### Author Topic: Resonant Cavity Space-Propulsion: institutional experiments and theory  (Read 57936 times)

#### RERT

##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #40 on: 02/08/2016 11:03 AM »
Dr.Rodal -

Frobnicat seems far more nimble than me at this stuff, but since you ask for some mathematical critique, I think I owe you a stab.

There are three frames involved: frame 0, where the object is initially at rest. Frame 1, where it has acquired its initial velocity, and frame 2, where it has acquired its final velocity.

The total mass-energy is thus m0c^2, and does not vary between frames: in fact I think your equation

m1V1/gamma1 = m2V2/gamma2 should be replaced by the conservation of the norm of the energy momentum vector, vis:

m0^2c^4 =
gamma1^2*m1^2*c^4-gamma1^2*m1^2*v1^2 =
gamma2^2*m2^2*c^4-gamma2^2*m2^2*v2^2

[I may or may not have this right, but there will definitely be mass-energy terms mixed with the momentum terms.] I'd take a stab that this is the kind of covariant formulation Frobnicat eluded to above. I won't comment on later parts of the analysis, since if my comment is correct the rest would not follow.

R.

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #41 on: 02/08/2016 12:56 PM »
Dr.Rodal -

Frobnicat seems far more nimble than me at this stuff, but since you ask for some mathematical critique, I think I owe you a stab.

There are three frames involved: frame 0, where the object is initially at rest. Frame 1, where it has acquired its initial velocity, and frame 2, where it has acquired its final velocity.

The total mass-energy is thus m0c^2, and does not vary between frames: in fact I think your equation

m1V1/gamma1 = m2V2/gamma2 should be replaced by the conservation of the norm of the energy momentum vector, vis:

m0^2c^4 =
gamma1^2*m1^2*c^4-gamma1^2*m1^2*v1^2 =
gamma2^2*m2^2*c^4-gamma2^2*m2^2*v2^2

[I may or may not have this right, but there will definitely be mass-energy terms mixed with the momentum terms.] I'd take a stab that this is the kind of covariant formulation Frobnicat eluded to above. I won't comment on later parts of the analysis, since if my comment is correct the rest would not follow.

R.
Relativity's Energy-Momentum Equation ( https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation ) is an identity between energy and momentum that is satisfied exactly (just like 1=1) if energy is conserved. If  Relativistic Momentum is conserved and if Relativistic Energy is conserved, it trivially follows that Relativistic Energy-Momentum is conserved. [*]

The equations are well-known:

Lorentz factor (https://en.wikipedia.org/wiki/Lorentz_factor)

γ = 1/ √[1- (v/c)2]

Momentum (https://en.wikipedia.org/wiki/Momentum#Relativistic_mechanics)
p = γ m v

which is the equation I used in my post on conservation of momentum,

where, in the above equation and in the ones to follow, m is the rest mass m=mo, the mass of an object in its rest frame.

KineticEnergy (https://en.wikipedia.org/wiki/Kinetic_energy#Relativistic_kinetic_energy_of_rigid_bodies)
K =  (γ -1) m c2

https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalence
PotentialEnergy = m c2 (the rest energy)

TotalEnergy =  E = KineticEnergy  + PotentialEnergy
=(γ -1) m c2 + m c2
= γ m c 2

Energy-Momentum Equation ( https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relation ) =

E2 = p2 c2 + m2 c4

or

m2 c4 = E2 - p2 c2

which is, and should obviously be, an identity (if you substitute the above values, you get the identity 1 = 1)

m2 c4 =(γ m c 2)2 - (γ m v)2 c2
=γ2 m2 c 4 - γ2 m2 v2 c2

γ2 m2 v2 c2 = (γ2-1) m2 c 4

v2/c 2  = (γ2-1) /γ2

1 = 1

which is just a trivial statement of the identity that one equals one, since the Lorentz Factor

γ 2 = 1/ (1- (v/c)2)  by definition

QED (quod erat demonstrandum)

[*] And if energy (and mass) are not conserved, as in a system in which negative mass is continuously created (or destroyed), it would be incompatible to demand conservation of energy, since mass-energy is not conserved in such a system.

If mass-energy is continuously created or destroyed, one should use a single reference configuration, and it looks better to deal with conservation of energy separately.  Also, then as already discussed here: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1488362#msg1488362 the InitialVelocity must be measured with respect to the same frame where the InitialMass of the object was measured.  This is an acceleration problem, hence the frame where the rest mass is measured is a privileged, non-inertial frame.   If other frames of reference are used, not only the Initial Velocity will be different, but the Initial Mass will be different too, if measured in any frame other than the object's initial frame of reference to measure (and keep track of) its changing mass.
« Last Edit: 02/09/2016 01:00 AM by Rodal »

#### frobnicat

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #42 on: 02/08/2016 09:53 PM »
Dr Rodal, you insist that you are here doing a study of a closed system composed of a single lump of mass, i.e. that there is no separation (separation in 2 parts from a single part, as would be the case for action/reaction) nor joining ("melting" of 2 parts in a single part, as would be the case for an inelastic collision/aggregation) nor bounce (2 parts exchanging momentum but still being separate before and after such interaction). Do I understand correctly your premise ?

If so, in a given frame, considering one lump of rest mass m1 at velocity v1 and associated γ1=γ(v1) before, and same singleton object of rest mass m2 at velocity v2 and associated γ2=γ(v2), taking both conservation of momentum and of (total) energy gives (following the equations you recall) :
γ1 m1 v1 = γ2 m2 v2  (CoM)
γ1 m1 c² = γ2 m2 c²  (CoE)
⇔ (since c²≠0)
γ1 m1 v1 = γ2 m2 v2
γ1 m1 = γ2 m2

γ1 m1 v1 = γ1 m1 v2
γ1 m1 = γ2 m2
⇔ (since γ1≠0)
m1 v1 = m1 v2
γ1 m1 = γ2 m2

Now, all depends on m1

m1=0, total mass of the closed system is 0 from start
since γ2≠0 ⇒ m2=0 : it must be that total mass stays 0
and v1 and v2 are independant

m1≠0, total mass of the closed system is not 0 from start
since m1≠0 ⇒ v1=v2 : it must be that velocity stays the same
and so γ1=γ2 and it follows that m1=m2

I don't see how you can start with a singleton lump closed system that's supposed to respect conservation of energy and conservation of mass in the framework of SR, even assuming possibility of negative rest mass (or imaginary rest mass, whatever) and not arrive at same conclusion. There appears to be a contradiction between your premise (closed system) and the conclusions you draw from equation of conservation of momentum alone, when a closed system needs both constraints to be taken together.

Also it is not clear how you consider mass...
.../...
where, in the above equation and in the ones to follow, m is the rest mass m=mo, the mass of an object in its rest frame.  Also, as already discussed here: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1488362#msg1488362 the InitialVelocity must be measured with respect to the same frame where the InitialMass of the object was measured.  This is an acceleration problem, hence the frame where the rest mass is measured is a privileged, non-inertial frame.   If other frames of reference are used, not only the Initial Velocity will be different, but the Initial Mass will be different too, if measured in any frame other than the object's initial frame of reference to measure its mass.
.../...

<<m is the rest mass m=mo, the mass of an object in its rest frame.>>
All right so we are not using so called relativistic mass mrel, and by avoiding the traps of mrel we are conforming to prescriptions of modern physics teaching. Fine with me. That means that whenever we talk about mass we can be confident that is not mrel(v) a function of velocity, i.e. a covariant value that depends on inertial frame of reference, but we talk on an invariant value, that has the exact same value for all observers. The fact that we are talking of this invariant mo mass appears clearly in the equations, as for instance momentum is given by p=γmov otherwise we would have p=mrelv. To me it then appear as a contradiction to use mo in the equations but to discuss those very same variables as if they were a function of velocity :
<<but the Initial Mass will be different too, if measured in any frame other than the object's initial frame of reference to measure its mass. >>

And I fail to see the physical meaning of  <<InitialVelocity must be measured with respect to the same frame where the InitialMass of the object was measured>> that again seem to imply the use of mrel that is a function of velocity wrt. observer, when all equations use the invariant mo that is not a function of velocity wrt. observer

But all those question are less important than the first part of this post : unless we are talking of a 0 total (invariant) mass object from start, in SR a closed system single object with mo≠0 just has an inertial trajectory of constant velocity and constant (invariant) mass, in this later case the hypothesis of occurrence of negative mass doesn't change the game.

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #43 on: 02/08/2016 10:01 PM »
...I don't see how you can start with a singleton lump closed system that's supposed to respect conservation of energy and conservation of mass in the framework of SR...
Stop right there  . Nowhere in the above considerations have I  considered conservation of energy.  I only addressed conservation of momentum, so far.

The post title said it 1) CONSERVATION OF MOMENTUM (not conservation of energy and 2) VARIABLE MASS in a closed system:

CONSERVATION OF RELATIVISTIC MOMENTUM FOR REACTION-LESS PROPULSION THROUGH VARIABLE INERTIAL MASS

On the contrary, it was stated that the equations imply continuous creation (or destruction) of negative mass, which is in violent contradiction with conservation of mass-energy (unless, of course FinalMass=InitialMass=0 for any deltaV).

« Last Edit: 02/09/2016 01:59 AM by Rodal »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #44 on: 02/08/2016 10:52 PM »
Dr Rodal, you insist that you are here doing a study of a closed system composed of a single lump of mass, i.e. that there is no separation (separation in 2 parts from a single part, as would be the case for action/reaction) nor joining ("melting" of 2 parts in a single part, as would be the case for an inelastic collision/aggregation) nor bounce (2 parts exchanging momentum but still being separate before and after such interaction). Do I understand correctly your premise ?

...
All right so we are not using so called relativistic mass mrel, and by avoiding the traps of mrel we are conforming to prescriptions of modern physics teaching. Fine with me. ...
When using the term "lumped mass" I meant it in the sense of a lumped parameter, and did not address in what sense (if it is at all physically possible) this may involve positive and negative masses inside.

Clearly, unless FinalMass=InitialMass=0, for any deltaV, the equations imply that the rest mass would be changing, from an initial value to a final value, which is in contradiction to the concept of relativistic concept of rest mass that is conserved, and clearly imply that mass-energy cannot be conserved in such a system.

The equations imply that either:

* mass-energy is conserved and hence the only way to satisfy conservation of momentum is with an initial mass = 0 and is always zero (the solution could be due to two masses, as in Bondi/Forward diametric drive, having equal absolute magnitude but opposite sign)

* mass-energy is not conserved: for example because the system composed of a positive mass plus a negative mass is such that the positive mass is immutable but that negative mass can be continuously created (or destroyed)

Therefore the best way to proceed is to continue to address the problem accounting separately for a positive rest mass that is immutable (conservation of mass applies to the positive mass), and separately, for a negative mass that can be continuously created or destroyed.

Clearly, neither conservation of mass or conservation of energy applies to the negative mass (that can be continuously created or destroyed) in this case: the rest mass of the negative mass is not constant.

If we have a system that can change its rest mass (by creation or destruction of negative mass), it seems to me that it would be best handled in a reference frame for the Initial Configuration, as in Lagrangian coordinates embedded in the material, for example when dealing with very large deformations and very large strains of a body.

« Last Edit: 02/09/2016 01:08 AM by Rodal »

#### RERT

##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #45 on: 02/09/2016 12:09 PM »
...
m2 c4 = E2 - p2 c2

....

Thank you for your exposition. The above equation is essentially what I quoted, assuming conservation of energy-momentum, in the three relevant frames.

As you say, QED - Quite Enough Done.

R.

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #46 on: 02/09/2016 05:30 PM »
Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?

1) Special Relativity: NO. The rest mass cannot be a function of the time coordinate, as Lorentz covariance would not be preserved.  Variation of rest mass cannot be due to kinematic (velocity or position) evolution.

2) Einstein's General Relativity (GR): It appears as NO.  It appears that a time-dependent variable mass would give rise to a time-dependent Energy Stress tensor, solely due to the mass variability with time, which is not consistent with Einstein's GR theory of gravitation.   Also it appears that Relativity's Energy-Momentum equation:

m2 c4 = E2 - p2 c2

may prevent general time-dependent variable mass.

Note: I need to review how does Woodward accommodate variable negative mass-energy in his theory (which I understand he states is consistent with Einstein's General Relativity), as it appears to me that there should be an issue with the time-dependent Energy-Stress tensor and with the Energy-Momentum equation in such a theory.

3) Scalar-Tensor theories of Gravity: YES,  through the introduction of a scalar field-dependence, variable mass is allowed:  a time-dependent Energy-Stress tensor is compatible with the theory (because of the scalar field).

4) Fifth-dimension (or higher-dimensional) field theories:  YES, it allows variable-mass.

CONCLUSION:  Variation of mass represents an additional degree of freedom, and hence field theories that can accommodate this concept are, for example, scalar-tensor theories of gravitation or five-dimensional or higher-dimensional field theories of gravitation that can accommodate this extra degree of freedom.

This is completely in agreement with Minotti's paper on the EM Drive

Scalar-tensor theories and asymmetric resonant cavities
Fernando O. Minotti
Grav. & Cosmol. 19 (2013) 201

that motivated this analysis, as Minotti uses a scalar-tensor theory of gravitation derived from Kaluza-Klein's theory.

It is also in agreement with Dr. White invoking 5th or higher dimensional theories for his Quantum Vacuum hypothesis.

« Last Edit: 02/09/2016 10:53 PM by Rodal »

#### X_RaY

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #47 on: 02/09/2016 06:36 PM »
Hi,
I did not follow the whole conversation during last few days.
Why is a variable mass related to any force toward the small end of the cavity? If there IS a lower or higher mass related to the EM field inside the resonator what is that meaning? The smaller diameter side of the cavity itself have had a lower mass because it consists of less volume of copper as the larger side.  Also the earth gravity is almost homogeneous over the size of the cavity. How it can generate a thrust in shifting the center of the mass of itself? A slightly other force composition in relation to the gravity field around ok but thrust generation?
IMHO Only a negative mass value would explain thrust generation against the background gravity field at all (repulsive energy). The direction of this force would be against the attractive gravity of the biggest mass nearby: the earth it self.
I think I have to study your the last posts.
« Last Edit: 02/09/2016 06:41 PM by X_RaY »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #48 on: 02/09/2016 06:51 PM »
Hi,
I did not follow the whole conversation during last few days.
Why is a variable mass related to any force toward the small end of the cavity? If there IS a lower or higher mass related to the EM field inside the resonator what is that meaning? The smaller diameter side of the cavity itself have had a lower mass because it consists of less volume of copper as the larger side.  Also the earth gravity is almost homogeneous over the size of the cavity. How it can generate a thrust in shifting the center of the mass of itself? A slightly other force composition in relation to the gravity field around ok but thrust generation?
IMHO Only a negative mass value would explain thrust generation against the background gravity field at all (repulsive energy). The direction of this force would be against the attractive gravity of the biggest mass nearby: the earth it self.
I think I have to study your the last posts.

1) According to Minotti's paper (quoted in my post above) the force on the EM Drive can be directed towards either end, depending on the electromagnetic mode shape

2) Minotti's paper (using a scalar-tensor unified theory of gravitation and electromagnetism) predicts negative energy-mass (violation of the Weak Energy Condition) in the EM Drive, which would be variable with power, with mode shape and with time (for time-dependence of power input).

3) The force in Minotti's paper is due to coupling with a scalar field in a unified theory of electromagnetism with gravitation, and not due to the Earth's gravitation.  The force of the Earth's gravitation is insignificant compared to the force of a small magnet.

4) Minotti's paper predicts, that for copper wall thickness ~1 mm, the thicker the copper (as long as significantly greater than the skin depth), the greater the force.

5) The force is not directly analogous to a Bondi/Forward diametric drive because the Bondi/Forward diametric drive force is due to two separate bodies without an electromagnetic field.  Instead, the force in Minotti's formulation is due to coupling of the electromagnetic field with a scalar field and it is and most dependent on the electromagnetic mode shape.  I brought the Bondi/Forward analogy only to illustrate how can a zero mass be achieved by a negative mass having same absolute magnitude as the positive mass.

6) The linear version of the unified theory used by Minotti predicts gravitational effects due to the Earth's magnetic field which are unreal.  Minotti briefly goes over the fact that perhaps a nonlinear version would cancel these unreal effects.
« Last Edit: 02/09/2016 10:08 PM by Rodal »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #49 on: 02/09/2016 07:33 PM »
..
Quote
...In order to have a non-dimensional scalar field φ of values around unity, in expression
(1) the constant G0 representing Newton gravitational constant is included...
Based on this statement in section 2. of the paper there is a (weak)coupling to the gravity and if so there is also coupling on the earth gravity field for this scalar. And yes gravity is a very weak force in comparison to the other forces inclusive electromagnetism.
I read the paper one or two years ago and it's an impressive idea. I have to read it again to follow your statements but its hard stuff and it will take a while.
That's correct.  Minotti also includes the effect of Earth's Magnetic field.  Perhaps it is best to visualize the small magnitude of the Earth's gravitational force by the fact that the force he derives is dependent on the electromagnetic mode shape, independent of EM Drive orientation with respect to the Earth.
« Last Edit: 02/09/2016 07:34 PM by Rodal »

#### ThinkerX

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #50 on: 02/10/2016 01:11 AM »
Ok, trying to wrap what's left of my mind around this:

Quote
4) Minotti's paper predicts, that for copper wall thickness ~1 mm, the thicker the copper (as long as significantly greater than the skin depth), the greater the force.

So, say you have two EM Drive units that are identical, except one has 'skin depth' of 1 mm and the other has 'skin depth' of say 3 mm.  According to this theory, the second device should perform significantly better.  Is that correct?

If so, this appears to be something within the capabilities of our DIY crowd.

But...

1 - would the increased weight of the device with the thicker skin offset the thrust measurements?  (I suspect I am missing something glaringly obvious here.)

2 - Does the entire skin need to be thicker, or just the end plates?

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #51 on: 02/10/2016 02:35 AM »
Ok, trying to wrap what's left of my mind around this:

Quote
4) Minotti's paper predicts, that for copper wall thickness ~1 mm, the thicker the copper (as long as significantly greater than the skin depth), the greater the force.

So, say you have two EM Drive units that are identical, except one has 'skin depth' of 1 mm and the other has 'skin depth' of say 3 mm.  According to this theory, the second device should perform significantly better.  Is that correct?

If so, this appears to be something within the capabilities of our DIY crowd.

But...

1 - would the increased weight of the device with the thicker skin offset the thrust measurements?  (I suspect I am missing something glaringly obvious here.)

2 - Does the entire skin need to be thicker, or just the end plates?
Actually Minotti's theory predicts that the force is proportional to the total thickness of the copper as long as it is significantly thicker than the skin depth (and the wall is "thin", not much thicker than 1 mm), for example at ~2 GHz, for copper, the skin depth is about 1 micrometer and the total thickness considered in his example was 1 mm.

Quote from: Minotti
Assuming a cavity with thin walls (but much thicker than the penetration depth ,
in order to the boundary conditions used to be correct) of mass surface density ...
There are no details in the literature as to the precise dimensions of the cavities
used in the experiments, so that an example roughly similar to the overall dimension
reported and with the proportions observed in the published photographs will be used.
Assuming a wall of thickness 1 mm, and a copper mass density of 8.9 × 103 kg/m3, we
have  = 8.9 kg/m2.

According to the theory, if another EM Drive with the same geometry, same copper material and operating at the same frequency and mode shape has a total wall thickness of 2 mm (0.079 in), the force should be two times greater than in the EM Drive with 1 mm (0.039 in) thick.

In this statement, both EM Drives should have uniform thickness: same thickness for walls as for end plates.

Yes, this should be carefully tested in experiments.
« Last Edit: 02/10/2016 02:48 AM by Rodal »

#### frobnicat

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #52 on: 02/10/2016 03:31 PM »
Dr Rodal, thanks for answering my comments about your work around "negative mass" creation and conservation of momentum. It was clear from the equations that you considered only conservation of momentum and didn't consider conservation of total energy, but from early posts (on the main EM drive thread) I had the impression that you were assuming some compatibility with conservation of energy, for instance (bold added by me for emphasis) :

.../...
Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.

Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass.  More on that later...

(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass  )

.../...
4) The EM Drive is a closed system, in which case the only way I see to conserve momentum-energy for acceleration of the EM Drive is to have creation of negative mass-energy in the EM Drive
.../...

I see two different problems. Possibility of negative mass, that is Weak Energy Condition breaking, is one thing. But modification of rest (invariant) mass in a closed system without a balanced counterpart in changes in kinetic energy is another one, it looks more like conservation of (total) energy breaking, whether the change appears as + or - mass.

As an example of the difference between those 2 hypothesis : we can apply usual SR for conservation of energy and momentum when considering a single particle of mass m1>0 splitting into two particles of mass m2>m1 and m3<0. The hypothesis of the existence of particle of mass<0 doesn't change the equations. But your approach seems to ignore one equation (conservation of energy) and hence gives the system a degree of freedom absent of this initial example. Negative mass deltas is then not specifically implicated, and indeed your solution space also shows positive (unbalanced) delta mass, i.e. actually either positive or negative total energy evolutions.

Your latest answer clarifies this as citing a scalar field or supplementary spatial dimension as required to make sense of such mass variation... I would have a hard time following in detail Minotti (or you following Minotti) on such topic outside of usual SR application, but maybe could understand a few words of how, one way or another,  energy is conserved in the end to say that the approach "conserves momentum-energy" ?

Otherwise how poor SR pedestrians are supposed to make sense of conservation of momentum alone ? It is my understanding than when positing one equation of conservation in SR, whether or not considering other constraints, the equation can have meaning in SR only if it is frame invariant. In other terms, and trying to be mathematically factual, when writing one conservation equation as
function( v1, ..., vk, m1, ..., mk)=0
applying a same arbitrary boost to all velocities
v1'=boost(v1)  ...  vk'=boost(vk)
then we should check that following expression still holds :
function( v1', ..., vk', m1, ..., mk)=0

And I think that your single momentum equation you start from doesn't respect that, so I don't see how it can bear physical meaning in a relativistic context and what is the value of the interpretations you draw from it.

« Last Edit: 02/10/2016 03:34 PM by frobnicat »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #53 on: 02/10/2016 04:34 PM »
Dr Rodal, thanks for answering my comments about your work around "negative mass" creation and conservation of momentum. It was clear from the equations that you considered only conservation of momentum and didn't consider conservation of total energy, but from early posts (on the main EM drive thread) I had the impression that you were assuming some compatibility with conservation of energy, for instance (bold added by me for emphasis) :

.../...
Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.

Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass.  More on that later...

(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass  )

1) The above statement that negative mass addresses the conservation of energy problem is correct in the specific instance of constant zero initial lumped mass.  Specifically, the initial condition of lumped rest mass=0, staying constant  (for example as a result of equal magnitude negative mass as positive mass) answers all your previous posts regarding conservation of energy, and it does so trivially, as the kinetic energy is zero for zero mass, and you cannot use the EM Drive as a generator if it has effective zero inertial mass. (Effectively I know that even photons, with zero rest mass have energy, so if you want you can throw an expression with the Plank constant there, and replace zero kinetic energy with very very small kinetic energy).

If my memory is correct, in your consideration of energy conservation you never considered that the rest mass could be zero.  You assumed (unstated) that the rest mass was greater than zero.  The concept which you addressed in your energy conservation statements, the EM Drive, has been discussed by Dr. White and by Dr. Minotti as involving negative energy-mass, so one should discuss the consequences of such negative energy-mass in considerations of energy conservation, instead of ignoring it, and assuming as in your considerations, that the energy-mass was positive, and constant.  In other words, your energy considerations for the EM Drive,  ignore the premise of these authors.

2) The argument that <<nobody has found experimental evidence of negative mass >> is a non-starter in this discussion because: eminent physicists like Kip Thorne, Hawking and others have discussed negative mass (to stabilize wormholes for example), so there is no "shame" in theoretically considering negative mass.  As to experimental evidence, whether Casimir effect and other types of negative energy can indeed be considered experimental evidence of negative energy is up for discussion, but again eminent physicists (for example in discussion of stabilization of wormholes posit the Casimir energy as the means for the negative energy).

And again, in your considerations of conservation of energy you are dealing with a concept where some authors (Dr. White and Dr. Minotti) explicitly state that they are considering negative energy !

Therefore, since your conservation of energy considerations ignore negative energy-mass, your considerations of energy conservation seem to be inapplicable to the concepts advanced by Dr. White and Dr. Minotti.
« Last Edit: 02/10/2016 06:16 PM by Rodal »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #54 on: 02/10/2016 04:39 PM »
...
I see two different problems. Possibility of negative mass, that is Weak Energy Condition breaking, is one thing. But modification of rest (invariant) mass in a closed system without a balanced counterpart in changes in kinetic energy is another one, it looks more like conservation of (total) energy breaking, whether the change appears as + or - mass.

As an example of the difference between those 2 hypothesis : we can apply usual SR for conservation of energy and momentum when considering a single particle of mass m1>0 splitting into two particles of mass m2>m1 and m3<0. The hypothesis of the existence of particle of mass<0 doesn't change the equations. But your approach seems to ignore one equation (conservation of energy) and hence gives the system a degree of freedom absent of this initial example. Negative mass deltas is then not specifically implicated, and indeed your solution space also shows positive (unbalanced) delta mass, i.e. actually either positive or negative total energy evolutions.

Your latest answer clarifies this as citing a scalar field or supplementary spatial dimension as required to make sense of such mass variation... I would have a hard time following in detail Minotti (or you following Minotti) on such topic outside of usual SR application, but maybe could understand a few words of how, one way or another,  energy is conserved in the end to say that the approach "conserves momentum-energy" ?

...
In the above post: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1489632#msg1489632, I already addressed the fact that I think that variable rest mass is incompatible with Special Relativity, and so it is perplexing why you are bringing Special Relativity (assuming this is what you mean by "SR") into the picture again, as if demanding that Special Relativity should be obeyed.

I thought this was clear:

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?

1) Special Relativity: NO. The rest mass cannot be a function of the time coordinate, as Lorentz covariance would not be preserved.  Variation of rest mass cannot be due to kinematic (velocity or position) evolution.

...

As to conservation of energy, I thought that this was also clear:

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?

...
2) Einstein's General Relativity (GR): It appears as NO.  It appears that a time-dependent variable mass would give rise to a time-dependent Energy Stress tensor, solely due to the mass variability with time, which is not consistent with Einstein's GR theory of gravitation.   Also it appears that Relativity's Energy-Momentum equation:

m2 c4 = E2 - p2 c2

may prevent general time-dependent variable mass.

Note: I need to review how does Woodward accommodate variable negative mass-energy in his theory (which I understand he states is consistent with Einstein's General Relativity), as it appears to me that there should be an issue with the time-dependent Energy-Stress tensor and with the Energy-Momentum equation in such a theory.

...

Also it is perplexing why you keep bringing up conservation of energy for a variable mass problem in a closed system, when it was stated repeatedly that any such variable mass in a closed system to make sense it would involve creation (or destruction) of negative energy-mass.

As to how variable mass can be addressed in scalar-tensor theories of gravitation, this has already been done prior to my posting.  I'll try to find the references...

In your discussion of conservation of energy in the EM Drive: you disregard the fact that authors like Dr. White and Dr. Minotti posit a solution that involves negative energy-mass, and instead you insist in considerations of energy conservation that involve the assumption of constant positive energy-mass, an assumption in contradiction with the assumptions of the authors of the concept (EM Drive) you are addressing in your consideration.

Rather than insisting on obeying Special Relativity and constant energy-mass, when discussing the EM Drive concept, it seems to me that it is better for me (and you too) to address the fact that the authors (Dr. White and Dr. Minotti) posit negative energy-mass, rather than disregarding the author's assumptions.
« Last Edit: 02/10/2016 10:44 PM by Rodal »

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #55 on: 02/10/2016 05:59 PM »
The following references using a particular scalar-tensor theory (https://en.wikipedia.org/wiki/Brans%E2%80%93Dicke_theory) (not the particular theory used by Minotti) treat the mass, instead of being constant, as a space-time dependent scalar:

Observable effects of a scalar gravitational field in a binary pulsar
Eardley, D. M.
Astrophysical Journal, vol. 196, Mar. 1, 1975, pt. 2, p. L59-L62.

Gravitational radiation, close binary systems, and the Brans-Dicke theory of gravity
Will, C. M. & Zaglauer, H. W.
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 346, Nov. 1, 1989, p. 366-377.

Relativistic Gravity in the Solar System. I. Effect of an Anisotropic Gravitational Mass on the Earth-Moon Distance
Will, C. M.
Astrophysical Journal, vol. 165, p.409

Also see section 7-7.1 of "the famous ADM paper", where the rest mass m is treated as varying slowly (*) with time:

R. Arnowitt, S. Deser, C. W. Misner, "The dynamics of general relativity," in: L. Witten, Gravitation: An Introduction to Current Research, (Wiley, New York, 1962) pp. 227-265.
http://arxiv.org/abs/gr-qc/0405109

(*) in cosmological time !
« Last Edit: 02/10/2016 07:24 PM by Rodal »

#### rfmwguy

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #56 on: 02/10/2016 08:21 PM »
Doc, the invitation extends to your crew here as well if anyone needs a lot of emdrive file storage space. Forgot to mention that on the other thread. Sorry for the oversight and interruption.

#### frobnicat

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #57 on: 02/10/2016 10:46 PM »
Dr Rodal, thanks for answering my comments about your work around "negative mass" creation and conservation of momentum. It was clear from the equations that you considered only conservation of momentum and didn't consider conservation of total energy, but from early posts (on the main EM drive thread) I had the impression that you were assuming some compatibility with conservation of energy, for instance (bold added by me for emphasis) :

.../...
Variable mass, implying the need for negative mass to self-accelerate, addresses both conservation of momentum and it also addresses conservation of energy.

Energy is conserved, and such a propulsion device is not a free-energy machine, because the greater the speed, the lower the mass.  More on that later...

(The practical problem of course is that up to now, nobody has found experimental evidence of negative mass  )

1) The above statement that negative mass addresses the conservation of energy problem is correct in the specific instance of constant zero initial lumped mass.

Yes, on that we agree. Mathematically a 0 mass lump has always 0 kinetic energy and needs 0 Force to accelerate or change velocity. But there is no EM drive related experiment claiming or hinting of a 0 initial mass of device. And more importantly all EM drive related experiment claiming positive anomalies record effective force≠0 on some massive object (mass>0). This is this force that raises problem of conservation of energy (relative to what is measured as explicit input power) for something that is not supposed to react on the walls of the lab or other object nearby like earth (through geomagnetic field for instance) if it is to be claimed as "anomalous".

Quote
Specifically, the initial condition of lumped rest mass=0, staying constant  (for example as a result of equal magnitude negative mass as positive mass) answers all your previous posts regarding conservation of energy, and it does so trivially, as the kinetic energy is zero for zero mass, and you cannot use the EM Drive as a generator if it has effective zero inertial mass. (Effectively I know that even photons, with zero rest mass have energy, so if you want you can throw an expression with the Plank constant there, and replace zero kinetic energy with very very small kinetic energy).

"The initial condition of lumped rest mass=0" is irrelevant for the devices tested so far. But, for sake of clarifying this hypothetical limit case, even if it was the case that we had a device with rest mass=0, if at the cost of 1kW injected power it is to give more than 3.33µN of effective force against some massive object and not reacting on the lab's walls (that is the claim of the experiments), then such 0 rest mass device answers none of my previous post regarding conservation of energy in conditions of stationary velocity and stationary thrust, as the kinetic energy plays absolutely no role in such argument, and I could still use an EM Drive as a generator even if it has effective zero inertial mass .

Quote
If my memory is correct, in your consideration of energy conservation you never considered that the rest mass could be zero.

No because when considering energy conservation in the context of stationary velocity and stationary thrust this is irrelevant as no change in kinetic energy is involved.

Quote
You assumed (unstated) that the rest mass was greater than zero.

I had no incentive to assume such, since it won't change the outcome. The device could be of positive, 0, or negative mass, the argument depends solely on a stationary frame invariant effect of given thrust/power>3.33µN/kW. Obviously the stationary requirement implies constant mass, as anything else than constant mass of the device would trivially imply exhaust. The device is claimed to be propellantless.

Quote
The concept which you addressed in your energy conservation statements, the EM Drive, has been discussed by Dr. White and by Dr. Minotti as involving negative energy-mass, so one should discuss the consequences of such negative energy-mass in considerations of energy conservation, instead of ignoring it, and assuming as in your considerations, that the energy-mass was positive, and constant.  In other words, your energy considerations for the EM Drive,  ignore the premise of these authors.

Well, on those threads about EM drive I was the first to mention the possibility of a tachyon exhaust to give some grounding (within known frameworks) of self powered propulsion better than 3.33µN/kW. I'm not afraid of imaginary rest mass, I'm ready to hear about negative energy or negative mass. But this is different than plain breaking of conservation of total energy.  3 + -2 = 1  fine, but 3 = 1 where are we heading ?

Quote
2) The argument that <<nobody has found experimental evidence of negative mass >> is a non-starter in this discussion ...

Just to be clear, while I tend to agree, this is not something I wrote nor put forward in my remarks, for the reason I'm not objecting that negative mass is a somehow legit hypothesis worth of discussion.

Quote
... because: eminent physicists like Kip Thorne, Hawking and others have discussed negative mass (to stabilize wormholes for example), so there is no "shame" in theoretically considering negative mass.  As to experimental evidence, whether Casimir effect and other types of negative energy can indeed be considered experimental evidence of negative energy is up for discussion, but again eminent physicists (for example in discussion of stabilization of wormholes posit the Casimir energy as the means for the negative energy).

Out of my domain of substantiated opinions. Serious names think the concept of negative mass or negative energy deserves a place in theoretical physics, fine, I don't object (how could I ?).

Quote
And again, in your considerations of conservation of energy you are dealing with a concept where some authors (Dr. White and Dr. Minotti) explicitly state that they are considering negative energy !

Negative energy is different from creation or annihilation of energy. I've become extremely skeptical of dr. White's views on advanced topics since I saw how he treated (or let treat by a collaborator, since it's "only" cosigned White) mundane classical action reaction system in an annex dealing with the crucial aspect of conservation of energy of propellantless device.

My "problem" with White's take on that, and I think with what you are embarking into with γ1m1v1=γ2m2v2 (m1≠m2), is not that there can be a m<0 or Δm<0 or E<0 or ΔE<0 term somewhere, it is that we can't account properly for some (not necessarily restricted to basic special relativity) definition of total energy Etot such that we can guarantee there is never Etot(t+Δt)≠Etot(t) and this is valid for all observers.

Quote
Therefore, since your conservation of energy considerations ignore negative energy-mass, your considerations of energy conservation seem to be inapplicable to the concepts advanced by Dr. White and Dr. Minotti.

My considerations of energy conservation, since I made them under the specific situation of stationary thrust and stationary velocity, quite don't care about the sign of energy or mass terms. They care about some lack of equality, the fact that so far we are not aware of a frame agnostic definition of total Energy for the whole system, in a deep space context (not reacting on lab's walls), such that we don't see Etot(t+Δt)≠Etot(t). While it's true I spoke mainly about apparent excess of energy, the same idea (stationary thrust at stationary velocity) can be applied to make apparent complete wipeout of some energy content, that is as problematic.

#### frobnicat

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #58 on: 02/11/2016 12:11 AM »
...
I see two different problems. Possibility of negative mass, that is Weak Energy Condition breaking, is one thing. But modification of rest (invariant) mass in a closed system without a balanced counterpart in changes in kinetic energy is another one, it looks more like conservation of (total) energy breaking, whether the change appears as + or - mass.

As an example of the difference between those 2 hypothesis : we can apply usual SR for conservation of energy and momentum when considering a single particle of mass m1>0 splitting into two particles of mass m2>m1 and m3<0. The hypothesis of the existence of particle of mass<0 doesn't change the equations. But your approach seems to ignore one equation (conservation of energy) and hence gives the system a degree of freedom absent of this initial example. Negative mass deltas is then not specifically implicated, and indeed your solution space also shows positive (unbalanced) delta mass, i.e. actually either positive or negative total energy evolutions.

Your latest answer clarifies this as citing a scalar field or supplementary spatial dimension as required to make sense of such mass variation... I would have a hard time following in detail Minotti (or you following Minotti) on such topic outside of usual SR application, but maybe could understand a few words of how, one way or another,  energy is conserved in the end to say that the approach "conserves momentum-energy" ?

...
In the above post: http://forum.nasaspaceflight.com/index.php?topic=39214.msg1489632#msg1489632, I already addressed the fact that I think that variable rest mass is incompatible with Special Relativity, and so it is perplexing why you are bringing Special Relativity (assuming this is what you mean by "SR") into the picture again, as if demanding that Special Relativity should be obeyed.

I thought this was clear:

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?

1) Special Relativity: NO. The rest mass cannot be a function of the time coordinate, as Lorentz covariance would not be preserved.  Variation of rest mass cannot be due to kinematic (velocity or position) evolution.

...

Yes, and that was clarifying, thanks. Thing is, you are starting a whole analysis by an expression of momentum conservation borrowed from SR (Special Relativity) and then apply it in a context where it is no longer frame invariant (in you own terms "Lorentz covariance would not be preserved") : what is the value left of a such a relativistic equation when it is no longer frame invariant ? In the (respectable) thought experiments you are developing here, I don't see what this equation brings, when saying that total energy can vary (which is outside SR), more than simply stating that momentum can vary directly (which is not more nor less outside SR). You end up with an analysis that doesn't enforce some form of conservation of total energy at all (it is not conserved) and that conserves momentum but restricted to only one privileged frame. That's not much left!

SR doesn't prevent Newtonian mechanics to be obeyed for systems with relative velocities <<c. GR doesn't prevent SR to be obeyed for systems in ~flat space-time. So if it does exist situations of variation of rest mass that cannot be due to SR kinematic evolution but due to such exotica as inflaton scalar field or 5th dimension I still would like (expect ? require ?) such situations to be compatible with central SR aspect of frame invariance, or else that well motivated non SR equations are used from scratch (and that such non SR equation do decay to SR ones as a limit case).

Quote
As to conservation of energy, I thought that this was also clear:

Is the concept of a time-dependent, variable "rest-mass" (mass that would be measured at rest), allowed by the following theories?

...
2) Einstein's General Relativity (GR): It appears as NO.  It appears that a time-dependent variable mass would give rise to a time-dependent Energy Stress tensor, solely due to the mass variability with time, which is not consistent with Einstein's GR theory of gravitation.   Also it appears that Relativity's Energy-Momentum equation:

m2 c4 = E2 - p2 c2

may prevent general time-dependent variable mass.

Note: I need to review how does Woodward accommodate variable negative mass-energy in his theory (which I understand he states is consistent with Einstein's General Relativity), as it appears to me that there should be an issue with the time-dependent Energy-Stress tensor and with the Energy-Momentum equation in such a theory.

...

Also it is perplexing why you keep bringing up conservation of energy for a variable mass problem in a closed system, when it was stated repeatedly that any such variable mass in a closed system to make sense it would involve creation (or destruction) of negative energy-mass.

Because for me "closed system" and "variation of total energy" is a contradiction in terms. Beyond that I can't quite follow you on GR ground.

Quote
As to how variable mass can be addressed in scalar-tensor theories of gravitation, this has already been done prior to my posting.  I'll try to find the references...

In your discussion of conservation of energy in the EM Drive: you disregard the fact that authors like Dr. White and Dr. Minotti posit a solution that involves negative energy-mass, and instead you insist in considerations of energy conservation that involve the assumption of constant positive energy-mass, an assumption in contradiction with the assumptions of the authors of the concept (EM Drive) you are addressing in your consideration.

Rather than insisting on obeying Special Relativity and constant energy-mass, when discussing the EM Drive concept, it seems to me that it is better for me (and you too) to address the fact that the authors (Dr. White and Dr. Minotti) posit negative energy-mass, rather than disregarding the author's assumptions.

Well, maybe it's better I leave that altogether. I certainly don't have time to dig seriously all those papers.
Just so that you understand my motives, that are not simple trolling (as I'm sure you know) but genuine perplexity (probably as much as your perplexity at my perplexity) :
Your equation for deltamass as a function of deltaV and Vinitial is exactly the same as that we would obtain if we were to consider in SR (with both CoE and CoM) an aggregation of a "lump" of mass Minitial merging at velocity Vinitial with an auxiliary lump of mass Mauxiliary at rest to yield an aggregated lump of mass Mfinal at velocity Vinitial+deltaV. So to me your "variation of rest mass" for a single lump is indistinguishable from a merge event between two lumps, hence qualifying the hypothetical varying mass single lump as "closed system" illusory.

A bit like if you were to invoke spontaneous mass creation from the fifth dimension to explain a turbo jet thrust, and you end up with same equation as when deriving it as air breathing. Albeit the "closed system" equation by spontaneous mass creation from fifth dimension works in only one privileged frame and breaks all relativistic frameworks otherwise (Galilean for a start), while the natural open air-breathing approach gives same prediction in the reference frame privileged before, but is also correct in all frames, and fully compatible with tried and proven frameworks. This is a lot of trouble just for asserting that it could conceivably be a closed system when, given the phenomenology of the considered equations, all indicates that it is open.

And this has nothing to do with signs of mass or deltas of mass, until we are speaking of the efficiency, and I agree that specifically negative energies do appear when dealing with self powered >3.33µN/kW because of the need to dump energetic debt (again : open system, not closed)

#### Rodal

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##### Re: Resonant Cavity Space-Propulsion: institutional experiments and theory
« Reply #59 on: 02/11/2016 12:30 AM »
...This is a lot of trouble just for asserting that it could conceivably be a closed system when, given the phenomenology of the considered equations, all indicates that it is open....
My God,  I posted with bold red signs and a moving banner, something titled "Under construction" and now you are stating that I am asserting that the EM Drive is a closed system that works on spontaneous and continuous creation of negative mass-energy

Considering what are the implications if the EM Drive would be a closed-system does not at all mean that one is "asserting" that it is

Such considerations are par for the course for anybody involved in R&D !

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