# Energy Conservation

## 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.  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 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 and clarified by user frobnicat  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.

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:

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. $f=ma$

$a=\cfrac{f}{m}$

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

2. $v=v$0$+ at$

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. $e=\cfrac{1}{2}mv^2$

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

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.

## Free-energy is a just a consequence of incorrectly assuming that constant acceleration will result from constant input power

This "paradox" is not longer a proper paradox (a statement that apparently contradicts itself and yet might be true), but like most paradoxes in Physics it just a result of unwarranted assumptions. It is a misunderstanding that arises from making the assumptions that

1) one can have constant acceleration at constant power ad infinitum and

2) that one can ignore the 1st and 2nd laws of thermodynamics.

Initially, that the acceleration cannot be constant at constant power may not be obvious. But once this becomes obvious (and @frobnicat made an excellent argument to explain this) to continue to use these assumptions becomes unwarranted and eventually it becomes a straw man argument. The so-called typical "attacking a straw man" argument creates the illusion of having completely refuted or defeated an opponent's proposition (that there can be an EM Drive) by replacing it with a different proposition (i.e., "stand up a straw man") (that EM Drive implies constant acceleration at constant power) and then to refute or defeat that false argument ("knock down a straw man") (that the EM Drive necessarily implies free energy) instead of the original proposition.

This is not a debunking proof, all that the "paradox" proves, is that one cannot have free energy: that the assumption of constant acceleration at constant power is untenable. It certainly does not prove that there cannot be an EM Drive that respects the 1st and 2nd Law of Thermodynamics.