Whether it is cow’s milk, coconut milk, olive oil, crude oil, citric acid, sulfuric acid, rubbing alcohol, or alcohol drinks, or any other type of the things I mentioned.
If you define a function of 0 and 1, over time of which a plane takes off, and define 0 and on the ground and 1, in the air. What happens between 0 and 1? Is the function defined? Does one consider this to be a continuous function?
Become an expert at knowing the difference. Also write nasty letters to the candy makers of “bad flavors” they make on purpose, or made a mistake in batches and pass the savings on to you, the consumer.
Furthermore, a click drag on that on accident just trying to see who flagged his OP brings up a small list. That with way more reactions, checked elsewhere just trail off quickly and don’t give a full list either. So, interesting but ultimately nigh useless. Except in Black theme and that text white on white background hidden names, exposure all at once.
Depends. When do we consider a plane to be “in the air”?
If it’s a set distance (i.e. the atoms of the plane’s wheels are x distance from the atoms of the ground), then yes, it’s a superposition of quantum states. The function will only ever have values of 0 and 1, nothing in between, BUT (!!!) the point in time at which the function switches from 0 to 1 will not be well-defined.
Spoiler for more info: [details=Spoiler]In quantum mechanics, position isn’t a fundamental quantity. It’s just an observable (a consequence of some underlying, more fundamental quantities). And the tricky part in quantum mechanics is that there is no way to precisely determine an observable using analytical/theoretical methods (using math).
In the case of position, the probability of it being within a certain range of values is given by the norm-squared of the wavefunction (@pedoviejo you most definitely know this, so I’m basically just saying this for other people who might not know).
So when finding the distance (difference in position) of two atoms, the probability of it being within a certain range of values would depend on the norm-squared of both wavefunctions (probably calculated the same way as multiple-dice rolls, but I’m not sure and I don’t have the energy to actually try to do the math right now).
Now we factor in the momentum of the plane upward (which is also just an observable!!! but a macro change in momentum indicates a change in the fundamental wavefunction, which means the norm-squared and position distribution should also be changing).
The probabilities will shift as you move along in time, because it’ll become more likely for the distance of the two atoms to be large.
So from a purely analytical/theoretical standpoint, our original function (0 on the ground, 1 in the air) would look more like this on the time axis:
t = 0: function is 0 (on the ground)
t = t_1: function has 90% chance of being observed as 0, 10% chance of being observed as 1
t = t_2: function has 80% chance of being observed as 0, 20% chance of being observed as 1
t = t_3: function has 70% chance of being observed as 0, 30% chance of being observed as 1
…
and so on. At some point (depending on how the atoms of the plane’s wheels and of the ground are constrained), we may see the function become undisputedly equal to 1.
BUT (!!!) quantum mechanics likes to fuck with people, so all that probability is thrown out the window whenever you observe. You might measure the distance at t = t_1 and find that the plane is already in the air (distance > x) even though there was only supposed to be a 10% chance of doing so.
So from a practical/empirical standpoint (which is still backed by the theory), the plane is in the air at the moment you measure it to be in the air.[/details]
If it’s defined using weight (i.e. the weight of the entire plane no longer rests on the ground), then it’s easier; we don’t necessarily have to talk about quantum mechanics at all. Just measure the lift that the plane generates. If lift >= weight, the plane is in the air and our function becomes equal to 1.
The question
is actually a funny one. We’re the ones who defined the function in the first place! So if we don’t explicitly say what happens between 0 and 1, then the function is undefined by definition (lol).