Think in the "S-Matrix" way, but be careful, the analogy is imperfect.
In the past 4D flat spacetime region with warp drive switched off the center of mass momentum of the enemy alien saucer is conserved. There is no propulsion without an ejected propellant there as Michael says because
Tuv(enemy ship)^,v = 0
,v is ordinary partial derivative
Pu(Past) = spacelike integral of Tuo d^3x
dPu(Past)/dt = 0
in that region from Noether's theorem where RIGID P10 (10-parameter Poincare group) is a symmetry group of the ship's dynamical action in that pre-warp region.
Note the spacelike integral is over a small finite 3D region.
Switch on PROPELLANTLESS PROPULSION WEIGHTLESS GEODESIC WARP DRIVE in a finite intermediate background Minkowski region. In that intermediate region RIGID P10 is no longer a symmetry group. There is local current conservation but no global "charge" conservation in that WARPED intermediate 4D region.
Unlike S-Matrix theory of HEP P10 is suspended in the "scattering region," i.e. there is no Dirac delta function of
&(Pu(ship past) - Pu(ship future)) in the "Feynman diagrams" assuming perturbation theory works here.
That is, for the enemy vessel's center or mass momentum although dPu(ship past)/dt = 0 prior to warp switch ON
That is although dPu(ship future)/dt = 0 after warp switch OFF
There is no reason to suppose Pu(ship past) = Pu(ship future)
But it is even more subtle than that, because even in simple physics, the total momentum changes when a force is applied. The situation here is that there is never a "force" applied in the GR Einstein paradigm because the motion of the enemy ship is always locally geodesic, i.e. g-force-free in warp drive. In GR only non-gravity forces like the EM Lorentz force and radiation reaction jerks will make g-forces pushing the ship off its local Levi-Civita connection timelike geodesic. Note torsion forces must be kept small same as tidal curvature forces in a star gate traversable wormhole time travel portal like we see, perhaps, at the Skinwalker Utah Ranch owned by Robert Bigelow of Las Vegas?
On Jun 11, 2007, at 6:12 PM, Jack Sarfatti wrote:
Michael Ibison gives a very interesting clever thought-provoking argument that propellantless propulsion is not possible. Like Nick Herbert's FLASH, which led to the no-cloning theorem of quantum information theory, I suspect that Ibison's idea, though incorrect, is incorrect for a very subtle reason that will lead to progress in the practical metric engineering of warp and wormhole.
Alleged Fact: We see UFOs fly and they have propellantless propulsion. Therefore, Ibison's argument is wrong, but how exactly is it wrong?
On Jun 11, 2007, at 1:26 PM, michael ibison wrote:
I have no problem with you posting my previous comments.
However, your present qualifications based on off-mass-shell virtual interactions (gravitational or otherwise) just obscure the point I am making but do not address it. My point is valid in the case where the initial and final states of the metric are Minkowski.
Yes, it appears so. You have the analog to the S-Matrix with asymptotically free "in" and "out" states at past and present infinity. In your case you have asymptotically flat 4D spacetime geometries with a perturbative model of warp drive switched on for a finite "time". You assume a flat background metric - what Roger Penrose calls the "linear graviton," i.e. huv is a small spin 2 tensor field representing the warp drive.
guv = (Minkowski)uv + huv(warp drive)
huv(warp drive) << (Minkowski)uv
Any near-field virtual interactions associated with the warp drive must be absent at those times. If not, then we are not discussing the same thing. If the ship is somehow 'dressed' by some local metric change, then that is not the same ship we started with, which was in Minkowski spacetime. I will wait until you have switched off all such engineered fluctuations of the metric. When you are quite finished we must be back in Minkowski spacetime and my statement applies.
It would seem so, but perhaps not. We live in a Higgs field(s), which is cohered virtual quanta forming the vacuum condensate. Indeed, in my model of gravity curvature tetrad 1-forms and torsion spin-connection 1-forms emergent from the Goldstone phase 0-forms of the post-inflation Higgs field(s) in the same way that the superflow field velocity 1-form emerges from the exterior derivative of a single Goldstone phase 0-form, therefore you simply cannot switch off the zero point ambient zpf dark energy density that is a Ricci source of curvature. The issue then is how strong is it on different scales and is it scale-dependent being large on the microscale of a fermi?
Remember the actual measured value of (10^-3 ev)^4 is only the IR long wave limit where an entire galaxy is approximated as a mathematical point in the FRW metric model.
Your objection / qualification reminds me of the "Newton's third law doesn't apply" argument often leveled at the case of magnetic interactions in the scattering of two charges. Whilst they are interacting, working out how there is conservation of momentum may be tricky and may depend on the choice of the EM SET. But we can avoid all those complications by confining attention to the times long before the charges are close, and long afterwards. Before they get close we can ignore all EM interactions, and so the mechanical energy and momentum are all that matter ;). Long after the scattering, one can ignore all near-field EM considerations, there are then no Lorentz forces, no hidden momentum, and no virtual photons. Then only the mechanical energy and momentum, and the energy and momentum of radiation matter.
Consequently, if the CoM of the charges is different in that final stage than it was in the initial stage, then one can be sure that there is radiation - which is the 'propellant'.
I have no idea what you mean by an exotic vacuum being a source or sink of momentum. Are you giving up on conservation of momentum?
Possibly. Depends what you mean by "momentum" global or local? GR raises still not settled questions about global conservation laws.
Let's go back to Noether's theorem of 1918.
Conservation of total global energy and linear momentum only holds when the RIGID continuous 4-parameter translation group is a symmetry group of the dynamical action of the relevant fields.
That is, x^u -> x'^u = x^u + a^u
where a^u is a constant 4-vector the same over the entire history of the universe!
This is very unphysical! It certainly violates locality!
Indeed, when we localize T4 i.e. let a^u -> a^u(x^v) we get Einstein's 1916 curvature field (with zero torsion gaps) as a consequence of a warped tetrad field that is the compensating spin 1 gauge 4-potential analogous to Au in EM. The spin 2 geometrodynamic connection is composite bilinear in the spin 1 tetrad fields. Note the QM spin addition rules from SU(2) group representation theory in Hilbert spaces of qubit fields
1 + 1 = 2,1, 0
3x3 = 5 + 3 + 1
OK how do we approximately represent the space ship that has a warp drive generator? It's basically a localized source field with a confined soliton structure. Let's call this the Psi source field and a U(1) EM field Au. Treat it as spin 0 for simplicity. Also we allow torsion fields so that the geometrodynamic connection is not symmetric Levi-Civita, but also has an antisymmetric contortion term.
The Einstein field equation is
Guv(geometry) + /\zpfguv(geometry) + kTuv(Psi(ship), Au) = 0
/\zpf is the ambient zero point dark energy/matter field.
dark energy is positive pressure
dark matter is negative pressure
when w < - 1/3
There is also a second torsion field equation coupled to the source angular momentum tensor.
e.g. Kibble 1961
It's complicated and its details are not important here for my qualitative points.
Because of the torsion field, in terms of the symmetric torsion free Levi-Civita connection covariant derivative ;
Guv^;v =/= 0 unlike 1916 GR.
In fact, assuming metricity, i.e. guv^.;v = 0
Guv^;v + /\zpf^,vguv + kTuv(Psi,Au)^;v = 0
this is the local conservation law for the 4D spacetime translational stress-energy current densities.
Note that Tuv ~ functional derivative of source (ship) action with respect to the metric guv variation.
There is a similar local law for the 4D space-time rotational torsion "vortex" current densities.
All derivatives of the source field Psi are covariant "minimal coupling" derivatives for both localized P10 (Poincare) and localized U(1) groups.
What did I mean by virtual vacuum current reservoir for center of mass momentum of ship?
Guv^;v = 0 to a good approximation, then
/\zpf(Dark Energy)^,vguv(geometry) + kTuv(Psi(Warp Drive Generator),Au(EM))^;v = 0
/\zpf(Dark Energy)^,vguv(geometry) = virtual vacuum translational current reservoir source and sink of linear momentum
Now in fact, you may not be able to make asymptotically flat states, but even if you can, there is no reason at all to assume that the total linear momentum of the Psi(ship) soliton source field (localized support in 4D background Minkowski spacetime) is conserved! Why? Because the total linear momentum, the global spacelike integral including both geometrodynamic and source & EM fields is not conserved.
That is, when you include the geometrodynamic field as a dynamical actor on equal basis with source ship and EM fields there is no global energy-momentum conservation law on spacelike slices in the intermediate warp drive finite spacetime regions.
Note, as an example of violation of global T4 conservation laws, the total energy of our expanding accelerating dark energy deSitter universe is not conserved! The dark energy density is constant on IR scale so that the total dark energy scales as a(t)^3 where a(t) is the FRW scale factor.
From the POV of Noether's theorem this is obvious because RIGID T4 is not a symmetry group of the total dynamical action of the universe.
So the above is my off-the-cuff back-of-the-envelope retort to your interesting argument. I could be wrong or not even wrong. However, I think your argument is interesting and provocative and should be debated in same way as Nick Herbert's FLASH argument. :-)
Non-conservation of energy or momentum that may appear in a vacuum interaction must be an artifact of the method of (perturbative) analysis. Space-translation invariance of the action is all we need to be sure that the momentum is exactly conserved at all times - vacuum fields or no vacuum fields. Hence the ship cannot move without propellant - regardless of any fancy warp-drive physics.
From: Jack Sarfatti [mailto:email@example.com]
Sent: Monday, June 11, 2007 2:55 PM
Subject: RE: Inertial mass, rest mass & zero rest mass
I wish you would make a public statement. :-)
I see what you say based on perturbation theory. However, I don't think we need real on-mass-shell propellant. Off mass shell virtual "dark energy" propellant inside vacuum is what is happening here. We do not need on light cone gravity waves in far field - it's all near geometrodynamic field. We can debate this. There will be exotic vacuum trace of the warp that is the momentum source & sink.
What your argument really shows is that warp drive is NONPERURBATIVE like the superconducting ground state cannot be derived in a finite number of terms in perturbation expansion.
Looking over what you have said recently on this topic, I am in complete
agreement with you.
Based on past discussions. I fear though that some folks may have come to
erroneous conclusions on the possibilities for space-travel based on warp-drive
ideas. To illustrate, consider:
i) Start with a system with no fancy metric, eg close to Minkowski spacetime.
ii) Switch on warp drive (bend metric etc) in vicinity of craft, and wait whilst
craft moves along geodesic of curved spacetime
iii) Turn off warp drive - spacetime is once again Minkowski.
Whatever qualities of the warp drive are employed, at the end of all this, it is
provably the case that the centre of mass (COM) of the total system cannot be
different than it was at the start. That is, one cannot use a warp drive to
conclude that the craft can get from A to B (whose coordinates are referred to
the starting and finishing MINKOWSKI spacetime) with no other reciprocal change.
Conservation of momentum demands that that there must be another mass that has
moved along the vector BA such that the COM is preserved. In other words, the
displacement cannot be achieved without propellant. This conclusion applies
irrespective of talk of fancy Alcubierre metric waves carrying the ship along.
Fancy warp drive physics do not get around the problem of the need for
propellant. Of course, the propellant could take the form of gravitational
radiation, but propellant there must be.
>From: Jack Sarfatti [mailto:firstname.lastname@example.org]
>Sent: Monday, June 11, 2007 11:25 AM
>Subject: Re: Inertial mass, rest mass & zero rest mass
>On Jun 10, 2007, at 9:19 PM, michael ibison wrote:
>> Jack: why did you send this to (just) me? Are you expecting a
>> - Michael
>>> -----Original Message-----
>>> From: Jack Sarfatti [mailto:email@example.com]
>>> Sent: Sunday, June 10, 2007 4:08 PM
>>> To: michael ibison
>>> Subject: Fwd: Inertial mass, rest mass & zero rest mass
>>> Begin forwarded message:
>>>> From: Jack Sarfatti
>>>> Date: June 10, 2007 2:05:30 PM PDT
>>>> To: MPOGO@aol.com
>>>> Subject: Re: Inertial mass, rest mass & zero rest mass
>>>> Don't evade the point here. It's important and it shows
>why all the
>>>> schemes suggested by
>>>> 1) Haisch, Puthoff, Rueda, Cole ... ZPE friction
>>>> 2) Mach's Principle - Woodward
>>>> 3) EM stress - Jim Corum
>>>> All schemes except for variations on the Alcubierre toy
>model - true
>>>> metric engineering the fabric of space will fail to explain UFO
>>>> evidence with zero g-force EVEN IF THEY WORKED AS ADVERTISED
>>>> The one solid reliable empirical reference here is Paul
>>> Hill's book as
>>>> Hal Puthoff & Eric Davis agree. The key idea in that book is the
>>>> "acceleration field," i.e. "geodesic weightless warp
>drive" in more
>>>> modern jargon.
"If we knew what it was we were doing, it would not be called research, would it?"
- Albert Einstein