# The role of probability

Is Probability the underlying law of nature, or does it only emerge from repeatedly recording observations of events that we cannot yet measure accurately enough?

OR put another way

If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?

ShayanJ
Gold Member
Is Probability the underlying law of nature, or does it only emerge from repeatedly recording observations of events that we cannot yet measure accurately enough?
In terms of physics, its an open question. In terms of philosophy, its a matter of taste! See here!
If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?
According to Quantum Mechanics, the problem is not with technology limitations and uncertainty principles are intrinsic to quantum system. But this is sometimes a matter of debate between different interpretations of QM too.

In terms of physics, its an open question. In terms of philosophy, its a matter of taste

The way I see it , is that interpretations are formalized to better understand certain concepts which allow us better to
understand nature.

An apple may taste different for different people , but most of us still concede that we call it an apple, through collective observations.
This does not mean that one day we might distinguish through "finer" observation that there is a subset of different kinds of apples.

Have we not limited ourselves through probability , by saying it looks a little different so its there is 90% probability that it IS an apple.
Are we not just smoothing the curve to connect the dots?

DrChinese
Gold Member
Are we not just smoothing the curve to connect the dots?

You can connect the dots a couple of different ways. Or not at all. There are several interpretations, and each leaves a different apple-like taste in your mouth. :)

None of them really involve throwing out the Uncertainty relations, though.

Johan0001
atyy
Is Probability the underlying law of nature, or does it only emerge from repeatedly recording observations of events that we cannot yet measure accurately enough?

OR put another way

If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?

It turns out that "OR put another way" is not correct. The answer to the first question is yes, it may be possible that nature is deterministic. But the answer to the second question is no, because the commutation relations underlying the uncertainty principle (plus a few other assumptions that are usually true in quantum mechanics) guarantee that the observables in the position-momentum uncertainty relation cannot be measured without disturbance, because they cannot even exist simultaneously.

atyy
According to Quantum Mechanics, the problem is not with technology limitations and uncertainty principles are intrinsic to quantum system. But this is sometimes a matter of debate between different interpretations of QM too.

Regarding the possibility of simultaneously accurate measurements of non-commuting canonically conjugate position and momentum, there isn't a "debate" between different interpretations, except maybe in special cases like 1D motion. The related theorems that hold in all interpretations are:
http://cds.cern.ch/record/275911/files/th-7492-94.pdf
http://en.wikipedia.org/wiki/Kochen–Specker_theorem

bhobba
Mentor
Is Probability the underlying law of nature, or does it only emerge from repeatedly recording observations of events that we cannot yet measure accurately enough?

Probability is a modelling tool defined by the Kolmogorov axioms - just like classical mechanics, relativity etc etc. Physical theories are basically mathematical models.

If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?

You misunderstand QM - it says that's impossible. If such occurred it would prove QM wrong and would be a major earth shattering discovery.

Thanks
Bill

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bhobba
Mentor
Have we not limited ourselves through probability , by saying it looks a little different so its there is 90% probability that it IS an apple. Are we not just smoothing the curve to connect the dots?

If you want to revolutionise QM by ridding it of probability - feel free. Many have tried - they all failed. The best that has been achieved is to have the underlying probabilities depending on other things like lack of knowledge in initial conditions (Bohmian Mechanics) or things going on at the sub-quantum level (there are a number that take that route eg Nelson Stochastics and Primary State Diffusion).

Although no one can prove we cant find a theory that does away with such things the fact so many have tried and failed, including really great figures like Einstein, strongly suggests its intrinsic. Of course no one can know what future progress will bring.

Thanks
Bill

Probability is a modelling tool defined by the Kolmogorov axioms - just like classical mechanics, relativity etc etc. Physical theories are basically mathematical models.

Interesting , thanks

Just a question. The third of the Kolmogorov axioms refers to "mutually exclusive events" .

When we apply probability to experimental outcomes of entangled particles , is it fair to call these events mutually exclusive.
Since they are " entangled" , and part of a single system as sometimes described?

bhobba
Mentor
When we apply probability to experimental outcomes of entangled particles , is it fair to call these events mutually exclusive. Since they are " entangled" , and part of a single system as sometimes described?

Correct. The usual terminology though is correlated.

This is an important point about locality in QM. 'Locality' is encapsulated in the so called cluster decomposition property:

It does not apply to correlated systems like EPR.

Whether such violates locality or not depends on your definition of locality.

Thanks
Bill

Correct. The usual terminology though is correlated.

This is an important point about locality in QM. 'Locality' is encapsulated in the so called cluster decomposition property:

It does not apply to correlated systems like EPR.

Ok I think I understand better .

Is this where the famous Bell inequality is violated?
1. In the entangled experiments the bell inequality is violated when the results show inconsistencies with predicted probability outcomes.
2 Inferring that FTL/instantaneous correlations must then be possible.

If a new technology were to be discovered in the near future, which could allow us to observe without disturbing the "observables" we currently measure. Then Heisenberg's uncertainty principle ΔXΔρ > ħ/2 could be further refined?

You misunderstand QM - it says that's impossible. If such occurred it would prove QM wrong and would be a major earth shattering discovery.

I am not saying intrinsic uncertainty could eventually be overcome, but it may become negligible.

http://www.sciencedaily.com/releases/2012/09/120907125154.htm

Our own Dr Chinese explains it brilliantly:
http://www.drchinese.com/Bells_Theorem.htm

Yes I read most of his links previously , and I must say.
I have not found a more comprehensive detailed description on the topic.
Thanks Dr Chinese and to you Bill.

bhobba
Mentor

If they mange to do it then QM will be overturned.

That said - be very careful of articles on the popular press - they often get things wrong.

Thanks
Bill

atyy
The third of the Kolmogorov axioms refers to "mutually exclusive events" .

When we apply probability to experimental outcomes of entangled particles , is it fair to call these events mutually exclusive.
Since they are " entangled" , and part of a single system as sometimes described?

Yes, the outcomes of measurements on any quantum system, including entangled systems, are mutually exclusive. It basically states that each measurement has a single definite outcome (except in the Many-Worlds approach). For example, if Alice and Bob measure whether their spins are up or down, they will get one of 4 definite results {up-up, up-down, down-up, down-down}. When the same measurement is repeated on another identically prepared system, the outcome will again be one of these 4 possible definite outcomes, but it may not be the same one as on the previous identically prepared system. The distribution of definite outcomes is given by the Born rule.

I am not saying intrinsic uncertainty could eventually be overcome, but it may become negligible.

http://www.sciencedaily.com/releases/2012/09/120907125154.htm

Wow is this article getting attention in the physics community? If those experiments can be repeated by other laboratories with the same result we have a break-through in QM indeed. The conclusion of that article is the same one as the original paper, it's not misinformation like it happens in many cases.

bhobba
Mentor
Wow is this article getting attention in the physics community? If those experiments can be repeated by other laboratories with the same result we have a break-through in QM indeed. The conclusion of that article is the same one as the original paper, it's not misinformation like it happens in many cases.

The article gives the wrong impression that they violating the uncertainty principle - they aren't. What they have done is fully explainable in QM - if it wasn't that would be BIG news - it isn't.

What they are doing is work on so called weak measurements:
http://en.wikipedia.org/wiki/Weak_measurement

Because it is weakly coupled to the system and does not disturb it there is a large uncertainty in the measurement result. To be specific what it is measuring is an average of if you took a large number of individual measurements.

Thanks
Bill

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vanhees71 and Tosh5457
Because it is weakly coupled to the system and does not disturb it there is a large uncertainty in the measurement result. To be specific what it is measuring is an average of if you took a large number of individual measurements.

Which is the better approach , many measurements with large uncertainty or few measurements with less uncertainty.
Which better describes nature?
My view is we learn from experience , the more times we do it , the better we can understand the holistic picture.
And that is what they are doing here.

On a roulette table rolling the zero 3 times in a row is less informative , than getting the average of the last 10000 spins.

The word "intrinsic" has been mentioned a lot without explanation of what it means. Using the example of position and momentum, here is a different look.

Momentum is the product of relativistic mass times velocity. Velocity is the rate of change of position. To measure the momentum of a particle precisely, you have to at least measure it's velocity precisely. But you can not measure velocity at a single point. You need to measure position at least 2 points and divide by the time it took to travel between the two points. The further apart the two points are, the more accurately you can determine it's velocity but then which of the points do you attribute measured velocity to? Point A, B, or between both points (don't forget uncertainty due to potential acceleration and deceleration)? The further apart the points, the higher the uncertainty associated with the velocity (and thus also the momentum). The smallest distance between two points is the Planck length, so that is the highest accuracy (smallest uncertainty) you can have for a position to assign to the velocity measurement.

Therefore "intrinsic" uncertainty between position and momentum is due simply to the fact that they are mathematically defined in a complementary manner, momentum being defined relative to the rate of change of position, ie momentum and position are not defined within the same basis. In short, the uncertainty between position and momentum comes from the fact that the definition of momentum involves the behaviour of a particle over more than one position. This is what "intrinsic" means.

bhobba
Mentor
Which is the better approach , many measurements with large uncertainty or few measurements with less uncertainty. Which better describes nature?

They both do, and are of equal value. The point is to understand what's going on - not to choose which is better.

My view is we learn from experience , the more times we do it , the better we can understand the holistic picture.
And that is what they are doing here.

The theory explains both - how you view it is purely up to you.

On a roulette table rolling the zero 3 times in a row is less informative , than getting the average of the last 10000 spins.

That depends on what information you want - do you want the average of the outcomes or the individual outcomes. You can do a lot more with the individual outcomes like calculate the standard deviation.

Thanks
Bill

ShayanJ
Gold Member
The word "intrinsic" has been mentioned a lot without explanation of what it means. Using the example of position and momentum, here is a different look.

Momentum is the product of relativistic mass times velocity. Velocity is the rate of change of position. To measure the momentum of a particle precisely, you have to at least measure it's velocity precisely. But you can not measure velocity at a single point. You need to measure position at least 2 points and divide by the time it took to travel between the two points. The further apart the two points are, the more accurately you can determine it's velocity but then which of the points do you attribute measured velocity to? Point A, B, or between both points (don't forget uncertainty due to potential acceleration and deceleration)? The further apart the points, the higher the uncertainty associated with the velocity (and thus also the momentum). The smallest distance between two points is the Planck length, so that is the highest accuracy (smallest uncertainty) you can have for a position to assign to the velocity measurement.

Therefore "intrinsic" uncertainty between position and momentum is due simply to the fact that they are mathematically defined in a complementary manner, momentum being defined relative to the rate of change of position, ie momentum and position are not defined within the same basis. In short, the uncertainty between position and momentum comes from the fact that the definition of momentum involves the behaviour of a particle over more than one position. This is what "intrinsic" means.

By this explanation, uncertainty principles should appear in classical mechanics too!!!

atyy
By this explanation, uncertainty principles should appear in classical mechanics too!!!
They do. They are all over the place if you look. Look up "Fourierhttps://www.physicsforums.com/wiki/Fourier_transform [Broken] duals", "Pontryagin duality", "conjugate variables".

A common example is that between time and frequency in wave mechanics, or that between action and density in hydrodynamics.

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