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http://www.people.fas.harvard.edu/~djmorin/book.html
Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. Solution: From A's point of view, B's clock is running slow by a factor gamma, on both the outward and return parts of the trip. Therefore, B is younger than A when they meet up again. This is the answer, and that's that. So if getting the right answer is all we care about, then we can pack up and go home. But our reasoning leaves one large point unaddressed. The "paradox" part of this example's title comes from the following alternate reasoning. Someone might say that in B's frame, A's clock is running slow by a factor gamma, and so A is younger than B when they meet up again. It's definitely true that when the two twins are standing next to each other (that is, when they are in the same frame), we can't have both B younger than A, and A younger than B. So what is wrong with the reasoning at the end of the previous paragraph? The error lies in the fact that there is no "one frame" that B is in. The inertial frame for the outward trip is different from the inertial frame for the return trip. The derivation of our time-dilation result applies only to one inertial frame. Said in a different way, B accelerates when she turns around, and our time-dilation result holds only from the point of view of an inertial observer. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." The moment a rational scientist comes to find the following excerpt consistent he becomes irrational, that is, he becomes a Believer: "For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev |
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Pentcho Valev wrote:
http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [snip crap] idiot http://www.hawaii.edu/suremath/SRtwinParadox.html http://sheol.org/throopw/sr-twin-01.html http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html Twin Paradox idiot Perhaps you are too stooopid to click on a link. Uncle Al will exercise the compassion to ram it up your butt, [In the Newtonian approximation to GR, the line element for "Newtonian coordinates" is to excellent approximation: ds^2 = -(1 - 2\phi) dt^2 + dx^2 + dy^2 + dz^2 where \phi is the Newtonian gravitational potential, c=1 The only deviation from Minkowski spacetime is in the time coordinate - using these coordinates the 3-space corresponding to a given value of t is Euclidean flat.] Twin Paradox: One twin travels relativistically, one twin stays home. They reunite. The traveling twin aged much less. The twin who travels through more space accumulates less time; also true for an orbit. Interval sqrt(t^2 - x^2 - y^2 - z^2) between the two events, expressed in inertial coordinate system (t,x,y,z), is conserved. Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the smaller sqrt(t^2) must be. The ratio by which the two aged when they are again local is identical in all reference frames: ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (units of c=1). Acceleration is irrelevant, demonstrated by Triplets. Three identical clocks as kits and not constructed until the experiment is running. Each clock has a short toggle switch. Individual spaceships carry a kit each. Set up the experiment. CLOCK 1: Our clock sits stationary in our inertial reference frame with its toggle sticking out. Touch the toggle and "off" state goes "on" or "on" state goes "off." Build it from parts just before needed, in the "off" state, zeroed. CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial frame and positioned far to our left. Clock 2 was built after all acceleration ceased during setup, set to zero, "off" state. It skims past Clock 1 (our clock) in vacuum free fall, toggles touch, both Clocks 1 and 2 are "on" and locally synchronized by touching. Elapsed time accumulates in each clock. CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial frame of reference, but 180 degrees counter in direction to Clock 2, far far to our right. It was built after all acceleration ceased during setup, set to zero, "off" state. An arbitrary time after Clocks 1 and 2 synchronize and turn "on" by touching, Clocks 2 and 3 brush past each other, both in vacuum free fall, touching toggles. Clock 2 is now "off," Clock 3 is now "on." Write down the elapsed time in "off" Clock 2. The spaceship with Clock 3 returns over the path taken by the spaceship with Clock 2. CLOCK 1: Our clock. It sits stationary in our inertial reference frame with a little toggle sticking out. Clock 3 vacuum free falls past, toggles touch. Clocks 3 and 1 are off. Write down elapsed times. No clock accelerated while "on" or while existing. BOTTOM LINE: Send results by radio. Numbers on paper don't change. Throughout the entire run three clocks were passive observers in vacuum free fall with zero acceleration. Compare elapsed times. Elapsed times #2+#3 does not equal #1, the local stationary reference frame summation. The sum of #2+#3 elapsed time is about 4.5% that than of #1's accumulated elapsed time. The Twin (Triplets) Paradox obtains without any clock having been accelerated. -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) http://www.mazepath.com/uncleal/qz4.htm |
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On May 12, 7:27*am, Pentcho Valev wrote:
http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. Solution: From A's point of view, B's clock is running slow by a factor gamma, on both the outward and return parts of the trip. Therefore, B is younger than A when they meet up again. This is the answer, and that's that. So if getting the right answer is all we care about, then we can pack up and go home. But our reasoning leaves one large point unaddressed. The "paradox" part of this example's title comes from the following alternate reasoning. Someone might say that in B's frame, A's clock is running slow by a factor gamma, and so A is younger than B when they meet up again. It's definitely true that when the two twins are standing next to each other (that is, when they are in the same frame), we can't have both B younger than A, and A younger than B. So what is wrong with the reasoning at the end of the previous paragraph? The error lies in the fact that there is no "one frame" that B is in. The inertial frame for the outward trip is different from the inertial frame for the return trip. The derivation of our time-dilation result applies only to one inertial frame. Said in a different way, B accelerates when she turns around, and our time-dilation result holds only from the point of view of an inertial observer. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." The moment a rational scientist comes to find the following excerpt consistent he becomes irrational, that is, he becomes a Believer: "For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev The difficulty you have is understandable but misguided. You believe that if you do not understand it, then it must be irrational. And therefore if it is deemed irrational by you, then it must be bogus science. Because you believe that you should be able to understand anything -- absolutely anything -- that is rational in science. It does not occur to you that the reason you do not understand it is that your gray matter has been replaced by solid bone. PD |
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The arbiter of whether a theory is valid or not is the empirical
data of observation and experiment. There has yet to be an observation that contradicts a prediction of special or general relativity. Both theories remain fruitful in helping us understand the behavior of nature all around (and a part of) us. Suggest you look at the Physics FAQs with respect to Relativity and Cosmology at: http://math.ucr.edu/home/baez/physics/index.html And: Are There Any Good Books on Relativity Theory? http://math.ucr.edu/home/baez/physic..._booklist.html |
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On May 12, 5:57 pm, PD wrote:
On May 12, 7:27 am, Pentcho Valev wrote: http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. Solution: From A's point of view, B's clock is running slow by a factor gamma, on both the outward and return parts of the trip. Therefore, B is younger than A when they meet up again. This is the answer, and that's that. So if getting the right answer is all we care about, then we can pack up and go home. But our reasoning leaves one large point unaddressed. The "paradox" part of this example's title comes from the following alternate reasoning. Someone might say that in B's frame, A's clock is running slow by a factor gamma, and so A is younger than B when they meet up again. It's definitely true that when the two twins are standing next to each other (that is, when they are in the same frame), we can't have both B younger than A, and A younger than B. So what is wrong with the reasoning at the end of the previous paragraph? The error lies in the fact that there is no "one frame" that B is in. The inertial frame for the outward trip is different from the inertial frame for the return trip. The derivation of our time-dilation result applies only to one inertial frame. Said in a different way, B accelerates when she turns around, and our time-dilation result holds only from the point of view of an inertial observer. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." The moment a rational scientist comes to find the following excerpt consistent he becomes irrational, that is, he becomes a Believer: "For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev The difficulty you have is understandable but misguided. You believe that if you do not understand it, then it must be irrational. And therefore if it is deemed irrational by you, then it must be bogus science. Because you believe that you should be able to understand anything -- absolutely anything -- that is rational in science. It does not occur to you that the reason you do not understand it is that your gray matter has been replaced by solid bone. PD the best one can do is to feel understanding real understanding is epiphenomenal, not real |
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Einstein desperately destroying his own rationality:
http://www.aip.org/history/einstein/...relativity.htm John Stachel: "How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair. We have no details of this struggle, unfortunately." Einstein's irrationality taught in Einsteiniana's schizophrenic world: the speed of light does not depend on the speed of the observer (Divine Albert said so), therefore the wavelengh does: http://sampit.geol.sc.edu/Doppler.html "Moving observer: A man is standing on the beach, watching the tide. The waves are washing into the shore and over his feet with a constant frequency and wavelength. However, if he begins walking out into the ocean, the waves will begin hitting him more frequently, leading him to perceive that the wavelength of the waves has decreased." http://www.pitt.edu/~jdnorton/teachi...ang/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)." Pentcho Valev wrote: http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. Solution: From A's point of view, B's clock is running slow by a factor gamma, on both the outward and return parts of the trip. Therefore, B is younger than A when they meet up again. This is the answer, and that's that. So if getting the right answer is all we care about, then we can pack up and go home. But our reasoning leaves one large point unaddressed. The "paradox" part of this example's title comes from the following alternate reasoning. Someone might say that in B's frame, A's clock is running slow by a factor gamma, and so A is younger than B when they meet up again. It's definitely true that when the two twins are standing next to each other (that is, when they are in the same frame), we can't have both B younger than A, and A younger than B. So what is wrong with the reasoning at the end of the previous paragraph? The error lies in the fact that there is no "one frame" that B is in. The inertial frame for the outward trip is different from the inertial frame for the return trip. The derivation of our time-dilation result applies only to one inertial frame. Said in a different way, B accelerates when she turns around, and our time-dilation result holds only from the point of view of an inertial observer. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." The moment a rational scientist comes to find the following excerpt consistent he becomes irrational, that is, he becomes a Believer: "For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev |
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Einsteinians know no limits: Another incredible "explanation" of the
wavelength shift (the wavelength SHOULD vary if the speed of light is to remain constant): http://www.fourmilab.ch/cship/doppler.html "To correctly calculate the Doppler shift for large velocities, we have to take into account the Lorentz contraction of spacetime. As we travel along the propagating wave, the rate at which we encounter peaks and troughs is affected not only by the ratio of our velocity to the speed the wave is travelling, but also by the Lorentz contraction in the direction of our travel. When we're approaching a wave, Lorentz contraction increases the Doppler shift we observe since the wave crests become increasingly contracted in space; consequently we measure a shorter wavelength. Since the Lorentz contraction increases without bound as we approach the speed of light, so the Doppler shift increases without bound, rather than merely doubling the frequency as we'd expect from classical physics. If we're receding from the wave, the Doppler shift is reduced by special relativity. Why? The Lorentz contraction is the same regardless of whether we're approaching an object or receding from it. The Lorentz contraction will, then, reduce the wavelength of the wave at the same time the Doppler shift is increasing it." The arguments Einsteinians use above are quite similar to the arguments the shopkeeper uses in proving that the parrot is both alive and beautiful: http://www.youtube.com/watch?v=4vuW6tQ0218 Owner: Oh yes, the, uh, the Norwegian Blue...What's,uh...What's wrong with it? Mr. Praline: I'll tell you what's wrong with it, my lad. 'E's dead, that's what's wrong with it! Owner: No, no, 'e's uh,...he's resting. Mr. Praline: Look, matey, I know a dead parrot when I see one, and I'm looking at one right now. Owner: No no he's not dead, he's, he's restin'! Remarkable bird, the Norwegian Blue, idn'it, ay? Beautiful plumage! Pentcho Valev wrote: Einstein desperately destroying his own rationality: http://www.aip.org/history/einstein/...relativity.htm John Stachel: "How can it happen that the speed of light relative to an observer cannot be increased or decreased if that observer moves towards or away from a light beam? Einstein states that he wrestled with this problem over a lengthy period of time, to the point of despair. We have no details of this struggle, unfortunately." Einstein's irrationality taught in Einsteiniana's schizophrenic world: the speed of light does not depend on the speed of the observer (Divine Albert said so), therefore the wavelengh does: http://sampit.geol.sc.edu/Doppler.html "Moving observer: A man is standing on the beach, watching the tide. The waves are washing into the shore and over his feet with a constant frequency and wavelength. However, if he begins walking out into the ocean, the waves will begin hitting him more frequently, leading him to perceive that the wavelength of the waves has decreased." http://www.pitt.edu/~jdnorton/teachi...ang/index.html John Norton: "Here's a light wave and an observer. If the observer were to hurry towards the source of the light, the observer would now pass wavecrests more frequently than the resting observer. That would mean that moving observer would find the frequency of the light to have increased (AND CORRESPONDINGLY FOR THE WAVELENGTH - THE DISTANCE BETWEEN CRESTS - TO HAVE DECREASED)." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev |
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Einsteiniana: Divine Albert said the speed of light is variable and
this is perfectly valid and makes good physical sense but we now say the speed of light is constant and that's it: http://math.ucr.edu/home/baez/physic..._of_light.html Steve Carlip: "Is c, the speed of light in vacuum, constant? At the 1983 Conference Generale des Poids et Mesures, the following SI (Systeme International) definition of the metre was adopted: The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second. This defines the speed of light in vacuum to be exactly 299,792,458 m/s. This provides a very short answer to the question "Is c constant": Yes, c is constant by definition! (...) Einstein went on to discover a more general theory of relativity which explained gravity in terms of curved spacetime, and he talked about the speed of light changing in this new theory. In the 1920 book "Relativity: the special and general theory" he wrote: "...according to the general theory of relativity, the law of the constancy of the velocity of light in vacuo, which constitutes one of the two fundamental assumptions in the special theory of relativity [...] cannot claim any unlimited validity. A curvature of rays of light can only take place when the velocity of propagation of light varies with position." Since Einstein talks of velocity (a vector quantity: speed with direction) rather than speed alone, it is not clear that he meant the speed will change, but the reference to special relativity suggests that he did mean so. This interpretation is perfectly valid and makes good physical sense, but a more modern interpretation is that the speed of light is constant in general relativity." Einsteiniana: An infinitely long body can safely be trapped inside an infinitely short container; the infinitely long body remains trapped inside the infinitely short container in an infinitely compressed state: http://math.ucr.edu/home/baez/physic...barn_pole.html "These are the props. You own a barn, 40m long, with automatic doors at either end, that can be opened and closed simultaneously by a switch. You also have a pole, 80m long, which of course won't fit in the barn. Now someone takes the pole and tries to run (at nearly the speed of light) through the barn with the pole horizontal. Special Relativity (SR) says that a moving object is contracted in the direction of motion: this is called the Lorentz Contraction. So, if the pole is set in motion lengthwise, then it will contract in the reference frame of a stationary observer.....So, as the pole passes through the barn, there is an instant when it is completely within the barn. At that instant, you close both doors simultaneously, with your switch. Of course, you open them again pretty quickly, but at least momentarily you had the contracted pole shut up in your barn. The runner emerges from the far door unscathed.....If the doors are kept shut the rod will obviously smash into the barn door at one end. If the door withstands this the leading end of the rod will come to rest in the frame of reference of the stationary observer. There can be no such thing as a rigid rod in relativity so the trailing end will not stop immediately and the rod will be compressed beyond the amount it was Lorentz contracted. If it does not explode under the strain and it is sufficiently elastic it will come to rest and start to spring back to its natural shape but since it is too big for the barn the other end is now going to crash into the back door and the rod will be trapped in a compressed state inside the barn." Einsteiniana: An observer sees the bug squashed; the bug sees itself alive and kicking. This does not refute Divine Albert's Divine Theory. Rather, this gloriously demonstrates the unlimited deductive power of Divine Albert's Divine Theory: http://hyperphysics.phy-astr.gsu.edu.../bugrivet.html "The bug-rivet paradox is a variation on the twin paradox and is similar to the pole-barn paradox.....The end of the rivet hits the bottom of the hole before the head of the rivet hits the wall. So it looks like the bug is squashed.....All this is nonsense from the bug's point of view. The rivet head hits the wall when the rivet end is just 0.35 cm down in the hole! The rivet doesn't get close to the bug....The paradox is not resolved." Selected Einsteinians (e.g. John Norton) are entitled to reject the important consequence of Einstein's 1905 false light postulate establishing the passage of time as an illusion. All other believers should, like Brian Greene, constantly procrusteanize their minds into conformity with the consequence establishing the passsage of time as an illusion: http://rescomp.stanford.edu/~cheshir...einQuotes.html Albert Einstein: "People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion." http://www.pitt.edu/~jdnorton/Goodie...age/index.html John Norton: "A common belief among philosophers of physics is that the passage of time of ordinary experience is merely an illusion. The idea is seductive since it explains away the awkward fact that our best physical theories of space and time have yet to capture this passage. I urge that we should resist the idea. We know what illusions are like and how to detect them. Passage exhibits no sign of being an illusion....Following from the work of Einstein, Minkowski and many more, physics has given a wonderfully powerful conception of space and time. Relativity theory, in its most perspicacious form, melds space and time together to form a four-dimensional spacetime. The study of motion in space and and all other processes that unfold in them merely reduce to the study of an odd sort of geometry that prevails in spacetime. In many ways, time turns out to be just like space. In this spacetime geometry, there are differences between space and time. But a difference that somehow captures the passage of time is not to be found. There is no passage of time. There are temporal orderings. We can identify earlier and later stages of temporal processes and everything in between. What we cannot find is a passing of those stages that recapitulates the presentation of the successive moments to our consciousness, all centered on the one preferred moment of "now." At first, that seems like an extraordinary lacuna. It is, it would seem, a failure of our best physical theories of time to capture one of time's most important properties. However the longer one works with the physics, the less worrisome it becomes....I was, I confess, a happy and contented believer that passage is an illusion. It did bother me a little that we seemed to have no idea of just how the news of the moments of time gets to be rationed to consciousness in such rigid doses.....Now consider the passage of time. Is there a comparable reason in the known physics of space and time to dismiss it as an illusion? I know of none. The only stimulus is a negative one. We don't find passage in our present theories and we would like to preserve the vanity that our physical theories of time have captured all the important facts of time. So we protect our vanity by the stratagem of dismissing passage as an illusion." http://www.geekitude.com/gl/public_h...50422141509987 Brian Greene: "I certainly got very used to the idea of relativity, and therefore I can go into that frame of mind without it seeming like an effort. But I feel and think about the world as being organized into past, present and future. I feel that the only moment in time that's really real is this moment right now. And I feel [that what happened a few moments ago] is gone, and the future is yet to be. It still feels right to me. But I know in my mind intellectually that's wrong. Relativity establishes that that picture of the universe is wrong, and if I work hard, I can force myself to recognize the fallacy in my view or thinking; but intuitively it's still what I feel. So it's a daily struggle to keep in mind how the world works, and juxtapose that with experience that [I get] a thousand, even million times a day from ordinary comings and goings." Pentcho Valev wrote: http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. Show that B is younger than A when they meet up again. Solution: From A's point of view, B's clock is running slow by a factor gamma, on both the outward and return parts of the trip. Therefore, B is younger than A when they meet up again. This is the answer, and that's that. So if getting the right answer is all we care about, then we can pack up and go home. But our reasoning leaves one large point unaddressed. The "paradox" part of this example's title comes from the following alternate reasoning. Someone might say that in B's frame, A's clock is running slow by a factor gamma, and so A is younger than B when they meet up again. It's definitely true that when the two twins are standing next to each other (that is, when they are in the same frame), we can't have both B younger than A, and A younger than B. So what is wrong with the reasoning at the end of the previous paragraph? The error lies in the fact that there is no "one frame" that B is in. The inertial frame for the outward trip is different from the inertial frame for the return trip. The derivation of our time-dilation result applies only to one inertial frame. Said in a different way, B accelerates when she turns around, and our time-dilation result holds only from the point of view of an inertial observer. (...) For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." The moment a rational scientist comes to find the following excerpt consistent he becomes irrational, that is, he becomes a Believer: "For the entire outward and return parts of the trip, B does observe A's clock running slow, but enough strangeness occurs during the turning-around period to make A end up older. Note, however, that a discussion of acceleration is not required to quantitatively understand the paradox, as Problem 11.2 shows." http://www.haverford.edu/physics/songs/divine.htm No-one's as dee-vine as Albert Einstein Not Maxwell, Curie, or Bohr! He explained the photo-electric effect, And launched quantum physics with his intellect! His fame went glo-bell, he won the Nobel -- He should have been given four! No-one's as dee-vine as Albert Einstein, Professor with brains galore! No-one could outshine Professor Einstein -- Egad, could that guy derive! He gave us special relativity, That's always made him a hero to me! Brownian motion, my true devotion, He mastered back in aught-five! No-one's as dee-vine as Albert Einstein, Professor in overdrive! http://www.youtube.com/watch?v=5PkLLXhONvQ We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Einstein's postulates imply That planes are shorter when they fly. Their clocks are slowed by time dilation And look warped from aberration. We all believe in relativity, relativity, relativity. Yes we all believe in relativity, 8.033, relativity. Pentcho Valev |
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On May 12, 4:15 pm, Uncle Al wrote:
Pentcho Valev wrote: http://www.people.fas.harvard.edu/~djmorin/book.html Introduction to Classical Mechanics David Morin Cambridge University Press Chapter 11, p. 14: "Twin A stays on the earth, while twin B flies quickly to a distant star and back. [snip crap] idiot http://www.hawaii.edu/suremath/SRtwi...r-twin-01.html http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html Twin Paradox idiot Perhaps you are too stooopid to click on a link. Uncle Al will exercise the compassion to ram it up your butt, [In the Newtonian approximation to GR, the line element for "Newtonian coordinates" is to excellent approximation: ds^2 = -(1 - 2\phi) dt^2 + dx^2 + dy^2 + dz^2 where \phi is the Newtonian gravitational potential, c=1 The only deviation from Minkowski spacetime is in the time coordinate - using these coordinates the 3-space corresponding to a given value of t is Euclidean flat.] Twin Paradox: One twin travels relativistically, one twin stays home. They reunite. The traveling twin aged much less. The twin who travels through more space accumulates less time; also true for an orbit. Interval sqrt(t^2 - x^2 - y^2 - z^2) between the two events, expressed in inertial coordinate system (t,x,y,z), is conserved. Given the invariant interval, the larger sqrt(x^2 + y^2 + z^2)is the smaller sqrt(t^2) must be. The ratio by which the two aged when they are again local is identical in all reference frames: ratio = sqrt(t^2 - x^2 - y^2 - z^2)/t (units of c=1). Acceleration is irrelevant, demonstrated by Triplets. Three identical clocks as kits and not constructed until the experiment is running. Each clock has a short toggle switch. Individual spaceships carry a kit each. Set up the experiment. CLOCK 1: Our clock sits stationary in our inertial reference frame with its toggle sticking out. Touch the toggle and "off" state goes "on" or "on" state goes "off." Build it from parts just before needed, in the "off" state, zeroed. CLOCK 2: In a spaceship traveling at 0.999c relative to our inertial frame and positioned far to our left. Clock 2 was built after all acceleration ceased during setup, set to zero, "off" state. It skims past Clock 1 (our clock) in vacuum free fall, toggles touch, both Clocks 1 and 2 are "on" and locally synchronized by touching. Elapsed time accumulates in each clock. CLOCK 3: In a spaceship traveling at 0.999c relative to our inertial frame of reference, but 180 degrees counter in direction to Clock 2, far far to our right. It was built after all acceleration ceased during setup, set to zero, "off" state. An arbitrary time after Clocks 1 and 2 synchronize and turn "on" by touching, Clocks 2 and 3 brush past each other, both in vacuum free fall, touching toggles. Clock 2 is now "off," Clock 3 is now "on." Write down the elapsed time in "off" Clock 2. The spaceship with Clock 3 returns over the path taken by the spaceship with Clock 2. CLOCK 1: Our clock. It sits stationary in our inertial reference frame with a little toggle sticking out. Clock 3 vacuum free falls past, toggles touch. Clocks 3 and 1 are off. Write down elapsed times. No clock accelerated while "on" or while existing. BOTTOM LINE: Send results by radio. Numbers on paper don't change. Throughout the entire run three clocks were passive observers in vacuum free fall with zero acceleration. Compare elapsed times. Elapsed times #2+#3 does not equal #1, the local stationary reference frame summation. The sum of #2+#3 elapsed time is about 4.5% that than of #1's accumulated elapsed time. The Twin (Triplets) Paradox obtains without any clock having been accelerated. -- Uncle Alhttp://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals)http://www.mazepath.com/uncleal/qz4.htm thanks, if i understand it right, space must have viscosity, a viscosity constant, function of speed, with respect to time |
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