Heisenberg "Uncertainty" as a reference frame effect

[dvandom]

Michael Dickson of the University of South Carolina gave a symposium talk today on the topic of how considering frames of reference more carefully can lead to scientific insight. Some of it was over my head, so I make no promises that I'm accurately representing his points, but I think I can manage to explain it at a level that most of you who read my LJ will be able to follow.

Background time, first.

A frame of reference is basically how you define what zero is. From where do you measure distances? What counts as "standing still" when you measure speed? Anything can be a frame of reference, but the best ones are those that aren't accelerating. These are called inertial frames. They can be moving, but not speeding up, slowing down, or changing direction.

All science works the same in every inertial frame, which is why they're so handy. If you're in an accelerating (or non-inertial) frame, things don't always work as well, and you have to start approximating. The more acceleration, the worse your approximations get. It's not all that bad, though. For accelerations up to anything a human can survive, you can measure things as well as a part in a billion and not really run into trouble. Most of you probably don't need to measure anything that well, and it wasn't until about 150 years ago that even theoretical "we might want to measure this well eventually" considerations even ran up against the non-inertial nature of being on Earth.

Around that time, though, it started to be possible to measure things really well, so long as you were in an inertial frame. It started to matter how low an acceleration had to be before it would be low enough to not screw up your measurements.

Okay, that's background. Inertial frames are good. We don't normally live in one, so at some point our approximations break down. Here's where we get into the meat of the talk.

The general point of the talk is that while we may normally assume our frame is inertial enough, it's worth carefully examining the ways in which it is accelerating, to see if that explains anything in a new way. Specifically, the example used was the Heisenberg "Uncertainty" (I prefer Indeterminacy) Principle.

Let's say you've got a frame in which you're measuring things. Your measuring device has to be connected to that frame to mean anything. Any measurement is going to require interaction, so your device (and the entire frame) will get a little "kick" when you make a measurement. For reasons that don't bear going into right now, the more precisely you want to measure something, the bigger that kick will be.

To someone standing outside your frame, every time you measure something, your frame will accelerate. In other words, every measurement you make will result in your frame becoming less of an inertial frame. If you measure position, that makes measurements of momentum less precise because you're violating the assumption of an inertial frame. And the more precisely you measure position, the more badly you break your inertial nature. And that is indeterminacy...you can't measure position without screwing up your measurement of momentum, and vice versa.

Now, if you're working with rulers and radar guns, you'll never measure one thing well enough to get in the way of your measurement of the other thing. Measurement devices that operate on a human scale are able to ignore a rather large amount of acceleration before their assumptions break down. But these days, scientist are able to measure things to within extremely small distances and extremely exact energies, and it's starting to matter on a practical level. Measuring that wavelength down to a femtometer just bumped your detector enough to make your measurement of momentum no good.

It gets better. Let's consider that outside observer. In theory, if they're in an inertial frame, they could see exactly what's happening in the lab, and not get messed up by the fact the lab is bumped. Classical mechanics assume that an inertial frame does exist somewhere, even if we can never find it. But say we were in that legendary zero-acceleration frame. How do we tell what's going on in the bumped lab?

We have to measure it.

So our frame gets bumped.

Congratulations, you just broke the inertial frame.

You cannot make a measurement that assumes an inertial frame without accelerating that frame and turns exactitude into approximation.

You can't avoid Indeterminacy.