From: Ross A. Finlayson (raf@tiki-lounge.com)
Date: Thu Jul 20 2000 - 16:44:24 MDT
hal@finney.org wrote:
> Scerir writes:
> > http://arxiv.org/abs/quant-ph/9810031
>
> This is a very helpful paper and provides a good background for
> understanding the Nature paper, which I think is quite misleading.
>
> It is curious that the Nature paper consistently uses the term
> "superluminal", when their data shows the far more dramatic effect of
> a *negative* velocity. A negative velocity is one where the output
> comes out before the input went in. It can be considered not just
> faster than light, but faster than infinity.
>
One way to look at this (it might not be the correct way) symbolically is that
the order type Ord (the proper class of all finite and infinite integers) is
not less than anything, or to permute the words, less than nothing. The
integers are still an ordered set, so in that interpretation one is negative
"Ord", and Ord negative one.
This is addressed by what is called the Burali-Forti paradox. Burali-Forti
says that the order type of Ord would have to be greater than Ord, yet as Ord
(the symbolic name) contains all these numbers, that the order type of Ord
would have to be in Ord.
So, perhaps it is not paradoxical. My opinion of paradoxes is that none exist
and that their qualification shows either logical inconsistency or
misapplication of terms.
>
> For example, they say, "this means that a light pulse propagating through
> the atomic vapour cell appears at the exit side so much earlier than if it
> had propagated the same distance in a vacuum that the peak of the pulse
> appears to leave the cell before entering it." The comparison here to
> vacuum propagation is meaningless. The peak of the pulse *does* appear
> to leave the cell before entering it - not just when compared to c, but
> independent of any velocity comparisons. Over and over we see the paper
> couching results in terms of comparisons to the speed of light, when in
> fact they are dealing with results that appear to propagate into the past.
>
> I think the authors are trying to present their results in this way
> in order to make them seem less dramatic, and thereby to make their
> explanation seem more plausible. They claim that this result is simply
> due to classical effects of interference between frequencies. They also
> claim (and here they are really wrong) that the shape of the pulse is
> preserved.
>
> In fact, as the quant-ph paper referenced above makes clear, the shape
> of the pulse is not and cannot be preserved. This becomes especially
> obvious if we consider a larger version of the experiment. Instead of
> 6 cm of gas, let's suppose we could build a chamber 6 meters long.
> Now the negative velocity region will be 100 times larger, giving the
> pulse a 6 us advance rather than 60 ns. That's the same as the width
> of the pulse itself!
>
> The question then immediately arises, if this would really work (as
> the Nature paper seems to imply), what would happen if you built a
> feedback system which upon receiving the time-advanced pulse, cut off
> the transmission of the original pulse, which hasn't even started yet?
>
> The quant-ph paper analyzes essentially this scenario, and unsurprisingly
> it shows that nothing bad happens. In fact, the output pulse does
> *not* depend on the shape of the input pulse. Rather, it is in effect
> *extrapolating* the pulse shape based on the amount of input it has seen
> so far. If you try to do the feedback, the change in the input pulse
> causes the output pulse to go into a damped oscillation.
>
> Furthermore, the front of the output pulse cannot be superluminally
> advanced over the front of the input pulse (the Nature paper does mention
> this at the very end, but they don't explain that it contradicts their
> earlier explanation of what is happening). This is not very apparent in
> the present data, where the acceleration is only about 1% of pulse width,
> but if we scale the experiment up, it will become glaringly obvious.
> With the 100 fold expanded version of the experiment, there is no way to
> have a reasonably shaped pulse which is 6 us advanced over the source, but
> which also has its front not advanced at all over the source. What you
> will get is a completely misshapen pulse, probably with a rapid rise,
> or perhaps some of the nonlinear ringing behavior shown in the quant-ph
> paper Scerir references above.
>
> To sum up, in the Nature experiment, the pulse shape can and does
> change because the front cannot be advanced. This doesn't show up very
> much on their current data but would become obvious if the experiment
> were scaled up. The explanation in terms of classical interference
> is misleading as it implies that scaling up the experiment would lead
> to further advanced pulses, which it would not; it would just lead to
> misshapen pulses. The quant-ph paper offers a much more coherent and
> lucid explanation of what is going on.
>
> Hal
About the rest of this, I can not claim to understand.
Relativity and the mass/energy/lightspeed equivalence relation appears to be
largely correct, I can't claim to have gathered empirical data, fromw hat I
understand the most obvious proof of that is redshift.
There is much current application of Cartan's, Dirac's, Pauli's, Majorana's,
et. alia's, mathematical explanation of many of these things, of which I can
say little.
In my opinion, physical laws are the same throughout the entirety of the
universe, there are just some of which we aren't aware.
Ross
-- Ross Andrew Finlayson Finlayson Consulting Ross at Tiki-Lounge: http://www.tiki-lounge.com/~raf/
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