it. There's a dirty little secret of science education here. It took a long time to make that nice, all wrapped up in a bow presentation of science that students receives up until the senior year of college or so. Newtonian mechanics is a prime example. Newton, as I mentioned, largely relied upon geometric reasoning. It wasn't until 50 years after his death that Newtonian mechanics was reformulated in terms of algebra and calculus. It took another 150 years or so to boil Newtonian mechanics down to the simple forms we use now. Vectors, for example, are a late 19th century refinement to Newtonian mechanics. Interestingly, just when physicists had finally come up with this all wrapped up in a bow presentation of Newtonian mechanics, other physicists were starting to find some rather big problems with Newtonian mechanics in the form of quantum mechanics and relativity.

He was going by the adage "if you can't say something nice don't say anything at all." I won't go by that adage. Your concept is nonsense. No matter how big a number you claim as the largest, and I'll just take your number and add one to it. My number is bigger than yours. There is no largest number.

That's just wrong. The bulge would be larger (but only slightly) if the earth was covered with water. If you were correct, the equatorial regions would be dry while the poles would be twenty miles underwater. That's even more wrong. Ignoring third body effects (tidal gravity) and rotational effects, self-gravitation acts to pull an object into a spherical shape. Always. A spherical shape is the shape that minimizes energy. Add in those other effects and the minimal energy shape will of course be something other than spherical. Increase the density of the primary body and self-gravitation will make the shape more spherical, not less. I suggest you look into Lagrangian and Hamiltonian dynamics.

Expressing this as [math]e^{i\pi}+1=0[/math] connects the two identity elements (0 and 1), the two most important transcendental numbers \pi and e), and [math]i[/math] all in one fell swoop. That is why many refer to this as the most important identity in all of mathematics. I would write that as [math]e^{ix}=\cos x + i\sin x[/math] Note the difference in appearance. This is apparently the target of the Feynman quote rather than Euler's identity. Feynman is far from the only one, and far from the first, who has been enamored with Euler's identity ([math]e^{i\pi}+1=0[/math]) or Euler's formula ([math]e^{ix}=\cos x + i\sin x[/math]).

The atmosphere also has tides. Defining tides a bit more loosely as any regular variations (i.e., after removing effects such as weather) in behavior, the atmospheric tides have thermal and gravitational components. The thermal tides dominate over gravitational tides in the case of the atmosphere. The upper atmosphere has a diurnal bulge. Density at a given altitude varies with local time of day, with a maximum at about 2 PM local time and a minimum at about 4 AM. These density variations affect the behaviors of vehicles in low Earth orbit (hence my interest in the tides). The atmospheric thermal tides result because the atmosphere is a compressible fluid and thus is highly sensitive to temperature. The atmosphere is heated mostly from the ground and in the ozone layer. It's the heating in the ozone layer that is the primary driver of upper atmosphere thermal tides. Thermal tides also exist in the lower atmosphere, but they're a bit more complex than the upper atmospheric thermal tides. Gravitational tides in the atmosphere can be seen after one removes the weather and the thermal tides. They are very small.

Uh, no. If the oceans were made of mercury the tides would be smaller. Mercury is more viscous than water and is more dense than water. The greater viscosity results in a greater lag and a smaller amplitude. The greater density results in a greater self-gravitation, which acts against the tidal potential from some third body. Think of it this way: The Earth tides would be much larger than the ocean tides were your analysis correct. It's the other way around; the Earth tides are smaller than the ocean tides.

Oh, please. Every internet forum has its own set of rules regarding what kinds of discussions are allowed and what to do with those who break the rules. They're allowed to do that; it's called freedom of speech. Freedom of speech applies to the owner of the website. It does not apply to the site's participants. Sites that allow complete freedom of speech tend not to hang around for very long. Spammers inevitably clog such sites with ads for Viagra and such. There are always going to be rules. There's a wide spectrum of internet forums that address issues of science and technology. Some such as Physics StackExchange, Engineering Tips, and the PhysicsForums that you mentioned cut things off at established science. Their rationale is that science and technology are hard enough subjects as is even without crackpots coming in a completely muddying the waters. Others (I'm not going to name any names; you can find them) are so beholden to the healing powers of crystals, what those nasty aliens will do next, or why the government and industry are conspiring against free energy devices that they don't tolerate anyone who questions whether their emperor is wearing any clothes. This site, scienceforums.net, sits somewhere between those extremes. The last part, "highly questionable speculations founded upon a false edifice" is a very apt description of cold fusion. As for the first part, "This state of affairs must surely come to an end. It must evolve into a system where scientific journals are free and accessible to the public", Why? What value is there in this? I certainly do like that many scientific articles now are freely available on the web, but does that personal value-added to me equate to a value-added to science? It is a bit of a stretch. There is a value added to science: This information is freely available to scientists, too. It's available to them even when they're at home or on vacation. A good number of scientists rarely, if ever, leave their work at work. The work from home, they work while they are on vacation, they even work while they're in the midst of a nasty divorce because they weren't paying enough attention to their spouse. One big problem with open access journals is who pays for it? Usually it is the authors of the articles. Example: PLoS Biology is a very high impact, open access journal run by a not-for-profit organization. This open access comes at a price, a very high price. The not-for-profit PLoS charges $2900 to the authors of an article published in PLoS Biology. Baloney. The scientific value added to science by allowing public access to scientific journals is zero. The days when an uneducated lone wolf could add anything of value to science started vanishing a couple hundred years ago. It is vanishingly small now. I challenge you to name one "major source of innovation and discovery" in the field of physics in the last 150 years. Not Michael Faraday. Although not formally educated, he was very much an insider. Not Albert Einstein, either. He was formally educated, and patent offices hire PhDs precisely because of that education. That said, there is a value added to society by allowing public access to scientific journals. We the taxpayers paid for a lot of the underlying research and we paid for a lot of the "free" peer review of the articles. We should have access to it because we funded it. But we aren't going to add value to the scientific process.

B.Rossi and D.B.Hall, "Variation of the Rate of Decay of Mesotrons with Momentum", Phys. Rev. 59, 223–228 (1941) Abstract: http://prola.aps.org/abstract/PR/v59/i3/p223_1 The Rossi-Hall experiment and a number of follow-ons looked at various short-lived particles created in the upper atmosphere by collisions of cosmic rays with the atmosphere. The Rossi-Hall experiment focused on muons (which the called mesotrons). Suppose you measure the flux (number of particles per second) of these short-lived particles at the top of a mountain and at sea level. You should observe more of those particles atop a mountain compared to at sea level because that increased elevation at the mountaintop gives those particles less time to decay. Measuring this particle flux was one of the key tests of special relativity. Ignoring relativistic effects, the time spent by those particles as the move from the mountaintop elevation to sea level is simply the altitude difference divided by the velocity. Divide this time by the half life of the particle and you get the expected number of half lives. This number of half lives should in turn dictate the ratio of the flux observed atop the mountain to that observed at sea level. To make this concrete, suppose the mountaintop elevation is 6300 feet (1920 meters), the particles are moving at 99.94 c, and the particles have a half life of 2.197 µs. A non-relativistic calculation would say that it takes the particles 6.409 µs to go from 6300 feet to sea level, or 2.917 half lives. A mountaintop flux of 538 particles per hour should mean a sea level flux of 71 particles per hour. That is not what was observed. The sea level flux was much higher than that predicted ignoring relativistic effects, about 500 particles per hour. So how to explain this from a relativistic perspective? One way is to look at it from the perspective of the Earth-bound observer. Time is dilated for those relativistic muons. The 2.197 µs muon half life becomes a time dilated 63.43 µs, so that 2.197 µs is only 0.101 half lives. Given a mountaintop flux of 538 particles per hour, the sea level flux should be about 502 particles per hour. Another way to look at it is from the perspective of the muon. From this perspective it is the Earth that is moving toward the muon at 0.9994 c. That 6300 foot difference from mountaintop to sea level becomes a paltry 218.2 feet. At 0.9994 c, it takes the Earth only 0.222 µs to cover this distance, or 0.101 half lives. That's the same as the Earth-bound observer explanation. Tests of time dilation are tests of length contraction. The two concepts go hand in hand.

The stationary observer will calculate the time needed for the light to reach the target as 10 seconds while to the person on the horse it's 8.660254 seconds. Your confusion arises from a number of misconceptions. #1, You can't measure the one-way transmission time (one-way speed of light). You can only measure round trip time. The assumption is that space is homogeneous. The speed of light is the same in all directions. (This is testable). #2, Simultaneity is also relative. That statement "while the two observers are at an equal distance away from the target" doesn't quite work in the relativity. So let's change the experiment so that the laser is triggered right as the rider goes by stationary observer. Here simultaneity does work because the rider and observer are (instantaneously) co-located. They are not however at the same distance from the target. #3, Distance is also relative. The stationary observer sees the target as 2,997,924.58 kilometers (10 light seconds) away. To the person on the 0.5 c horse, the target is only 2,596,278.84 kilometers (8.660254 light seconds) away.

From that site: Both of these postulates [the two postulates of special relativity] are vague, contradictory, and the elements within them are poorly defined. The results of many experiments performed since these postulates were first proposed in 1905 demand that their wording be altered and their elements to be more carefully defined in order to more accurately reflect reality. Oh my. Where's the :rofl: emoticon when you need it? The postulates are very specific (= very testable) and are in concordance with one another. The results of experiments since 1905 are consistent with the results predicted by relativity. How much more wrong could that site be? You have found one of a boatload of crackpot sites. I strongly suggest that you stop wasting your time and learn some real science instead.

At first quarter, the moon rises more or less in the east at about local noon and sets more or less in the west at about local midnight. At sunset the first quarter moon is close to its maximum elevation and is more or less in the south (assuming you live in the northern hemisphere). If you saw the moon in the west just after sunset you were probably looking at a waxing crescent moon rather than first quarter moon. Today (Jan 30, 2012), the moon is 45% of full, so it is one day shy of quarter moon.

That's a bit disingenuous. Poincare and Lorentz approached the problem presented by Maxwell's equations from a Newtonian perspective: That somewhere out there is some absolute truth. Their ether frame was not any old random inertial frame. They were looking for the one true inertial frame, or "God's frame". By the time they had worked the bugs out of their Lorentz Ether Theory, this one true inertial frame was just as unobservable as it was in Newtonian mechanics (which also assumes the existence of "God's frame").

No. How did you arrive at that conclusion? Any two co-moving frames will agree on time.

You'll see that written in many places, but it is essentially nonsense. There is no such thing as a rest frame of a photon. The idea doesn't make sense. At age 16 Einstein started thinking about what it would be like to be riding along with a beam of light. He realized back then that things got a bit paradoxical, maybe even nonsensical. Realizing that this concept was nonsense was what finally let Einstein see relativity ten years later.

Your conclusion does not follow from the premises. I cut your post off with the words "and at the same time" because that is the source of your error in understanding. One of the key consequences of relativity is that even simultaneity is relativity. There is no universal "at the same time". You are wasting your time trying to disprove relativity mathematically. You aren't going to be able to that. The mathematics of special relativity is very sound. What you should be doing is trying to understand that mathematics. Just because the mathematics of special relativity is very sound does not mean that it is right. After all, the mathematics of Newtonian mechanics is also very sound. Just because a theory is internally consistent does not mean it is correct. Scientific theories have an extra constraint: They have to describe reality. Experiment upon experiment have shown that it is relativity theory, not Newtonian mechanics, that describes what transpires at very high speeds.

Correct. Incorrect.

Your understanding is incorrect. A request: Stop with the font/size games. Just use the defaults. That was a bit terse. The people on the Earth will see the rocket's clock as running slow. The people on the rocket with see the Earth-based clocks as running slow.

Yes. The laws of physics are the same in all inertial frames of reference.

Correct. You could even have the rocket moving at 99.9999% the speed of light with respect to some reference, and the motion of the rocket will still have no effect. There is no absolute reference frame by which to judge something's speed. Everything is relative. In the case of this experiment, that the rocket is moving with respect to something else has zero impact on the outcome of the experiment.

Try rephrasing that question. As it stands it's pretty much gobbledygook. You aren't communicating.

Huh? You really should learn the subject you are trying to criticize before you criticize it. As a starter, suppose you see two space ships each moving directly away from you, but in opposite directions, with each space ship going at 3/4 the speed of light as perceived by you. The people on each space ship will perceive that they are moving away from you at 3/4 the speed of light. They will also perceive that they are moving away from the other space ship at 24/25 the speed of light -- not 1.5 times the speed of light as Newtonian mechanics would suggest.