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microwaves and ftl transmission

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fenc...@aol.com

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Dec 11, 1996, 3:00:00 AM12/11/96
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Please help! Early last week while traveling in my car I caught the last
part of the Canadian news program "As It Happens" in which someone was
claiming to have sent a "modulated microwave carrier wave" at approx 4.7
times the speed of light. I did not get a name or an institution involved
with this work. What is this about and how is it possible? I would
appreciate an e-mail to fenc...@aol.com as well as a post.

Korac

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Dec 12, 1996, 3:00:00 AM12/12/96
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It probably is of the same source as some papers I saw from a
microwave journal that some guys claimed to be able to use phase velocity
to transmit pulses. It looked dubious at best, since no error margins in
their equipment and data analysis was given. It all hinged on detecting
a pulse a fraction of a nanosecond before it should have been detectable.
Such high speed risetime detection is tricky. I hope somebody does
discover a way to modulate something faster than light, but since
microwaves ARE light, I don't think this is it. Hope for tachyons and
"subspace" things.

*******************************************************
"Those that give up essential liberty for a little
security, deserve neither liberty nor security."
- B.Franklin

"When ID's are mandatory, its time to leave the planet."
- Lazarus Long
(a.k.a. R. Heinlein)
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Kimberly J Allen

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Dec 12, 1996, 3:00:00 AM12/12/96
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Probably the velocity of the carrier wave (4.7 c) was the *phase* velocity.
Phase velocity = omega/k.
Group velocity = d(omega)/dk

The phase velocity can (and in many cases, does) exceed the speed of light.
Because it carries no information, it doesn't violate causality. The group
velocity carries the wave's information, and must be less than c.

Kim Allen

Emory Bunn (a.k.a. Ted)

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Dec 12, 1996, 3:00:00 AM12/12/96
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In article <58pi3n$d...@agate.berkeley.edu>,

Kimberly J Allen <kal...@oceanside.ucsd.edu> wrote:
>The phase velocity can (and in many cases, does) exceed the speed of light.
>Because it carries no information, it doesn't violate causality. The group
>velocity carries the wave's information, and must be less than c.

There are actually some circumstances under which the group velocity
exceeds c, but it turns out that even under those circumstances there
is no actual information being transmitted superluminally.

For more information, you could look at

http://physics1.berkeley.edu/research/chiao/research.html

which describes research done on this and other subjects at Raymond
Chiao's lab in Berkeley. (A former member of the Chiao group,
Aephraim Steinberg, used to be a regular presence in the physics
newsgroups. If he's still lurking, maybe he'll be inspired to tell us
the story.)

-Ted

Doug Natelson

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Dec 12, 1996, 3:00:00 AM12/12/96
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kal...@oceanside.ucsd.edu (Kimberly J Allen) writes:

>
>Probably the velocity of the carrier wave (4.7 c) was the *phase* velocity.
>Phase velocity = omega/k.
>Group velocity = d(omega)/dk
>

>The phase velocity can (and in many cases, does) exceed the speed of light.
>Because it carries no information, it doesn't violate causality. The group
>velocity carries the wave's information, and must be less than c.
>

>Kim Allen

Watch out; that's not strictly true. See, for example,
Chiao, R.Y. "Superluminal (but causal) propagation of wavepackets
in transparent media with inverted atomic populations." Phys Rev A
_48_ B34 (1993).

The abstract:

The propagation of limited-bandwidth signals, such as Gaussian wave
packets, tuned to a transparent spectral region far below the resonance of
an inverted two-level atomic medium, can be superluminal, i.e., with phase,
group, and energy velocities all exceeding the vacuum speed of light c.
Causality is not violated, however. Little distortion and gain can accompany
this propagation.

____

According to this paper and its brethren, there are several different
'velocities':

phase velocity -- speed of crests of infinite plane waves
group velocity -- speed of center of bandwidth-limited wavepacket
energy velocity -- speed at which energy stored in some wavepacket
propagates (can be weird in inverted media, where
the wave can 'borrow' energy from the medium
front velocity -- speed at which a rising edge of a step function
would travel if formed as a wavepacket (requires
arbitrarily high frequencies)

I'm probably leaving out some, too, since I'm not remotely an expert
in the field. It would seem that the front velocity is what really
determines information transfer.

Doug Natelson
nate...@embezzle.stanford.edu

Yehuda Naveh

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Dec 13, 1996, 3:00:00 AM12/13/96
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On 12 Dec 1996, Doug Natelson wrote:

> The arguments are really interesting, and the answer is that yes,
> it is possible for the center of a wavepacket to traverse a tunneling
> barrier at effectively greater than c.

The crucial point is that a tunnel barrier is always dispersive - it's
biased towards UV. Therefore, the center of the wavepacket does not have much
meaning, at least not in terms of group velocity. The dispersiveness is also
true for photonic tunneling (the equations are the same). So I don't see how
a symphony would remain the same symphony after crossing the barrier.

The issue of tunneling time (how long is the particle in the barrier) is
really controversial, mainly, I think, because there is no agreement on
definitions. There are a few other ways to think of the tunneling time,
not only in terms of wavepackets.

You might want to look at:
R. Landauer and T. Martin, Rev. Mod. Phys. 66, 217
(1994). "Barrier interaction time in tunneling".

-Y


Doug Natelson

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Dec 13, 1996, 3:00:00 AM12/13/96
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Yehuda Naveh <yeh...@hana.physics.sunysb.edu> writes:

>On 12 Dec 1996, Doug Natelson wrote:
>
>> The arguments are really interesting, and the answer is that yes,
>> it is possible for the center of a wavepacket to traverse a tunneling
>> barrier at effectively greater than c.
>
>The crucial point is that a tunnel barrier is always dispersive - it's
>biased towards UV. Therefore, the center of the wavepacket does not have much
>meaning, at least not in terms of group velocity. The dispersiveness is also
>true for photonic tunneling (the equations are the same). So I don't see how
>a symphony would remain the same symphony after crossing the barrier.

This is a very good point, which Steinberg et al. make very carefully:
There's some initial uncertainty in the starting point of each particle
one sends through (if you want to think of it that way), and the fast
particles have a better chance of making it, since tunneling is more
probable for more energetic particles.

You're also right to point out that there are multiple ways to define
'tunneling time'. One could imagine a particle with spin tunneling, and
applying an infinitesmal magnetic field in the barrier region, and
looking at how much the spin had precessed in the particles far to the
right of the barrier, for example.

Getting back to dispersion, though: things get even muddier if one
considers tunneling of photons through a population-inverted medium.
In that case, the wavepacket can 'borrow' energy from the medium
along the way, and the final wavepacket can be as large as the incident
one and of the same width, but with a peak that has advanced more
rapidly than c. Again, the claim is that causality is still not a
problem -- see Chiao et al., "Tachyon-like excitations in inverted
two-level media", Phys Rev Lett _77_ 1254 (1996).

Would someone who understands the causality proofs care to post an
explanation of them? I'm not sure I'd do a decent job.

Doug Natelson

john baez

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Dec 15, 1996, 3:00:00 AM12/15/96
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In article <58pm1m$d...@nntp.Stanford.EDU>,

Doug Natelson <nate...@embezzle.stanford.edu> wrote:
> kal...@oceanside.ucsd.edu (Kimberly J Allen) writes:

>>The group velocity carries the wave's information, and must be less than c.

>Watch out; that's not strictly true.

I.e., it's false. It is, however, a widespread misapprehension spread
by bad textbooks. The phase velocity exceeds c more commonly than
the group velocity, but the group velocity also exceeds c in some media.
Indeed, why shouldn't it? It's merely defined as d omega/dk, where your
medium can have waves in it like

exp(i(omega t - kx))

One can cook up media with "anomalous dispersion" for certain values
of k - i.e., media where omega is a function of k that makes d omega/dk > c
for some values of k. This actually led to a bunch of objections to
the theory of special relativity back around 1910. But as Sommerfeld,
Brillouin and others pointed out, you still can't communicate faster than
c!

If you were trying to communicate faster than the speed of light,
you'd need to get a "propagation velocity" greater than c. This is
also called the "signal velocity", and it's basically the same as what
Natelson is calling the "front velocity":

> front velocity -- speed at which a rising edge of a step function
> would travel if formed as a wavepacket (requires
> arbitrarily high frequencies)

though it's more precise if you don't require that the wave be
a *step* function. Just take any wave that's nonzero inside a given
region and zero outside. (If it's shaped like a step function at first,
it won't usually stay a step function, because dispersion will smear it
out.) The idea is that the region where the wave is nonzero can't
grow in size faster than propagation velocity. The propagation velocity
is defined as the smallest velocity for which that's true.

The postulate of causality in relativity is that the propagation velocity of
ANYTHING - sound, electromagnetism, the strong force, the weak force,
gravity - is less than or equal to c.

The classic introduction to these concepts is:

Brillouin, Leon, 1889-
Wave propagation and group velocity. New York, Academic Press, 1960.
Series title: Pure and applied physics; vol. 8.

It has lots of nice pictures of actual experiments.

Another good introduction is Chapter 22 of Sommerfeld's textbook
on optics, the chapter entitled "Phase velocity, signal velocity,
group velocity".

Sommerfeld, Arnold, 1868-1951.
Optics. Translated by Otto Laporte and Peter A. Moldauer.
New York: Academic Press, c1964.
Series title: Sommerfeld, Arnold, 1868-1951 Lectures on theoretical
physics; vol. 4.

By the way, if anyone wants to really learn physics thoroughly, they should
read Sommerfeld's books. This guy was in many ways the "conscience" of
physics when quantum mechanics was being developed. Apparently whenever
someone like Bohr or Heisenberg got sloppy and screwed up, Sommerfeld would
correct them. So his books are a good place to get the straight dope.
Also, they are delightful to read. In his book on optics he explains
why oil slicks on puddles of water look iridescent, why paper is white,
and even the difficult problem of what boundary conditions for Maxwell's
equation are needed to describe something that's "black". Learn physics
from the man who taught the greats!


steve

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Dec 18, 1996, 3:00:00 AM12/18/96
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On 11 Dec 1996 04:19:13 GMT, fenc...@aol.com wrote:

>Please help! Early last week while traveling in my car I caught the last
>part of the Canadian news program "As It Happens" in which someone was
>claiming to have sent a "modulated microwave carrier wave" at approx 4.7
>times the speed of light. I did not get a name or an institution involved
>with this work. What is this about and how is it possible? I would
>appreciate an e-mail to fenc...@aol.com as well as a post.

Check out the UK BBC TV web site. Last week there Horizon programme
covered the posibility of time travel and interviewed the guys who
have made this claim and played their mozart tape. You can download
the transcript of the programme and i suspect it has all the
references.

john

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