Posted: Sep 02, 2011 8:44 am
heisenbinker wrote:If we carry out the thought experiment for the uncertainty principle : i.e. the photon hitting the electron under a microscope.
For this experiment to be of quantum nature the observation is compulsory and the photon has to hit the electron.
Now, say you want to observe the position at time 't'.
And say for convenience sake you can setup the experiment and perform it instantly.
Two separate points i would like to make are
1) For the photon to hit the electron it has to travel a distance 'd' and collide with it. The time taken would be d/c. where c is the speed of light. So the observation is made at t+ d/c. The time for the photon to be observed by the observer can be neglected from the fact that the observer is watching on the plane adjacent to the collision, an infinitely small distance away.
2) There is a probability that your photon will not hit the electron instantly because the photon has a linear (?) trajectory and miss the electron since we don't know where it is. This probability should depend on all possible points in space that can be occupied by the electron and how fast the photon can traverse through this space (by means of rebounds or whatever) which is certainly finite, hence at time t you will never ever determine the position x certainly.
Am i right in thinking this?
welcome
except you havent yet said what exactly is your equipment for measuring time?. The problem with time is that there is no uniquely independent way of even measuring it, it can be done only in relation with something else. 1). true, there is gap between measurement and observation, but it again depends on your experimental setup, how do you make an observation.
2). While there is the issue of probability without doubt, you could consider averaging over some n trials.
thirdly, the uncertainty principle has relations between energy and time, position and momentum, angular position and angular momentum. So theoretically one could get position and time accurately, it now depends on your experiment.