November 12, 2011
hello sir, im a 12th grade student and im having trouble explaining the uncertainity of the velocity as in comes in the uncertainity principle by Heiseinberg , and what about speed of light , uncertainity in the measurement of the velocity of light , does this make sense ???
1. uncertainty relation between momentum and position which is basically a speed and position uncertainty hence depending on what uncertainty you have for position you get the uncertainty on time **and vice a versa**
2. in case of uncertainty between energy and time it is so in absense of relativity. In relativistic situations one can not define the position of photons (light) very sharply because they have zero mass and speed of light velocity. That means Energy-time uncertainty becomes a speed-time uncertainty for mass-less particles such as photons and momentum-time uncertainty for particles with mass such as electrons and mesons moving at very high speed (relativistic speeds).
SO for photons which are always relativistic when the “error” (actually uncertainty) in position is smaller than the wavelength you can determine the position of the photons to the accuracy of the wavelength, this is called ray-optics or wave-optics because we can define light rays as we can define a sharp position for the photons, ofcourse for small wavelengths.
But for small wavelengths that is very high freq. waves of light there is still an uncertainty between speed and time. The first case was speed and position now the 2nd case is speed and time. These two cases which in non-relativistic situation different cases are essentially the same thing for high energetic photons because there is a position and time in speed.
That just means if one (say position) is uncertain the other (time) has to be proportionately certain. eg if you take a picture with an intense source of light and the target of which you are taking the pic moves, it creates a fuzzy or smeared out impression. If you move your hand when pic is taken your hand’s image is funny, its smeared out. That is so, since there is speed = (distance, time) uncertainty, if one becomes sharply known the other becomes equally uncertain. In the picture usually the distance is what is uncertain since the time is already fixed. That means the image is not sharp but is fuzzy across a distance.
In summary for the relativistic quantum mechanics two separate uncertainty equations have become condensed into only one uncertainty relation, one between the distance and time.
[for photons momentum and energy are correlated, since photons are massless it still has a momentum because there is energy, so all uncertainty equations are valid in the scheme of theory but what is essentially playing is a consistent inter-relation among different physical quantities which become clear as per the situation.]
eg In a picture taken with a camera a moving train appears fuzzy and smeared out but stationary targets are depicted with better accuracy. That is the relative speed between the camera and the targets brings additional distance uncertainites into the image because the time is sharply known through the act of the taking the picture ..