What happens if we throw a dice from same position, with same force, by creating a vacuum environment on earth? Will it be predictable now i.e. will the dice have same results all the time?
If answer to the question is no, I have another question, Why in quantum mechanics we say a particle for example electrons are in two states. We only get a probabilistic value of position, that does not mean, its in two states at a time. The way we see it may be destroying the probabilistic character.
In a pure Newtonian model, you can indeed make a prediction of the outcome if you know the inputs. But in this case there is a good deal going on. Rotation of the dice, how the dice leave the throwing surface, linear velocity, angle of impact to the landing surface, the coefficient of restoration from the landing surface, etc. You have removed air resistance which is would be a very low impact to the physics model. The problem is that the results would be governed by Chaos theory than quantum mechanics. Even a slight change in any variable would cause completely different outcomes.
You can predict it, you don't really need the vacuum either. This is actually one way that people cheat with dice: https://youtu.be/t1dTadFlyDE
We used to play dice a lot when I was a kid, and sooner or later most of us figured out ways of cheating with trick rolls. The simplest of these works by reducing the amount of rotation the die will have like in the video, but also restricting how much the die bounces in your hand and throwing in a consistent way. But in principle I don't see why you couldn't build a machine to cheat more elaborately.
An idealized die thrown on an ideal flat plane is pretty easy to predict. I personally would do it by running a Monte Carlo to build a model, and then running future throws through that model. It would be 100% correct.
For the real world, I suspect there are three major sources of error:
The question is whether the ideal model can predict the real world. I suspect if the table is reasonably flat, the dice are even, the air is still, it would work quite well. Not 100% maybe, but probably %99 with a good thrower robot.
The die roll is actually a pseudorandom number generator. It is a deterministic, mechanical process, but the output is produced in an obfuscated way from two inputs, or seeds: The particular imperfections of the table, and the particular characteristics of each throw (no two human throws are exactly the same, and that probably does have quantum mechanical causes). If you can supply the same seed, you should get the same result.
Another analogy is the hash: The roll is the hash function. The output is the die result. The input is the throw (vector momentum and and angular momentum imparted). The surface is the salt.
Dice are a very good PRNG (or hash) because it is well known that the resulting distribution is flat. If a human is throwing, you can even treat them as true random. But true randomness comes from the randomness inherent in our musculoskeletal system, not the mechanics of die roll.
Why in quantum mechanics we say a particle for example electrons are in two states. We only get a probabilistic value of position, that does not mean, its in two states at a time. The way we see it may be destroying the probabilistic character.
Heisenberg's principle says that the exact location and speed of a particle cannot be known. Not only by us humans, but it is generally indeterminate. This appears to be a fundamental property of the universe. In that sense, it literally is in two places at the same time, but of course the mistake made here is assuming that the electron must be a point mass simply because we derived the probability cloud by modeling it as one.
However, when you have a large number of particles glues to each other, their location probabilities (for instance) combine in a way that reduces the spread. A die is made of an absurdly large number ($10^{23}$ ish) of protons, neutrons and electrons, and so the spread is tiny. Of course, you can't know the exact location of the die, but when the error is fractions of the size of an atom, you won't notice. That's why we pretend uncertainty does not exist on the macro scale: It's usually just averaged away and has too little effect.
In simple terms: random is random. The more particles that interact the more random the end state is likely to be unless you can influence the interactions in some way to limit the outcome. You could drop a coin in a vacuum and probably get it to land a certain way every time. In this case you've removed the randomness of turbulence from the air and the balance of a coin is such that it has a strong tendency to land on only one side or the other. Without air you could probably get it to fall flat and not bounce hard enough to rotate it after impact. For example drop it from 2 cm with head up, and you'll probably get heads every time.
For a die you have 6 sides and can rest stably on either of sides, unlike a coin. You could use "trick dice" which have the center of gravity modified. But for normal die their symmetry make random rotations easier to achieve after the first impact. You could modify the surface material so there is no bounce (like a metal die landing on a magnet, or onto something sticky). Then you could drop the die so it does not rotate while falling and doesn't bounce and rotate randomly.
I'm not sure how you are trying to relate this to QM. The probability of what state a particle is in collapses once it is measured.
The throwing of the dice in the vacuum will have the same outcome as throwing in air as long as their symmetry is true. No one value from 1 - 6 will favor the other. All possibilities will have an equal probability of occurring. The force of gravity will still be a force. Not like the dice will be in a weightless environment. Just no air pressure. The dice will still fall towards the center of earth.
Quantum mechanics tells us where we are likely to find the particle and that we can never be certain of its present location, only the probability it will be there. {When we refer to two different states we are not referring to usually referring to location but to angular momentum, spin +1 or -1, Clockwise or counterclockwise.}
Also about 80 years ago, scientists discovered that it is possible to be in two locations at the same time—at least for an atom or a subatomic particle, such as an electron. For such tiny objects, the world is governed by a sometime non-intuitive set of physical laws known as quantum mechanics. At that size range, every bit of matter and energy exists in a state of blurry flux, allowing it to occupy not just two locations but an infinite number of them simultaneously.
Electron tunneling is an example that the laws of probability support quantum physics because tunneling has an option like passing through a barrier that is impossible for classical mechanics. And indeed we observe tunneling through physically impossible barriers.
In contrast to probability theory, Quantum Mechanics is a theory with dynamical solutions of specific differential equations with imposed physical boundary conditions. There is nothing random about these solutions. Thus QM is not based on probability theory as the events are not random and are not from the distributions appearing in the studies of probability theory.
I refer you to the following post on this site for additional information on Proability Theory vs QM Why is quantum mechanics based on probability theory?
Dice is a purely classical object, if one starts from a known boundary condition, the Newton's law differential equations should return you the same result every time. However, electrons are quantum object, in the sense that they are very fragile. Once you measure the position, i.e. shining light on the electrons, you impart momentum so that the result would be different everytime as you literally change the physics parameters of a single electrons. Whereas, classical object are much more robust as they are macroscopic object composed of quantum objects, entangled to a reservoir "environment".
We only get a probabilistic value of position, that does not mean, it's in two states at a time.-yes, it doesn't mean it is in two states at the same time. Many people use this wrong sentence to describe quantum superposition probably because they've remained classical from their heart. It's utterly nonsense to say that the electron is at many places at the same time. Rather, the electron has the possibility to be at both places at the same time. BTW, how is this related to the dice?? – Oct 26 '15 at 19:08