Probabilities in quantum mechanics (and other areas)

[Gilded]

Ok, so one day randomness came to mind. Randomness in the aspect of flipping a coin; basically about 1/2 probability of getting tails. But, it is not actually random in the aspect of physics since you could calculate the momentum the coin has, and all the other factors like gravity etc., eventually getting the result of the flip (without seeing the actual result of course). So, I tried to think of a thing that has an actual random factor to it, and the only thing that came to mind is a radioactive decay (like would be the case in the Schrödinger's cat experiment).

 

Any others? I'm just probably silly to forget about all the other nice randomy thingies flying about. :<

[Severian]

Classical physics is completely deterministic, so there are no effects of this nature. Only quantum mechanical effects have this, such as radioactive decay. This was Einstein's big objection to QM ("God does not play dice.").

 

Interestingly, even using the radioactive decay to 'trigger' heads or tails according to some well specified rule (eg. if it decays with 3s then its heads, if not its tails) you would still be able to predict the probability of getting heads, so QM still has predictive power.

[Gilded]

From what I've heard, the nucleus "doesn't know" it's age or any of it's conditions, and can decay just about any time. Let's take a gram of uranium; most likely after the time of the half-life (let's say 4 billion years), there is 0.5g left. But, there is a probability of 0.1g of it decaying within a week, it's just VERY unlikely (as you said, there is a possibility of predicting the probability).

 

I phrased my thread starting post quite wrong, as I mostly wanted to know if there is an event that one could say there is an absolute 50% chance. Let's say, there is an absolute 50% chance of a nucleus decaying within 3 seconds, and an absolute 50% chance of decaying within the following two seconds. So, this is actually possible with the decay of a nucleus? Of course, I was looking for completely random events too, but mainly the absolute 50/50 probability (as these don't seem to exist in classical physics).

[swansont]

Let's say, there is an absolute 50% chance of a nucleus decaying within 3 seconds, and an absolute 50% chance of decaying within the following two seconds. So, this is actually possible with the decay of a nucleus? Of course, I was looking for completely random events too, but mainly the absolute 50/50 probability (as these don't seem to exist in classical physics).

 

If a nucleus has a 50% chance of decaying in 3 seconds, then the other 50% probability requires infinite time. The half-life is 3 seconds.

[julien]

I thought a coin could be taken as similar to a spin 1/2 particle (in the sense there are only 2 possible outcome), then, the probabilities given by QM are for example [math] p(+)=cos(\alpha)^2[/math]...which is 1/2 on average, but how can alpha be found...? Maybe all the parameters (gravity, wind, momentum, starting kick ....) can be but into only one real parameter (alpha)....but QM does NOT give the result knowing alpha (unless p(+)=0,1 of course, but this happens with measure 0)....at least at my knowledge of QM...

 

But I also get stuck on that : let throw N times a +/- coin, getting statistical results like s(+)=N(+)/N, s(-)=N(-)/N (surely near to 1/2).....if s(+)>s(-), does that imply that for the next time p(-)>p(+), p(-)=s(-) or does there exist an analytical link between the statistics of the last N coin's result, and the probability for the next one ?

 

Thanx

[swansont]

Random events won't have a causal link. "Dice don't have memory" is one way of saying it. The fact that many people think that they do, and other misunderstandings about probability, are why casinos are money-makers.

[julien]

That's almost true (I begin to believe the reality always is a superposition of true/false...this is brain aching)...but i suppose it is just a hypothesis for calculation and simplification, since :

 

let's play and imagine a toy model :

 

a coin falling in a kind of jam...(this could for exemple modelize a sort of magnetisation response to a certain medium)......then the coin will be no more balanced for the next trial, favorizing one side...more balanced for the next time if falling on the defavorized side...so in this case the outcome modifies the "balanceness" of the coin, and hence the probability.....

 

starting with a balanced coin (as hypothesis), one could deduce the new probabilities knowing the history of outcomes...u agree with this toy model ? (a bit naive I admit, but this is not to win money at lottery, just a mind game)

 

Hence in this model the probabilities have memory, but nothing is told about the results...