Interesting stuff. Either there's something odd with these experiments, or there's something odd with the laws of physics. Without a PhD in physics I can't judge, but it does seem like an extraordinary claim, and those require extraordinary evidence, so right now my money is on an experimental artifact. Exciting though, feels like reading a Greg Egan novel

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On the other hand, I do think we can figure out just how extraordinary the claim is using basic high school physics. Does a propellantless drive necessarily violate conservation of energy? So I went and played around a bit, and came up with this high school-level thought experiment involving a bowling ball rocket. So, for everyone else who'd like a concrete example and some numbers that anyone can understand to go with Jason's explanation, read on

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**Bowling ball rocket**A bowling ball rocket is an ordinary rocket (a mass driver), with bowling balls for fuel. These are of course high-tech aerospace grade bowling balls: they mass only 4 kg each, and they have a spring attached that is coiled up and held in that position with a bit of string. The spring on each bowling ball stores 24 J of potential energy and has no mass.

The bowling ball rocket itself has an empty mass of 8 kg, and it carries two bowling balls for fuel. It hovers in space somewhere conveniently far away from everything else, and next to it is us, wearing space suits and measuring things.

So, here's the initial situation:

m_b1 = m_b2 = 4 kg mass of each bowling ball

m_r = 8 kg mass of rocket

v_r = 0 m/s velocity of rocket

v_b1 = 0 m/s velocity of bowling ball 1

v_b2 = 0 m/s velocity of bowling ball 2

And the energy balance looks like this

E_kin = 1/2 * m_r * v_r + 1/2 * m_b1 * v_b1 + 1/2 * m_b2 * v_b2 = 0 J

E_pot = 2 * 24 J = 48 J

E = 0 J + 48 J = 48 J

Notation note: I'm using primes in the following to denote instances of time, not derivatives.

*First bowling ball*Now, the rocket uses its robot arm to place one bowling ball against the back side of its hull, with the spring touching the hull, and then it cuts the string. The spring uncoils, pushing away the bowling ball in the backward direction, and the rocket in the forward direction. All the potential energy in the spring is converted into kinetic energy.

Now, we want to know the new velocities (relative to our still stationary selves) of all the objects involved:

v_r' = ? velocity of rocket after first bowling ball launched

v_b1' = ? velocity of first bowling ball after launch

v_b2' = ? velocity of second bowling ball after launch of first

Since the second ball is still on board the rocket, we know that v_b2' = v_r'. Also, this is an ordinary rocket, so energy is conserved, so the total kinetic energy of all the objects must equal the amount of energy stored in the spring. That gives us

1/2 * m_b * v_b1'^2 + 1/2 * (m_r + m_b) * v_r'^2 = 24 J

Secondly, momentum is conserved, so we have

m_b * v_b1' + (m_r + m_b) * v_r' = 0 kg*m/s

Solving these equations, we get

v_r' = 1 m/s

v_b1' = -3 m/s

v_b2' = 1 m/s

We can also calculate the kinetic energy (again relative to our stationary selves) of the various objects in the system:

E_kin_r' = 1/2 * m_r * v_r'^2 = 1/2 * 8 * 1 = 4 J

E_kin_b1' = 1/2 * m_b1 * v_b1'^2 = 1/2 * 4 * 9 = 18 J

E_kin_b2' = 1/2 * m_b2 * v_b2'^2 = 1/2 * 4 * 1 = 2 J

Also, we can calculate the momenta

p_r' = m_r * v_r' = 8 * 1 = 8 kg*m/s

p_b1' = m_b1 * v_b1' = 4 * -3 = -12 kg*m/s

p_b2 = m_b2 * v_b2' = 4 * 1 = 4 kg*m/s

*Second bowling ball*Now, the rocket launches its second bowling ball. Rocket and second bowling ball together had 6J of kinetic energy, and 24J of kinetic energy is added by the spring, so the total kinetic energy of rocket and ball 2 must be 30J after the second launch:

E_kin_r'' + E_kin_b2'' = 30 J

1/2 * m_r * v_r''^2 + 1/2 * m_b2 * v_b2''^2 = 30 J

Momentum is again conserved:

m_r * v_r'' + m_b1 * v_b1'' + m_b2 * v_b2'' = 0 kg*m/s

Solving this (exercise for the reader

), with v_b1'' = v_b1', we get

v_r'' = 1 + sqrt(2) ~= 2.41 m/s

v_b1'' = -3 m/s

v_b2'' = 1 - 2 * sqrt(2) ~= -1.82 m/s

E_kin_r'' = 1/2 * m_r * v_r''^2 = 12 + 8 * sqrt(2) ~= 23.3 J

E_kin_b1'' = 1/2 * m_b1 * v_b1''^2 = 18 J

E_kin_b2'' = 1/2 * m_b2 * v_b2''^2 = 18 - 8*sqrt(2) ~= 6.7 J

p_r'' = m_r * v_r'' = 8 + 8*sqrt(2) ~= 19.3 kg*m/s

p_b1'' = m_b1 * v_b1'' = -12 kg*m/s

p_b2'' = m_b2 * v_b2'' = -7.3 kg*m/s

So that's an ordinary rocket, and everything works as expected.

**Moving frame of reference**There's one more interesting property of this: it works from a moving frame of reference. If we had not been stationary in our space suits, but had done our measurements while moving along at 1 m/s relative to the starting speed of the rocket, then energy and momentum would still have been conserved.

In that case, we start with an initial kinetic energy of 1/2 * 16 kg * 1 m^2/s^2 = 8 J and momentum of 16 kg * -1 m/s = -16 kg*m/s (we're moving at 1 m/s relative to the rocket, so we measure the rocket moving at -1 m/s relative to us). After the first bowling ball is released, we measure velocities

v_r' = 0 m/s

v_b1' = -4 m/s

v_b2' = 0 m/s

which gives a kinetic energies

E_kin_r' = 1/2 * m_r * v_r'^2 = 1/2 * 8 * 0 = 0 J

E_kin_b1' = 1/2 * m_b1 * v_b1'^2 = 1/2 * 4 * 16 = 32 J

E_kin_b2' = 1/2 * m_b2 * v_b2'^2 = 1/2 * 4 * 0 = 0 J

The total kinetic energy is now 32 J, which equals the initial 8 J plus the 24 J contributed by the spring. Energy is conserved. For momentum we get

p_r' = m_r * v_r' = 8 * 0 = 0 kg*m/s

p_b1' = m_b1 * v_b1' = 4 * -4 = -16 kg*m/s

p_b2 = m_b2 * v_b2' = 4 * 0 = 0 kg*m/s

So the total is -16 kg*m/s, which equals what we had initially as well. Momentum is also conserved in this moving frame of reference. I'll leave the situation after the second bowling ball is launched for the reader.

**Magic spring rocket**So, now let's try a propellantless rocket. We replace our aerospace grade bowling balls with magic springs. Those are just the springs from the bowling balls, still storing 24 J of energy, but now without the bowling balls attached. They have no mass whatsoever, but when they uncoil, they still push the rocket ahead.

*First magic spring*So, we go back to our unmoving reference frame, reset the rocket to 0 m/s, and have it trigger its first magic spring. Assuming that the magic springs conserve energy, this converts 24 J of potential energy into 24 J of kinetic energy, which is added to the rocket. Its kinetic energy relative to us space suited observers will become

1/2 * m_r * v_r'^2 = 24 J

from which we get velocity and momentum

v_r' = sqrt(6) ~= 2.45 m/s

p_r' = m_r * v_r' = 8 * sqrt(6) ~= 19.6 kg*m/s

Now here's something odd, because momentum has not been conserved. Apparently our magic spring has transferred 19.6 kg*m/s of momentum somewhere else. If I understand the reasoning a bit, this is supposed to be taken care of by mass-energy equivalence, which requires the extended concept of momentum from Special Relativity, and is beyond the simple Newtonian physics we're using here.

*Second magic spring*Now, the rocket triggers the second magic spring. This adds another 24 J of kinetic energy, for a total of 48 J, giving velocity and momentum

v_r'' = sqrt(12) ~= 3.46 m/s

p_r'' = m_r * v_r'' = 27.7 kg*m/s

There are two interesting observations here: the delta-v we got from the second magic spring is less than what we got from the first magic spring (1.01 m/s vs. 2.45 m/s). Also, the momentum change is less, 8.1 kg*m/s vs. 19.6 kg*m/s. But energy is conserved. This is one type of propellantless rocket.

**Constant thrust magic spring rocket**TheTraveller

claimed that the EMDrive gives constant thrust at a constant power input. For the magic coil rocket, that would mean that each coil gives the same delta v. Let's see what happens with the total energy of the system if we assume that the second coil gives as much of a velocity change as the first:

v_r = 0 m/s

v_r' = sqrt(6) ~= 2.45 m/s

v_r'' = 2 * sqrt(6) ~= 4.90 m/s

E_kin = 1/2 * m_r * v_r^2 = 0 J

E_kin' = 1/2 * m_r * v_r'^2 = 24 J

E_kin'' = 1/2 * m_r * v_r''^2 = 96 J

So, here we have a situation where we put in two coils of potential energy, for a total of 48 J, but we're getting 96 J of kinetic energy back for it, at least relative to an unmoving observer. Constant acceleration, but no conservation of energy. That's a second type of propellantless rocket, and this is what ppnl is describing when (s)he says you can't have constant acceleration without violating conservation of energy.

So, which of the two types of propellantless drive is the EMDrive? According to the whitepaper linked by TheTraveller:

Thus as the velocity of the waveguide increases in the direction of thrust, the thrust will decrease until a limiting velocity is reached when T=0.

So, apparently it's the first type. Which means that it doesn't necessarily violate conservation of energy, at least, based on Newtonian physics.

There's one more issue though. According to AdrianW (in

Reply #216), while the first propellantless rocket type doesn't violate conservation of energy, it implies that it now matters from which reference frame you are measuring. So let's reset the type 1 rocket one more time, fire our suit thrusters to get us up to 1 m/s relative to the rocket, and measure the initial situation:

v_r = -1 m/s

E_kin = 1/2 * m_r * v_r^2 = 4 J

p_r = m_r * v_r = -8 kg*m/s

After the first spring, we get

v_r' = sqrt(6) - 1 ~= 1.45 m/s

E_kin' = 1/2 * m_r * v_r'^2 = 4 * (sqrt(6) - 1)^2 = 28 - 8 * sqrt(6) ~= 8.40 J

p_r' = m_r * v_r' = 8 * (sqrt(6) - 1) ~= 11.6 kg*m/s

So, from this perspective, we again lost 19.6 kg*m/s of momentum by uncoiling the first spring, but now energy isn't conserved! We get different results when measuring from different moving frames of reference! That is a violation of Galilean relativity!

This can only work if there is some very special observing velocity at which everything works out, and a rule that says that observers at other velocities need to compensate for their velocity relative to the special one. But if that is the case, then we should be measuring different values when the Earth is moving in the same direction as this special velocity, compared to six months later when it is moving in the opposite direction. Which we probably would have noticed by now.

**Conclusion**So, assuming Newtonian physics, which none of the actual physicists working on this are doing of course, it appears that a propellantless rocket either violates conservation of energy, or requires one frame of reference to be special. That's a very extraordinary claim. Now if someone can explain to me how dr. White sidesteps this issue (in the simplest terms possible) I'd be much obliged

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