Sometimes I get stuck in details when trying to communicate my vision of fundamental physics. This usually begins with positive energy and a desire to look stuff up and see how they correspond to my ideas. I fill notebooks with equations and I draw images whenever I find paper and pens. After a few days of work, I seem to run out of steam and the process is stalled. There is always something terribly wrong in all this, and for all the nice lines I draw between various dots of knowledge, the picture becomes increasingly blurry and incomprehensible. It always ends in a terrible mess of scattered potentials. Nothing stable and reliable ever manifests, and I end up with nothing to say.
A month later, I do it all over again.
What usually helps me terminate these bouts of communication is when I stumble upon something that makes it obvious that my thinking is better left playing around inside my head, and I better leave others alone with their ideas. Today, the reality check looked like this:
Suppose it is desired to measure the position and speed of an object – for example a car going through a radar speed trap. It can be assumed that the car has a definite position and speed at a particular moment in time. How accurately these values can be measured depends on the quality of the measuring equipment – if the precision of the measuring equipment is improved, it will provide a result that is closer to the true value. It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.
In 1927, Heisenberg proved that this last assumption is not correct. Quantum mechanics shows that certain pairs of physical properties, such as for example position and speed, cannot be simultaneously measured, nor defined in operational terms, to arbitrary precision: the more precisely one property is measured, or defined in operational terms, the less precisely can the other. This statement is known as the uncertainty principle. The uncertainty principle isn’t only a statement about the accuracy of our measuring equipment, but, more deeply, is about the conceptual nature of the measured quantities – the assumption that the car had simultaneously defined position and speed does not work in quantum mechanics. On a scale of cars and people, these uncertainties are negligible, but when dealing with atoms and electrons they become critical.
The above is from Wikipedia’s article Introduction to quantum mechanics. So what is wrong in this picture? It is a standard description of a basic quantum concept, so it should not be a problem. Maybe it isn’t, and I’m just seeing ghosts, or I am just too dense to get it. I don’t know, but …
It can be assumed that the car has a definite position and speed at a particular moment in time.
How can one assume such nonsense? How can we build a resonable argument based on the assumption that a moving object can have both “speed” and “position” measured simultaneously? Do we really need Heisenberg to tell us that’s impossible, not only on a quantum level, but impossible all together?
Isn’t it obvious that to measure the speed of object X, going from a to b, requires object X to change position? And does this not tell us that as long as object X stays at position a, we cannot define its speed because the damn car, or particle if you will, doesn’t have any speed. It simply refuses to travel along our points of measurement. But sure enough, if it just sits there, we can say a lot about its position. In fact, it has to be perfectly still when we define its position. As soon as object X starts rolling, position is lost, but we can now say something about its speed.
At “a particular moment in time”, object X can never have speed at all.
Moment in time cannot be measured as moment in space.
It might be assumed that the speed of the car and its position could be operationally defined and measured simultaneously, as precisely as might be desired.
Is this really what any sensible person would assume to be possible? I’m afraid it is, and if so, I must be the craziest nutcase alive. How could I ever communicate efficiently with a person who assumes “speed” can be measured when the object is perfectly still in a definite “position”?
No can do.
So the groundbreaking proof by Heisenberg, the awesome insight everyone had been unable to get until 1927, was that in the realm quantum mechanics, it was impossible to measure these two properties simultaneously. And so we were given the uncertainty principle. All hail to the power of Heisenberg because he was way smarter than I will ever be, so I’m not roasting him by any means. What troubles me is the possibility that people today, almost 100 years later, goes around thinking that the classical world is different from the quantum world in this respect. I suspect most of you are thinking that this uncertainty is a particular case of “weird quantum effects” or conditions. And while you do that, I’m here thinking it is not a special case at all, but bleedin’ obvious in the moment you say it out loud:
– What is the exact position of a car in motion?
– At what speed does a car in the parking lot move?
If this is one of the corner stones of Quantum Mechanics, no wonder it is assumed to be incomplete.
And yes, it is way more complicated than this, it is much more complex, I have made a sloppy interpretation of the article, no one who doesn’t know QM correctly can understand it, I’m over simplifying the statements, it is not about conventional “speed” and “position” of classical objects, it depends on how we define the relevant concepts, and the realm of quantum effects is totally different from that of classical effects.
I know all of that.
And still …it makes no sense at all.
Not to me.