Probabilities

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hi all.

I am reading John Gribbins popular science book 'In search of Schrodingers cat' at the moment and would be interested in your opinions or explanations of the following questions

What are the origins of the probabilities that form a fundamental part of Quantum Theory.

there is no explanation in the book, so far. It seems taken as a given that the probabilities just 'are'.

For instance, when an electron or other packet of energy is emitted from the atom, the suggestion is that there is no way to confidently predict the moment precisely. I am aware of the concept of half lives.

Could it be said that the probabilities exist because the events that cause the atom to emit a packet of energy are not predictable or detectable using current scientific instruments? do we have to use probabilities for this reason?

Could the emmission of particles be caused entirely by the environment in which it resides? for instance, our solar system

Could the probabilities be different in another part of the cosmos where the environmental conditions are different?

my knowledge of QF is very basic and I am aware that these questions may be a bit simplistic

thank you

Dan

Edited by danielj

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Probabilities are just a very useful interpretation of the square of the wavefunction.

There are other interpretations.

It's similar to the following:

Suppose your friend rolls a baseball along a channel from one end to the other,

Now suppose that at some time t after he has set the ball in motion you whack down with a baseball bat.

You can calculate a probability that you will hit the ball, which decreases with the speed of the ball and increases with the time your bat spends down on the channel.

Wave function probabilities are like that, for a given segment of space.

Edited by studiot

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thank you.

i will read up on wave function.

Dan

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You can improve the model by noting that the ball must be somewhere so the total probability of it being on the channel equals one.

Further if the channel is tilted down the ball will accelerate so the speed of the ball will increase as it rolls down and therefore the probability of hitting it will decrease.

Alternatively the channel may be tilted upwards so the ball will slow.

The model, of course is to compare the probability of hitting the ball with the probability of finding the electron in a given segment of space.

You can even extend the model to probabilities curves that rise and fall with a hump, like an electron orbital.

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Not quite true studiot.

With QM there is also a probability that the ball is outside the channel ( tunneling ).

Originally the wave interpretation of electron orbitals dictated that only orbitals with whole number waves were allowed as you cannot have partial waves.

It was Max Born who supplied the probability amplitude interpretation.

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Not quite true

Actually it is, but it is only an analogy to help explain where probabilities fit into QM.

If you take the one dimensional Schrodinger equation the particle must be somewhere along the single axis you have.

But that axis is homeomorphic to a segment of itself so it is legitimate to use a finite interval to represent the full line.

The process of normalisation maps the whole line to the interval (0.1).

Originally the wave interpretation of electron orbitals dictated that only orbitals with whole number waves were allowed as you cannot have partial waves.

Are you not thinking of boundary conditions here?

Whole number waves have no meaning on an infinite line.

Edited by studiot

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What are the origins of the probabilities that form a fundamental part of Quantum Theory.

We have no explanation, at this stage it is just a fact of nature.

Mathematically it is similar to classical statistical physics where probabilities and averages come in as we are dealing with a large number of particles. We want to describe the relation between the microscopic properties and the bulk macroscopic properties. As one cannot practically keep track of all the molecules in say a gas, you look at the average properties of the particles.

The big difference is that in quantum mechanics probabilities, averages and similar are also needed for single particles and not just large collections. Moreover, classical statistical physics is really based on our inability to keep track of everything precisely, quantum mechanics is built into nature and tells us that we cannot measure everything precisely even in principal.

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[...] Could it be said that the probabilities exist because the events that cause the atom to emit a packet of energy are not predictable or detectable using current scientific instruments? do we have to use probabilities for this reason? [...]

This was debated at the beginnings of quantum mechanics. The present consensus (with fringes as for any consensus) is that particles are random by their very nature, and the uncertainty does not result from our limited capability to observe or predict their behaviour.

In other words, the particle(s) determines itself when it is "asked" to do so by the observation, but not before.

One key hint was given by entangled particles. You can observe the random polarization of two entangled photons that can be vertical, horizontal, right, left... for both. Individually random but both are linked.

If it worked anly for vertical vs horizontal, one could claim that the photons decided upon emission what polarization they choose. Then, right vs left detectors would detect 50% of the vertically polarized photons, 50% of the horizontally, without correlation at both detectors.

But the same source of photon pairs gives the correlation with left vs right polarized detectors.

Then, the simplest (there are other attempts) interpretation is that the polarization is really undefined until the pair decides for vertical, horizontal, right, left at the detectors.

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thank you.

I find it very difficult to get my head around randomness. Effect with no cause? I understand that for progress to be made, it can be neccessary to accept these things and move on regardless. Perhaps it is a feature of the human brain that I find randomness unsatisfactory.

Are there any theories that attempt to explain the random nature of atomic behaviour?

dan

Edited by danielj

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Are there any theories that attempt to explain the random nature of atomic behaviour?

Quantum mechanics deals with the random and probabilistic nature of physics at the atomic scale. If you are looking for some theory that produces this probabilistic nature as some emergent phenomena, then there is no accepted theory in mainstream physics. There are some more speculative ideas here like Bohmian mechanics.

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Quantum mechanics deals with the random and probabilistic nature of physics at the atomic scale. If you are looking for some theory that produces this probabilistic nature as some emergent phenomena, then there is no accepted theory in mainstream physics.

There is no theory, but there is evidence.

http://www.economist.com/blogs/babbage/2012/08/neutrinos-and-solar-storms

Also some normally unstable particles were stopped indefinitely from decaying when properly isolated in magnetic traps.

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There is no theory, but there is evidence.

That suggests that neutrinos may have some effect on decays, as neutrinos have something to do with the weak force this is plausible, but I remain very skeptic about this. Anyway, these results change decay rates, but the process of radioactive decay is still random.

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That story is extremely doubtful to be polite. First, the measurements are difficult to make. Then, one team made measurements at one place, and an other team on an other continent re-interpreted the data 20 years later, with some filtering, without seeing the disappeared experiment that had by far not been designed for the new claimed accuracy, nor interviewing the experiment's authors.

The re-processed data contains fluctuations; the more recent authors analyze some fluctuations that confirm their claim and neglect others that don't. It's visible with naked eye on the curves. This does not fit science.

The authors believe to see a seasonal variation and claim it must relate with Sun's distance, while billions of effects depend on the season.

A scientist has taken the accurate curves of power produced by the RTG of a space probe that went both near Venus and Jupiter - a distance change better observable than Earth's eccentricity - to observe that the decay rate evolved exactly as expected. No effect of Sun's distance.

When searching for a simple experiment that a students team could make on a satellite, I considered checking this "effect" versus the changing distance to Sun over an orbit. The radioactivity specialist I consulted answered to forget said claim.

So: don't take this for firm evidence, and don't build any theory on such claims.

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That story is extremely doubtful to be polite. First, the measurements are difficult to make. Then, one team made measurements at one place, and an other team on an other continent re-interpreted the data 20 years later, with some filtering, without seeing the disappeared experiment that had by far not been designed for the new claimed accuracy, nor interviewing the experiment's authors.

The re-processed data contains fluctuations; the more recent authors analyze some fluctuations that confirm their claim and neglect others that don't. It's visible with naked eye on the curves. This does not fit science.

The authors believe to see a seasonal variation and claim it must relate with Sun's distance, while billions of effects depend on the season.

I have no idea what are you talking about.

So why are you introducing some "20 years ago" fairy tale, that has nothing to do with article.. ?

Ephraim is professor on the Purdue University

http://www.physics.purdue.edu/people/faculty/ephraim.shtml

This does not fit science.

Science is constantly making experiments.

Prepare Chlorine-36, prepare Manganese-54, and start recording decay rate whole year.

If you will have steady decays per second while long term observation, you will have proof and counter-argument for Fischbach & Jenkins observations.

A scientist has taken the accurate curves of power produced by the RTG of a space probe that went both near Venus and Jupiter - a distance change better observable than Earth's eccentricity - to observe that the decay rate evolved exactly as expected. No effect of Sun's distance.

You obviously didn't take into account that RTG uses Plutonium that's decaying by emitting alpha particle. That might have meaning.

I would expect RTG to have voltage/current stabilizers. Also RTG are using Peltier effect that's very little efficiency.

They're not designed to be detector of decays per second, but to be power source.

What I noticed is that Manganese-54 decays by both beta decay- and beta decay+, and electron capture:

Isotope Manganese-54
Protons 25 Neutrons 29
Mass 53.9404 [u]
Nucleus Energy 50232.3 [MeV]
Parent 50232.3 Daugther 50231.5
Alpha decay prohibited (-8.7587 MeV)
Proton emission prohibited (-7.55958 MeV)
Neutron emission prohibited (-8.93835 MeV)
Manganese-54 -> Iron-54 + e- + Ve + 0.69713 MeV
Manganese-54 -> Chromium-54 + e+ + Ve + 0.355216 MeV
Manganese-54 + e- -> Chromium-54 + Ve + 1.37721 MeV


Chlorine-36 also decays both by beta decay- and beta decay+, and also electron capture:

Isotope Chlorine-36
Protons 17 Neutrons 19
Mass 35.9683 [u]
Nucleus Energy 33495.6 [MeV]
Parent 33495.6 Daugther 33494.9
Alpha decay prohibited (-7.64155 MeV)
Proton emission prohibited (-7.96448 MeV)
Neutron emission prohibited (-8.57926 MeV)
Chlorine-36 -> Argon-36 + e- + Ve + 0.709681 MeV
Chlorine-36 -> Sulfur-36 + e+ + Ve + 0.120219 MeV
Chlorine-36 + e- -> Sulfur-36 + Ve + 1.14222 MeV

That's why I suggested Ephraim to try also Copper-64 that's also both beta decay- and beta decay+.

When searching for a simple experiment that a students team could make on a satellite, I considered checking this "effect" versus the changing distance to Sun over an orbit. The radioactivity specialist I consulted answered to forget said claim.

Wrong. You should perform such experiment regardless of his opinion. But use various radioactive materials. There are proton emitters, neutron emitters, positron emitters, electron emitters, alpha emitters, gamma emitters. Each one should be independently checked at various distances from the Sun. And of course they should not be used to power on whole satellite!

So: don't take this for firm evidence, and don't build any theory on such claims.

Actually I know Ephraim Fischbach. We were talking about his experiments with neutrinos. He asked me what experiments I would like him to perform and I suggest few, that you would definitely call highly speculative..

Edited by Sensei

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Sorry studiot, I wasn't trying to be critical of your explanation.

I was offering an example of the 'strange' consequences of QM and a historical footnote.

Don't read more than I wrote into it.

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@Danielj

We have learned to allow probability and other statistical techniques to exist alongside deterministic formulae and to pick and choose the most expedient for a particular job in hand.

Engineers even manage to mix the two with so called 'Limit State Design Theory'.

Remember also that there are two types of variable, discrete and continuous. Probabilities defining orbitals is a fine example of mixing the two since the variables in the Schrodinger equation are continuous, but we are trying to describe 'an electron', which is discrete.

Hi, MigL

I can't cut and paste or quote using this machine so just to say 'No Problemo :-)'

Edited by studiot

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Sensei, you believe what you want, and even that Solar neutrinos influence radioactivity if you wish...

Read again the paper, look at the curves, observe that the correlation with flares is not visible.

Consider that solar flares don't change essentially the neutrino flux from our Sun.

That the paper wants to see an effect on some alpha emitters - just like 238Pu is. Read the other paper about the RTG: your objections are already addressed there, of course.

That an annual variation has billions of possible explanations, the distance to Sun being just one.

And, yes, the authors re-analyzed data that was then already 20 years old.

Maybe you wish to believe in that paper, but it's bad science.

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Do you know how neutrino detector is working?

Perfectly stable Chlorine-37 is hit by neutrino that must have >0.814 MeV and it's changing to Argon-37, which is unstable element and decays back to... Chlorine-37 by electron capture. Argon-37 has half-life ~35 days.

Cl-37 + Ve + 0.814 MeV -> Ar-37 + e-

Ar-37 + e- -> Cl-37 + Ve + 0.814 MeV

Detector can observe flashes leaved by decaying Argon, or count argon gas molecules.

Chlorine based detector is working exclusively with neutrinos that exceed 0.814 MeV (which is quite a lot for Sun fusion f.e. p+ + p+ fusion is producing just 0.42 MeV).

If Argon-37 wouldn't be decaying, or have half-life significantly longer, this reaction could remain completely unnoticed.

I am working on application that will automatically analyze the all 3143 isotopes and show me all possible materials that could be used as neutrino detectors.

Edited by Sensei

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And these neutrino detectors have shown no surge during solar flares nor storms. As expected, since the neutrinos originate at the nuclear fusion reactions deep in the Sun, not at the shallow surface. That's one bizarre claim in the original paper, the other being that one sees variations in the radioactive decay curve without solar activity, and solar activity without effect on the radioactive decay.

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And these neutrino detectors have shown no surge during solar flares nor storms. As expected, since the neutrinos originate at the nuclear fusion reactions deep in the Sun, not at the shallow surface.

Chlorine-37 based neutrino detector is triggered by neutrinos that have >0.814 MeV energy.

Which means neutrinos produced by decay of Beryllium-7 (these have up to 0.862 MeV), or decay of Boron-8 (these have up to 17 MeV).

If neutrino have less energy, detector is not triggered.

It doesn't mean that neutrino was not emitted.

It could be emitted but remained unnoticed.

That's one bizarre claim in the original paper, the other being that one sees variations in the radioactive decay curve without solar activity, and solar activity without effect on the radioactive decay.

Purdue University even patented their method in the US:

Edited by Sensei

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And? You would like neutrinos of lower energy to be produced in any significant amount, as compared to those from 7Be and 8B which result from the very proton-proton cycle at the core? I'm perfectly confident that this would be noticed from long.

Neutrinos are emitted in decays that produce energy, that would have been noticed. Better: light nuclides and their decays are all known.

Also, you'd like neutrinos of lower energy to trigger radioactiv decay more efficiently than those from the proton-proton cycle?

That's becoming unrealistic... The reasonable path is that the core emits nearly all neutrinos, including the ones capable of triggering reactions, that these neutrino flux is independent of solar flares and storms, which dont' influence decay on Earth - as the original paper shows, if one reads the curve objectively.

Patents prove that a clerk accepted the text. In the US, he must be convinced that the invention works, with all associated uncertainties, in Europe not even. In France at a time when inventions had to look feasible to be patented, a clerk refused the electric transformer. A patent is not a proof of valid concept.

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And? You would like neutrinos of lower energy to be produced in any significant amount, as compared to those from 7Be and 8B which result from the very proton-proton cycle at the core? I'm perfectly confident that this would be noticed from long.

It's well known fact, if you would know subject.

~85% of neutrinos are coming from p+ + p+ collisions, and are not possible to detect by Chlorine-37 based neutrino detector.

Be-7 + e- -> Li-7 + Ve + 0.862 MeV (15% of all neutrinos)

B-8 is responsible for just 0.1% from 15% of all neutrinos (small quantity, but large max energy possible).

http://en.wikipedia.org/wiki/Solar_neutrino

http://en.wikipedia.org/wiki/File:Proton_proton_cycle.svg

Energy 0.420 MeV from p+-p+ collisions, doesn't mean that neutrino takes it all. They share it randomly with positron.

0.42 MeV is sum of energy of neutrino + kinetic energy of positron.

Also, you'd like neutrinos of lower energy to trigger radioactiv decay more efficiently than those from the proton-proton cycle?

I am just saying about neutrinos detection methods. If detector didn't detect anything it doesn't mean that there was no particle there passing through it.

I am considering neutrinos from proton-proton collisions as "low energy neutrinos".

18 MeV max from B-8 versus 0.42 MeV max. That's huge difference, 43 more energy.

Lower energy neutrinos is 5.6(6) times more than those with larger energy (Be-7) and >5000 times more than from B-8.

Detection of neutrinos is harder, but their quantity per cm^2 is higher. Higher probability of collision with some nucleus.

And we don't know for sure how they influence unstable isotopes.

Chlorine-37 example shows that they can influence even STABLE isotope.

That's becoming unrealistic... The reasonable path is that the core emits nearly all neutrinos, including the ones capable of triggering reactions, that these neutrino flux is independent of solar flares and storms, which dont' influence decay on Earth - as the original paper shows, if one reads the curve objectively.

You're just repeating your personal opinion.

I told you- prepare isotopes and check it by yourself.

Then you will have experimental verification.

Edited by Sensei

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And all these neutrinos are produced at the core as I already said, in an amount propotional to these from 7Be, independently of solar storms and flares. How the heck should effects at Sun's surface change the neutrino flux to influence radioactivity on Earth?

No, I won't make any further check on that. The curve interpretation in the original paper is flawed. The mechanism shows no relationship with neutrino emission.

There would be many thousands of claims to be checked, less unrealistic than this one.

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