Integrate the product of the energy density and the adjacent element of the surface area over the whole inner surface. The NET result will be the force. Is it zero? If the walls are perfectly conducting, it should be. However, since there are asymmetrical non-zero losses in the warm copper, maybe not.
Alright, but how would that be inherently better than the collimated Photon Rocket?
Because a gravitational acceleration is created which is directly proportional to the time derivative of the power dissipation.
What exactly is being dissipated. This sounds a lot like saying gravity exists because of increasing entropy or energy disipation via matter.
I am inclined to think that the energy dissipation is with regards to the vacuum energy. That is the vacuum loses energy when acting on matter in free-fall. So energy conservation free falling matter accelerates and gains energy and the vacuum loses energy.
(Not sure how this fits in but when that matter impacts the planet surface it loses its kinetic energy to entropy or thermal aspects much of which can escape the planets surface and travels into the solar system away from the planet. )
However, this energy loss of the vacuum seems permanent while the matter is gathered, (reducing the dance of the matter in equilibrium with it) the more matter is gathered. If energy is given to the matter to allow it to escape the gravity well, the well dissipates, and the matter separated speeds up in time. Almost like the separation of the matter allows the energy to be given back to the vacuum. (Red shift of light escaping a gravity well is light giving some of its energy to the vacuum?)
It seems tempting to view the vacuum in a gravity well as being devoid of energy similar to the Casimir force where plates are attracted via an energy defecit between them. However, this Casimir force is supposed to be different from gravity is it not?
So how does this figure into your power dissipation? Is it power being dissipated from the vacuum, where this extra energy seems to be appearing via propellant-less acceleration? So if we keep harvesting it, creating our own black hole. Basically devoiding the vacuum of its energy? Dissipating the vacuum?
I'm beginning to think that the EMdrive isn't translationally invariant or temporally invariant, longitudinally. It is rotationally invariant as seen when spinning the drive around its longitudinal axis.
I'm beginning to think that the EMdrive isn't translationally invariant or temporally invariant, longitudinally. It is rotationally invariant as seen when spinning the drive around its longitudinal axis.
That's an interesting idea - what if you were to spin the EMdrive around its longitudinal axis (since it is axisymmetric) - what would be the result of doing that?
Because a gravitational acceleration is created which is directly proportional to the time derivative of the power dissipation.
So the longer that field takes to dissipate without further power input into the cavity, the more propulsive this thing is?
No, it's a time derivative (a rate), not an integral. The higher the rate of change in power, the greater the acceleration, and thrust.
Because a gravitational acceleration is created which is directly proportional to the time derivative of the power dissipation.
So the longer that field takes to dissipate without further power input into the cavity, the more propulsive this thing is?
No, it's a time derivative (a rate), not an integral. The higher the rate of change in power, the greater the acceleration, and thrust.
So how do you maintain the rate of change in the power, in order to produce/sustain the acceleration?
You can't just keep jacking up the power forever - presumably that's just happening at startup, and then after that your power feed level is steady. Can you just cycle the power? If the rate of change of power is negative (ie. power level is dropping) then is the thrust or acceleration negative?
There are ultra-short pulse lasers, like Femtosecond-pulse Lasers. There are even long-wave versions of these. If this short-pulsed approach were taken using microwaves, then could that provide the high rate of change in power to give better acceleration?
http://ieeexplore.ieee.org/document/7442760/
https://en.wikipedia.org/wiki/Ultrashort_pulse
Why do I think that I need to accelerate in order to travel to the stars? I don't. I can get there by friction too. I can slow down in a particular direction and I can still go to places unseen. If that doesn't make any sense, research about how we all travel through spacetime at c. If I slow my passage through time, I increase my passage through space.
I'm beginning to think that the EMdrive isn't translationally invariant or temporally invariant, longitudinally. It is rotationally invariant as seen when spinning the drive around its longitudinal axis.
Integrate the product of the energy density and the adjacent element of the surface area over the whole inner surface. The NET result will be the force. Is it zero? If the walls are perfectly conducting, it should be. However, since there are asymmetrical non-zero losses in the warm copper, maybe not.
Alright, but how would that be inherently better than the collimated Photon Rocket?
Because a gravitational acceleration is created which is directly proportional to the time derivative of the power dissipation.
What exactly is being dissipated. This sounds a lot like saying gravity exists because of increasing entropy or energy disipation via matter.
I am inclined to think that the energy dissipation is with regards to the vacuum energy. That is the vacuum loses energy when acting on matter in free-fall. So energy conservation free falling matter accelerates and gains energy and the vacuum loses energy.
(Not sure how this fits in but when that matter impacts the planet surface it loses its kinetic energy to entropy or thermal aspects much of which can escape the planets surface and travels into the solar system away from the planet. )
However, this energy loss of the vacuum seems permanent while the matter is gathered, (reducing the dance of the matter in equilibrium with it) the more matter is gathered. If energy is given to the matter to allow it to escape the gravity well, the well dissipates, and the matter separated speeds up in time. Almost like the separation of the matter allows the energy to be given back to the vacuum. (Red shift of light escaping a gravity well is light giving some of its energy to the vacuum?)
It seems tempting to view the vacuum in a gravity well as being devoid of energy similar to the Casimir force where plates are attracted via an energy defecit between them. However, this Casimir force is supposed to be different from gravity is it not?
So how does this figure into your power dissipation? Is it power being dissipated from the vacuum, where this extra energy seems to be appearing via propellant-less acceleration? So if we keep harvesting it, creating our own black hole. Basically devoiding the vacuum of its energy? Dissipating the vacuum?
Dissipation of the internal energy of the EMdrive. Reducing its mass. Its mass isn't constant. Neither is its momentum. The way I'm thinking now is that the velocity is remaining constant, and it's the mass and the momentum that's changing. I'll see if that holds up over the course of a lot of thinking.
The wavelength spreading haunts me. I see the answer right in front of me. I've read about this, I've studied it, I've seen it in different contexts*, and yet it eludes me.
* http://forum.nasaspaceflight.com/index.php?topic=42978.msg1735887#msg1735887
Why do I think that I need to accelerate in order to travel to the stars? I don't. I can get there by friction too. I can slow down in a particular direction and I can still go to places unseen. If that doesn't make any sense, research about how we all travel through spacetime at c. If I slow my passage through time, I increase my passage through space.
I'm beginning to think that the EMdrive isn't translationally invariant or temporally invariant, longitudinally. It is rotationally invariant as seen when spinning the drive around its longitudinal axis.
I see a contradiction in my post, and it is probably related to the mass defect that I believe must be there, so I know I'm not understanding yet.
Just for clarification, I'm treating the electromagnetic waves as the internal forces, and I'm treating the cavity losses as the external forces. The resultant is the partially standing wave.
I do understand how the unequal losses at each end set up the unequal amplitudes (and I showed the math for how that happens in a slide) of the counterpropagating waves, and which the sum of the two is a partial standing wave. That's internal and external forces at play. It conserves momentum.
The results reveal that the cutoff frequency has a red-shift with the increase of the grating depth. Figure 6(c) depicts the group index c/vg as a function of the incident frequency at a given grating depth. It is found that the group velocity vg (≡∂ω/∂β) can be slowed down significantly when the incident frequency approaches the cutoff frequency. The quasi-period-stub structure is introduced to enlarge the slow light frequency range.
Why do I think that I need to accelerate in order to travel to the stars? I don't. I can get there by friction too. I can slow down in a particular direction and I can still go to places unseen.
I really think that Time is just a non-physical construct imagined by us, and that Entropy is the more representative and more physically meaningful concept. Time simply marks the changes in Entropy, and progression of Time is really just progression of Entropy. Relativistic effects on Time are actually just relativistic effects on Entropy and its rate of change. We define all Observation through our own mental process of Observation, which is simply based on a a sequence of Entropy-correlated states.
So when you say "if I slow my passage in time, then..." - I'd argue that it's better to think in terms of "if I slow my Entropy changes, then..." - ie. it's better to re-think and re-work everything temporally-related in terms of entropy instead.
Not trying to be metaphysical or philosphical here, just going with Occam's Razor. (It's actually Time which is metaphysical, while Entropy is physical)
Why do I think that I need to accelerate in order to travel to the stars? I don't. I can get there by friction too. I can slow down in a particular direction and I can still go to places unseen.You seem to be confused. Slowing down is still accelerating. The same relativistic effects happen. Also, if you are going to talk about friction, it needs to be friction on some external medium. This may sound a bit pedantic, but it is important to be clear when discussing things like this.
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Your description quite trivially does not match reality, so it fails Occam's Razor. The only correlation between entropy and time is that as time progresses forward, the rate of change of entropy is greater than or equal to 0. As a very explicit example, if you have a block of wood sitting somewhere, entropy is increasing very slowly. If you then light the wood on fire, entropy is increasing many orders of magnitude faster, yet no clocks nearby will run at a different rate. Time is therefore quite real and distinct from entropy.
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Your description quite trivially does not match reality, so it fails Occam's Razor. The only correlation between entropy and time is that as time progresses forward, the rate of change of entropy is greater than or equal to 0. As a very explicit example, if you have a block of wood sitting somewhere, entropy is increasing very slowly. If you then light the wood on fire, entropy is increasing many orders of magnitude faster, yet no clocks nearby will run at a different rate. Time is therefore quite real and distinct from entropy.
...
There have been a lot of theories I have seen posted recently, and I have just skimmed most of them. Generally there are a lot of suggestions like this one for radical changes to physics, yet no attempt to even check if basic mechanics is still consistent under them. I get some people are just brainstorming or thinking out loud, but this seems to be significantly adding to the noise floor in the thread.
The Entropy state of our brain is what I was referring to when I said our "mental process of observation" - that is what allows us to note the passage of Time. The block of wood has its own entropy state independent of our brain - so yes, it can vary for the block of wood (catches on fire or doesn't), and that doesn't affect the entropy state of our brain.
But there is the Overall Entropy state of Our Local Universe - and the entropy state of a clock is more correlated to this Overall Entropy state of Our Local Universe than it is to the entropy state of the block of wood (burning or not), or the entropy state of our brain.
Sorry to divert conversation with discussion of Physical-vs-Metaphysical. But Time is metaphysical, while Entropy is physical.
We are only able to mark time due to changes in Entropy - because we are only able to think/remember/Observe due to changes in Entropy (inside our brains).
The passage of time is independent of entropy. entropy cannot measure the passage of time, only the direction.

No. The entropy change in our bodies, in the block of wood, etc. affect the local entropy of the universe, so burning a block of wood increases the rate at which entropy increases, and if entropy could be used instead of time, that means a nearby clock (with a mechanical mechanism electrical mechanism, or any other principle of operation) should run faster.
Completely false. Time is physical. You cannot write the laws of physics without time. You cannot use entropy to fully describe an elastic collision between 2 balls, but you do need to use time to do so.

I skipped most of the stuff you talked about observation and brains because it is quite obvious that the chemical balance inside our brains does not actually affect the rate that time passes. This sentence though goes a step further into utter contradictory nonsense. Remembering stuff inside our brains would mean an increase in order, and a local decrease in entropy (enabled by the increase in entropy caused by digestion and metabolic processes, our bodies maintain an internal equilibrium, so the positive entropy change ends up generally leaving our bodies along with the waste heat.).

While I agree with your intent above or at least the bulk of it, in this last.., "yet no clocks nearby will run at a different rate. Time is therefore quite real and distinct from entropy.", I question the logic.
Clocks are not time. Clocks measure/record change, within an agreed upon rate. I agree that entropy as you describe above, does not change the way clocks measure/record any rate of change... But clocks are not time. Time is a construct of the mind we use to communicate how we observe and experience change. A construct for which we use clocks as descriptive rulers. IOW Change is real and time is a construct of the mind used to communicate, the measurement, observation and experience of change.
This is most times a nit picking distinction (almost certainly in this case), because the concept is critical to our understanding of everything else, "under the sun" and to communication itself. However sometimes in these discussions the tendency to attribute to "Time" some sort of inherent independent reality, as if it were causative rather than a descriptive construct, seems to confuse at least to some extent, many of the other concepts and possible mechanisms being discussed.