October 2, 2011
a matter of relativistic quantum mechanics resolved (in my mind): why do we see a blurry, smeared picture where if you moved your hand a little your digital camera gives you a fuzzy thing in motion, it follows from Energy-time uncertainty which has two forms in relativistic quantum mechanics **extremely fast moving quantum-objects**
1. if the quantum is say an electron, it’s got mass, energy-time uncertainty becomes momentum-time uncertainty.
2. if the quantum is photon (visible light) the ET uncertainty is speed-time uncertainty, because photon has no mass in it’s rest frame.
**In qmech its a relatively massive particle, so electron will show same effect as photons given their rest mass or rest energy is very uncertain, in a situation where it is so, a fact some relativists do not understand. There are many energy variables now given that mass is also energy as per relativity. the more you go towards general relativity the more complicated it becomes. **
Since we take pictures with visible light which are massless-quantums in their rest frame, this means for a sufficiently small time the speed will be very uncertain from point 2 above. This is the case when we are taking a picture and something moved, depending on how fast it moved the allowed time for the camera goes from a small number to a very very small number. Very slowly moving objects are blurred very little. The same reason why-when you take pictures from a car because of relative motion the picture gets blurred. It’s the relative motion (from Galilean relativity we see everyday).
Now the speed of the photon bunch registered with the camera is very uncertain **in general this means the energy of these bunch is very uncertain, “a saving paradox” for theory of Relativity, since relativity proclaims a fixed speed for photon.
Since speed is distance/time and time is precise by the shutter or whatever of the camera, the more precise this time is the more there is motion between target and camera, this only means distance is very very uncertain. The camera doesn’t know for sure where exactly the light came from if the speed of shutter is fast or the relative speed between camera and target whose picture is taken is larger. This reflects in the picture being blurred, you expected the position of the target to be somewhere but the uncertainty showed up.
In general for such a situation energy-time uncertainty meant a distance-time uncertainty. Quantum Mechanics as we know now, explains pretty much everything we know today, except the few problems which is why Physics survives. These problems are the reason Physics community has something to work on.
The above example I gave is a remarkable nature of Quantum Mechanics known as “Correspondence principle”. It says for everything that happens at the scale of the quaantum there exists a possibility that in some form or other this effect is carried to the scale of our existence and beyond. That is why we feel electromagnetic force, that is why sun-light causes diffraction, that is why CMBR creates dots on your TV screen, that is why we can convert quantum signals into something we can see or hear. That is why we see particle tracks in bubble chamber. Radioactivity causes harms that are perceptible on a human and animal body and so on. It is the scale which is small necessarily, for where quantum processes are valid and it is carried along to a larger scale. If it were wrong at the scale we could never properly explain it, thankfully we understand so much quantum mechanics. The novice often confuses the scale with size, energy, time and error and thinks everything has to be small, not all of them in a given situation have to be small. There is a little novice in all of us reg. what is the nature of quantum mechanical scale and the nature of the correspondence scale, but that is why it is that much more exciting that we see these effects on an everyday basis. It would be plain wrong*! to assert that quantum mechanics does not correspond to everyday phenomena. Some of the very basic phenomena in our everyday lives are basic quantum mechanics, some of whose forms were present from time immemorial, classical mechanics was insufficient to explain these but pat came along quantum mechanical understanding so we did not dig down and said “well I always saw that and thought to myself my knowledge of wave-mechanics does not explain it, we needed also the particle kinematics, intimately interwoven before we realize such an understanding”.
*! A wrong notion our great popularizers have been carrying forth to this day. The problem if you recognize is that the true popularizers are scarce but when it comes to the hand of the unimaginably inspired smart alecs it gets mystified again. As physicists it is our reponsibility to demystify nature, not to clog the knowledge already gained, because we are very good in taking offense but not to understand why there was offense in the first place. I have often heard smart alecs saying they are inspired fools a term they get from great minds. Socially fine.