I've always thought it was unfair that this is impossible. It's not like you're getting something for nothing - you are still required to expend energy. So why does the universe have to be such a dick about converting electricity directly into motion?
Following the Noether theorem, conservation of momentum follows from uniformity of space (translation symmetry), i.e. for an experimental result it doesn't matter whether it takes place here or some light years away. Although we have some astronomical hints for that and it is a compelling hypothesis (in light of Occams razor) this is not necessarily the case. Finally, the concept of conservation of momentum is a theory for which we have compelling evidence in that nobody has been able to falsify that. But this doesn't necessarily mean that this holds for all times.
Where can I read more about how/why this is impossible? Isn't it just the reverse of a solar sail to send out the photons yourself rather than catching them? It seems like shining a flashlight in one direction should produce thrust in the other. Is that not true or is it something different at work here?
>> It seems like shining a flashlight in one direction should produce thrust in the other. Is that not true or is it something different at work here?
That is absolutely true. Electromagnetic radiation effectively has momentum. Take the energy in joules and convert it to mass via E=mc^2 and then plug it in the momentum equation p = mv but using c as the velocity and you get p = E/c. Change in momentum over change in time is force, so we can then get to F = P/c. I believe the units are Newtons, Watts, and meters/sec. So with 300 Megawatts you can produce a whole Newton of force!
I used this on a physics final once, but hid the work because the prof expected us to use formulas for radiation pressure derived from electromagnetics and I had missed that lecture. Later I derived the general case of my approach and it matched the EM derived formulas. 50/50 if he would have appreciated it or marked it down. The question was "a 50mW laser is reflected off a mirror, what force is exerted on the mirror due to the beam?". Note that the change in momentum is doubled for reflection vs emission or absorption.
> the prof expected us to use […] and I had missed that lecture
You just gave me a wave of nostalgia. That’s how I survived all of my math and physics classes. If you develop an intuitive understanding of the material, you can derive things as needed from a few core principles you do remember. A bit sad when learning is the way to subvert an educational system, though.
I am not sure that I buy that. Charging the battery moves molecules from one electrode to the other. The number of atoms in the battery doesn't change. Do they really get heavier by virtue of changing their arrangement?
If you use that logic (and maybe it is right) then it seems to me as though pushing a rock up a hill makes it ever so slightly heavier too.
Maybe that's my complete lack of intuition about non-classical stuff though.
Yes, they do get heavier by virtue of changing their arrangement. And yes, pushing a rock up a hill makes it - well, the rock will get slightly lighter in weight by virtue of being further from the Earth (classical inverse square law of gravity) - but the total mass of the rock-Earth system (assume you used solar power so you didn't take the energy from a terrestrial source) will slightly increase.
This is my understanding: say you have a spring which is just two positive particles. When you compress it, bringing the particles closer, you're storing energy in the EM field (E²+B²) near the particles. When you accelerate the spring, you're also accelerating the energy, which requires extra energy. This feels the same as the spring becoming heavier.
This is just a microscopic explanation for the general principle that energy has mass. I've never done the math to confirm that the extra energy to accelerate the compressed spring corresponds to the extra mass from stored energy.
When oxygen combines with hydrogen to form water, it gives off energy equivalent to the change in mass (water molecules are oh-so-slightly less massive than their constitute oxygen and hydrogen atoms). A battery produces power by converting molecules into different molecules with more binding energy (i.e. lighter molecules that have given up more energy/mass).
> Isn't it just the reverse of a solar sail to send out the photons yourself rather than catching them?
No, that'd be the case if it were open but it isn't. As I understand it, it's an entirely closed system. That's what's controversial, there's nothing coming out of this "thruster", not even photons.
Wouldn't it be relatively straightforward to repeat the Chinese test in a garage? We're talking a whopping 70 millinewtons here, so equivalent to the weight of 7 grams. Some shrews are lighter than that.
I checked again. Some insider said the Chinese machine does produce 80 millinewtons, but it's less efficient than the NASA one since they take way more power input.
> It seems like shining a flashlight in one direction should produce thrust in the other. Is that not true or is it something different at work here?
Yes, there does seem to be something else. Classical mechanics cannot explain thrust from shining a flashlight inside your spaceship. But "the EmDrive converts electric power into thrust ... by bouncing microwaves around in a closed container"
The momentum those photons are carrying implies a change in momentum to the emitter that is equal and opposite. Conservation of momentum applies even though the emitted substance is electromagnetic radiation, not matter particles.
What's weird about this device is that the radiation chamber is completely closed---the microwaves emitted are then re-absorbed by the chamber, but the claim is that the net momentum of the chamber has changed... Somehow. If it is true, it'd be a violation of conservation of momentum (unless the microwaves are somehow passing momentum to something else, which is why people are talking about quantum mechanics possibly coming into play).
We're well beyond my physics knowledge here. (See IANAP above!) So, I have questions.
Is momentum the only type of energy a photon has?
By allegory: Suppose a cannonball can be red hot, or cool. Separately, it can be flying or at rest. So, there are four cannonball types: hf, hr, cf, and cr.
The hot, flying cannonball has the most energy and the cool, resting cannonball has the least. Yet, the momentum of both flying cannonballs is equal--temperature is orthogonal.
Is all that right?
If it is, then... I thought photons contain some energy that is similarly orthogonal to momentum.
...I guess I don't recall learning that, so maybe I just made it up. But, I have seen videos of laser pointers that can burn paper--they don't seem to have recoil. If the energy that is burns that paper is ... momentum, then I've clearly misunderstood the SCALE of mechanical energy vs. thermal energy. But if the thermal (or something?!) energy is ... separate, then... Well, then we're back to the original point: most of the energy you use to create a photon isn't translated into momentum, so light isn't the propellant you're looking for.
NB I don't have a comment about the microwave chamber other than "NFW.".
Each photon can be completely described by three values. Where is it? Which direction is it traveling? What is its energy? For photons, unlike the cannonball, there are no additional places to store energy.
So, what does that mean for the laser example? Because you are absolutely right that lasers can ignite paper. Photons carry both energy and momentum, but the two cannot be separated. If the paper takes the energy, it must also take away the momentum. The key equation for light is "E = pc", energy equals momentum times the speed of light. The more the energy, the more the momentum. Reduce the energy (or transfer it into the paper
Let's start playing with some numbers. I like drinking tea, and I don't like waiting very long for the water to boil. So, I take out my 1 megawatt laser, and bring a cup of water to boil in about 0.5 second. The lasers you have seen igniting paper are usually 50 milliwatt, so we are talking 20 million times stronger. If there is an effect, surely it would be visible here.
So, that E=pc formula still works here. Because I am transferring energy to my cup of water, I must also be transferring momentum. The question is, how much momentum? To determine this, I rearrange the formula to p = E/c. Using the magic of google to handle the unit conversions, I find that I have about 0.001 pounds of force. The friction of the cup against the table is far, far more than enough to keep the cup from showing any reaction whatsoever.
You are asking absolutely great questions. It is fun to hear somebody not accepting things at face value, comparing to known experiences, and figuring out how to make them fit. Keep up the great work.
Let's see, I think a million watts is a bit more than we need to 235 mL of water in 0.5 seconds.
A calorie (not a Calorie) is the amount of energy it takes to raise 1 ml of water 1 deg C. Suppose 15C water (pipes run through the ground which is cool).
Is that right? While a megawater later is overkill for your cup of tea, it is NOT overkill for ten cups of tea (in half a second)?
For some reason, I always thought of a megawatt as BIGGER. Or, I guess I thought of boiling water as SMALLER.
In any case, there's still something I don't get here.
Obviously if you are trying to change the velocity of your spacecraft and all you have is a cup of water and a megawatt laser, you're not going to point the laser into space, you're going to point it at the cup. (Which happens to be roughly and conveniently conical.)
Picture this: point your megawatt laser at your friend's spacecraft and her cup of water... She'll get delta-V when her water boils, but that's AFTER you already got a little (very little) recoil from firing the laser.
I guess I don't understand the relationship between momentum and mass when mass is zero.
You are correct, and I was wrong in the amount of energy necessary to bring the water to a boil. I was using wolfram alpha, "energy to boil a cup of water", which probably then gave me the energy needed to boil it all away, not just to bring it to a boil.
It takes a tremendous amount of energy to heat things, overall. For example, compare the energy in a bullet to the energy in a warm cup of water. A 20g bullet moving at 400 m/s has 1600 joules of energy. That amount of energy, when used to warm a cup of water, would only warm it by less than 2 degrees Celsius.
Let's start with your last statement, on the relationship between energy, momentum, and mass. The most common formula is E=mv^2/2. This works for objects with mass that are moving slowly. Now, by "moving slowly", I mean "relative to the speed of light". The fastest object made by man, the Juno spacecraft, moves at about 140,000 km/hr, which is a paltry 0.00013c. This formula still works here.
If we want to know what happens at faster speeds, we need to dip into special relativity. There are some messy derivations, but one critical formula that comes out of it is E=sqrt(m^2c^4 + p^2c^2). If you imagine a ninety-degree triangle where the shorter sides are the mass of an object and the momentum of an object, then the long edge is the energy. Increasing either mass or momentum will increase the energy.
Suppose we start dialing down the momentum in this equation. After some math, (http://en.wikipedia.org/wiki/Binomial_theorem ), we arrive at E=mc^2 + mv^2/2. This is the origin of the famous E=mc^2. We now have two terms, the rest energy, and the kinetic energy. Note that the other term is the more familiar form of kinetic energy, which is why it works in everyday life.
Now, suppose we go the other route and set m=0. Then we get E=pc. Even though one side of the triangle (mass) has been reduced to zero, the other side (momentum) still gives it a non-zero energy. I apologize if that is more math than you had been hoping for, but eventually one always runs into some math.
A few things on the spaceship. You are absolutely right on the thinking of it. As soon as the laser switches on, it starts applying force. If my friend's spacecraft is one light-second away, I don't need to wait one second for the laser to reach her before feeling anything, because the light itself carries momentum away. In fact, if I wanted, I could just fire the laser out into space. I get propelled one way, and to balance out the momentum, the photons are travelling in the opposite direction.
> Is momentum the only type of energy a photon has?
Well, momentum is not a type of energy.
But then, for photons and any other massless thing, the momentum is a function of the particle's energy. It's mass that make it possible[1] for the momentum to vary.
[1] IANAP and don't know the exact causation relation here. Talking about causation probably does not even make sense, but I'm not sure of that.
Not quite. It's the ability to travel at different velocities that allows the momentum to vary for particles with mass. But massless particles like photons always travel at the speed of light, so that option is not open to them. Therefore, their energy and momentum are always proportional.
A flashlight in space does propel itself, but that's not really a related question. A more related question is why does a flashlight in a fixed mount inside of a windowless spacecraft not propel the spacecraft (or, similarly, why does a fan inside of a sealed, ventless housing attached to an airplane wing not function as an engine.)
Of course, if there's some way this does work despite what we think we know about physics, its a pretty gigantic breakthrough (well, at least, understanding and practically applying it would be -- otherwise its just an anomaly that provides a pretty gigantic question mark...)
