Can Probability collapse down to Certainty,in classical macro systems??

[Pratt]

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!

 

 

Edited January 11, 2011 by Pratt

[swansont]

People have built flippers that will apply a well-known force/torque to a coin and flip it a predictable number of times.

[TonyMcC]

People have built flippers that will apply a well-known force/torque to a coin and flip it a predictable number of times.

I wonder what would happen if the coin was wide and thin and a force was calculated to make it land on edge? I am thinking of imponderables such as air currents.

[swansont]

I wonder what would happen if the coin was wide and thin and a force was calculated to make it land on edge? I am thinking of imponderables such as air currents.

 

That's a tougher problem. Making it land heads or tails has a relatively large margin of error. Pretty big angle you can overshoot or undershoot.

[TonyMcC]

My first thought was if the calculations are properly formulated and applied there was certainty from the begining - i.e. there never was only probability.

However in real life every now and then something might happen to upset this conclusion. e.g. a bird might swoop down during the process and collide with the coin. Perhaps in every physical application of a logical conclusion there is, however slight, some degree of uncertainty? Just musing!

[steevey]

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 .

 

 

 

Of course you can determine probable things. If I start with a U.S. quarter with heads facing the ceiling and rotate the coin 180 degrees, it will be tails, and EVERY time I start on heads and rotate the coin 180 degrees it will ALWAYS be tails.

 

When you can't determine the the certainty of things in advanced mathematics or physics, its either because your missing a variable, or the variable you have is continuous, meaning it represents multiple numbers at a time or even all real numbers or all possible numbers to infinity. In either case, there is no known way to determine a single possible outcome. For instance, when you flip a coin in the air, you have no idea how much momentum and what angle your putting into the coin as well as some air resistance, so there's no way you can determine the outcome. But if you did know all of those factors before oyu flipped the coin, you could determine the outcome.

 

 

[lemur]

how do you prevent it from bouncing and flipping some more after landing? Do you catch it at a specific height? How do you insure the exact position at which it is caught?

[steevey]

how do you prevent it from bouncing and flipping some more after landing? Do you catch it at a specific height? How do you insure the exact position at which it is caught?

 

Those are some of the factors you'd have to know about in order for you yourself to determine the outcome. Those factors are already there, so the outcome will be determined whether you know it or not.

 

 

 

[lemur]

Those are some of the factors you'd have to know about in order for you yourself to determine the outcome. Those factors are already there, so the outcome will be determined whether you know it or not.

Oh, I see. You're already warming up to your big general philosophical argument that everything happens deterministically. I was literally just asking about how the machine catches the coin so that it doesn't bounce. And just in case you really want to get into the determinism discussion, how do you deal with multiple factors that influence each other while influencing the outcome. E.g. if the coin's flipping speed affects the density of air pocket it creates as it flips, how do you predict the synergism between the two variables except by statistically keeping track of large numbers of flips using the same machine/process; and even then, wouldn't there ALWAYS be variation in the results? You can't build a machine that always flips heads, can you?

[swansont]

Oh, I see. You're already warming up to your big general philosophical argument that everything happens deterministically. I was literally just asking about how the machine catches the coin so that it doesn't bounce. And just in case you really want to get into the determinism discussion, how do you deal with multiple factors that influence each other while influencing the outcome. E.g. if the coin's flipping speed affects the density of air pocket it creates as it flips, how do you predict the synergism between the two variables except by statistically keeping track of large numbers of flips using the same machine/process; and even then, wouldn't there ALWAYS be variation in the results? You can't build a machine that always flips heads, can you?

 

If the variation is small, then the answer is yes. If, say, the variation accounts for the effect of a few degrees of rotation,

[lemur]

If the variation is small, then the answer is yes. If, say, the variation accounts for the effect of a few degrees of rotation,

So what factors prevent such variation from synergizing into full-blown interdynamism?

[Sisyphus]

So what factors prevent such variation from synergizing into full-blown interdynamism?

 

What?

[steevey]

Oh, I see. You're already warming up to your big general philosophical argument that everything happens deterministically. I was literally just asking about how the machine catches the coin so that it doesn't bounce. And just in case you really want to get into the determinism discussion, how do you deal with multiple factors that influence each other while influencing the outcome. E.g. if the coin's flipping speed affects the density of air pocket it creates as it flips, how do you predict the synergism between the two variables except by statistically keeping track of large numbers of flips using the same machine/process; and even then, wouldn't there ALWAYS be variation in the results? You can't build a machine that always flips heads, can you?

 

If you can control ALL the factors, you can make whatever result you want every time. But, do you know how to control the wave function of an electron or the power of gravity that Earth has? No. So you specifically don't know what the outcome will be, even though all those factors are there. You can't see air either, but it's the reason we're alive right now. Same with the factors that determine things.

 

 

But otherwise, no, I wasn't warming up to that at all, it was more of a tangent.

Edited January 17, 2011 by steevey

[lemur]

What?

What, you don't appreciatize my vocabulation? "Synergy" refers to interaction effects and "interdynamism," well, I guess you just have to break that one down into "inter" and "dynamism." Forgive me for constructing words from roots. It's common in some languages to build words from the ground-up, my personal language for example.

[steevey]

What, you don't appreciatize my vocabulation? "Synergy" refers to interaction effects and "interdynamism," well, I guess you just have to break that one down into "inter" and "dynamism." Forgive me for constructing words from roots. It's common in some languages to build words from the ground-up, my personal language for example.

 

As long as we're calling peopel out not for the sake of the topic, what do you say about my response to you?

Edited January 17, 2011 by steevey