I m posting one of my thought experiment here,which is as follows.Please have a look through it and give suggestions or make out errors if dere is.......(some confusion is dere wid the moment of inertia of a disc(a coin in dis case).If its given wrong,please correct it......
COLLAPSING OF PROBABILITY INTO CERTAINTY IN CLASSICAL MACRO-SYSTEMS:-
Thought experiment:-'Tossing of a coin' :-----
When we toss a coin, we force it up and it performs both rotational motion and translation motion. In our views, we find out the probability of whether a head will come up or a tail. But, if we carefully investigate the motions under certain given parameters, it may be possible to predict with certainty, whether the coin will come up with a head or a tail! Our aim is to relate this event mathematically to 'collapse down' the probability into certainty .
Let the mass of the coin be 'm' and radius be 'r'.
Let we apply a force 'F'.
Let the force required to rotate the coin by 180 degree(pi radians) be 'f'.['f' is an arbitrary constant dependent upon the properties of the coin]
The moment of inertia of the coin(a circular disc) I =1/2*m*r^2.
The coin goes to a height 'h' vertically due to Fsinz . It rotates due to Fcosz.
So total distance traversed(d)=2h.
If it makes 'n' rotations, then 2*pi*r*n = 2h
=>n= h/r*pi.
Let the coin is tossed up with an initial angle 'z'.
Now, Fsinz= mg
Let angular acceleration be 'a'.So, Fcosz =I*a=I*r*g [ g is acceleration due to gravity].
Solving these two equations, F= g*sq.root(m^2+I^2*r^2)
Now, from initial position, total angular change =n*pi
So, for n*pi angular change, required force =nf = Fcosz=g*sq.root(m^2+I^2*r^)*cosz .
So, n = Fcos /f = {g*sq.root(m^2+I^2*r^2)*cosz}/ f.
Now, if n = 2m+1 , for all mE Z+, then certainly n is odd, and the coin will come up with the opposite face of that of the initial(If initially before tossing, coin is having head, it will come up with tail and vice-versa).
If n= 2m,for all mE Z+ , the certainly n is even and the coin will come up with the same face of that of the initial(if initially coin is with head, it will come up with head after tossing).
If n= K.x (where k= 2m or 2m+1,for all mE Z+), then if x<5 or x=5, then n= K.
Else if x > 5, then n= k+1.
Hence, we can determine whether the coin will come up with head or tail with a strong probability of 1!!
This implies, we can predict the toss certainly under careful mathematical investigation, with the said parameters and equations!