From the FAQ on emdrive.com:
"Q. Does the theory of the EmDrive contravene the accepted laws of physics or electromagnetic theory?
A. The EmDrive does not violate any known law of physics."
How can this be?
Suppose you have a 1000 kg vehicle propelled by an EmDrive.
In one frame of reference the vehicle accelerates from 0 m/s to 1 m/s. An observer in this frame of reference concludes that the EmDrive must have consumed a minimum of ((1000)*(1)^2)/2 - ((1000)*(1)^2)/2 = 500 J.
In another frame of reference the vehicle accelerates from 10 m/s to 11 m/s. An observer in this frame of reference concludes that the EmDrive must have consumed a minimum of ((1000)*(11)^2)/2 - ((1000)*(10)^2)/2 = 10,500 J.
Energy is not being conserved.
I know this is the 10th thread and this has probably been covered previously but it seems that there are only two positions a reasonable person can take:
1.) The EmDrive does not work; the observed effects are all within experimental error.
2.) The EmDrive works; all errors have been accounted for; energy and momentum are not conserved.
Does anyone hold the position:
3.) The EmDrive works; all errors have been accounted for; energy and momentum are conserved.
If so, can you explain how?
Yes when calculating a change in velocity of a boost of 1m/s then 1/2*m*v^2 for 1/2*m*(0+1)^2 is much smaller than 1/2*m*v^2 for 1/2*m*(10+1)^2.
To truly get down to the mystery of why a constant boost can give such a difference in energy you have to consider the potential energy.
http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.htmlTo simplify matters you can consider a ship in an elliptical orbit around the sun. At the aphelion of its orbit it has some decreased velocity due to its increased potential energy. If a burn is initiated here the burn will be less efficient. The reason being is because the fuel has a lot of wasted potential energy. As it is released from the ship it has a long ways to fall.
Rather if you let the ship fall into the gravity well the ship speed will increase and the fuel when released will be at a much lower potential energy.
There is another subtle matter here hidden in the physics. For the maximum efficiency you want to release your fuel at exactly the speed the ship is flying at. Why? So that the fuel gains no potential energy.
Letting the ship fall into a gravity well is two fold. It decreases the potential energy of the fuel and increases the velocity of the ship. Increasing the velocity of the ship increases the efficiency of fuel exhausted at high velocity (you must fire the fuel off at a higher specific velocity for it to come to a stop relative to the gravitational potential well). The larger the gravitational potential one falls into the better.
What about where there are no gravitational wells. How then does the ship change velocity with out accelerating its own fuel. Every bit of energy used to accelerate the fuel/ship increases the speed. The larger the speed the faster the fuel needs to be kicked out for the fuel to come to a rest. A rest you ask? With respect to what frame? Probably the same reason a photon rockets efficiency increases as the ship reaches c the photons kicked out increase in efficiency. Or the photons caught and reflected come to a complete stop or completely red-shifting.
Relativistic solutions to directed energy
Neeraj Kulkarnia, Philip M. Lubina, and Qicheng Zhanga
aDepartment of Physics, University of California, Santa Barbara, CA, USA
...
Thus, a photon striking the sail of a spacecraft moving arbitrarily close to c transfers all its energy to the kinetic energy to the
spacecaft. The situation seems to indicate the efficiency approaches 1 as v → c...
By the way there are 2 types of gravitational assists. One is falling into a gravitational well and then using your thrusters (increasing their efficiency). The other is depending on how you approach a gravitational body and how you leave it you can swap kinetic energy between the two bodies i think.