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DStahl
2003-Jan-13, 01:07 AM
The Walker-Dual experiment; phase, group, and signal velocities; superluminal phase velocity and superluminal gravitational propagation have all cropped up in a couple different threads. I'd like to draw the discussion together under one heading, and invite Tim Thompson, Agora Basta, David Hall, JS Princeton, Wiley, and all the others who have engaged the topic to explore it some more here.

The story so far:

Tom Van Flandern contends that the 1997 Walker-Dual experiment is evidence for superluminal propagation of gravity. The W-D paper did demonstrate velocities for electrical and gravitational phase propagation in excess of the speed of light (references and links at the bottom of this post). This was predicted by Feynman's 1963 calculations, and does not contradict conventional theory. Walker and Dual also tentatively reported superluminal group electrical wave propagation, and wrote that this may violate causality. However, conventional explanations note that both phase and group velocity may exceed c without violating special relativity or causality--see the reference to Mathpages, provided by Wiley, below.

In 2000 William Walker wrote a paper describing superluminal electrical wave propagation in the near-field realm, ie one wavelength or less from a dipole emitter. He then proposed that magnetic and gravitational fields would behave similarly. Near the end of his paper he made some of the same claims as Van Flandern:

"Light from the sun is not observed to be collinear with the sun's gravitational force. Astronomical studies indicate that the earth's acceleration is toward the gravitational center of the sun even though it is moving around the sun, whereas light from the sun is observed to be aberated (sic). If the gravitational force between the sun and the earth were aberated then gravitational forces tangent to the earth's orbit would result, causing the earth to spiral away from the sun, due to conservation of angular momentum. Current astronomical observations estimate the phase speed of gravity to be greater than 2X10<sup>10</sup> c. Arguments against the superluminal interpretation have appeared in the literature [9, 10]." (emphasis added)

(The last sentence references a paper by Steve Carlip, and one by Ibison, Puthoff, and Little--see links below.)

And onward to new stuff...

I emailed Thomas Chen about the following enigmatic paragraph in the Walker-Dual paper, which seems to be the only place they challenge conventional physics:

"The analysis of the group speed of a longitudinally oscillating electrical field is currently inconclusive. The group speed is commonly thought to be equal to the speed of light, but preliminary analysis indicates that the group speed is much faster than light which is not thought possible due to causality violation."

Dr. Chen kindly replied as follows (quoted by permission):

"The sentence you ask me to comment on is correct in saying that the group speed is larger than the speed of light, if one takes the definition of group speed literally. But on the other hand, it is wrong by concluding a violation of causality."

"Please note that a superluminal group speed does not imply a superluminal transmission of information. The concept of group speed is artificial; by definition, it should not be applied to the 'near zone', but only in a spatial region where there is wave propagation in the usual sense. Otherwise, an artificial definition is being taken too seriously, and ad absurdum."

"My take on unravelling the logical structure of this seeming paradox is as follows."

"In the near zone, there is a superposition of a lot of outgoing and incoming waves, all propagating with speed of light. Due to these superpositions, it is not possible to observe an individual wave. If the source is modulated, it is in all real experiments done so with a frequency so small that the particles in motion (mass in GR, charges in electromagnetic radiation) exhibit a velocity much lower than the speed of light."

"Since the outgoing and incoming waves are all modulated by a low frequency signal, but propagate extremely fast, all one can measure is the average phase difference between a massive number of in- and outgoing waves. The averaged phase differences amount to the modulation signal of the source."

"Therefore, there is at this stage no clash with causality, because all waves in question do indeed travel with the speed of light."

"Now, the key question is whether the modulation signal travels faster than the speed of light. This is a little more tricky. The simplest modulation signal is a sine curve. One will see that the phase difference expected to be measured in a distance away from the source suggests superluminal propagation, as proposed by Walker and Dual."

"The quintessence of the problem, however, is that there is no way one can transmit information by single sine modulation. Any true information content must possess some decently complicated Fourier spectrum. We should thus in fact define 'information' as a signal with some decently elaborate Fourier spectrum."

"Hence, if we now assume a signal with some fairly sophisticated Fourier spectrum (think of a radio broadcast), the question becomes: Does that information travel superluminally in the near zone?"

"The answer is: It is never possible to tell."

"Why? It's because in order to decode the information, one must Fourier transform the measured signal. But in order to do that, one must require a certain amount of time, it's not possible to perform a Fourier transform by measuring a signal for only one moment."

"So, it is necessary to 'listen to the signal' for an extended time interval before one can determine its Fourier decomposition, and thus decipher the information it contains (the 'information' is the same as the Fourier spectrum of the modulation, and as I said above, a single spike in the spectrum doesn't count as information). How long does one have to listen? The time necessary for doing the Fourier transform is approximately the inverse of the 'typical
frequency' of the information signal."

"But this implies that it is not possible to measure how fast the signal propagated if one is closer to the source than a wavelength of the TYPICAL MODULATION FREQUENCY (not the wavelength corresponding to the speed of light!!!). However, the wavelength of the modulation frequency is much larger than the diameter of the near zone that corresponds to the speed of light. So in a distance of some wavelengths (corresponding to the modulation frequency) away from the source, one is already in the radiation zone with respect to the speed of light, and one will measure a propagation velocity of the signal in agreement with the speed of light."

"This is in fact a hidden form of a Heisenberg uncertainty principle: The more spectral content a transmitted signal contains, the longer one has to measure it for an accurate Fourier analysis, and the farther away from the source one must move in order to determine the propagation speed of the signal."

"The one single most important concept to emphasize in the discussion of the seeming paradox arising with the Walker-Dual experiment is the Heisenberg uncertainty principle: It is not possible to state at the same time that a signal has a certain frequency, and that it is located at a sharp position in space."

"In quantum mechanics, it's the exact same statement: There, the frequency corresponds to quantum mechanical momentum, and the ususal Heisenberg principle says that momentum and position can't be measured with infinite precision at the same time. In quantum mechanics, the precision limit is bounded by Planck's constant h. In Fourier analysis, it's 1 instead of h. Most people believe that Heisenberg's uncertainty principle is a special feature of quantum mechanics."

"It is actually a very deep insight that in all natural phenomena where some form of wave propagation occurs, there is a kind of a Heisenberg uncertainty principle. Something that is not widely known except among mathematicians working in the field (I am quite sure, not even among physicists), is the following fact: The Heisenberg uncertainty principle is NOT a mysterious physical law special to quantum mechanics, and discovered by Prof. Heisenberg, which is inexplicable and mysterious. This is in contrast to the Schrodinger equation, which is truly as miraculous as nature itself."

"The truth is: The uncertainty principle is a generally valid mathematical theorem in the theory of Fourier analysis (this mathematical field is called harmonic analysis, a deep and beautiful area with many surprises). It states that the product of the standard deviations of any pair of conjugate Fourier variables (i.e. wave vector and position vector, or energy and time, or frequency and time, etc) is bounded below by 1 (depending on the normalization with factors pi etc)."

"Whenever you are given a physical system described by Fourier theory, of which wave propagation is a prominent example, you will ALWAYS have an uncertainty principle. The catch is to find out how it must be formulated. In the case of information transmission versus causality, it's as explained above."

--------

Now THAT'S an explanation! (Incidentally, BA, Dr. Chen delved into the forum before giving his permission to quote, and was very complimentary about the discussion: "I have looked at the web forum, and have enjoyed the constructive and engaged discussion, I very much encourage it to continue.")

A technical discussion of some of the same issues, with math, is given by Mohammad Mojahedi and Kevin J. Malloy in "Superluminal But Causal Wave Propagation" linked below.

So, from all this I would say that not only is the Walker-Dual experiment fully explained in the framework of conventional physics--and should be removed from Van Flandern's list of experiments supporting superluminal gravity--but the later work of William Walker on superluminal near-field propagation is easily explained as well: "In the near zone, there is a superposition of a lot of outgoing and incoming waves, all propagating with speed of light. Due to these superpositions, it is not possible to observe an individual wave."

Van Flandern is mistaken in using Walker-Dual as support for superluminal gravitation.

References:

Mathpages: Phase, group, and signal velocity (http://www.mathpages.com/home/kmath210/kmath210.htm) and Lead-lag frequency response (http://www.mathpages.com/home/kmath249/kmath249.htm)

Short description of retarded field theory in electromagnetism, with animated applet, courtesy of Wolfgang Christian: http://webphysics.davidson.edu/Applets/Retard/Retard_FEL.html

"The Speed of Gravity: Repeal the Limit II" by Tom Van Flandern: Metaresearch org (http://www.metaresearch.org/cosmology/gravity/speed_limit.asp)

"Gravitational Forces with Strongly Localized Retardation" by William Walker, Jurg Dual, and Thomas Chen: abstract in html, (http://arxiv.org/abs/gr-qc/9610049) full paper in pdf (http://arxiv.org/pdf/gr-qc/9610049)

"Propagation Speed of Longitudinally Oscillating Gravitational and Electrical Fields" by William Walker and Jurg Dual: abstract in html, (http://arxiv.org/abs/gr-qc/9706082), full paper in pdf (http://arxiv.org/pdf/gr-qc/9706082)

"Experimental Evidence of Near-field Superluminally Propagating Electromagnetic Fields" by William D. Walker: abstract in html, (http://arxiv.org/abs/physics/0009023) full paper in pdf (http://arxiv.org/ftp/physics/papers/0009/0009023.pdf)

"Aberration and the Speed of Gravity" by Steve Carlip: abstract in html, (http://xxx.lanl.gov/abs/gr-qc/9909087) full paper in pdf (http://xxx.lanl.gov/PS_cache/gr-qc/pdf/9909/9909087.pdf)

"The Speed of Gravity Revisited" by Ibison, Puthoff, and Little: abstract in html, (http://arxiv.org/abs/physics/9910050) full paper in pdf (http://arxiv.org/ftp/physics/papers/9910/9910050.pdf)

"Superluminal but Causal Wave Propagation" by Mohammad Mojahedi and Kevin J. Malloy: full paper in pdf (http://www.grc.nasa.gov/WWW/bpp/pdf/Mojahedi-JPC.pdf)

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JS Princeton
2003-Jan-13, 08:29 AM
Good recap, DS. I would say that Chen basically gives an excellent discussion of the issue. I would say, however, that the data from the last experiment involving gravitational waves due to Jupiter basically nail the lid on the coffin of infinite speed of light for me.

2003-Jan-13, 01:42 PM
there once was and old dud'
who listebed for a thud
from Jupiter afar, close to a star
but his beat was incomplete
so he settled for a stain on a sheat

AgoraBasta
2003-Jan-13, 06:40 PM
DStahl,

While Chen definitely states a lot of correct and straightforward info, he's hardly comprehensive enough on the general point since modulation is not at all necessary for signal transmission. One may simply stress the transmitter with a short "delta pulse" and record signal delay from the receiver, no time-consuming encoding is necessary; furthermore, since we need no more than one single bit to measure the transmission speed, his mention of delta-f/baud-rate issue can't apply. The original W/D scheme didn't provide for such a single-bit operation mode, while a simple mod can do that. Cheers!

<font size=-1>[ This Message was edited by: AgoraBasta on 2003-01-13 17:21 ]</font>

AgoraBasta
2003-Jan-13, 06:56 PM
On 2003-01-13 03:29, JS Princeton wrote:
I would say, however, that the data from the last experiment involving gravitational waves due to Jupiter basically nail the lid on the coffin of infinite speed of light for me.For me, it so far appears more like a first nail in the lid of the coffin of Kopeikin's reputation...
But we shall see...

cable
2003-Jan-13, 07:29 PM
why should it be modulated ??
an EM wave may act remotely on an antennae, even if it's a non modulated CW.
we can detect the presence/absence of a pure CW.

DStahl
2003-Jan-13, 10:51 PM
Phase and group waves contain no information that is not dependent on their component luminal waves: they cannot transmit information faster than light. That's one of the points made by Chen. However, Van Flandern contends that the propagation of gravity does indeed transfer information faster than light: it "tells" the vector of interaction where and how to interact. This is what Van Flandern means when he defines the speed of gravity: "The 'speed of gravity' refers to whatever causally links the source of gravity to the 3-space acceleration of a target body." (emphasis added) This plain-language definition of an information-carrying wave was given a name by Sommerfield and Brillouin: the "front" wave, as detailed in "Superluminal but Causal Wave Propagation" by Mojahedi and Malloy. The authors explain the mathematical description of the front wave, and demonstrate that:

"...under no circumstances the so called 'front velocity' may exceed the speed of light in a vacuum, and in fact under all circumstances the 'front velocity' is exactly luminal. In other words, the requirement of Einstein causality that no 'signal' (information) can be transmitted superluminally is satisfied in all cases, since the 'front velocity' is always luminal. This means that the presence of the genuine information should not be associated with the pulse maximum, half maximum, or the envelope, but indeed is contained within the singularities (points of non-analyticity) of the pulse."

"The mathematical proof that no signal (information) may be detected sooner than t<sub>0</sub> = x/c can be seen via contour integration of an expression such as Eq. (8)..."

I won't try to type in the relevant equation in html, because that would make my eyes bleed--you'll have to look at the Mojahedi-Malloy paper. But the point is, Van Flandern is confused: he's claiming that experiments such as Walker-Dual and the later Walker paper, both of which deal explicitly with phase and group velocities, show something of import about front velocity as defined by Sommerfield-Brillouin and presented by Mojahedi-Malloy.

It's a bait-and-switch: the experiments Van Flandern cites are not relevant to the physical quantity Van Flandern is dealing with.

cable, I would think that for an unmodulated signal 1.) there would be no phase velocity, and possibly no group velocity, definable; and 2.) the information carried by the wave would be defined only by the non-analytic signular points where the field transmitter "turns on" and when it "turns off"--and so a receiver must wait until the entire signal has been transmitted before knowing the full "information" content of the field. (In this case I suppose that would be a simple sum of the constant field vector over the elapsed time, since there is no other information carried.)

But all EM waves are modulated, strictly speaking, even if one proposes a theoretically monochromatic transmission--ie simple sine waves. After all, the definition of an electromagnetic wave is a field that varies over time, eh? And since Walker-Dual explicitly used oscillating fields they were explictly using modulated waves.

That's what Chen was getting at, I think, when he said that "...there is no way one can transmit information by single sine modulation. Any true information content must possess some decently complicated Fourier spectrum. We should thus in fact define 'information' as a signal with some decently elaborate Fourier spectrum."

Such a signal may well produce superluminal phase or group velocities, but as Mojahedi and Malloy point out, that violates neither special relativity nor causality. Van Flandern's superluminal gravity, on the other hand, does violate special relativity, as he himself admits.



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Wiley
2003-Jan-13, 10:56 PM
DStahl,

Thanks for the post and for emailing Dr. Chen. Very enlightening reply.



DStahl wrote:
Van Flandern is mistaken in using Walker-Dual as support for superluminal gravitation.


I certainly agree with that.

Wiley
2003-Jan-13, 11:02 PM
On 2003-01-13 14:29, cable wrote:
why should it be modulated ??
an EM wave may act remotely on an antennae, even if it's a non modulated CW.
we can detect the presence/absence of a pure CW.



Some sort of modulation scheme is required to transfer information. If I understand your example correctly, you're suggesting switching from CW to say CCW polarizations. This is modulation. This would be an example of "spatial" modulation as opposed to "temporal" modulation we are familiar with from AM and FM radio.


<font size=-1>[ This Message was edited by: Wiley on 2003-01-13 18:02 ]</font>

Wiley
2003-Jan-13, 11:04 PM
On 2003-01-13 13:40, AgoraBasta wrote:
One may simply stress the transmitter with a short "delta pulse" and record signal delay from the receiver, no time-consuming encoding is necessary; furthermore, since we need no more than one single bit to measure the transmission speed, his mention of delta-f/baud-rate issue can't apply. The original W/D scheme didn't provide for such a single-bit operation mode, while a simple mod can do that. Cheers!



Can you explain this in more detail? Because it sounds like modulation to me.

DStahl
2003-Jan-13, 11:06 PM
The pleasure is mine, Wiley. We live in a wonderful time--Ben Franklin would have had to wait a month or more to ask a question and get a reply from Voltaire; I can ask questions of physicists in New York, Stockholm, and Geneva and hope for a reply in hours. And when I get something like the message from Dr. Chen, which explains a link between Heisenburg uncertainty and Fourier analysis...well, it's just spectacular. The pleasure is INDEED mine!

<font size=-1>[ This Message was edited by: DStahl on 2003-01-14 04:19 ]</font>

AgoraBasta
2003-Jan-13, 11:45 PM
On 2003-01-13 18:04, Wiley wrote:
Can you explain this in more detail? Because it sounds like modulation to me.Sure this can be treated as modulation if you wish to consider the Fourier-image of delta-pulse or of any high slew rate front fed into transmitter. But why should one wish that?

What I say is - induce as abrupt a jerk as possible in the transmitter dipole, then read out the time delay till when receiver dipole reacts. This may be done in my scheme, but not in original W/D.

Tim Thompson
2003-Jan-16, 12:16 AM
DStahl: I'd like to draw the discussion together under one heading, and invite Tim Thompson, Agora Basta, David Hall, JS Princeton, Wiley, and all the others who have engaged the topic to explore it some more here.

I didn't want y'all to feel ignored, but it seems I have little to offer in addition. I do remember deriving Heisenberg's uncertainty principle in a general form, though not in the manner alluded to by Chen. So I poked around and found the proof in the mathpages collection ("Fourier Transforms and Uncertainty (http://www.mathpages.com/home/kmath488/kmath488.htm)"). This proves the theorem Chen mentioned, as well as providing the connection to Heisenberg's uncertainty. I was unaware of this until Chen mentioned it, very spiffy.

cable: we can detect the presence/absence of a pure CW

I too have pondered this notion, but two things come to mind. First, a pure CW signal does not constitute information in the sense that Chen is talking about. The Fourier transform (http://aurora.phys.utk.edu/~forrest/papers/fourier/) of a pure CW is a delta function (http://mathworld.wolfram.com/DeltaFunction.html), which only conveys the "information" you already mentioned, that the CW exists.

Second, and perhaps most interesting, is that all real CW signals have to turn on. You can postulate in a mathematical model, the instantaneous transition from nothing to CW. But in the real world, that can't happen. Any real transmitter will ring as it sets up the CW signal, and that ringing constitutes the kind of modulation that Chen is talking about.

This also leads to AgoraBasta's suggestion, "as abrupt a jerk as possible". Even the most abrupt of jerks will be accompanied by ringing fore & aft, which constitutes the modulation Chen describes.

Is Walker-Dual unexplained? I should think not. The results seem to be in line with theoretical expectations. The real problem is that most people don't properly understand what the theoretical expectations are.

Is gravity superluminal? It does not appear to be so over any meaningful measure of distance. I like Carlip's explanation ("Aberration and the Speed of Gravity (http://xxx.lanl.gov/abs/gr-qc/9909087)", Physics Letters A 267: 81-87, March 13, 2000), and note (as does Carlip) that there are astronomical observations relevant to the near-field speed of gravity in binary pulsar timing, which shows that the speed of gravity even there is within a few percent of the speed of light.

I see nothing here that challenges standard physics, though the topic is quite interesting nonetheless.

DStahl
2003-Jan-16, 02:46 AM
Thanks, Tim. I just heard from Jurg Dual; since Walker left the Institute in Geneva Dual has not pursued the vibrating-systems work further.

I'm reading through the Ibison, Puthoff, and Little paper in hopes of posting a summary of their refutation of Van Flandern's reasoning on the visible-eclipse-versus-gravitational-conjunction observations. Discussions like this serve me well as they spur me to pursue my self-education...I have a genuinely selfish motive! More soon.

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AgoraBasta
2003-Jan-16, 09:35 AM
On 2003-01-15 19:16, Tim Thompson wrote:
This also leads to AgoraBasta's suggestion, "as abrupt a jerk as possible". Even the most abrupt of jerks will be accompanied by ringing fore & aft, which constitutes the modulation Chen describes.Who cares of ringing if the very start of any response constitutes the bit we need as info? Sure we need elaborate technique to discern that event, but that's almost entirely a technological issue.

BTW, Tim, I still await you comment on this related matter (http://www.badastronomy.com/phpBB/viewtopic.php?mode=viewtopic&topic=3430&forum=1&start=45) in the other topic.

2003-Jan-16, 10:55 AM
<a name="3-1-16"> page=3-1-16 aka "OH YUCK?"
TODAY IS THURSDAY? hurray hurray
and on this day.. far away
in CH59 i will say
to my mini corder just Cm's away
Hay mini? Gravity Waves
& students behave.. in very predictable ways
include in my note, Telekinisis, & teleVision,
just to bar .. any indisision.. or REM revision
yeah? 3:01 A.M. January 16, 2003 {so 3am will be poetry HR }(BWUW)

Fruh-Batz
2003-Jan-16, 12:53 PM
Hey HUb', you got some more of this stuff?

It's great /phpBB/images/smiles/icon_smile.gif

Yul
2003-Jan-16, 07:07 PM
The latest from TVF

http://www.metaresearch.org/media%20and%20links/press/SOG-Kopeikin.asp

DStahl
2003-Jan-16, 10:11 PM
Van Flandern: "... the physical quantity heretofore called 'the speed of gravity', which has already been proved by six experiments to propagate much faster than light, perhaps billions of times faster."

"In 1825, Laplace determined that the minimum speed of gravity consistent with observations was at least 10 million times the speed of light, c."

The full equations describing retarded fields were not known in 1825, so Laplace could not have used them to correctly find the propagation speed of gravity. The retarded-field equations were formalized very late in the 19<sup>th</sup> century, I think, and in the first quarter of the 20<sup>th</sup> century it was shown that they stem from the conservation laws and the symmetry required by Noether's Theorem. When TVF uses this calculation by Laplace it is exactly like relying on Newton's calculations for the precession of the orbit of Mercury: an anachronism long superseded both in theory and in observation.

TVF: "A 1997 laboratory experiment by Walker & Dual showed that gravitational signals propagated much faster than light signals."

We've disposed of that one.

The remaining point--the difference between the aberration of sunlight and the vector of gravitational attraction--has been explained nicely in the framework of lightspeed gravitational propagation by Ibisen, Puthoff, and Little.

Really, Clifford Will's challenge to Kopeikin et al is much more substantial. I don't understand how Van Flandern can use something like the Laplace calculation or the Walker-Dual experiment and keep a straight face. Maybe his proposal is really an elaborate satire?