Mowgli

Yes' date=' just that the relativisitic formula for it is different. As the shockwave passes you, the frequency as you measure it is infinite. But immediately after the shockwave passes you, the frequency rapidly decreases. In my animation, the instant the luminal shockwave hits you is when you see the object at B'. As you see the phantoms move away from B', the observed frequencies move from gamma, x-ray, uv, visible all the way to RF. Since the angular position is a function of time, you can think of the frequency evolution in terms of the angle, which is what agrees well with the available data. So as for the luminal boom, true, you cannot measure the frequency of the shockwave, but immediately after the shockwave passes you, you can start measuring the frequencies. For the superluminal explosion, what I was suggesting though was, [i']ignore[/i] the frequencies altogether, and think of when the waves will reach you. Did you say the shockwave travelled faster than sound? I didn't know that... Interesting. Why? Or, is it the footprint of the sonic boom that travels faster than sound?

Acutally, the trajectory I assumed for the superluminal object is more general that it looks. Let me explain why. Imagine a superluminal object going in some random direction (but still in a straight line). This line of flight has a point of closest approach to us. What my calculation says is that we won't see it until the object is close to this point (point B' in my second post above). At this point, the observed emission of the object is in the gamma region (the luminal boom alluded to earlier). Then the spectrum quickly moves through the x-ray, visible region on to RF (which concides with what we observe in GRB afterglows). As time tends to infinity, the phantom objects are so deep in the RF region that we won't see them at all; we may see only some microwave radiation. So, whatever be the direction in which the superluminal object is moving, as long as it is moving roughly in a straight line, our perception of it is roughly similar (but with different time constants depending on the distance and the speed). I didn't want to bring up this part of my speculation because it calls for even bigger leaps of faith, but now is probably a good time to do so. Let's suppose, hypothetically, that our universe is a collection of possibly superluminal objects (galaxies) moving in random directions and ask ourselves the question how we and our telescopes will observe it. It is not difficult to show that most of these objects will look as though they are receding from us close to the speed of light (as measured by their redshifts), there will be a significant amount of low frequency isotropic radiation, there will be symmetric radio sources and occassional gamma ray bursts and so on. In short, our perception will be pretty close to what we do perceive! I know this sounds far-fetched, but please remember, when I said the laser dot on the ceiling would appear at two place at the same time, that sounded quite far-fetched as well. Now, tell me, is it any wonder that I called my book The Unreal Universe? One quick question to tickle your brain - if there is a superluminal explosion, how would we perceive it? For example, imagine a star explodes at say 12 light years from us, the debris is thrown around in a spherical shell that moves away from the center of the star at a constant superluminal speed of say 2c. What will we see?

Yes, the invariant mass is a tough nut to crack. I thought about it for a while, and could not find a real chink there. I have a notion that the concept is sufficiently cyclic that it is self-consistent. I wanted to write a small simulation to illustrate this, and will do it when I have some time. (Take a particular decay, say D to Kpi, assume the daughter momenta to be well measured, assume some other daughter masses, and consequently their energies, and estimate the width of the D peak.) I have to admit though that I'm not very hopeful that I will be able to prove my point. (Why would the particle misidentification - switch the Kaon and pion, I mean - broaden the D peak?) This is one of the things I may not be able to explain away easily. About neutrino mass squared, looking at the papers again, I see that the measurements are like -2 +- 3 eV2, quite consistent with zero. As an aside related to this, I read this little story about standards of evidence and the need to examine our biases. Imagine that a study done on tooth decay and smoking, and a significant correlation is found between them. Assume that eighty percent of smokers are found to have bad teeth, while only forty percent of non-smokers have bad teeth. Based on this, it is concluded that one of the ways of avoiding bad teeth is not to smoke. When I first read this story, the conclusion sounded completely reasonable to me, until the bias was pointed out later. Did it fool you as well? It's important to identify and avoid biases in sciences especially when it may not be obvious. Yes' date=' that is the paper I was referring to. As I mentioned earlier, my model is not (yet) a complete theory. Figuring out how thousands of very intelligent scientists consistently went wrong over a hundred years is not something I can reasonably expect to complete in my lifetime - not fair on myself. Nonetheless, let me try it this way - why not take my model for its own merit in how well it explains the astrophysical phenomena, and how much simpler it is compared to the current models? Given that we use different physics (QM or SR) at different length and speed scales, we may suspend our disbelief for a while. After all, as you pointed out, my picture of how we perceive superluminality doesn't apply to particles. In fact, the subnuclear particles are not "perceived" at all, and they exist only as a result of our acceptance of scientific realism. But this is another topic altogether. What is required is the assumption that the speed of light/sound is independent of the source' date=' which is true for wave propagation. I should come back to my main point, which is that SR applies to our perception of motion. This is more or less obvious if we look at its original derivation making use of light travel time effects. So, saying that SR applies to the space and time after we take out the light travel time effects is not consistent with its derivation. What is done afterwards in Einstein's article is an assertion that our perception [i']is[/i] the absolute reality. My argument is merely that we should be mindful of the distinction between the absolute reality and our percpetion of it. If we are, then we can find an elegant explanation for certain astrophysical and cosmological phenomena. Thank you for taking my ideas seriously and spending the time and effort to think and talk about them.

Since this thread has been idle for a while, I thought I would some other ideas related to it. I would really like to hear from the resident experts, if they have any comments, criticism or any other kind of feedback or suggestions. In thinking about the hypothetical superluminal object, one may rightly criticize that there is no point in discussing it; after all, nothing is supposed to travel faster than light. That brings us to the basic question -- what is so important about light that it should figure in the basic structure of space and time? In order to understand the importance of light in our space and time, let's consider a different space-time -- for instance, one created by echolocation. It's not difficult to work out how the (blind) bat would perceive moving bodies. It turns out that the bat will think that nothing can move faster than the speed of sound. (A supersonic object moving away from the bat can never be sensed because the sound the bat emits will never reach the object, and there will be no reflection. An approaching supersonic object will pass the bat before the reflected sound reaches it, and will become a receding object.) It can also be shown that there will be a time dilation and length contraction in echolocation as predicted in special relativity (SR), again with the speed of light replaced with that of sound. Now, if the bat were intelligent enough to theorize about space and time, the theory it would have come up with would have been uncannily similar to SR with the speed of light replaced with that of sound. In this case, we can clearly see that the bat is making a theory about its perceived reality because we know what the underlying absolute reality is -- it is the reality as we (humans) sense it using a faster mode (light). It stands to reason that our space-time also must have perceptual effects. We can either attribute the effect that the finite speed of light has in our perception of moving bodies to the properties of space and time (as in SR), or we can try to "take them out" from our perception of motion. It turns out that we cannot take them out because multiple configurations can result in the same perception; it is an ill-posed problem with many valid solutions. The next best thing we can do (that I could think of) was to work forward; ie, guess a configuration and work out how we would perceive it, much like I did in the case of echolocation. I considered a hypothetical superluminal object and worked out in detail what our perception of it would be. The "luminal boom" it creates explains neatly many of the puzzling features of a Gamma Ray Burst (GRB) including the time evolution of the afterglow. The aftermath of the luminal boom (asymptotically low frequencies) explains the spectra, the observed symmetry and other time/angle dependent features of radio sources (DRAGNs). I made some predictions about their kinematics, verified some of them with existing data. I also provided some other predictions, which, if observed, will falsify my model. (Because if a model cannot be falsified, it's no model at all.) For instance, a clear movement in the angular position of the core of a DRAGN (which would be the position of the so-called host galaxy) would invalidate my model. Or, the appearance of a superluminal "knot" in one of the jets with no counterpart in the opposing jet will also prove that my model is wrong. I can point you to my article (which I optimistically called a journal article) if you are interested in the technical details. Despite the success of my model in describing these phenomena, it is still a tough sell because the current belief is that SR applies to the absolute reality. In other words, once you take out the light travel time (LT) effects that I described in the preceding paragraph, what is left is the space-time that is assumed to obey SR. (Actually, one of the experts in this forum said that to me earlier.) It is an understandable assumption because, frankly, the LT effects are not that hard to work out, and it is not conceivable that the great minds of the last century didn't work them out and see their implications. The only explanation I can think of is that they were kind of blinded by the assumption that our perceived reality was the absolute reality, and that their theories applied to the absolute reality. (Is this one way of describing scientific realism?) The real point that I'm trying to make is that SR applies to our phenomenal reality, not to its noumenal causes. This is a philosophical stance, and physics journals are not ready (perhaps rightly) to just take my word for it Looking at it philosophically, one can say that there is a noumenal reality of which our phenomenal perception is all based on light. Furthermore, our cognitive model for the phenomenal reality is space. Space is a cognitive representation of the photons falling on our retina, much like sound is a representation of pressure waves in the air, temperature is a model for molecular movements and smell is a model for chemical concentrations. We cannot imagine space to be a model only because we have no "higher" sense modality, and a consequent model, to understand it, which we did in the case of sound, smell and temperature. Given that space is created out of light input, it becomes immediately obvious why the speed of light is a fundamental property of our perception of space. So clearly, light and its speed are the most important things in our reality. What do you think? There is quite a bit more to it than what I can post here (related to neuroscience, evolutionary biology, etc.); after all, I wrote a full-length book about it...

When something is in an orbit, gravity and acceleration kind of cancel each other - hence weightlessness. I think the equivalence principle says that such a frame is in fact an inertial frame so that SR applies.

Actually, the "phantom" objects will be identical only if the superluminal object doesn't change during its flight. In my second post with the algebra, if you look at the first figure, let's say the light rays from A- and A reach the observer at the same instant in time, giving him the impression that he is seeing two objects. In "reality," he is seeing the object as it was at two different instants in time, say t- and t. During the time interval between t- and t, the object may have changed. So you can expect only a rough symmetry. In fact, I was a little concerned about CPL's use of the word "identical" in the thread title, so I put a disclaimer in my first post stating: "(If the object doesn't change during its flight, the two "phantom" objects are identical to each other.)"

We can measure only the angular speed. In order to translate that to a linear speed measurement, we need to estimate the distance to the line of flight y. This estimate is model dependent, and is always done in such a way that the real speed is subluminal and the phantoms are in fact two distinct objects. It can be shown that as long as the angular rates are not identical, one can always find a distance y to the system such that the real speed (of an assumed symmetric back to back ejection) is subluminal, even if one of the sides may have apparent superluminal speed. This is indeed how they calculate the upper limit on the distance y in astrophysics, by enforcing Lorentz invariance. I can show you proof if you like. I was thinking more in terms of radio sources (like Cygnus A, as attached) and their spectra rather than gravitational lensing. If I remember right, the jet to the right of the core (the tiny red dot at the center) is a nearly continuous and collemated "ejecta" of over 5000 light years, which implies long memory or coordination over great distances. (Or, was it in M87?)

It is a "luminal" boom, as shown in the attached picture, which is another way of looking at the animation. In this picture, the circles represent the wave that the moving object (say the first peaks) emits. What is also of interest is how the frequency as measured at O changes. It starts at infinity and rapidly decreases. In fact, in the animation in the previous post, the color of the "phantom" objects is supposed to represent their redshift as seen by the observer, although it is not done to scale. I didn't post the algebra behind it yet, but the spectrum and its time evlution predicted in this "luminal" boom can explain GRBs with remarkable simplicity. (Except, of course, that the explanation violates Lorentz invariance.)

This post gives the algebra behind the animation. First, let's define the notations used using the following figure. Here, the object is traveling along the thick horizontal line at a speed [math]\beta[/math]. The black dot in the animation (where the object first appears to the observer) is B'. B is the point of closest approach. Let's set the time [math]t=0[/math] when the object is at the point B. The line of flight (at its closest point B) is at a distance of y from the observer at O. A is a typical point at a distance x from B. [math]\theta[/math] is the angle between the line of flight and the observer's line of sight. [math]\phi[/math] is that the angle that the object subtends at the observer's position O with respect to the normal. Let's set [math]c=1[/math] to simplify the algebra, so that [math]t_o[/math], the observer's time is [math]t - y[/math]. (A- is another representative point where [math]t, x[/math] and [math]\phi[/math] are negative.) With these notations, we can write down the following equation for the real position of the object at time [math]t[/math]: [math] x = y\tan\phi = \beta t [/math] Or, [math] t = \frac{y\tan\phi}{\beta} [/math] A photon emitted by the object at A (at time [math]t[/math]) will reach O after traversing the hypotenuse. A photon emitted at B will reach the observer at [math]t = y[/math], since we have chosen [math]c = 1[/math]. We have defined the observer's time [math]t_o[/math] such that [math]t = t_o + y[/math], then we have: [math] t_o = t + \frac{y}{\cos\phi} - y [/math] which gives the relation between [math]t_o[/math] and [math]\phi[/math]. [math] t_o = y\left( \frac{\tan\phi}\beta + \frac{1}{\cos\phi} - 1\right) [/math] Expanding the equation for [math]t_o[/math] to second order, we get: [math] t_o = y\left(\frac\phi\beta + \frac{\phi^2}{2}\right) [/math] (Call this equation Q.) The minimum value of [math]t_o[/math] occurs at [math]\phi_{0}=-1/\beta[/math] (which defines the position of the black dot in the animation, the point B') and it is [math]{t_o}_{min} = -y/2\beta^2[/math]. To the observer, the object first appears at the position [math]\phi=-1/\beta[/math]. Then it appears to stretch and split, rapidly at first, and slowing down later. The quadratic equation Q above can be recast as: [math] 1+\frac{2\beta^2}{y}t_o = \left(1+\beta\phi\right)^2 [/math] which will be more useful later in the derivation. (Call this equation U.) The angular separation between the objects flying away from each otheris the difference between the roots of the quadratic equation Q: [math] \Phi \,=\, \phi_1-\phi_2 [/math] [math] \,=\, \frac{2}{\beta}\sqrt{1+\frac{2\beta^2}{y}t_o} [/math] [math] \,=\, \frac{2}{\beta}\left(1+\beta\phi\right) [/math] making use of the ``useful'' equation U above. Thus, we have the angular separation either in terms of the observer's time ([math]\Phi(t_o)[/math]) or the angular position of the object ([math]\Phi(\phi)[/math]) as illustrated in the next figure, which illustrates how the angular separation is expressed either in terms of the observer's time ([math]\Phi(t_o)[/math]) or the angular position of the object ([math]\Phi(\phi)[/math]). The rate at which the angular separation occurs is: [math] \frac{d\Phi}{dt_o} \,=\, \frac{2\beta}{y\sqrt{1+\frac{2\beta^2}{y}t_o}} [/math] [math] \,=\, \frac{2\beta}{y\left(1+\beta\phi\right)} [/math] Again, making use of the useful equation U. Defining the apparent age of the formation [math] t_{age} = t_o - {t_o}_{min}[/math] and knowing [math]{t_o}_{min} = -y/2\beta^2[/math], we can write: [math] \frac{d\Phi}{dt_o} \,=\, \frac{2\beta}{y\sqrt{1+\frac{2\beta^2}{y}t_o}}[/math] [math] \,=\, \frac{2\beta}{y\sqrt{1-\frac{t_o}{{t_o}_{min}}}}[/math] [math] \,=\, \sqrt{\frac{4\beta^2}{y^2}\,\times\,\frac{-{t_o}_{min}}{t_o-{t_o}_{min}}}[/math] [math] \,=\,\sqrt{\frac{2}{y\, t_{age}}} [/math] Note that in order to go from the angular rate to the speed (even the apparent speed), we need to estimate [math]y[/math], which is model-based. Now, can you tell me why the object doesn't appear at two places if [math]\beta < 1 [/math]?

Okay, I will start with an animation first to make it interesting. I will post the notations and algebra in the next post. In the figure below, we have a (purely hypothetical) superluminal object - the white circle flying across the animation at ten times the speed of light. As it flies by, it emits light. We consider the light rays (the red lines with small red circles at the end) coming towards the observer at the bottom-center of the animation. As we can see, the first ray of light that reaches the observer is emitted at a point close to the point of closest approach to the observer, indicated by a black dot that appears when the ray reaches him, say at time=[math]t_o[/math]. The rays emitted before this first ray reach the observer after [math]t_o[/math]. This reversal of the order in which the rays reach the observer gives rise to the perception of two objects moving away from the black dot. (If the object doesn't change during its flight, the two "phantom" objects are identical to each other.) Now, my question is, if we see two objects in a symmetric formation in the night sky, can we be sure that they are really two, and not our perception of one object in motion? Of course we can if we say that nothing can really travel faster than light. Assuming hypothetically that we didn't know about SR and its constraint on the speed, is there any way we could work out the "real" speed from our observation of the rate of angular separation? My feeling is that there are at least two configurations (one superluminal object going in one direction or two objects - superluminal or otherwise - going in opposite directions) which will result in the same observation.

Shall I post the equations for a hypothetical superluminal object with the understanding that it is essentially the same as the laser dot problem? I have those already worked out. The main difference between the two is that in the laser dot problem, we know the height of the ceiling. In the other problem, we have to guess the distance of the object. I also think I should start a new thread because this discussion is straying too far from the topic of this thread on -ve index left-handed materials. If it is okay with the moderators, can I start a thread on "Hypothetical Superluminal Objects"?

I sent you a private message about it because I thought my cv or publication list was of little interest to this forum.

Correct me if I'm wrong, but I thought a frame in free fall in a gravitational field is an inertial frame where SR applies. Of course, I understand that I have to account for the Sagnac effect, but there are no GR effects.

So if there was another earth on the other side of the sun, there wouldn't be any SR effects between our earth and the other one, right? Thanks.

A quick question: two satellites in the same orbit around a gravitational body - are they supposed to have zero relative velocity? What if they are at diametrically opposite points, so that one is traveling at a velocity v and the other at -v, where v is the orbital speed?

Attempts to disprove SR did not fail, they got much less press. Like the links to the two challenges I posted in this thread, which went unaswered. The usual response from the experts is that they have neither the time nor the inclination to figure out what the challenger's mistake is. But one of the challenges actually offered $50,000 to make it worth their time! Assuming this is not a rhetorical question -- by model independent I meant an experiment where extra corrections were not made to the measurements' date=' and where the undilated time duration was known accurately and independently. To recap the thread history, I was one of the first ones to point out to the original poster that SR was mathematically consistent. ie, if he accepted the coordinate transformation in SR, there was no way he was going to find an inconsistency with its predictions. The orginal poster got a little upset and complained of a religious attitute when it came to SR. I agreed with him and told him that there was a bit of religiousness in the way in which modern physics is taught, where criticism is not tolerated. This criticism (of the teaching methods of modern physics) landed me in all kinds of trouble. Paradoxically perhaps, the trouble I got in is proof enough to the impatience with which mainstream physics treats criticism. IMHO, physics will be better served when the experts are more inclined to periodically reexamine the basic assumptions and interpretations of its theories. Then again, it is only my opinion; experts should and will do what they damn well please, as one of them rightly pointed out. And finally, I don't think time dilation is a global hoax either. I do have some concerns about its origin, interpretation and magnitude. If you would like to know why, please take look at my article that I posted earlier.

I think what Einstein meant was that space and time were cognitive constructs, phenomenal or perceptual reality rather than the noumenal cause behind it. Would you happen to have the context in which AE said it so that what he meant is clear? If so, could you post it? If not, wonder why you didn't have a qualifier like "I think Einstein meant..." or "In my opinion..."

Likewise, blind faith is indicated when people accept whatever theory they are taught without ever examining the assumptions that go into making the theory. There was one poster, supporting SR using rather colorful language, who couldn't understand why pure SR time dilation is impossible to measure. Wonder why you wouldn't accuse him of lack of understanding -- because he supports your faith? (Apologies to the poster for this uncharitable use of his post.) Honestly, do we have to go down this road? I can happily accept and live with my ignorance. What does it matter that space contracts and time dilates when I can't even define what space and time are? Like someone far wiser than you and me pointed out, "Space and time are modes by which we think, not conditions in which we live."

Don't get upset about accusations of faith, swansont; after all this is a forum that routinely accuses people of ignorance and lack of education and whatnot if they dare to question the mainstream! Anyways, if you are really interested in the alternative, it is attached. It concentrates on two rather poorly understood astrophysical pheneomena, and finds a simple explanation for them outside the assumptions and consequences of SR. Admittedly, it doesn't analyze and explain every experimental support in a new framework, which is not something one can do while holding on to a day job to pay the bills. unreal-article.pdf

These are the other combinations of GR and SR I have seen so far: Around the world atomic clock (J.C. Hafele and R.E. Keating (1971)), where GR effect was about 150 ns and SR about 50. Sagnac was +/-150 ns depending on the direction of flight, giving a prediction of about 40+/-20 ns in one direction and about 300+/-20 in the other direction. The experimental verification was of the order of one sigma in both cases (which is not that impressive given the huge error in the first prediction where GR and Sagnac more or less cancelled off). TWTT flight tests (2003), where the GR effect was about -20ns and SR was about 5ns (both linearly increase from zero to the stated values as a function of the flight time). The Sagnac effect was a wavy function of time. Again, GR/SR is about 4 throughout the time range. Not really all possible combinations of gravitational and kinematic effects, but I do get your point. But don't you get the feeling that there should be bigger structure in which all the three effects can be neatly accommodated? Wouldn't you at least want to think along that line? If your answer is no, then that's what I mean by orthodoxy or religiousness in physics.