I’m going to look up spin states in pairs of particles. I don’t know much about that.
What I was referring to was complementary properties of a single particle. Velocity and position is the most well known pair of complementary properties.
“In physics, complementarity is a fundamental principle of quantum mechanics, closely associated with the Copenhagen interpretation. It holds that objects have complementary properties which cannot be measured accurately at the same time. The more accurately one property is measured, the less accurately the complementary property is measured, according to the Heisenberg uncertainty principle. Further, a full description of a particular type of phenomenon can only be achieved through measurements made in each of the various possible bases — which are thus complementary. The complementarity principle was formulated by Niels Bohr, a leading founder of quantum mechanics.”
—Wikipedia
I listened to a physics lecture and the physicist explained that this complementary property is actually wrong. Finding the speed or position means the particle has lost its quantum properties and is part of the classical physics world as a corpuscular particle. Thus we cannot talk in terms of quantum mechanic then. It is rather a failing of classical physics, its limit, rather than quantum mechanic, because quantum mechanic is accurate and very precise, without resort to such probability or ambiguity to find results or approximate them. Thus it is not quantum mechanic that imposes this rule.
What it is is that there is not a well defined border between classical physics and quantum mechanics. That switch from multiple state at once to a defined state is not clear.
also the other nuance is that if a particle is quantum, if it is in a certain state, once read, it changes its state and gives a different state than what it was right before the reading.
But it is not a rule proper to quantum mechanic that we cannot read both position and velocity at the same time, it is more a misconception due to the issue of transition area between the quantum physics to the classical physics.
“Measurement disturbs the system.” In more detail, this misconception holds that each particle really does have definite values for both position and momentum, but these definite values cannot be deter- mined because measurement of, say, a particle’s position alters the value of its momentum. (It is related to the idea of a classical picture underlying quantum mechanics mentioned in item 6.) This is a particu- larly common misconception because some arguments due to Heisenberg (“the gamma ray microscope”) and Bohr can be interpreted to support it. It is another attractive idea rendered untenable through tests of Bell’s theorem [9]. (This idea is also shown to be incorrect through “quantum eraser” arguments, as in reference [14].)
http://www.oberlin.edu/physics/dstyer/TeachQM/misconnzz.pdf
http://physicshelpforum.com/showthread.php?t=2714
Misconception – You cannot simultaneously measure both the position and the momentum of a particle.
Correct Physics – This is the wrong phrasing of Heisenberg’ s Uncertainty Principle (HUP), which actually states that the position and momentum are not simultaneously determined. This has a very different meaning than what is stated above. Uncertainty is a property of the quantum state and not determined by how measurements are done. No matter how a measurement is taken one cannot change the inherent uncertainty determined by the quantum state of the system.