So many books I have gone through and my idea doesn't come to conclusion.
It is said the uncertainty comes to do disturbance during measurement.
But I feel and believe that even if we don't measure, uncertainty exists there. This is nature. Want to clear my idea through discussion.
Regards
Nityananda Das
Respected sir, uncertainty principle does not speak about measurement induced errors. Measurements change the system to their eigen state that is though different story. As per I understand, the statement should be.. "Two canonically conjugate variables can not be simultaneously and precisely DEFINED (not measured)". It is an uncertainty of nature. We can not even mathematically define two canonically conjugate variables (i.e position and momentum) at the same time with infinite precision.
Thanks
Arka
Dear Arka
This is the same thing that I understand. But in some places I have seen the concept of measurement.
Again, you see the Gamma ray microscope ( thought experiment).
What the message from this thought experment ? Not clear to me.
Love and Regards
Nityananda Das
Dear Nityananda Das,
In my opinion most of the uncertainties come from the modeling phase or identification of the model parameters, then uncertainties can appear during the control of the system notably through uncompensated disturbances. This is why it is imperative to successfully build the model by a judicious choice of the type of representation. As for the introduction of uncertainty when measuring the parameters, this path may exist in the two phases mentioned above.
Best regards
Properly reporting an experimental result along with its uncertainty allows other people to make judgments about the quality of the experiment, and it facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an uncertainty estimate, it is impossible to answer the basic scientific question: "Does my result agree with a theoretical prediction or results from other experiments?" This question is fundamental for deciding if a scientific hypothesis is confirmed or refuted.
PLEASE See :
Introduction to Error Analysis, the Study of Uncertainties in Physical Measurements, 2nd Edition
Authors:
Taylor, John
Dear Ahmad,
You are absolutely right that each experment has error and the results approach the theoretical predicted outcome.
But I am talking about in a different angle of physical understanding.
For example , position and momentum, the two canonically conjugate variables have there uncertainties inherently, or by nature these are uncertain , independent of measurement. As Mr Arka Bandopadhyay has commented.
Regards
Nityananda Das
This is more about human limits. Our abilities are limited and so are our instruments. So, what we propose or measure cannot be absolutely right.
Respected Sir,
In quantum mechanical systems, measurement itself affects the result, so, gives birth of the confusion. This is as much as I understand. [ We may refer to Feynman Lecture on Physics third volume, double slit experiment part for better understanding (or may be for better confusion). In Gasiarowicz's book the general uncertainty formulation for any two variables which can be Fourier transformed(canonical conjugate) tries to address this mathematically. ]
Dear Sujoy
Please think in a different way . I think uncertainty is by nature. But I am not confirmed. That's why I placed the question. I have gone through the references you placed. But see, if you don't want to measure , can you think a pure sinusoidal wave extended over infinite extension ? It means , if you can think it then it is possible to exist delta p = O. But that means infinite energy . Can I think like this ?
Regards
Nityananda Das
Sujoy Datta , Nityananda Das I am glad to inform you that both of you are the scholars (child of intellect, as sir use to say) of Prof. A Mookerjee.
Arka, how can I miss that fact! I myself arranged all the thesis (nearly 50) in the wardrobe of Sir's house. Furthermore, he has a very fundamental paper on Feenberg perturbative model using Feynman diagram, if I am not wrong. Sir always have some memories with every student and never misses the chance to share that with others.
:D
Dear Arka
I don't believe that uncertainty Principle isn't related to measurement. You also agree with this.
Anyway , I would like to know from Sujoy about his thinking on uncertainty Principle.
Regards
Nityananda Das
Sir, I am sure that uncertainty is not related to error in measurement but the measurement itself. It's not the capacity of machine or human being that is related to uncertainty. It is the measurement when changing the result itself is the clue of uncertainty, I feel. This phenomenon is absent in real world, if we take a picture of a running dog at a moment and note the speed at the same time none of these two measurements, position and velocity in interfering each other. But in quantum world, the scenario is different, a measurement of a electron's trajectory (position) spoils its wave nature, i.e, measurement itself interfering into the result. Same problem leads to the Schrodinger cat paradox.
Let us think of a quantum free particle, it has equal probability of been found everywhere, everytime. So, uncertainty of space is infinite at every moment. How about its momentum? Momentum is constant, so zero uncertainty there. Now product of these two uncertainties is a finite number(zero times infinity).
If we put a number to anything, like the spreading of sinusoidal wave to +-infinity , we are really making it a measurable quantity. It's ok in real world but in quantum world it spoils the game as measurement itself affects the result. In measurement theory, we can always associate a operator with any observable (measurable quantity) irrespective of classical or quantum system but due to the measurement's effect in result itself makes the operator model so important in quantum world, so important that many have the wrong idea that operator is a solely quantum mechanical idea.
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