Can probability gives exact results?

[eljose79]

perhapas it sounds contradictory but this is an example:
let suppose we have a continuous probability distribution given by r(x) then the maximum value (the most probable ) is given by

dr(x)/dt=0 then if we make several meassures and have some numbers by taken the mean value ...would we have the exact value of it?..yes you always have an error but if it goes as g(n) with
n=infinite g(n)=0 then the error would be 0 so the theory is exact..(i think this happens in statistical mechanics)..why not in quantum physics?..

 

[ahrkron]

I'm not sure I understand what you mean. Would it be correct to paraphrase you as: "Can we beat the Heisenberg Uncertainty Principle (HUP) by using lots of measurements?" ?

Assuming that is your question, the answer is we cannot, because:
1. The HUP deals with what happens on *each* experiment and, mainly,
2. The way the HUP comes about is precisely throough the probability distributions: the conjugate pairs (position and momentum, energy and time, etc) are formed, precisely, by variables related in such a way that, when the probability distribution of one of them becomes narrow, the prob. dist. for the other widens.

When you tune your experiment to have a very well defined value for, say, the position, the probability distribution for momentum gets wider. There can be a well defined central value for both distributions, but that is not the point of the HUP. Instead, the important part is how far your measurements will be from that central value.

Think for example in the difference between the two following estimates from a car repair shop:
1. "Your car repair will cost $305.00, give or take $2.00 because the price of such screws recently changed and we don't have those prices right now"
2. "The repairs will be around $300, maybe $100 more or $100 less, depending on what we find when we open the dashboard"

In both cases you may have the correct central value, but the error is as important a quantity.

 

[tacman]

Probability can give exact results in certain situations, but it is not always the case. In the example given, the maximum value of a continuous probability distribution can be determined by finding the point at which the derivative is equal to 0. This can give an exact result, but it is not always possible to find the derivative or make precise measurements in real-life scenarios.

Additionally, the concept of "exactness" in probability can be subjective. While the error may approach 0 as the number of measurements increases, it does not guarantee an exact result. There will always be some level of uncertainty or error in probabilistic calculations.

In the field of quantum physics, the Heisenberg uncertainty principle states that it is impossible to know both the position and momentum of a particle with absolute certainty. This inherent uncertainty makes it difficult to obtain exact results in quantum mechanics.

Furthermore, quantum systems are inherently probabilistic and do not always behave in a predictable manner. This is due to the nature of quantum mechanics, where the behavior of particles is described by wave functions rather than deterministic equations. As a result, exact results may not always be achievable in quantum physics.

In summary, while probability can give exact results in certain cases, it is not always possible to have complete certainty or exactness in probabilistic calculations. Factors such as measurement errors, inherent uncertainty, and the probabilistic nature of quantum systems all contribute to the limitations of obtaining exact results in probability theory.