A highly technical article on why motion blur occurs. Its a quantum mechanical stationary state. Whats a stationary state? A stationary state is just a snapshot of a time. But according to Heisenberg’s uncertainty relation of time vs energy (a daunting conundrum, because of time) when time is sharply measured, energy cycles are incompletely observed. Thats what we see in blurred images.
The energy cycle is not yet complete. which is to say, the error in energy is more and more when time is sharply measured equaling to instants. This is the case, because we are using high profile modern camera where shutter speeds can be so sharp they render the energy cycles incomplete. That is they take those instants when the position of any point is no more point but spread like a wave. The points (or sharp images) appear very blurred, or stretched out.
[This article is in the process of further review e.g. speed of light having a spread has to be dismissed or not]
A matter of Relativistic Quantum Mechanics resolved, in my mind; why does one see a blurry, smeared picture, e.g. if one moves one’s hand, a little, while taking a picture, a digital camera, gives a fuzzy thing in motion.
— It follows from the energy-time uncertainty relation, which corresponds to two forms, in Relativistic Quantum Mechanics, (R.Q.M.)
First off, what is R.Q.M.; Relativistic Quantum Mechanics pertains to extremely fast moving quantum-objects.
A quantum-object is a really small particle, usually an elementary particle such as an electron or even the atom. The more massive the quantum becomes, the lesser maximum speed such objects can move at, due to energy of motion converting into more and more mass, at higher and higher speed.
So, even though, technically, a molecule can be a quantum object, it can not move as fast as the electron, if enough energy can be imparted, to such an object.
For particles that are this small, speed is usually measurable in terms of the speed of light in vacuum, as these tiny objects attain speeds, that can quite match, that of light itself, sometimes both speeds being refereed to in vacuum.
When speed of these tiny objects, is even a bare 10%, of the speed of light in vacuum, these objects deviate, from the behavior, they would other wise show in the classical realm. In the former situation of really slow particles, the speeds add up as if they are additive in a normal way, but when the speeds become even as significant, as a mere 10%, compared to speed of light, the simple additive nature is lost, the speeds rather add up in more sophisticated way, given by something called as the Einstein’s velocity addition formula.
Similarly when the speed rises even to 10% — of vacuum speed of light, the particle’s mass keeps on increasing, as the speed can’t increase arbitrarily. These new kinematics behavior, are ingrained into whats called the Special Theory of Relativity.
So while these objects are Quantum Mechanical in nature, due to their small size, that is, their existence turned from being totally deterministic to probabilistic, coming from the statistical nature of the wave function, now they become Relativistic by nature. Together these objects obey therefore the Relativistic Quantum Mechanics.
So, when quantum objects, move at relativistic speeds, two situations arise.
- if the quantum is say an electron, it’s got mass, energy-time uncertainty gives rise to momentum-time uncertainty.
- if the quantum is photon — the quantum of visible light e.g., the energy-time uncertainty becomes; speed-time uncertainty, as photon has zero mass.
In Quantum Mechanics, electron is 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. Although, the more one goes towards general relativity, the more complicated it becomes.
Since we take pictures with visible light, which are mass-less-quanta, 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. This is the same reason why — when one takes pictures from a car, because of relative motion, the picture gets blurred. It’s the relative motion — from Galilean Relativity, that 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-over-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, one 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 a few problems, which is why Physics survives. These unsolved problems are the reason Physics community has something to work on.
The above example I gave, is a remarkable nature of Quantum Mechanics, and it is known as “Correspondence Principle”. It says “for everything that happens at the scale of the quantum, 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 our 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 — see note below, to assert the fallacy, 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“.
Note — A wrong notion our great popularizers, have been carrying forth, to this day. The problem if one recognizes, is that the true popularizers are scarce but when it comes to the hand of the unimaginably inspired smart Alec’s, it gets mystified again. As physicists, it is our responsibility, to demystify nature, not to clog the knowledge which is already gained. We are very good in taking offense, but not to understand, why there was offense in the first place. I have often heard smart Alec’s saying they are inspired fools a term they get from great minds.
In my last 3 weeks of conscience churning and even before the OPERA results were out, I had hit upon the fact, that, Relativity and Quantum Mechanics aren’t completely consistent with each other. This I had described in many articles — of mine, eg one article written 2 years ago — I had been thinking about this, a long time ago, about 3 years ago — and 6 months ago, I found the answer, but only recently I came across the answer, with almost complete clarity.
The Energy-time uncertainty for photons, leads to a speed-time uncertainty. See article, here.
Also a relation to OPERA anomaly is plausible.
Shouldn’t that be the answer to the OPERA anomaly of speed excess? Because, if the time is precisely known, it will only make the speed uncertain, by an amount depending on what the precision of time is. Also when speed is uncertain with time certain, it only makes distance uncertain, as in the case of “high profile camera blurring the clarity of picture” for exact same reason. Do we know the exact value of these “newer” uncertainties? Cos if we do the 1st thing we should have done is check them with the OPERA anomaly.