I can do better; I can make something move at *infinite* speed. Give me a yardstick and an axe. If I chop off the last third of the yardstick, then the center of the stick moves forward six inches in EXACTLY ZERO TIME.
Of course, a sane person might point out that neither the 18" mark or the 12" mark has moved, but a person looking for attention might insist that the center shifts from the 18" mark to the 12" mark in ZERO TIME, and that should count as motion!
Unless I've grossly misunderstood something, that's quite analogous to what these guys have done. Moreover, you *know* it has to be a trick, because all of their experiments are done with electromagnetic waves, which means Maxwell's equations have to hold, which means you've got Lorentz invariance built into the setup.
First, if I understand the paper correctly, all they're doing is getting the group velocity of a wave to move faster than c; the front velocity is still subluminal (as it must be). Therefore it *is* a trick, analogous to my trick with the yardstick.
As for why it *must* be a trick, these waves satisfy Maxwell's equations, which imply that the speed of light is bounded. Amid all the talk of "exceptions to special relativity", I haven't heard any talk of "exceptions to Maxwell's equations".
I think you may have your terms reversed, the front velocity of a wave front is associated with the phase velocity, which can easily be greater than c, while having a group velocity greater than c is done only in cases of anomalous dispersion.
The key to the Nimitz and Stalhofen setup is that they have a region 'd' where the wave undergoes quantum tunneling. It is not obvious that Maxwell's equations apply here, and it is well known that there are situations where the predictions of GR are different than the predictions of QM differ.
Maxwell's equations would imply that the wave takes a finite amount of time to cross the region 'd'.
Quantum mechanics imply that the tunneled wave appears across the distance 'd' instantaneously.
The paper claims that the time taken is zero.
My complaint with the paper is that they are so stingy with details that it isn't clear *exactly* what they are doing, and without that level of detail it is hard to know what is going on.
I could well have my terms reversed. What I tried to say was that they seem to be measuring the time between the arrival of successive maxima, and this is a pretty contrived definition. What you'd want to measure is the speed of the wavefront, and that (it seems to me) has to be governed by Maxwell's equations, so it can't exceed c.
The one and only thing I'm absolutely sure of here is that you understand this stuff far better than I do, so if you disagree with the above, I expect you're probably right.
Actually measuring the time between sucessive maxima is a pretty common thing to do, although in this setup I don't think it gives a useful answer. What they seem to be doing is measuring the difference in time between reception at two antennae, without giving the details of what they are measuring. They may be measuring the phase difference between two maxima, and as long the dispersion is low, that's a defensible thing to measure.
An additional problem is that a term such as "speed of the wavefront" isn't well defined, and there is endless confusion over if a phase or group velocity has been measured. There is no problem with phase velocities being greater than c, but things get hairy with group velocities greater than c, such as in areas of negative dispersion.
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branchandroot
no subject
Date: 2007-08-21 10:24 pm (UTC)no subject
Date: 2007-08-21 10:32 pm (UTC)no subject
Date: 2007-08-21 11:09 pm (UTC)speed. Give me a yardstick and an axe. If I chop off the
last third of the yardstick, then the center of the stick
moves forward six inches in EXACTLY ZERO TIME.
Of course, a sane person might point out that neither the
18" mark or the 12" mark has moved, but a person looking
for attention might insist that the center shifts from the
18" mark to the 12" mark in ZERO TIME, and that should
count as motion!
Unless I've grossly misunderstood something, that's quite
analogous to what these guys have done. Moreover, you
*know* it has to be a trick, because all of their
experiments are done with electromagnetic waves, which
means Maxwell's equations have to hold, which means you've
got Lorentz invariance built into the setup.
no subject
Date: 2007-08-21 11:59 pm (UTC)no subject
Date: 2007-08-22 12:05 am (UTC)no subject
Date: 2007-08-22 01:46 am (UTC)is getting the group velocity of a wave to move faster than c;
the front velocity is still subluminal (as it must be).
Therefore it *is* a trick, analogous to my trick with the
yardstick.
As for why it *must* be a trick, these waves satisfy Maxwell's
equations, which imply that the speed of light is bounded.
Amid all the talk of "exceptions to special relativity", I
haven't heard any talk of "exceptions to Maxwell's equations".
no subject
Date: 2007-08-22 02:03 pm (UTC)The key to the Nimitz and Stalhofen setup is that they have a region 'd' where the wave undergoes quantum tunneling. It is not obvious that Maxwell's equations apply here, and it is well known that there are situations where the predictions of GR are different than the predictions of QM differ.
Maxwell's equations would imply that the wave takes a finite amount of time to cross the region 'd'.
Quantum mechanics imply that the tunneled wave appears across the distance 'd' instantaneously.
The paper claims that the time taken is zero.
My complaint with the paper is that they are so stingy with details that it isn't clear *exactly* what they are doing, and without that level of detail it is hard to know what is going on.
no subject
Date: 2007-08-22 03:10 pm (UTC)to say was that they seem to be measuring the time
between the arrival of successive maxima, and this
is a pretty contrived definition. What you'd want to
measure is the speed of the wavefront, and that (it
seems to me) has to be governed by Maxwell's
equations, so it can't exceed c.
The one and only thing I'm absolutely sure of here is
that you understand this stuff far better than I do, so
if you disagree with the above, I expect you're probably
right.
no subject
Date: 2007-08-22 04:26 pm (UTC)An additional problem is that a term such as "speed of the wavefront" isn't well defined, and there is endless confusion over if a phase or group velocity has been measured. There is no problem with phase velocities being greater than c, but things get hairy with group velocities greater than c, such as in areas of negative dispersion.