# Do planes fly faster in the dark?

You read it right, "do planes fly faster in the dark".

The question is one that raises the problems that are assumed to plague quantum mechanics to the macro world. Or rather, they've been there all along, you just never notice them. The reason you don't is fidelity. The "larger" something is, the bigger the fault tolerance we have for it. If a double bass player misses his finger placement by 1/64th of an inch, then we don't care, it's close enough. If a quarter violinist misses her finger placement by the same measure, we cringe at the horror that is a screaming rather than singing violin. Take cars. A dent in your huge pickup truck is less likely to bother you than the same size dent in your Smart. Or take your food. You're likely to allow your girlfriend to steal a chip from your plate at the start of the meal, but when you only have three left, she better keep that fork at home.

Fidelity is a measure of imprecision. Something with high fidelity has high precision, and low fidelity stands for low precision. People who can still remember the day of the HiFi set (which were common goods less than 10 years ago) will known what I'm talking about. "High Fidelity, had something to do with my radio, right?" Amongst other things, yes.

Now, let us look at the real difference between quantum and macro (or "classical") mechanics. Most obviously, at the quanum level things are ridiculously small. You cannot comprehend how small things are, because numbers to explain just how small things are mean nothing to you. If I tell you "a single hydrogen atom is so small you need to line up well over 20,800,000,000 to cover a centimenter", this means nothing to you, you cannot conceive this number as anything real. To give you an idea of how small things are at the quantum level, let me put it differently: at the quantum level things are so small that the only way to "see" what's going on destroy the thing we're interested at and then looking at the destruction pattern. Kind of like dropping a drop of red ink so small your camera can't see it on a white sheet of paper, so that you can at least see the splatter pattern in the hopes that you can tell something about the drop that way.

Things in quantum mechanics are so small that you need HUGE machines to detect things. You can't just create a very powerful microscope, because microscopes require particles to bounce off what you're looking at, to create visible patterns in the microscope's viewer. At the quanum level, using for normal microscop that relies on light (photons) to find out something about a single flying photon, is a bit like shooting a gazillion-billion-trillion footballs at one more football. it doesn't work, they'll collide and you'll never know what the heck was going on with that one football you were interested in.

But this post started with something else. Do planes fly faster in the dark?

In quantum mechanics there are two basic "rules": 1) You cannot measure both the position and the momentum (the "speed in a particular direction" of something) at the same time, and 2) things don't have a "position", they only "probably exist" at many positions (which are fairly close to each other) at the same time.

the first rule is something that holds from the quantum to the classical level, and is only a fidelity problem. A car running at 50 mph over a strip of tarmac is not traveling at 50 mph over tarmac. In fact it is more than likely that the majority of the time it will be running just above or just below 50 mph. We cannot measure the exact speed of a car, because we measure speed using two measuring points, and then calculate the speed by dividing the distance between the two points, by the time it took the car to cover that distance. The more precise you want the speed from moment to moment the shorter you need to make the intervals, but you run into a problem that speed for just single point does not exist, because a) the distance covered would be 0 and b) the time taken would be 0. And 0/0 is not 0 but every number conceivable, *at the same time*.

This is actually a fun bit of math so let me show you that a division by zero is not impossible, it's just completely unworkable because you get every number possible back, together with every other number possible: "zero" is a conceptual number that does not exist in nature, it's an invention of man. If I have two pears and I remove two of them, then in real life there are not "zero pears" because in order to "be" there needs to be at least one instance. Instead, "there are no pears". Nevertheless, we can do math with "zero", and it usually behaves like a normal number, except during division when it screws up things fantastically...

There are three rules that zero behaves properly on, being +, -, and x: a+0 = a, a-0 = a, ax0 = 0. It's this last rule that is of interest, because we can express + in terms of -, and x in terms of / : a+b = c tells us that c-a = b and c-b = a. Likewise, axb = c means that c/a = b and c/b = a. So what does this mean if we do the proper replacements? ax0=0 means that 0/a = 0 and 0/0 = a. And here we are confronted with the marvel that is the "not a real number" fact. if "zero" was a real number then there would only be one possible way to do this last bit of arithmetic - 1/2 is a half, and nothing else. But "zero" is not a real number, instead it tells use that 0/0 is "some number", and we can fill in any number we like in the answer field, and then say "but I also like ..." and fill that in as well, and then go "but wait, I also like ..." and fill that in as well! So 0/0 = 0, 0/0 = 1, 0/0 = 1297, 0/0 = i (the complex number), 0/0 = ... etc. etc. etc... And so a division by zero is not "impossible", the result is just completely useless.

Back to our fidelity. Speed at a single point does not exist, but physics claims that momentum does. Momentum is measured in energy transfer. If the car is travelling with 1 mph and hits a large sheet of metal set up perpendicular to the direct the car is travelling in (like a wall across the road) then the sheet will dent. If the car is travelling with 100 mph when it does this, the sheet will probably not just bend but distort wildly and fly off. The momentum of the car when it hits the sheet, so the amount of energy that is transfered from the car upon impact, is much lower at 1 mph than at 100 mph.

But hang on, the crash is not instantaneous. The car is transfering energy for as long as it takes for it to stand still, and that does not take the conceptual 0 seconds. In fact momentum at a point in time is also fiction, as impacts are temporal. Even at the quanum level, energy transfer is not instaneous but takes a certain (relativistically small) amount of time. All we have in both quantum and classical physics is a way to analyse momentum by measuring crash-energies, with the only justification to say "there is momentum at some moment in time" being that the fidelity is chosen so that the interval of fidelity is "the same as" a moment. For a car traveling at 100 mph a 0.5 second interval is pretty momentuous, all of a sudden the car stands still and the metal sheet is flying through the air. For a quantum particle traveling at light speed, a 0,000000000000000001 second interval for energy transfer is also pretty momentuous, but it's not a zero-interval.

So now we can finally go to the original question! Do planes fly faster in the dark?

When in daylight, airplanes are constantly bombarded by photons from above, constantly transfering downward energy to the plane, effectively making the engines generate enough power to not just fly horizontal, but also create enough upward lift over the wings to compensate for the combination of gravity and sunlight. What if there is no sunlight, can planes fly faster on the same engine output because the power needed to overcome the constant photon bombardment can go to horizontal flight?

Hahaha, sure they can, but the effect is so small that it doesn't matter, what a silly question.