Sci-fi Alcubierre Drive and exotic matter/Casimir Effect
Becca Heisler
limits of general relativity. I am VERY new to this field of physics
and physics in general, so I have some questions:
1)Is the Alcubierre/Broeck Drive feasible in terms of physics?
2)What is exotic matter (matter with a negative mass?), and why is it
needed for this drive?
3)If the Casimir Effect produced great enough quantities of exotic
matter, would it be used to produce heat energy able to do work, a
pressure to propel something like a very high-tech piston, or a direct
distortion of spacetime around the ship itself?
4)Assuming that the theory works, and that the Casimir Effect could
generate sufficient quantities of exotic matter (after about a
thousand years of R&D), what is a good ship design that incorporates
the Alcubierre/Broeck drive?
5)Are there alternative theories for obtaining exotic matter, such as
mining it around a black hole?
Chris Hillman
On Wed, 5 Jun 2002, Becca Heisler wrote:
> I am a science fiction writer looking for a warp drive within the
> limits of general relativity.
You will be be disappointed, then! No such thing is known, and currently
this circumstance appears unlikely change. Indeed, even if gtr is wrong
(as in some sense it must be, because it is not a quantum theory--
however, many believe it almost surely must be the preferred classical
field theory limit of any viable quantum theory of gravity which may
happen along later in the new century), there are various arguments
suggesting that warp bubbles are physically impossible. These arguments
are not completely compelling (at the level of say "perpetual motion is
impossible"), as far as I can see, but they are much more compelling than
the rather weak suggestions that warp bubbles -might- exist, which have
been long on speculative flights of the imagination, but very lacking in
specific physical mechanisms.
> I am VERY new to this field of physics and physics in general, so I
> have some questions: 1)Is the Alcubierre/Broeck Drive
First of all, it is essential to understand that the Alcubierre warp
bubble spacetime (1994)
http://xxx.lanl.gov/abs/gr-qc/0009013
and the closely related Van Den Broeck warp bubble spacetime (1999)
http://xxx.lanl.gov/abs/gr-qc/9905084
are Lorentzian manifolds, but they are -not- in any reasonable sense
"solutions" to the Einstein field equation (EFE), although in the popular
press they have been described as such. IOW, despite what you may have
read, warp bubles are -not- repeat -not- in any sense "a prediction of
gtr"! Or even "compatible with gtr" as most physicists understand that
term!
To understand this, you need to know that the EFE, the field equation of
gtr, relates two "quantities", like this:
G_(ab) = 8 Pi T_(ab)
Mathematically speaking, both quantities are "second rank symmetric tensor
fields" defined on a Lorentzian manifold ("spacetime"), which is a "smooth
four-manifold" M equipped with a (Lorentzian) "metric tesnor" g_(ab), but
they nonetheless have profoundly different natures (which is of course
exactly why the EFE is "interesting"):
1. The Einstein curvature tensor G_(ab) at the left hand side (LHS) is
completely determined by the Riemann curvature tensor R_(abcd), i.e. by
"the curvature of spacetime" (but not conversely), -completely
independently- of any physical interpretation of any kind, much less a
particular theory of gravitation. Let me restate this for emphasis: the
tensor field g_(ab) which is part of the purely mathematical definition of
our Lorenzian manifold (M,g), determines the Riemann curvature tensor
R_(abcd), and a kind of "averaging" then produces G_(ab) from R_(abcd).
No physics is anywhere in sight on the LHS of the EFE!
2. The stress-momentum-energy tensor T_(ab) on the right hand side (RHS)
-does- have a direct physical interpretation in gtr. Basically,
(a) a "perfect fluid" gives a very particular type of contribution to
T_(ab), which is determined by a theory of perfect fluids (which is
independent of gtr, but can be fixed up to work on curved spacetimes),
(b) an electromagnetic field gives another very particular (quite
different) type of contribution to T_(ab), according to a prescription
which was determined by Maxwell as part of his theory of EM (again
independent of gtr, but later fixed up to work on curved spacetimes),
and so forth--- at least in principle. Since gtr is a classical field
theory rather than a quantum field theory, there aren't too many
"realistic" classical field theories to throw into the mix along with
various idealized types of "matter" which might be present in some region
of spacetime! Be this as it may, the point is that you add up all the
T_(ab) terms coming from all the various types of matter and
nongravitational fields which are present, and put that on the RHS of the
EFE.
Now, a common student error is to think that you can turn this around,
that you can start with any old Lorentzian spacetime, compute the tensor
G_(ab), then divide by 8 Pi and call the result "T_(ab)". Of course, -if-
you could always interpret this alleged "T_(ab)" as a
stress-momentum-energy tensor, gtr would be entirely -vacuous-! This is
because this would mean that -any- Lorentzian manifold is a "solution" to
the EFE! Needless to say, in mathematical physics, equations for which
-anything- is a "solution" are completely useless!
Of course, the point is that requiring that T_(ab) arise "in the usual
way" from matter or nongravitational fields such as an EM field places
-very stringent conditions- upon the our Lorentzian manifold (M,g)
together with any additional vector and tensor fields which might be
defined on M in order to represent the distribution of matter and of any
nongravitational fields. In fact, solving the EFE is not only not
trivial, but it is quite challenging!
Actually, it's even harder than I've yet indicated. To see why, suppose
we are seeking a solution where the only nongravitational field is an EM
field, and no "matter" is present. Such a solution is called an
"electrovacuum solution" or "Einstein-Maxwell" solution. To find one, you
not only need to find a Lorentzian manifold (M,g) and an EM field F_(ab)
which satisfies the "curved space Maxwell field equation", but when you
compute T_(ab) according to the prescription of Maxwell, and compare with
the G_(ab) computed purely mathematically from the R_(abcd) computed from
the metric tensor g_(ab), then T_(ab) and G_(ab) must satisfy the EFE.
So anything more complicated than a vacuum solution (no matter or
nongravitational fields of any kind) really involves a complicated
(nonlinear!) -simultaneous- solution, not just of the EFE, but of
additional field equations (or equations defining, say, the properties of
a perfect fluid).
(Actually, it's even trickier than -this-, but you get the idea...
suffice it to say, it's a bit of a miracle that tens of thousands of exact
solutions of the EFE are known.)
For more about the EFE, see
http://math.ucr.edu/home/baez/gr/gr.html
http://xxx.lanl.gov/abs/gr-qc/0103044
http://math.ucr.edu/home/baez/PUB/efe
Now, long ago physicists noticed that the T_(ab) terms which arise from
good approximations of various forms of "matter" and from realistic
classical field theories (i.e., EM) satisfy certain "energy conditions".
This is independent of gtr per se. It turns out that the class of
Lorentzian spacetimes with putative T_(ab) which satisfy these energy
conditions turns out to be a -very- small subset of the class of all
Lorentzian spacetimes. The point is, no warp bubble spacetime satisfies
any of the energy conditions (when you compute G_(ab), divide by 8 pi, and
try to interpret the result as T_(ab)), so they cannot possibly arise "in
the usual way" from well-understood, realistic theories of states of
matter or nongravitational classical fields such as EM fields.
For more about the T_(ab) terms arising from realistic physical theories
(as incorporated into gtr), see
http://math.ucr.edu/home/baez/PUB/tensor
For more about the energy conditions, see
http://math.ucr.edu/home/baez/PUB/dominantenergy
> feasible in terms of physics?
Certainly not in terms of theoretically well-understood physics, much less
experimentally well-tested physics! The concept of a warp bubble fell
firmly into the realm of "highly speculative theoretical proposals" from
the start, and within a few years had move into the even murkier realm of
"highly dubious and speculative theoretical proposals", as arguments
accumulated that such things cannot exist.
Caveat: it is true that when one attempts with suitable caution to mix up
quantum theory with gtr (this turns out to be very tricky!), then
well-established theory confirmed by replicable experiments (e.g. the
"Casimir force") show that some quantum systems can exhibit a kind of
"negative energy density" and other features which would violate the
classical energy conditions of gtr. However, this does -not- imply that
such quantum effects can be used to create "warp bubbles"!
> 2) What is exotic matter
A theorist's plaything.
> (matter with a negative mass?),
More like "hypothetical stuff with negative energy density", or even
better, "any hypothetical stuff which, if it existed, would violate at
least one of the classical energy conditions".
"Matter" as that term is commonly understood, of course, has -positive-
energy density.
> and why is it needed for this drive?
In warp bubble spacetimes, G_(ab) is nonzero, so these cannot possibly be
-vacuum- solutions in gtr (the only kind whose definition, G_(ab) = 0, is
in a sense purely mathematical, indepedently of gtr). Thus, if they were
solutions of the EFE, they would have to be nonvacuum solutions.
However, the Einstein tensors, inside the "walls" of the "bubble", simply
is not compatible with the classical energy conditions. (This was in fact
noticed by Alcubierre.) It turns out that this is true not only for the
Alcubierre and Broeck spacetimes, but (at least subject to some
hypotheses) for -any- spacetime containing a superluminal warp bubble.
These results go by the name of "superluminal censorship theorems".
Furthermore, it seems that so-called "quantum inqualities" would
apparently prevent warp bubbles from being realized using something like
the Casimir effect because it would require amazingly stupendous amounts
of energy. The Van Den Broeck spacetime actually arose in an attempt to
overcome this objection, but Van Den Broeck introduced a new kind of
apparently "unphysical" region in the "walls" of the "bubble" in order to
achieve this trick, and thus this bubble is apparently physically
unrealistic for, if anything, even -more- reasons than Alcubierre's
spacetime, since the alleged "energy reduction" never brought the numbers
into the reasonable realm--- as I recall, it was more like "reducing" the
energy requirement from the mass-energy of several thousand galaxies,
mysteriously turned into -negative- mass-energy and concentrated in a tiny
-tiny- region, to the mass energy of several thousand suns, all this for a
bubble which could move a busload of people from Paris to Beijing at an
"effective speed" of twice the speed of light.
Also, it turns out that (at least subject to some technical conditions)
superluminal warp bubbles, if they exist, would behave much like time
machines. Most contemporary physicists doubt very much that time machines
are physically possible, although as yet no rigorous proof exists, and at
least one prominent physicist (Igor Novikov) thinks that they -can-
exist, albeit with mysteriously circumscribed capabilities. But this is
-extremely- speculative, and in my view, any suggestion that time machines
are realizable should be regarded with great sceptism.
And as if this were not enough, the Alcubierre and Broeck spacetimes and
indeed (technical quibbles deleted) apparently -any- spacetime containing
a superluminal warp bubble would require the existence of "tachyonic
energy transport", something for which there is absolutely no experimental
evidence and which is highly suspect even in theory. Again, most
physicists would immediately dismiss anything requiring tachyonic energy
transport as physically impossible. This last (warp bubbles need
tachyonic stuff) is the most elementary objection of all, because it rests
upon a simple "eigenthing analysis" of the Einstein tensors of these
spacetimes.
"Superluminal" warp bubble: warp bubble spacetimes allow for the
possibility of a bubble which forms, accelerates away and eventually in a
sense "goes superluminal", accompanied by various phenonena somewhat
analogous to a sonic boom. The above arguments focus on showing that even
if something like a warp bubble could be -formed- and even if it could
then be made to -move along-, it could never "go superluminal". I was
interested in trying to study -subluminal- bubbles, which might not be
subject to some of the above objections. In fact, however, in the
Alcubierre and Broeck spacetimes even subluminal bubbles which never "go
superluminal" suffer from some terrible properties which tend to suggest
that the basic "Alcubierre trick" (a kind of "bump function blending" of
two or more legitimate solutions of the EFE, which apparently almost
always produces a spacetime with "unphysical" properties) may be fatally
flawed. As a matter of fact, studying the properties of such "blends"
might make a good jumping off point for a Ph.D. student interested in
working in general relativity, -provided- that doing thesis research in
gtr is a good idea, which for a theoretical physics student might not be
true--- but that's another story.
You can also look here
http://www.lns.cornell.edu/spr/
for previous posts by myself and others summarizing such theoretical
arguments against the physical existence of warp bubbles, together with
references to the approximately one dozen papers which have appeared on
the subject, almost all devoted to arguing that such things are
impossible. (No new papers have appeared for quite a while so I think the
naysayers have won their case, at least for the forseeable future.)
> 3) If the Casimir Effect
As I said, the Casimir effect -does- exhibit some properties suggestive of
exotic matter. However, it turns out that so-called "quantum inqualities"
would apparently prevent warp bubbles from being realized because it would
require so much energy. As I said, there are other, more or less
independent arguments which suggest that warp bubbles cannot be physically
realized.
> a direct distortion of spacetime around the ship itself?
Look up Alcubierre's original paper and then the papers cited in my long
extinct posts here. In a sense, as MG pointed out, "space" is compressed
in front of the bubble and expanded behind. However, I stress again that
these are just Lorentzian manifolds, and this is really verbal shorthand
for the behavior in these spacetimes of another quantity, the "expansion
scalar" h(X), which can be defined purely mathematically for any vector
field X (in this case, defining the world lines of a family of observers)
on (M,g). There is really -no- known physical interpretation known for
these manifolds, and they certainly are -not- in any sense "solutions" of
the EFE.
> 4) Assuming that the theory works, and that the Casimir Effect could
> generate sufficient quantities of exotic matter (after about a
> thousand years of R&D), what is a good ship design that incorporates
> the Alcubierre/Broeck drive? 5)Are there alternative theories for
> obtaining exotic matter, such as mining it around a black hole?
Exotic matter and black holes are completely different concepts. They
really have little if anything to do with each other, according to current
theory. Or perhaps I should say, they aren't really comparable concepts
because black holes are theoretically -very well established-, and the
observational evidence for the existence of astrophysical objects with all
the properties of black holes is now accepted as -overwhelming- (and also
steadily growing in size and sophistication), whereas exotic matter is
speculative even in theory, and at present there is absolutely -no-
experimental or astronomical evidence I know of suggestive of warp bubbles
or time machines or tachyonic stuff.
Chris Hillman
Home page: http://www.math.washington.edu/~hillman/personal.html
Aaron Bergman
<Pine.OSF.4.33.020605...@goedel3.math.washington.edu>,
Chris Hillman <hil...@math.washington.edu> wrote:
> Some poor uncited soul wrote:
> > 2) What is exotic matter
> A theorist's plaything.
That's a bit harsh. There are known violations of most of the energy
conditions.
I would say that the present state is that warp drives and the like look
unlikely but aren't ruled out at this point.
Aaron
--
Aaron Bergman
<http://www.princeton.edu/~abergman/>
Chris Hillman
Becca Heisler (not "uncited" in my post) asked:
> > > 2) What is exotic matter
I answered:
> > A theorist's plaything.
Aaron Bergman replied:
> That's a bit harsh. There are known violations of most of the energy
> conditions.
Hmm... just to make sure we're all on the same page, how do -you- define
"exotic matter"?
And what can you say about the -experimentally- known violations? I
mentioned the Casimir effect, for example, but to produce this you need
overwhelming amounts of ordinary matter arranged in a fairly constrained
geometric configuration (basically plates or wedges or something like
that, agreed?), whereas the Alcubierre and Broeck spacetimes require
-huge- amounts of -isolated- negative energy density (in the walls of the
bubble) with no regions of positive energy density anywhere in sight,
much less "flanking" the negative energy density regions. At the opposite
extreme, as we both know, an appropriate "cosmological constant" results
in a -uniform- negative energy density -everywhere-.
So AFAIK known ways of getting "exotic matter" don't enable one to
-concentrate- the stuff in an -isolated- region, away from
"overcompensating" amounts of ordinary matter/fields. But such apparently
illegal concentrations of isolated negative energy density are apparently
required simply to -create- an Alcubierre type warp bubble. (Never mind
persuading it to move off in some direction.)
> I would say that the present state is that warp drives and the like look
> unlikely but aren't ruled out at this point.
We agree on this, then, except that I might be a bit more pessimistic.
As I mentioned, some years ago I thought a bit about possible experimental
configurations for producing in a lab a tiny -subluminal- Alcubierre type
warp bubble, perhaps only for a very brief time. This may explain why I
am, it seems, more pessimistic than you are!
Uncle Al
Becca Heisler wrote:
>
> I am a science fiction writer looking for a warp drive within the
> limits of general relativity. I am VERY new to this field of physics
> and physics in general, so I have some questions:
> 1)Is the Alcubierre/Broeck Drive feasible in terms of physics?
It has its problems.
1) Where/how do you obtain and contain "negative mass?"
2) Warp bubble boundary conditions seem inimical to communicating
across the bounding brane interface. How do you navigate and steer?
How do you know when to stop? (Cf: supercavitating torpedoes.)
3) What happens to stuff pierced by the interface as the warp
bubble inflates and deflates?
> 2)What is exotic matter (matter with a negative mass?), and why is it
> needed for this drive?
Look up the papers and commentary thereupon. Science has no handle on
"negative mass." Anti-matter is ordinary mass.
http://arXiv.org/
http://arXiv.org/multi
Google
Alcubierre Broeck 159 hits
> 3)If the Casimir Effect produced great enough quantities of exotic
> matter, would it be used to produce heat energy able to do work, a
> pressure to propel something like a very high-tech piston, or a direct
> distortion of spacetime around the ship itself?
The Casimir effect is macroscopically worthless (though there is the
Scharnhorst effect across *small* spans
http://arXiv.org/abs/gr-qc/0107091
Google
"scharnhorst effect" 89 hits
Casimatter - nothing but minimal thickness mirror walls and 110 nm
optical path transparent dielectric spacers - runs the biggest
imaginable numbers into utter nothingness.
Two plane parallel infinitely conductive grounded perfect mirrors at 0
K brought into close proximity will act as an etalon, excluding
electromagnetic modes of quantum zero point fluctuations of the
vacuum. The surrounding radiation pressure then pushes in harder than
the attenuated cavity radiation pressure pushes out, leading to a net
"attraction" of the plates - the predicted and experimentally measured
Casimir effect.
(pi)^2(h-bar)(c) (pi)^2(h-bar)(c)
F = - ----------------(A) E = - ----------------(A)
(240)d^4 (720)d^3
where (MKS)
h-bar = 1.054572x10^(-34) J-sec (NIST)
c = 299,792,458 m/sec (NIST)
d is the separation in meters
A is the area in meters
The energy is the integral over distance of the force (though the
derivation arcutally goes in the opposite direction). E =
[4.3338x10(-28) J-m](A/d^3), which gives joules as expected.
If the plates are made of metal with finite conductivity at a finite
temperature, we have corrections versus composition, wavelength, and
separation:
http://xxx.lpthe.jussieu.fr/abs/quant-ph/9907105
http://xxx.lpthe.jussieu.fr/abs/quant-ph/0002061
(We won't worry about alternate geometries or dieletric walls.)
The metal with the best deep UV reflectance is aluminum (better than
90% to 110 nm). The only dielectric spacers good in the deep UV (to
about 105nm and 115 nm respectively) are lithium fluoride and
magnesium fluoride. AIP Handbook says we need 70 nm of Al at 120 nm
for 99% of maximum reflectivity. A 60:40 fluoride alloy to match the
linear thermal coefficient of thermal expansion of Al, given weighted
measured refractive indices at 120 nm, needs to be 37 nm thick for a
half-wave cavity. (Gedankenexperiment)
Casimatter is then vacuum deposition of alternate layers of 70 nm Al
and 37 nm fluoride alloy to create a contiguous stack of optical
pathlength-canceling half-wave etalons at 120 nm. 600 paired layers
sum to 64 microns, the thickness of a human hair, which is reasonably
doable in the real world. (If anybody has a clever idea for pulling
this off in bulk with vacuum spacing, I'd like to hear it. Pure
aluminum is very soft metal, and it absolutely requires *immediate*
fluoride salt overcoating to retain deep UV reflectivity.)
Consider a 2-cm diameter and high right cylinder. The 107 nm
metal-dielectric pair thus stacks 186,915 times, each with pi cm^2
area, to give 58.72 meters^2 of 120 nm optically-gapped Casimir
effect. This impresses me as a hefty area at a close approach
squeezed into a small package.
Plug in the numbers for Casimir energy. I get 1.13x10^(-5) Joules or
2.79x10^(-6) calories for the whole volume. One part per trillion
relative vs the mc^2 energy equivalent mass of the cylinder is 21.48
cal/gram energy/mass. Thus the "negative mass-energy" of a 2-cm
diameter and high solid Casimatter cylinder fabricated at the limits
of composition is about 10^(-20) of its rest mass. Feel free to
recalculate with more significant figures.
The correction factor for aluminum finite conductivity (temperature is
irrelevant at 120 nm gap) is 65% to give 1.75 microcalories zero point
fluctuation energy exclusion throughout the entire 6.26 cm^3 volume.
A hundred millionth of a trillionth isn't a sparrow fart in a
hurricane much less infinite energy or a warp drive.
> 4)Assuming that the theory works, and that the Casimir Effect could
> generate sufficient quantities of exotic matter (after about a
> thousand years of R&D), what is a good ship design that incorporates
> the Alcubierre/Broeck drive?
A multi-level sales opportunity, then flee town with the cash.
> 5)Are there alternative theories for obtaining exotic matter, such as
> mining it around a black hole?
Ain't no such. If you could travel to a black hole you would already
have a solution, yes? Wear your sunblock when you visit.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
"Quis custodiet ipsos custodes?" The Net!
Aaron Bergman
<Pine.OSF.4.33.020608...@goedel3.math.washington.edu>,
Chris Hillman <hil...@math.washington.edu> wrote:
> Becca Heisler (not "uncited" in my post) asked:
>
> > > > 2) What is exotic matter
>
> I answered:
>
> > > A theorist's plaything.
>
> Aaron Bergman replied:
>
> > That's a bit harsh. There are known violations of most of the energy
> > conditions.
>
> Hmm... just to make sure we're all on the same page, how do -you- define
> "exotic matter"?
Something that violates an energy condition.
> And what can you say about the -experimentally- known violations?
There aren't many, but who knows? There are a bunch of known effects
that violate most (all?) of the energy conditions. Besides, people can
be clever. Barcelo and Visser showed that you can get interesting
effects with just an ordinary scalar field.
Jeffery
Aaron Bergman <aber...@princeton.edu> wrote in message news:<abergman-E98F85...@news.bellatlantic.net>...
> > > 2) What is exotic matter
>
> > A theorist's plaything.
>
> That's a bit harsh.
I agree it's harsh to accuse theorists of playing with exotic matter.
There is no serious theory in particle physics or cosmology that
predicts negative mass. Negative mass was invented by wormhole
enthusiasts.
Wormholes, warp drive, time travel, all that stuff is utterly
impossible. It's not predicted by any serious theory in physics. It
violates the weak energy condition. It requires negative mass which
does not exist. Time travel intrinsically involves paradoxes, but that
doesn't stop people from letting their imaginations run wild with Gott
time machines, and similar nonsense. Now if someone invents a theory
with the sole purpose of trying to predict these things, then that
does not count as a theory that predicts these things, because it was
invented for the sole purpose of doing that!
I mean, for instance, supersymmetry was invented to solve the
hierarchy problem, and predicts supersymmetric particles. That's a
theory predicting something. If someone modifies general relativity
for the sole purpose of allowing wormholes, and postulates negative
mass for the sole purpose of allowing wormholes, just because they
think it would be really neat if wormholes existed, that does not
count as a theory that predicts wormholes.
I think warp drive was invented by Gene Roddenberry as a plot device
because special relativity is SO inconvienent.
Aaron Bergman
jeffery...@hotmail.com (Jeffery) wrote:
> Aaron Bergman <aber...@princeton.edu> wrote in message
> news:<abergman-E98F85...@news.bellatlantic.net>...
> > > > 2) What is exotic matter
> >
> > > A theorist's plaything.
> >
> > That's a bit harsh.
>
> I agree it's harsh to accuse theorists of playing with exotic matter.
> There is no serious theory in particle physics or cosmology that
> predicts negative mass. Negative mass was invented by wormhole
> enthusiasts.
We're not talking about negative mass; we're talking about exotic matter.
> Wormholes, warp drive, time travel, all that stuff is utterly
> impossible. It's not predicted by any serious theory in physics. It
> violates the weak energy condition. It requires negative mass which
> does not exist. Time travel intrinsically involves paradoxes, but that
> doesn't stop people from letting their imaginations run wild with Gott
> time machines, and similar nonsense. Now if someone invents a theory
> with the sole purpose of trying to predict these things, then that
> does not count as a theory that predicts these things, because it was
> invented for the sole purpose of doing that!
You evince little idea about the issues involved. Suffice it to say that
real scientists have written real articles about all these issues.
Robert Low
>Wormholes, warp drive, time travel, all that stuff is utterly
>impossible. It's not predicted by any serious theory in physics. It
>violates the weak energy condition.
No it doesn't. See the Goedel cosmology.
> It requires negative mass which
>does not exist. Time travel intrinsically involves paradoxes, but that
No, it doesn't. See John Earman's 'Bangs, crunches, whimpers
and shrieks: singularities and acausalities in relativistic
spacetimes' for a fairly detailed analysis.
DickT
> Becca Heisler wrote:
> > I am a science fiction writer looking for a warp drive within the
> > limits of general relativity. I am VERY new to this field of physics
> > and physics in general, so I have some questions:
> > 1)Is the Alcubierre/Broeck Drive feasible in terms of physics?
<snip excellent presentation>
That was a terrific post, Uncle Al. I just wanted to point out that
the negative energy isn't required to be of the same order of
magnitude as the payload, and that people who have fiddled around with
the equations, like David Waite, claim to have reduced the negative
matter requirement to a miniscule amount. You have showed how to
produce a miniscule amount. The Aclubierre-Casimatter-Uncle Al
spacedrive survives at a sufficient level for a hard science fiction
story!
Regards,
Dick
[Moderator's note: i.e., good enough to fool most people. - jb]
Chris Hillman
On Mon, 10 Jun 2002, Aaron Bergman wrote:
> Though failing to cite himself, it was secretly Chris Hillman who wrote:
> > Hmm... just to make sure we're all on the same page, how do -you- define
> > "exotic matter"?
> Something that violates an energy condition.
OK, that's basically the same "definition" I was using. (Not a -real-
definition, I think, since "energy condition" does not AFAIK have a
standardized definition, just a bunch of examples of an incompletely
defined concept.)
> > And what can you say about the -experimentally- known violations?
> There aren't many, but who knows? There are a bunch of known effects
> that violate most (all?) of the energy conditions. Besides, people can
> be clever. Barcelo and Visser showed that you can get interesting
> effects with just an ordinary scalar field.
BTW, I cited that paper in the long extinct post in which I summarized
essentially all the papers which have appeared in that field, for which
the OP can search in the s.p.r. archive.
As far as I can tell, a classical "scalar field" is another theorist's
plaything! E.g. we know the contribution to T_(ab) of a classical
(minimally coupled) massless scalar field, and we have an exact solution
to the EFE, the Janis-Newman-Winacour mcmsf solution, but we have no
evidence of an astrophysical object corresponding to such a beast. I -am-
vaguely aware that the classical limit of some quantum fields might be
scalar fields, e.g. IIRC a pion flux can -in principle- be described by a
-massive- scalar field, but AFAIK that isn't very -realistic-. I repeat
the point: AFAIK there's no known way of producing something which in gtr
can be treated as a scalar field, which can be -concentrated- in an
-isolated- region and also makes a -nonneglible- contribution to the
geometry of spacetime, all of which are apparently required for the
formation of warp bubbles. IOW, contrary to some press releases
concerning the work of Alcubierre and Van Den Broeck, there is nothing
like even a hypothetical -physical mechanism- anywhere in sight for trying
to produce one of these things (or seeking them in Nature*).
(Same for Reissner-Nordstrom electrovac solution, except that we have no
doubt that the classical EM field is a good description of lots of stuff
and is even astrophysically important.)
Chris Hillman
Home page: http://www.math.washington.edu/~hillman/personal.html
(*: CVDB and myself did independently consider the possible formation of
warp bubbles during gravitational collapse, and I produced a linearized
argument suggesting that if that happened, the bubble would produce
gravitational radiation. In principle that might provide a possible
"surprise" [c.f. the survey paper by Thorne on gravitational radiation]
when (if) second generation LIGO and LISA (respectively) begin
observations. However, AFAIK nothing ever really came of our
speculations, and AFAIK neither of us ever provided a convincing argument
that this could really happen even in theory.)
Chris Hillman
Becca Heisler asked:
> > > > 2) What is exotic matter?
I replied:
> > > A theorist's plaything.
Aaron Bergman commented:
> > That's a bit harsh.
Jeffery Winkler declared:
> I agree it's harsh to accuse theorists of playing with exotic matter.
^^^^^^
I never "accused" anyone of anything, and Aaron never said I had :-/
> There is no serious theory in particle physics or cosmology that
> predicts negative mass. Negative mass was invented by wormhole
> enthusiasts.
I think you might be confusing negative energy density with negative mass
matter. Since, as I and others already pointed out, the possibility of
negative energy density was experimentally verified via the Casimir effect
long before Morris-Thorne "wormholes" came along, it is not true that this
notion was "invented by wormhole enthusiasts".
(Becca: you can look on the s.p.r. archive for a post by John Baez on how
negative mass matter would behave, for example in Newtonian gravitation.)
> Wormholes, warp drive, time travel, all that stuff is utterly
> impossible.
(Becca: I hope you noticed that I didn't say anything so dogmatic. I said
that the current literature on the subject relates all three concepts---
ooops... actually I forgot to mention wormholes!--- and strongly suggests
none of these things can be physically realized. But it's early days yet,
so things could change.)
> It's not predicted by any serious theory in physics.
Novikov, Krasnikov, and some others have -seriously- speculated on the
possibility of time travel. I don't know whether Novikov would say that
he quite has a -theory- predicting the possibility of time travel,
however.
> It violates the weak energy condition.
Among others.
> It requires negative mass which does not exist.
Negative energy density. Which -does- exist. That's been experimentally
verified, as Aaron and others already pointed out!
I thought I had made it clear that the problem is not negative energy
density as such, but the geometric -configuration- of
stress-momentum-energy which would be required by an Alcubierre type warp
bubble, and which does not appear to be constructible using anything like
the Casimir effect, for the reasons I already described.
> Time travel intrinsically involves paradoxes, but that doesn't stop
> people from letting their imaginations run wild with Gott time
> machines, and similar nonsense. Now if someone invents a theory with
> the sole purpose of trying to predict these things, then that does not
> count as a theory that predicts these things, because it was invented
> for the sole purpose of doing that!
This claim is false as stated. What matters is not the "intention" of the
inventor(s) of the theory, but whether or not the theory is -testable-.
Maybe this is what you meant to say?
> I mean, for instance, supersymmetry was invented to solve the
> hierarchy problem, and predicts supersymmetric particles. That's a
> theory predicting something.
I think the missing word here is again "testable".
> If someone modifies general relativity for the sole purpose of
> allowing wormholes, and postulates negative mass for the sole purpose
> of allowing wormholes, just because they think it would be really neat
> if wormholes existed, that does not count as a theory that predicts
> wormholes.
"Modifies general relativity"? No--- there is a misunderstanding here
which raises another point I forgot to mention when I was discussing the
EFE in my response to Becca's questions.
Namely, given -any- classical relativistic field theory defined by a
Lagrangian, you can -always- compute the contribution of the stress-energy
of this field to T_(ab), the RHS of the EFE. The answer is unique.
Then, there is a way of incorporating the field theory into gtr; the
result is that one has fixed up the original field theory to take account
of the gravitational effects of the field energy. One can also throw in
other fields like the EM field and also idealized models of states of
matter, such as a perfect fluid. This process of incorporating a classical
relativistic field theory into gtr isn't completely straightforward
because you can get significantly different coupled field equations
depending on whether you let the new field "couple" to curvature or not.
For example, the classical field theory of a massless scalar field is
defined by a Lagrangian, which gives a covariant field equation, and this
can be incorporated into gtr via two popular prescriptions, called
"minimal coupling" and "conformal coupling", plus many others.
The point is that gtr is a very general relativistic classical field
theory of gravitation which is by construction capable of incorporating
any relativistic classical field theory of a nongravitational field, and
will account for the gravitational effects of the field energy of such a
field. In this respect it is somewhat analogous to thermodynamics.
Neither gtr nor thermodynamics by themselves ever tells the whole story
about theory X, but they do give unified and experimentally well-verified
descriptions of gravitational (heat) effects.
In particular, if a theory comes along which allows its stress-energy
tensor contribution to take on the very peculiar geometric configuration
of "eigenthings" which is characteristic of Alcubierre type wormholes, gtr
will incorporate it just fine, at least -formally-, without any
"modification" of the EFE. I trust it is clear by now why this does not
contradict what I said earlier about it being (at present) incorrect to
characterize warp bubbles (or wormholes or time machines) as a
"prediction" of gtr.
Gordon D. Pusch
> Uncle Al <Uncl...@hate.spam.net> wrote in message
> news:<ae0pon$eu5$1...@inky.its.caltech.edu>...
>> Becca Heisler wrote:
>>
>>> I am a science fiction writer looking for a warp drive within the
>>> limits of general relativity. I am VERY new to this field of physics
>>> and physics in general, so I have some questions:
>>> 1)Is the Alcubierre/Broeck Drive feasible in terms of physics?
> <snip excellent presentation>
>
> That was a terrific post, Uncle Al. I just wanted to point out that the
> negative energy isn't required to be of the same order of magnitude as
> the payload, and that people who have fiddled around with the equations,
> like David Waite, claim to have reduced the negative matter requirement
> to a miniscule amount.
You appear to be using a rather odd definition of "miniscule," unless you are
interpret it to mean "miniscule compared to the mass of the visible universe."
The most optimistic result so far reduces the required negative energy from
several thousand galaxies worth to only "a few solar masses" --- which is
certainly not "miniscule" by most people's standards !!!
Also, it should be noted that since the ADM mass of _ALL_ the "Warp Bubble"
spacetimes considered in the literature vanishes _identically_ (since the
assumed spacetime outside of the "bubble" is flat), so in a sense their
"gross tonnage" is =ZERO= --- i.e., any "positive" energy they carry
must be balanced by an equal amount of "negative" energy in some other
part of the "bubble." This strongly suggests that the amount of "negative"
energy required can =NEVER= be made "miniscule" --- it will always be
_AT LEAST_ as large as the mass/energy of the "payload."
(It also suggests that the "Warp Bubble" spacetimes are "pathological"
in much the same way that Newtonian "mass dipoles" are pathological:
Nothing in Newtonian theory *forbids* a negative mass from being eternally
gravitationally accelerated toward an equal and opposite positive mass that
eternally runs away from it with the exact same acceleration, so that the
two masses maintain an unchanging relative separation, their potential
energy remains constant, and their total kinetic energy remains zero ---
but no one takes this "solution" to Newton's equations of motion very
seriously !!!)
> You have showed how to produce a miniscule amount. The Aclubierre-
> Casimatter-Uncle Al spacedrive survives at a sufficient level for a hard
> science fiction story!
You have missed Uncle Al's point, which is that the =TOTAL= mass of a chunk
of "casimatter" is still _POSITIVE_, and is negligibly different from the
total mass of the bulk materials the chunk of "casimatter" is made out of.
In fact, it is a straightforward Weiskopfian "Search For Simplicity" order-of-
magnitude argument to show that the "Casimir Effect Correction" must always
be small compared to the energy equivalent of the heat of formation of the
material, let alone its total mass/energy. Proof: Allow two chunks of the
same material to be attracted toward each other by the "Casimir force" until
they are stopped by their repulsive short-range core of the intermolecular
potential. The resulting state is hardly different from a single chunk of
the bulk material. Now, pull a single chunk of bulk material apart into
two chunks, breaking a certain number of molecular bonds in the process;
the energy required to do so is approximately given by the energy of the
intermolecular bonds one has broken during this he process, which can
easily be estimated from the heat of formation of the material. The energy
equivalent of the heat of formation of the material is in turn much much
smaller than its total mass/energy. Since the "Casimir force" is weaker
than the intermolecular force, the "Casimir Energy" released when the two
chunks come together must be smaller than the amount of energy required to
break a chunk of bulk matter into two chunks, which is in turn much much
smaller than its total mass/energy. (This argument is consistent with the
"Casimir Force" merely being a bulk-material analog of the van der Waals
force between molecules, as discussed in the current "Casimir Effect"
thread.)
-- Gordon D. Pusch
perl -e '$_ = "gdpusch\@NO.xnet.SPAM.com\n"; s/NO\.//; s/SPAM\.//; print;'
Paul Reilly
> to the EFE, the Janis-Newman-Winacour mcmsf solution, but we have no
Winicour. (My thesis advisor)
Chris Hillman
Sigh...
mv Janis_Newman_Winacour_mcmsf_Agnese_LaCamera.mpl
Janis_Newman_Winicour_mcmsf_Agnese_LaCamera.mpl
And just this morning, there was I recoiling from the awful prospect of
proofing my GRTensorII database of 950 charts for possible inclusion in an
on-line database; you just reminded me why this is such an awful prospect
:-/ Thanks for the correction, though!
(Did you notice that "Exact Solutions" spells some author names
inconsistently? I suspect I may have found the name misspelled there.
Otherwise I must have transcribed it incorrectly myself, yuk. Anyway, I
hope all names will be spelled correctly in the new edition, since this
inconsistency is maddening.)
Aaron Bergman
<Pine.OSF.4.33.020610...@goedel1.math.washington.edu>,
Chris Hillman <hil...@math.washington.edu> wrote:
> As far as I can tell, a classical "scalar field" is another theorist's
> plaything!
The Higgs could very well be a scalar field. Scalar fields are common in
quintessence models. String theory predicts a number of scalar fields.
The point is not that I think hat warp drives are just around the
corner. I just don't think they've been ruled out.
FineS137
>> like David Waite, claim to have reduced the negative matter requirement
>> to a miniscule amount.
>The most optimistic result so far reduces the required negative energy from
>several thousand galaxies worth to only "a few solar masses" --- which is
>-- Gordon D. Pusch
I think you are referring to Chris VanDenBroeck's result. He was referring to
David Waite's result. (mine)
Van den Broeck's result was based on manipulating a term that he introduced
into the metric dealing with what you might think of as a gravitational length
contraction. My result is based on manipulating the lapse function, which deals
with what you might think of as a gravitational time dilation. His result
reduces it to a few solar masses. Mine reduces it arbitrarily.
-David Waite
Chris Hillman
On Sat, 15 Jun 2002, Aaron Bergman wrote:
> Chris Hillman <hil...@math.washington.edu> wrote:
>
> > As far as I can tell, a classical "scalar field" is another theorist's
> > plaything!
>
> The Higgs could very well be a scalar field. Scalar fields are common in
> quintessence models. String theory predicts a number of scalar fields.
I think you just proved my point! By "theorist's plaything" I mean a key
element of a theory whose most characteristic predictions have not yet
been experimentally tested. While the theories you mentioned are
"testable" in the sense that they do result in predictions which in
principle can be tested, AFAIK the relevant predictions have not yet been
tested. Put another way, AFAIK the best evidence we currently have
supporting the existence of the hypothetical fields you mentioned is along
the lines of "they play essential roles in the simplest theories we've yet
come up with which in theory have a chance of surviving still hypothetical
experimental tests".
> The point is not that I think hat warp drives
"Hat" warp drives?
> are just around the corner. I just don't think they've been ruled out.
I think we agree on this, assuming that by "hat warp drive" you mean some
special case of the warp bubbles I was discussing.
Chris Hillman
Home page: http://www.math.washington.edu/~hillman/personal.html
[Moderator's note: "hat" is presumably a typo for "that." -TB]
FineS137
>...people who have fiddled around with
>the equations, like David Waite, claim to have reduced the negative
>matter requirement to a miniscule amount. ...
For those interested in how this is done, it goes as
follows. Alcubierre wrote a general warp drive metric that included a
"lapse function" as he calls it. Usually the lapse function is taken
to be 1 everywhere and energy calculations are previously made were
based on a special case of his metric where that was the case. What I
did was write the warp drive metric transformed to an accelerated ship
observer's coordinates and reintroduced a variable lapse function into
the metric expressed for the ship observer's coordinates. I then
calculated the Einstein tensor from that metric to get the
stress-energy tensor. It turned out that the element corresponding to
coordinate frame energy density varied as 1/A^4 where A is that lapse
function. Otherwise the energy density agreed with Alcubierre's
expression which was found for A = 1 everywhere. I then went and
recalculated the quantum inequality for the case that A was some value
other than 1 in the negative energy region. It turns out that
increasing the value for A in this region increases the allowed
thickness for the negative energy region which also contributes to a
lower magnitude for a total negative energy requirement. Others I have
discussed this with have suggested giving A boundary conditions to A
of A = 1 both at the location of the ship and far from it so that the
crew's proper time doesn't lapse from their homeworld's time, but all
that is required to reduce the negative energy magnitude is for A to
be large in the region where it is located. For mathematical details
see pages 166 - 173 at
http://home.aol.com/zcphysicsms2/chap13.htm#166
David Waite