Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: cheryl j on 25/01/2015 16:31:22
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Sometimes in discussions with people about various unexplained phenomena they seem to use the uncertainty principle or quantum mechanics in general as an argument for "anything is possible" because the universe is not determined.
Does "probabilistic" actually mean not determined? Whether you're changing the outcome of a completely deterministic classical event, or changing the quantum probability distribution to a slightly different probability distribution, are you not still monkeying with the physical laws? Is there room "within" the probability distribution to sneak in certain things (like say free will) that might contradict classical determinism? You might not notice such a violation once, but wouldn't you notice over time, like someone playing with loaded dice?
What does determinacy mean in terms of quantum mechanics and physical laws?
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The way I see it is to abandon classical mechanics as a model of the truth, and start with quantum mechanics. Assume that the world is quantised and fuzzy, then see what happens when you get lots of small particles in one place.
Dice are a good starting point for understanding the phenomenon of indeterminacy. As we know from the double-slit experiment, a single particle can be anywhere, and the smaller the particle, the broader its wave function (i.e. the probability of its being at any particular point). Now a single throw of one die can give you any result from 1 to 6 - an absolutely flat wave function. If you throw two dice, you are more likely to get a score of 7 than any other number - the wave function of the ensemble has a peak. If you throw n dice, the score will approach 3.5 n as n increases: the peak gets sharper, until I can confidently bank on 3,500,000,000,000 plus or minus about 10 if you throw a billion (that is, an imperial billion) dice.
So: you can't predict the position of a single atom at a given moment, to any better accuracy than the diameter of the atom itself, but the indeterminacy of the position of a cannonball is negligible compared with its diameter because it consists of a hell of a lot of atoms stuck together, like one throw of 10,000,000,000,000,000,000,000,000 dice.
Thus classical (deterministic) mechanics is consistent with and can in principle be derived from quantum mechanics, but you can't do it backwards.
I gather you are a teacher. Try a bit of spread betting with your class. Give then 50 dice each and ask them to record a single throw (what noisy fun!). Get them to bet 10 cents on a spread of the class average - any number in the range 1.000 to 6.000 plus or minus 0.02 - but reserve 3.480 - 3.520 for the house (yourself). See how quickly the parents complain!
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Thank you. That is helpful. Would you say you subscribe to something like "adequate determinism"? http://en.wikipedia.org/wiki/Determinism
(last entry under varieties)
Why are some interpretations of quantum mechanics consider deterministic and others not if they all essentially predict the same kinds of things? http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (see chart, first column) I'm sure I should be able to glean this from the explanations but it doesn't seem obvious to me.
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Could we have a probabilistic charge density distribution for the electron that marries the thinking of Schrodinger and Born? In such a case there would be a maxima and minima that would coincide with the peaks and troughs of the wave.
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Does "probabilistic" actually mean not determined?
In classical physics that's true. However in quantum mechanics things are different. If, in principle, an outcome can be predicted with certainty, as is the case of throwing a die if the initial conditions are known perfectly, then the outcome is deterministic. In chaos theory one can adjust the initial conditions and get varied results making the result probabilistic. However its still a classically determinisitic system as all systems are in classical mechanics. Stephen Hawking says ..that the microscopic world of quantum mechanics is one of determined probabilities.
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I'm not sure, but I think you can apply statistics to see 'determinism' in populations too. A 'free will' is then the individual outcome of a dice, whereas you will get some sort of a average from treating them in a 'clump'. At least that's how I see it.
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I'm usually referring to HUP when discussing free will, but I think you could use throwing a dice for it too? Because you can't use the dice before to decide what the next will show you, although with enough throws you can define (statistical) probabilities.
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Thank you. That is helpful. Would you say you subscribe to something like "adequate determinism"? http://en.wikipedia.org/wiki/Determinism
(last entry under varieties)
Why are some interpretations of quantum mechanics consider deterministic and others not if they all essentially predict the same kinds of things? http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (see chart, first column) I'm sure I should be able to glean this from the explanations but it doesn't seem obvious to me.
No!
I don't get drawn into interpretations or philosophy. The way I see it, quantum mechanics is our best mathematical description of what actually happens. Nothing more or less. When we discover a new phenomenon we try to describe it in terms of the maths we know, and if that appears to imply nonconformity with the conservation and symmetries previously observed, it turns out (so far) to be productive to look for or predict the properties of particles we haven't previously noticed.
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How do stochastic processes or functions work? I tried reading the wikipedia article, but it was tough sledding. What makes a process stochasitc, allowing for different outcomes, rather than everything kind of averaging out with big numbers or multiple trials? Whats a markov chain?
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"A stochastic process is simply a probability process; that is, any process in nature whose evolution we can analyze successfully in terms of probability." and "Stochastic models can be contrasted with deterministic models. A deterministic model is specified by a set of equations that describe exactly how the system will evolve over time. In a stochastic model, the evolution is at least partially random and if the process is run several times, it will not give identical results. Different runs of a stochastic process are often called realisations of the process.
Deterministic models are generally easier to analyse than stochastic models. However, in many cases stochastic models are more realistic, particularly for problems that involve ‘small numbers’. For example, suppose we are trying to model the management of a rare species, looking at how different strategies affect the survival of the species. Deterministic models will not be very helpful here, because they will predict that the species either definitely becomes extinct or definitely survives. In a stochastic model, however, there will be a probability of extinction, and we study how this is affected by management practices.
In recent years, the distinction between deterministic and stochastic models has been blurred slightly by the development of chaotic models. A chaotic model is a deterministic model that is extremely sensitive to the values of some of the parameters in the model. Making a very small change to the values of these parameters can make the outcome of the model completely different extinction, and we study how this is affected by management practices."
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Phieew :)
Weird, tried to copy it from a pdf and...
And a Markow chain is a situation in where you assume the current configuration of a system to define the next. It's without 'memory' of all sequences before leading to the current that you study. "It can thus be used for describing systems that follow a chain of linked events, where what happens next depends only on the current state of the system."
And I'm pretty doubtful to the definition in where a chaotic model is a 'deterministic' btw. It's non linear to my thinking.
And a probability of something is to my mind defined by the statistics preceding. So 'pure probability' should then be our definition, gained from what statistics we have. Or? Can we prove it ideally, and prove it valid for all possible circumstances, possibilities of different physics etc?
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Thank you. That is helpful. Would you say you subscribe to something like "adequate determinism"? http://en.wikipedia.org/wiki/Determinism
(last entry under varieties)
Why are some interpretations of quantum mechanics consider deterministic and others not if they all essentially predict the same kinds of things? http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics (see chart, first column) I'm sure I should be able to glean this from the explanations but it doesn't seem obvious to me.
No!
I don't get drawn into interpretations or philosophy.
I can appreciate that, and I wasn't really attempting a philosophical discussion about it, but trying to get a better understanding on whether quantum uncertainty or randomness actually "filters up" with the potential to change the outcome of macroscopic, thermodynamically irreversible events. Is that a nuts and bolts question with an answer, or is a matter of interpretation? When I read things by physicists like Hawking or Sean Carroll, they sound an awful like determinists when looking at the big picture.
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"A stochastic process is simply a probability process; that is, any process in nature whose evolution we can analyze successfully in terms of probability." and "Stochastic models can be contrasted with deterministic models. A deterministic model is specified by a set of equations that describe exactly how the system will evolve over time. In a stochastic model, the evolution is at least partially random and if the process is run several times, it will not give identical results. Different runs of a stochastic process are often called realisations of the process.
Is that because new random variables are being continually fed into the chain, or because you didn't know what the set of random variables was at the start?
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Not as I read it Cheryl. I think one has to see it as a result of probabilities. And the 'split' seems slightly artificial, as you're perfectly correct in that 'things happen'. A probability is just a mathematical way of expressing somethings chance of happening. And the way to define that should be through the statistics you have. On the other hand? I'm not sure. You could also possibly define it purely mathematically? https://en.wikipedia.org/wiki/Statistical_mechanics
If you do as I do and define a arrow on one side, something 'without it' on the other, you too might get a feeling of some of those mathematical rules we find actually has to exist 'as is', on the side without a arrow. Similar to the way we think of constants, as guiding the evolution of a universe. Wish I knew.
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How do stochastic processes or functions work? I tried reading the wikipedia article, but it was tough sledding.
Is this the one that you read? http://en.wikipedia.org/wiki/Stochastic
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