Energy Conservation

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There is no energy paradox and there is no free energy

Todd (@WarpTech) resolves the energy "paradox" showing that it is due to a failure to take into account the increase in mass of the system:

See: [1] and [2], Todd writes:

The issue of a perpetual motion machine goes away when you accept that if the system has input power and no expulsion of mass, then mass is going to increase with time.

m(t) = m0 + Pin*t/c^2

Therefore, if F/Pin = N/kW is a constant, the acceleration will vary inversely to the mass as a function of time.

a(t) = a0/(1 + (Pin*t)/(m0*c^2))

F = m(t)*a(t) = m0*a0

v(t) = a0*t/(1 + (Pin*t)/(m0*c^2))

Now, the kinetic energy can never exceed the input energy.

Pin*t = m0*c^2 * (sqrt(m0*(a0*t)^2 / m(t)*v(t)^2) - 1)

It’s similar to special relativity, but for low velocity, taking relativistic mass into consideration. Even though the speed is far from c, mass is still increasing as energy is input to the system and is NOT expelled.

________

Consider another problem: assume an on-board power plant with 100% mass to RF conversion efficiency. Would the mass lost in the power plant would balance the mass gained in the thruster(aside from waste in the thruster)?

That is correct. The mass would remain constant if the on-board energy storage were 100% converted into stored RF energy and thrust. However, constant mass in this case still does not lead to free energy. The kinetic energy + stored RF energy can never exceed the initial stored energy of the on-board power plant.

As every engineer knows there is no free-energy, not even from the Quantum Vacuum. The thrust from a photon rocket is mistakenly taken to be F = P/c. This is wrong. The thrust of a photon rocket will depend on the change in frequency as the light leaves the material medium and enters vacuum. It's easy enough to show that inside a material, the momentum density D x B, depends on the properties of the medium.

D x B = eR*e0*E x uRxu0*H

where eR and uR are the relative permittivity and permeability in the material, and e0 and u0 are in vacuum.

eR >> u0, uR >> u0

When the light leaves the medium and enters the vacuum;

D x B = e0*E x u0*H

So where did the extra "relative" momentum go? This physics is being totally neglected in the equation F = P/c. That ratio is a back of the envelope calculation of the momentum of light in free space. It has nothing to do with how well light can push on a material as it exits.


Implications of Constant Thrust

Doctor White has proposed that the EM Drive is capable of producing constant thrust at a constant power output. User frobnicat has shown (in the following text and image) that if this were to be true, then the EM Drive could be utilized as a source of unlimited energy. [1] This of course constitutes a violation of Conservation of Energy.

"As often remarked : for any propellantless device yielding "given constant thrust for given constant power" (ie. a definite thrust/power ratio) there is a velocity relative to a power feedback loop system above which net power surplus can be generated (indefinitely, wear apart). This velocity is simply the inverse of the thrust/power ratio : V (m/s) = power (W) / thrust (N)." -frobnicat [2]

On the assumption that the results provided by the various experimenting groups are valid, then one of the following two options as provided by user deltamass[3] and clarified by user frobnicat [4] must be true. The options are as follows:

Option 1: Energy is conserved, but there is a preferred rest frame. In essence, the drive has a maximum change in velocity (a decreasing acceleration curve) that it can impart irrespective of its starting velocity. The idea of a preferred rest frame is at odds with general relativity.

Option 2: An apparent breach of conservation of energy is possible, where the mechanism by which conservation of energy is maintained is as yet unknown. An example of a possible solution to this problem is that the drive could in some way be emitting tachyons.[5]

Tachyons are fictional particles that can travel faster than the speed of light. Sending signals faster than light, leads to violations of causality, see: Tachyonic Antitelephone.

Since option 1 leads to a violation of general relativity and option 2 leads to a violation of causality, one concludes that, with constant input power supplied to the EM Drive, the acceleration cannot be constant. As remarked by WarpTech the acceleration must decrease with increasing velocity, as per Newton's 2nd law:[6]

Acceleration = Thrust / Mass = Power / (Mass*Velocity)

So, for constant input power to the EM Drive (and constant vehicle mass), the vehicle's acceleration must decrease in inverse proportion to the vehicle's velocity. To achieve constant acceleration, increasing power must be supplied to the EM Drive, in proportion to the increasing velocity.

Kinetic Energy Implications

This is a basic back-of-the-envelope debunk. It is not framed as a proof, it simply shows that the Em drive *cannot* work without new physics.

Given:

1. [math]f=ma[/math]

[math]a=\cfrac{f}{m}[/math]

if this device can produce a constant force then it will produce a constant acceleration and velocity will increase linearly in accord to:

2. [math]v=v[/math]0[math] + at[/math]

which will be proportional to the amount of energy provided to the device.

However the amount of kinetic energy KE in the device will evolve over time according to:

3. [math] e=\cfrac{1}{2}mv^2 [/math]

So here we have the core problem. Because the increase in KE over time is exponential, and the velocity and energy input is linear then at some point we will have more energy in the system than we put in.

Kvt.png

There is no way to rescue this proposition other than to say either the energy comes from somewhere else, ie the quantum vacuum OR that the device can somehow sense how fast it is going and therefore does not let you keep accelerating. This second rescue proposition appears to have already failed experimentally. The Earth is currently moving at approximately 390 km/s in the direction of the constellation Leo. If this device somehow was not frameless then there would have been a significant variation when the experiment was tried in different directions. There was not.

In Summary

If this device works, new physics is involved. Either the quantum vacuum is not as passive as we thought or special relativity falls, or both.



See Talk:Energy_Conservation for more discussion on this.

References