h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

Heisenberg's Uncertainty Principle

If Heisenberg's Uncertainty Principle states that it is impossible to know both the position and velocity of an object at the same time, but that it is possible to measure either the position or velocity separately, then it must surely be possible for two observers to take simultaneous measurements.

If one observer measures the velocity, while at precisely the same time, the second observer measures the position, then this does not so much break the HUP but bends it! Neither observer is breaching the HUP, but together they provide both the position and the velocity.

As for the photon used to measure the electrons position causing the electron to change velocity, then surely there are ways around this as well. If the electron was 'illuminated' by photons fired from all directions simultaneously, then the net effect of any one photon would be cancelled by the equal and opposite effect of the diametrically opposed photon.

Again this would allow the position and velocity to be aquired.

Surely, Heisenberg's Uncertainty Principle can't be that easy to negate. So where does this go wrong or is there a loophole in the logic.

There's a loophole in the logic - just simply imagine that the two observers you talk about are directed by one person, who's trying to find velocity and position at the same time. On a more fundamental level, the uncertainty principle is driven by the actual interactions of particles. Although photons are massless and chargeless, they have to react with the observed particle (eg. and electron) in some way for any information to be deduced so the state of the electron is disturbed. Then if somebody actually tries to fire off a beam of photons at the electron he will not be able to find either the position or the velocity to an arbitrary accuracy because the other observer has already observed it - the vary act of observation destroys the state being observed.

Your idea of firing photons from all direction simultaneously is also interesting. But you have to think about what source these photons will come from. Lasers? Discharge lamps? Whatever method, it will be impossible to have a coherent source of photons point at the same spot from all 360 degrees - photons are emitted from light in wavepackets, and it is entirely impossible that a single wavepacket from one side will reach the desired electron at exactly the same time as an exactly similar wavepacket from the other side.

The problem with thinking about the Uncertainty Principle is that we live in a macroscopic world and it seem scounterintuitice to think that when we measure something we are actually change it becuase everything is just so big. It all gets much more interesting on the quantum level that you have to deal with in this case.

Sadly the picture painted in the main article is too simplistic, lots of books and some teachers/lecturers use it as a way to make HUP seem more intuitive. The main fallacy is that it treats the object under observation as a particle having a real (absolute) position and momentum at the same time. Quantum mechanics however says that an object (electron for example) is not a concentrated point (or very small) particle but rather a diffuse wave packet and if you try to pin it down so that you can reduce the uncertainty in its position then you increase the uncertainty in its momentum and vice versa.

The issue is not one of measurement that we can overcome by clever techniques, but that an object does not have an absolute position and momentum at the same time. I sometimes think of it as a sausage shaped balloon, each end representing the value of position and momentum. If you squeeze one end to a sharply defined point, ie. measure the position or momentum then you inflate the other end, ie. make that value more imprecise.

Hope this makes some sense