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[EL]
Randy wrote {{{ [Randy] I'm going to ask you again, politely, to please look at my derivation, in which I took: - one wave moving at speed v1 - another wave of higher frequency moving at speed 1.5*v1 - summed together they give a wave packet with peaks wherever they are in phase (wavelength 3*lambda1 where lambda1 = wavelength of first wave) and showed - the peaks of that wave packet propagate at 3*v1 This demonstrates that by taking a sum of waves with the property that higher frequency wave move faster, I get a wave packet that moves much faster than any individual wave. - Randy }}} And per his request I decided to include his example here to test its physical validity while having confidence in Randy's mathematical knowledge. His example is included complete with his comments and my comments would be interleaved. {{{ [Randy] Suppose we have a really simple wave composed of two frequencies, f1 and f2. Let us suppose that f2 = 2f1. Let us also suppose that the speed of propagation for wave 1 is v, and for wave 2 is 1.5v. So the higher frequency wave (wave 2) has 50% higher velocity. The wave is described by S(x,t) = cos(2*pi*f1*(x/v1 - t)) + cos(2*pi*f2*(x/v2 - t)) You should first make sure you believe that. Each term describes a wave which is: - constant for x - v*t = constant - for fixed t, has spatial period (wavelength) v/f = lambda - for fixed x, has temporal period 1/f1 - has phase 0 at x = 0, t = 0. The first wave has a wavelength of v1/f1 = lambda1, the second has a wavelength of v2/f2 = (1.5*v1)/(2*f2) = (3/4)*lambda1 }}} [EL] This is a very small glitch and here is the correction. v2/f2 = (1.5*v1)/(2*f1) {{{ [Randy] So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave 1, and the packet is in phase every 4*lambda2 = 3*lambda1. If you fix time t, you will see the waves add up constructively at x=0 and every 4*lambda1 afterward. These peaks will move as the wave moves. The rate of advance of the peaks will be the group velocity, as it is the motion of our coherent pulse. So let's analyze what happens as time evolves. Suppose it is no longer time 0, but a little later, time T. }}} [EL] Here I would like to emphasize on the word "later". In fact, relativity did not screw anything else than the conception of time and certainly every thing else consequently. The classical calculation of wave modulation represented by Randy is quite legitimate but the problem is in the interpretation of time "what happens where". Bare with me because this example should be a perfect example to see what relativity destroyed, it destroyed the ability of quality minds to distinguish between reckless sequencing and the impeccable precision of logical event sequencing. {{{ [Randy] The phase of wave 1 is f1*(x/v1-T) and of wave 2 is f2*(x/v2-T) = 2*f1*(x/(1.5*v1)-T) These phases are equal where f1*x/v1 - f1*T = 1.33*f1*x/v1 - 2*f1*T or f1*T = 0.33*f1*x/v1 or x = 3*v1*T }}} [EL] As you have noticed that I emphasized on the word "later", I would like to drive the attention of the reader to some facts. When we draw a graph representing a wave with time on the x-axis and amplitude on the y-axis, we should pay attention to the meaning of zero time and positive time more than zero where zero time comes first and more than zero time comes "later". This means that looking at the wave graph we should imagine the wave evolving towards the left side and not to the right side as in oscilloscopes where raster scanning begins at the left side of the screen. The implication of this fact is so great but quite overlooked by many physicists and almost all mathematicians who take the hype O thesis from physicists for granted. Randy demonstrated that x = 3.v1.T, where the product of velocity and time is a distance of course and that distance is where identifiable group-wave-peaks may appear in LATER. I shall not discuss the out-of-synchronisation artefacts of oscilloscopes here again as you can read it up in this thread. Now I shall focus on the paper graph and what the physical meaning of wave modulation means. It is quite easy to confuse the Time versus Amplitude chart with velocity chart where Time is versus distance. If you can avoid that confusion then that is precisely what we need from the reader here. {{{ [Randy] The place where the waves are in phase has moved by a distance 3*v1*T in time T. }}} As you can read in Randy's own statement, he used the expression "a distance in time T". We know that the velocity v1 is the distance per unit time traversed by the wave W1. We know that the velocity v2 is the distance per unit time traversed by the wave W2. To understand how the modulation proceeds we need a spatial reference GATE through which the two waves propagate and modulate. That gate is an infinite plane placed orthogonal to the waves' propagational direction axis, assuming that they are coincident in direction. T must be a multiple of time units in which a finite portion of each wavelength is propagating through the medium and across our referential gate. Now that portion of the wave is what advances in one time unit. So what does that distance [3.v1.T] mean? Randy said that there is a periodically repeating event at which the two waves become in phase once more and then go out of phase for some time. Here are Randy's own words again. "So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave 1" Naturally W2 is given to be faster than W1 such that every 4 cycles of W2 correspond to 3 cycles of W1. The resulting modulation IS a consequence of those two physical velocities of wave propagation in Length over time dimensions. {{{ [Randy] Thus, the peak appears to be moving forward at 3*v1, despite the fact that one wave is moving at v1 and the other at 1.5*v1. As the whole thing has a spatial periodicity of 3*lambda1, you will find that all of the peaks, spaced 3*lambda1 apart, are similarly marching forward at 3*v1. }}} [EL] This is the crux of the confusion. Here we ask; what is it that is moving forward and relative to what? In this particular case, as time advances, the difference in the two velocities causes the in-phase event to show up at our referential gate at regular time intervals when 3 cycles of W1 have passed through the gate or 4 cycles of W2 have passed through the gate. This means that the frequency of the in-phase event is a Third of the frequency of W1 or a Quarter of the frequency of W2 if we assumed proper time to dominate such frequencies. Let us call this in-phase frequency F, then; F = f1/3 = f2/4 Hence f2 = 4/3 f1, which contradicts our premise where we assumed that f2 = 2 f1. Something hidden must be screwed up here; can you guess what is it? TIME. Good guess! If wave number one was 1000 Hz and wave number two was 2000 Hz then our referential gate must be THE OBSERVER through which relative velocities cause a frequency shift, such that 1000 complete cycles are introduced less frequently than 2000 complete cycles being introduced more frequently. Here we propose a standard time window of one proper second in which 1000 complete cycles of wave number one happens and 2000 complete cycles of wave number two happens concurrently. By taking the proper time window during which W1 passes through the gate of observation at its own velocity as our standard time frame we realise that W2 introduces 3000 complete cycles rather than 2000 because the velocity of observation is 1.5 times faster. This means that from the Observational gate's point of view the number of complete cycles of W2 within one time window is 3 times greater than the complete cycles encountered from W1 and it is not the velocity of anything at all. When those two waves interfere the less frequent wave becomes an envelope for the more frequent wave Such that each composite wave is W1 subdivided into 3 cycles of W2. This modulated wave becomes a moving reference envelope inside which the other wave is moving and we end up with (v2/v1).(f2/f1) being a dimensionless product of ratios that would yield the number 3 that means nothing in physical essence. You can see clearly that we could have taken the faster wave as the reference to which modulation is happening less frequent rather than more frequent. So we have the observational freedom to see the faster wave slipping forward inside the slower wave or to see the slower wave as a peristaltic motion moving backwards over the faster wave as a modulation of some constant peak amplitude. Here I would like to make a historical declaration. The observational gate that I have proposed does not observe any velocities once both wavefronts have arrived and being observed, and all that that gate could observe is the frequency of events because the gate is stationary in the space of both wave velocities. You could repeat this exercise by assuming a gate on a railway and let one train be 1.5 times faster than the other train but both arrive at the gate simultaneously. Let the size of the cars be twice longer on the slow train and record your observations regarding the coincidence of car-joints on both trains. The gate-observer may have a clock but all he may observe is a frequency of coincidences and no velocities are perceived at all. The true velocities are what the trains' wheels make on the iron railway. This in-phase frequency (car-joints on both trains coinciding) may be (as in our example) the frequency of 3 cars on the slow train or 4 cars on the fast train. Now we have two lambdas and one frequency so how can you decide on a single velocity? 3 cars take 3 times as much as one to pass on the slow train and 4 cars take 4 times as much as one to pass on the fast train. The static length of 3 slow cars is equivalent to 6 fast cars not 4 and that is what Lorentz Fitzgerald contraction is all about. Time dilation follows if we compare times and fix the lengths. So this idiotic game of juggling numbers makes no physics and makes no science. We can hybridize mathematics and physics and come up with negative dispersion, time dilation, length contraction, black holes and big bangs, but for what end is this clownish path taking us Randy? What is so funny and pleasing in ****ing with innocent minds? There are so many people out there that believe that such fiction is true and real. I am seriously asking why. Why the academic establishment allows this comedy? Are all scientists becoming incompetent to realise and figure out how this modern wave of fiction is screwing with their sanity and sound logic? I see Lemmings, plenty of them, all the time and everywhere. Rarely do I see like those men that made the solid foundations on which we stand today. Lemmings and clones are what the academic institutions are producing today. Perhaps it is time for humans to go extinct and rid nature from the asshole species. EL {{{ [Randy] The fact that their point of coincidence can move forward faster than either wave alone is a consequence of the shorter wave moving faster than the longer one. In other words, of the longer wave having higher index of refraction, or of dn/df being negative. If the longer wave moved faster (had lower index of refraction), you would not get this "superluminal" effect. You can do everything I just did in the more general case of a complex, multi-frequency wave packet and an arbitrary slope. You can further work out that there is no information being propagated at speed v1. This has nothing to do with relativity. It's pure classical wave physics, analyzing sines and cosines. - Randy }}} |
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"EL" wrote in message
om... - one wave moving at speed v1 - another wave of higher frequency moving at speed 1.5*v1 - summed together they give a wave packet with peaks wherever they are in phase (wavelength 3*lambda1 where lambda1 = wavelength of first wave) and showed - the peaks of that wave packet propagate at 3*v1 This demonstrates that by taking a sum of waves with the property that higher frequency wave move faster, I get a wave packet that moves much faster than any individual wave. So what? This demonstrates absolutely nothing that is in violation of relativity. The superlimunal propagation of the wave packet depends on the prior existence of its constituents that add to make it up. So, it can easily race along at greater than c if those constituent trains are already in existence. But no information is being transferred, because all of the info encoded in each train is already spread throughout all space, from the origin to the target. The constituent trains need to reach the target first (at speed c), in order to form the "red carpet" along which the wave packet can then travel at any speed. Minor Crank |
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[EL]
Randy wrote {{{ [Randy] I'm going to ask you again, politely, to please look at my derivation, in which I took: - one wave moving at speed v1 - another wave of higher frequency moving at speed 1.5*v1 - summed together they give a wave packet with peaks wherever they are in phase (wavelength 3*lambda1 where lambda1 = wavelength of first wave) and showed - the peaks of that wave packet propagate at 3*v1 This demonstrates that by taking a sum of waves with the property that higher frequency wave move faster, I get a wave packet that moves much faster than any individual wave. - Randy }}} And per his request I decided to include his example here to test its physical validity while having confidence in Randy's mathematical knowledge. His example is included complete with his comments and my comments would be interleaved. {{{ [Randy] Suppose we have a really simple wave composed of two frequencies, f1 and f2. Let us suppose that f2 = 2f1. Let us also suppose that the speed of propagation for wave 1 is v, and for wave 2 is 1.5v. So the higher frequency wave (wave 2) has 50% higher velocity. The wave is described by S(x,t) = cos(2*pi*f1*(x/v1 - t)) + cos(2*pi*f2*(x/v2 - t)) You should first make sure you believe that. Each term describes a wave which is: - constant for x - v*t = constant - for fixed t, has spatial period (wavelength) v/f = lambda - for fixed x, has temporal period 1/f1 - has phase 0 at x = 0, t = 0. The first wave has a wavelength of v1/f1 = lambda1, the second has a wavelength of v2/f2 = (1.5*v1)/(2*f2) = (3/4)*lambda1 }}} [EL] This is a very small glitch and here is the correction. v2/f2 = (1.5*v1)/(2*f1) {{{ [Randy] So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave 1, and the packet is in phase every 4*lambda2 = 3*lambda1. If you fix time t, you will see the waves add up constructively at x=0 and every 4*lambda1 afterward. These peaks will move as the wave moves. The rate of advance of the peaks will be the group velocity, as it is the motion of our coherent pulse. So let's analyze what happens as time evolves. Suppose it is no longer time 0, but a little later, time T. }}} [EL] Here I would like to emphasize on the word "later". In fact, relativity did not screw anything else than the conception of time and certainly every thing else consequently. The classical calculation of wave modulation represented by Randy is quite legitimate but the problem is in the interpretation of time "what happens where". Bare with me because this example should be a perfect example to see what relativity destroyed, it destroyed the ability of quality minds to distinguish between reckless sequencing and the impeccable precision of logical event sequencing. {{{ [Randy] The phase of wave 1 is f1*(x/v1-T) and of wave 2 is f2*(x/v2-T) = 2*f1*(x/(1.5*v1)-T) These phases are equal where f1*x/v1 - f1*T = 1.33*f1*x/v1 - 2*f1*T or f1*T = 0.33*f1*x/v1 or x = 3*v1*T }}} [EL] As you have noticed that I emphasized on the word "later", I would like to drive the attention of the reader to some facts. When we draw a graph representing a wave with time on the x-axis and amplitude on the y-axis, we should pay attention to the meaning of zero time and positive time more than zero where zero time comes first and more than zero time comes "later". This means that looking at the wave graph we should imagine the wave evolving towards the left side and not to the right side as in oscilloscopes where raster scanning begins at the left side of the screen. The implication of this fact is so great but quite overlooked by many physicists and almost all mathematicians who take the hype O thesis from physicists for granted. Randy demonstrated that x = 3.v1.T, where the product of velocity and time is a distance of course and that distance is where identifiable group-wave-peaks may appear in LATER. I shall not discuss the out-of-synchronisation artefacts of oscilloscopes here again as you can read it up in this thread. Now I shall focus on the paper graph and what the physical meaning of wave modulation means. It is quite easy to confuse the Time versus Amplitude chart with velocity chart where Time is versus distance. If you can avoid that confusion then that is precisely what we need from the reader here. {{{ [Randy] The place where the waves are in phase has moved by a distance 3*v1*T in time T. }}} As you can read in Randy's own statement, he used the expression "a distance in time T". We know that the velocity v1 is the distance per unit time traversed by the wave W1. We know that the velocity v2 is the distance per unit time traversed by the wave W2. To understand how the modulation proceeds we need a spatial reference GATE through which the two waves propagate and modulate. That gate is an infinite plane placed orthogonal to the waves' propagational direction axis, assuming that they are coincident in direction. T must be a multiple of time units in which a finite portion of each wavelength is propagating through the medium and across our referential gate. Now that portion of the wave is what advances in one time unit. So what does that distance [3.v1.T] mean? Randy said that there is a periodically repeating event at which the two waves become in phase once more and then go out of phase for some time. Here are Randy's own words again. "So every 4 wavelengths of wave 2 corresponds to 3 wavelengths of wave 1" Naturally W2 is given to be faster than W1 such that every 4 cycles of W2 correspond to 3 cycles of W1. The resulting modulation IS a consequence of those two physical velocities of wave propagation in Length over time dimensions. {{{ [Randy] Thus, the peak appears to be moving forward at 3*v1, despite the fact that one wave is moving at v1 and the other at 1.5*v1. As the whole thing has a spatial periodicity of 3*lambda1, you will find that all of the peaks, spaced 3*lambda1 apart, are similarly marching forward at 3*v1. }}} [EL] This is the crux of the confusion. Here we ask; what is it that is moving forward and relative to what? In this particular case, as time advances, the difference in the two velocities causes the in-phase event to show up at our referential gate at regular time intervals when 3 cycles of W1 have passed through the gate or 4 cycles of W2 have passed through the gate. This means that the frequency of the in-phase event is a Third of the frequency of W1 or a Quarter of the frequency of W2 if we assumed proper time to dominate such frequencies. Let us call this in-phase frequency F, then; F = f1/3 = f2/4 Hence f2 = 4/3 f1, which contradicts our premise where we assumed that f2 = 2 f1. Something hidden must be screwed up here; can you guess what is it? TIME. Good guess! If wave number one was 1000 Hz and wave number two was 2000 Hz then our referential gate must be THE OBSERVER through which relative velocities cause a frequency shift, such that 1000 complete cycles are introduced less frequently than 2000 complete cycles being introduced more frequently. Here we propose a standard time window of one proper second in which 1000 complete cycles of wave number one happens and 2000 complete cycles of wave number two happens concurrently. By taking the proper time window during which W1 passes through the gate of observation at its own velocity as our standard time frame we realise that W2 introduces 3000 complete cycles rather than 2000 because the velocity of observation is 1.5 times faster. This means that from the Observational gate's point of view the number of complete cycles of W2 within one time window is 3 times greater than the complete cycles encountered from W1 and it is not the velocity of anything at all. When those two waves interfere the less frequent wave becomes an envelope for the more frequent wave Such that each composite wave is W1 subdivided into 3 cycles of W2. This modulated wave becomes a moving reference envelope inside which the other wave is moving and we end up with (v2/v1).(f2/f1) being a dimensionless product of ratios that would yield the number 3 that means nothing in physical essence. You can see clearly that we could have taken the faster wave as the reference to which modulation is happening less frequent rather than more frequent. So we have the observational freedom to see the faster wave slipping forward inside the slower wave or to see the slower wave as a peristaltic motion moving backwards over the faster wave as a modulation of some constant peak amplitude. Here I would like to make a historical declaration. The observational gate that I have proposed does not observe any velocities once both wavefronts have arrived and being observed, and all that that gate could observe is the frequency of events because the gate is stationary in the space of both wave velocities. You could repeat this exercise by assuming a gate on a railway and let one train be 1.5 times faster than the other train but both arrive at the gate simultaneously. Let the size of the cars be twice longer on the slow train and record your observations regarding the coincidence of car-joints on both trains. The gate-observer may have a clock but all he may observe is a frequency of coincidences and no velocities are perceived at all. The true velocities are what the trains' wheels make on the iron railway. This in-phase frequency (car-joints on both trains coinciding) may be (as in our example) the frequency of 3 cars on the slow train or 4 cars on the fast train. Now we have two lambdas and one frequency so how can you decide on a single velocity? 3 cars take 3 times as much as one to pass on the slow train and 4 cars take 4 times as much as one to pass on the fast train. The static length of 3 slow cars is equivalent to 6 fast cars not 4 and that is what Lorentz Fitzgerald contraction is all about. Time dilation follows if we compare times and fix the lengths. So this idiotic game of juggling numbers makes no physics and makes no science. We can hybridize mathematics and physics and come up with negative dispersion, time dilation, length contraction, black holes and big bangs, but for what end is this clownish path taking us Randy? What is so funny and pleasing in ****ing with innocent minds? There are so many people out there that believe that such fiction is true and real. I am seriously asking why. Why the academic establishment allows this comedy? Are all scientists becoming incompetent to realise and figure out how this modern wave of fiction is screwing with their sanity and sound logic? I see Lemmings, plenty of them, all the time and everywhere. Rarely do I see like those men that made the solid foundations on which we stand today. Lemmings and clones are what the academic institutions are producing today. Perhaps it is time for humans to go extinct and rid nature from the asshole species. EL {{{ [Randy] The fact that their point of coincidence can move forward faster than either wave alone is a consequence of the shorter wave moving faster than the longer one. In other words, of the longer wave having higher index of refraction, or of dn/df being negative. If the longer wave moved faster (had lower index of refraction), you would not get this "superluminal" effect. You can do everything I just did in the more general case of a complex, multi-frequency wave packet and an arbitrary slope. You can further work out that there is no information being propagated at speed v1. This has nothing to do with relativity. It's pure classical wave physics, analyzing sines and cosines. - Randy }}} |
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![]() "Minor Crank" wrote in message news:IEInb.53464$Fm2.33079@attbi_s04... "EL" wrote in message om... Troll alert. Look at bottom of http://users.pandora.be/vdmoortel/di...rsenLogic.html Dirk Vdm |
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"Dirk Van de moortel" wrote
in message ... "Minor Crank" wrote in message news:IEInb.53464$Fm2.33079@attbi_s04... "EL" wrote in message om... Troll alert. Look at bottom of http://users.pandora.be/vdmoortel/di...rsenLogic.html Understood. I don't have the whole thread visible from this server, but I was responding to the wrong person, because of EL's confusing posting habits. Sorry, Randy. Minor Crank |
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"Minor Crank" wrote in message news:IEInb.53464$Fm2.33079@attbi_s04...
"EL" wrote in message om... - one wave moving at speed v1 - another wave of higher frequency moving at speed 1.5*v1 - summed together they give a wave packet with peaks wherever they are in phase (wavelength 3*lambda1 where lambda1 = wavelength of first wave) and showed - the peaks of that wave packet propagate at 3*v1 This demonstrates that by taking a sum of waves with the property that higher frequency wave move faster, I get a wave packet that moves much faster than any individual wave. So what? This demonstrates absolutely nothing that is in violation of relativity. The words above are mine, before EL's comments. I agree of course. That was the point of my calculation: To show that if dv/df is positive (dn/df is negative), then you can get superluminal group velocities. It rapidly devolved into rants about the evils of the term "negative dispersion", which eventually highlighted that EL could not maintain any consistent view of what is meant by dn/df, dispersion, or the slope of a curve. My favorite part in this discussion is where he gives data from one dispersion curve and announces that because the delta-n's between his irregularly-spaced tabulated values are not constant, "there is no ****ing slope". So I recommended getting away from all discussion of derivatives and slopes entirely and just concentrating on what happens when the shorter wave moves faster. I can't make sense of the resulting rant. It still seems to be something about relativity and time. As far as I can tell, he's upset that the wavelengths of my two waves are in a 4/3 relationship rather than a 2/1 relationship as the frequencies are, and suspects this is some product of the evil modern physicists. It is really a product, of course, of the fact that in my hypothetical medium, the two waves do not have the same velocity. Therefore wavelength is not inversely proportional to frequency. - Randy |
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EL wrote:
[EL] Randy wrote {{{ [Randy] I'm going to ask you again, politely, to please look at my derivation, in which I took: - one wave moving at speed v1 - another wave of higher frequency moving at speed 1.5*v1 - summed together they give a wave packet with peaks wherever they are in phase (wavelength 3*lambda1 where lambda1 = wavelength of first wave) and showed - the peaks of that wave packet propagate at 3*v1 This demonstrates that by taking a sum of waves with the property that higher frequency wave move faster, I get a wave packet that moves much faster than any individual wave. http://gregegan.customer.netspace.ne...ETS/20/20.html [snip] -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) "Quis custodiet ipsos custodes?" The Net! |
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Uncle Al wrote in message ...
http://gregegan.customer.netspace.ne...ETS/20/20.html [snip] [EL] Al, How can you post while being in coma! Man you are a comatose for so long that I began to believe that you descended from a vegetable. You just reposted a link to an applet that was completely and legitimately refuted by exposing the out-of-synch trick being used to fool idiots of your high calibre, sir. Go look at your picture and take your head out of your arse. EL |
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Minor Crank correctly wrote:
So what? This demonstrates absolutely nothing that is in violation of relativity. The superlimunal propagation of the wave packet depends on the prior existence of its constituents that add to make it up. So, it can easily race along at greater than c if those constituent trains are already in existence. But no information is being transferred, because all of the info encoded in each train is already spread throughout all space, from the origin to the target. The constituent trains need to reach the target first (at speed c), in order to form the "red carpet" along which the wave packet can then travel at any speed. Exactly. SR does not say that things (effects - whatever you like) can not happen faster than light. It says information can not be sent faster than light - it is only be being able to send information you run into the causality problems of FTL. Thanks Bill |
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Thread | Thread Starter | Forum | Replies | Last Post |
Empirically Confirmed Superluminal Velocities? | Robert Clark | Astronomy Misc | 42 | November 11th 03 03:43 AM |