Bad physics

You may have heard of the "EmDrive", a gadget that supposedly provides thrust by bouncing microwaves around in a metal can.  It's sort of like trying to power a spaceship by having the crew play ping-pong

Now there's a new "theoretical explanation" of this quite possibly nonexistent effect.  It was published in European Physics Letters by Michael E. McCulloch.  It's completely flaky, and normally I'd ignore it, but for some reason the normally respectable mag Technology Review decided to mention it.  So people are starting to talk about it, not realizing how goofy it actually is!

McCulloch talks a lot about the Unruh effect, so you should learn a bit about that.   It's never been detected, but most physicists believe in it, because it's a consequence of special relativity and quantum mechanics.   When you put these theories together, they predict that an accelerating observer will see a faint glow of thermal radiation.

Why hasn't it been detected?   Because it's predicted to be very, very  weak.   Absurdly weak!

For example, suppose you accelerate at a trillion gee - a trillion times more than a falling object on Earth.  Then the theory predicts you'll see thermal radiation at a temperature of 40 billionths of a degree Celsius above absolute zero.   That's so faint nobody knows how to detect it!

What if you sit there watching someone else accelerate past you?  What will you see then? 

There are arguments about this, but whatever happens, it'll be too small to detect under most circumstances.  Chen and Tajima have proposed an experiment to accelerate a single electron at 10 septillion gee  (that is, 10^25 gee).  That might be enough for something interesting to happen.  However, the EmDrive gadget is nowhere near as intense. The version NASA built is weaker than a typical microwave oven.
This has not stopped McCulloch from claiming that the Unruh effect "explains" the EmDrive! 

He also claims it explains the rotations of galaxies, eliminating the need for dark matter.  He also claims that it explains the accelerating expansion of the Universe, eliminating the need for dark energy.  He also claims that it explains the Pioneer anomaly - a small mysterious acceleration that some spacecraft have encountered as they go far out into the Solar System. 

None of this makes any sense.  In fact, I can barely believe I'm even talking about it!  But it fooled the folks at Technology Review, so let me quote a bit of McCulloch's paper, and comment on it:

McCulloch (2007) has proposed a new model for inertia (MiHsC) that assumes that the inertia of an object is due to the Unruh radiation it sees when it accelerates [...]

So the inertial mass of an object is caused  by the Unruh radiation?   Okay... yup, that's certainly new.   Let me just say there's no evidence for this.

[...] radiation which is also subject to a Hubble-scale Casimir effect.

Oh, good, the Casimir effect!  As if things weren't confused enough already.  The Casimir effect is a very real thing: a force between very nearby metal plates, caused by the fact that the electric field can't easily penetrate a conductor.  It's a reasonably large force when the plates are a few nanometers apart, but it rapidly becomes weaker as you move them farther apart.   So now imagine they're as far apart as most distant galaxies we can see....

In this model only Unruh wavelengths that fit exactly into twice the Hubble diameter are allowed, so that a greater proportion of the waves are disallowed for low accelerations (which see longer Unruh waves) leading to a gradual new loss of inertia as accelerations become tiny.

The Hubble diameter is very roughly the size of the observable Universe.  Now he's saying that at rather small accelerations the Unruh effect is so tiny that the thermal radiation has wavelengths even larger than the size of the observable Universe.  That's true.  And that of course means that this effect is even more absurdly weak than in the example I gave. 

But he's also saying that something like the Casimir effect takes place, where the size of Universe plays the role of distance between the metal plates in the usual Casimir effect.   In other words, when an object accelerates fast enough that the Unruh radiation it sees fits inside the Universe, the Unruh effect "kicks in" and gives the object a kick, or makes its mass get bigger, or something.

Again, two things stand out: 1) it doesn't work like this, and 2) even if it did, the effect would be so tiny that... why are we even talking about it?  Even the pathetically weak thrusts the EmDrive supposedly creates - less than 100 micronewtons in the latest experiments - are like a thundering herd of giant elephants compared to what we're talking about here. 

The difficulty of demonstrating MiHsC on Earth is the huge size of [the Universe] in Eq. 1 which makes the effect very small unless the acceleration is tiny, as in deep space. One way to make the effect more obvious is to reduce the distance to the horizon and this is what the emdrive may be doing since the radiation within it is accelerating so fast that the Unruh waves it sees will be short enough to be limited by the cavity walls in a MiHsC-like manner.

So now it's the radiation inside the can that's "accelerating so fast" that it sees Unruh radiation... which is limited in wavelength by the size of the can... which somehow makes the whole can get a push when the Unruh radiation fits into the can.

In short, we've got a Rube Goldberg machine where all the parts involve brand new theories of physics with nothing backing them up, and all the actual effects cited are absurdly tiny.

But that's not all!   One amusing thing is that while the Unruh effect involves quantum mechanics, Planck's constant - the number that shows up in every calculation in quantum mechanics - never shows up in this paper.  So McCulloch is not actually doing anything with the Unruh effect!  Instead, he's making up brand new stuff, like this:

Normally, of course, photons are not supposed to have inertial mass in this way, but here this is assumed.

So his photons have mass - and on top of that, the mass changes with time: see his Equation 4!

Verdict: this paper is a stew of nonsense served with a hefty helping of warmed-over baloney.   And yet we see in the Daily Mail:

Have scientists cracked the secret of NASA’s 'impossible' fuel-free thruster? New theory could explain the EmDrive that may one day take man to Mars in 10 weeks

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