Newton: Quantum, I'm Sure

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�� The basic Newtonian laws in classical physics are deterministic. Given the forces acting and the motion of a system, you can predict the position and momentum and of course the velocity of an object at any time and also the future. However, in the microscopic world which comprises of particles not perceivable by our eyes as in electron and proton, quantum theory shows that the simultaneous measurement and hence the specific description of the position and momentum of a particle in an experiment or in theory is not feasible. This is the first part of the amazing Heisenberg uncertainty principle (HUP). The second part deals with the uncertainty relationship between time and energy. In short, the uncertainty in the position, Dx and the uncertainty in momentum, Dp of a particle is given by the inequality:

Dx Dp > h/2p

where the momentum p is within an uncertainty of Dp and the position x of a particle at the same time to within an uncertainty Dx and h is the Planck's constant. Using common sense, the exact position of a particle should be determinable by measuring its momentum and the time it has taken to travel by means of highly sophisticated tools depending on the accuracy you need. Unfortunately, our common sense and knowledge are gain through daily experiences with the macroscopic world, i.e. with objects we can actually see. �

�� The wave function of a particle is a combination of many different wave functions with different momentums. HUP is a fundamental law of physics. The more accurate you make the position measurement, the more uncertainties you will have regarding its momentum (and vice versa). �

�� The reason you do not observe the effects is because they are small. For example, if you know the position of your computer to within 1mm, you can only know its momentum to within 10^-30 kg m/s. Note that the inequality above implies that the uncertainty in large objects such as a bowling ball or the Earth can be ignored since the inequality can also be written as Dx Dv > h/(2mp); momentum, p = mass, m x velocity, v (p = mv). Hence, Newtonian physics which includes F = ma is only applicable to large objects (to ignore Heisenberg's principle) with low speed (to ignore relativistic effects). Similarly, your car could suddenly move to the other side of the street, but the probability is around 10^-500. You could suddenly find yourself in space, but the probability is again extremely small. �

�� The second part is more important. It states that you cannot know both energy and time simultaneously. The result is that energy conservation can be violated for a short period of time. But the bottom line assures the conservation. This turns out to be important in electromagnetic interactions since in Quantum Electrodynamics (QED), the interaction is carried by photons which have the wrong amount of energy. ��

�� A quote from Albert Einstein: ��

�� Common sense is the deposit of prejudice laid down in the mind before the age of 18.�

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