Heisenberg Uncertainty Principle clarification

[Joker93]

I found these two examples in a books which demonstrate Heiseberg's uncertainty relation:

1)http://data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVwAAACRCAMAAAC4yfDAAAAAhFBMVEX///8AAADj4+OcnJxnZ2e9vb3GxsaXl5f4+Pj8/Px2dnasrKzV1dWQkJDt7e309PTn5+fb29vOzs7T09OkpKRVVVXBwcG3t7dsbGyEhIRgYGC4uLigoKCLi4vJycmAgIBwcHBMTExDQ0MvLy89PT0nJycaGhoNDQ1ISEgWFhY1NTUhISEMTPorAAAI2klEQVR4nO2dC3ujqhaGEW8Y5KaokURN2+nMnn3+//87oml6S1tNTES27zxphsRQ+gWBtVgAACuDYGE0dxEsJoRzl8BmCJ+7BDZD6NwlMJcNujKDPJ+kHDbC5f7aLLIpymElAnsAQFZckQWtJiuNZVTMr6nT1OHlWVAyXXGsArqAu6CMQIwvzmNtdL+glRWU+md6ubhrm3selGE/z2qyyd2L8wjXge55WF0HQS0q9u7OHie0u9po34EegvYnd9Lffdob82G+dmffwupYP9GytyfwdsyH17HCIGDFuufGGdP9r2OFIUAn/tv9p3TqER9TtymNpSSOM/xOj8LVPBtD7DjO4IvXFncc7iru7Wi1deTgq93VmzsGLe6Ike7aoY0hFZkYYXSNsjhWxukVkWK1f0cwrjLS4gpf8H+PsXe6rX6xOLlBpmPFpZuM3aAYsxP4N8h0fB9VXzMHZyyGiAuSzMLxriniWjnZY4649W7qYsyOOeKy8NrQHeMwR1xqXzCpOeIWYzzsy8AYcS3U1hhxI2KhGWGGuCiqLNT2PuLyovhWO1heHeRrJDcQF4HDx1/iOA9KgS9GA4j+tdA600wuLsYYMPye0ul5wPKzjLvGWo/jpOKyyFNx2j6n8VuE7KT935+NSD/d/rtgwgKYwtHVOKG4FJeb8+/kjrMJv5jmtXGU8NIuTiguSr96hwnxlfVV2qgtOFaym4wWRmDn9ORk4qKr+iM7J9anERdJ2VyVARZXfdxQphAX4WZMhMI5mJVxeFOIW33ZhQ3HyqB9Qzo0O6vusam8RNx40uFTVC3cSf7JLsLZc5bpYf1ocVGhhocwDmLpdffzzKq2R/W6kJHiFrKaPookIkuOWsC7TzOrWlzdMowSl2XJTUZOLMmW261VQXsnY0nlq8bNMfx79g7tyH6/0JaXu6BCIC+B91rvxHBxGbtHaD3cFGyJ+uK4i7hI3u7Vk/ZN7gBxXXIn50pShfvl2Wte/8DvltNtnM6R+r24iKvDHVtDBqUq2KKmJeJnKeUzrxT7982y/dLpZP1e3Pj+a23qqtrvlzN6oFAIARmECL4JMiZZ18KZ0qG9BcJaeZ6n+BLb4J7ek3peXDOW44bhfm/gdz+E3rlQf9IxorkyZHqAiq4OE0qXW4ff4YeVGfX2FVqRcKE1+D1ZYGRnTQPlKUpp32nI/WCsDDa5BaTF1fIqDofBGxPWCRnSyP4MJOTkix6AO7+4ubugteM8HCHu3CvcKMtyuKTeGI6pua/r7GjotoTiQ/pkgMI+ffo2RJ8+dUFxnz7d40mfPjXqdZ9+SXKdlK+bI/TZu6eNq/rs3ZNvPO3TJzOvz949mVNBn/3J9eb36dPgo+guD09RzrhPJx/S8Ut6776X41icX2PEhScxor4ZPqXR+fRJLHY+HX2Vpn36fXaUv0+/vn/8OP8qTc+n6dA0//DnfUzDM2kay6dltbkLItQ3wsPWG8ijkQNLE+E8yBbsbzCXsGNhdhpagAnDeZ1xzpc3zZYbvijU7Wqs4YX8TB8VYqI/9wUqlYLf1thibiPhK77z584PI22F/XFGjRoagRr2gSLGicu41NMQJeVDKmU34i2C9kEowDUQ3Ah/6aA5tHuDBtXXN2hxkyIUPi6gj4l4UkZ00INmf+8K33gN5ePE0eJC6Qm+d1nRSGTGLlqp4xz0szHipuSCLQGo4pwEgfTzgEC/LjgxolUYEXFzD/gGX2Ko+lK7rfy95Nr9UyTAnTgC8zJKk8S9qNYajI5yLIEZ4oozi1YXjRZXDxJNENe6fZmYYFQ7Sg0QF8c/X7MwDv3T/OJGxIih6aSYspoHH6zqy3oMEZeW8/7+22CIuMOnw5aEIeKuq9ZvyCruDTHUIXslhojLrz571USOx2rNLa6dx4EfR+6ziwsaK+tux/ziAnH58ZWGY4C4AO6FZW6xIyaIC4S00L8ADBG3pVrewtSfMUXcSFrYr5kirm4b5i7B5JgjbhQuZtXLUMwRl9q306s54i5wr4WfMEZcZqHX3BRx0dJ3FzuHKcHPVvp1BwVq3hy0MeQ7thBmY5tgCCGxRtu+dYsUeGNv9g5rvXCU3T+2yKJNXnPZRQ+hX29f7GeyDknbBv8685mbYtH4NiIQa1OTeEhBB8gD8L0NdgQiYZRL5YMtgOqeEcQ2jW/FY/VHLyOIHlm3+tsDDo1bRWmYJUHTVmEPKPL3fuVB9rS3Ov5OH52TFEDxRmv6EHF8AAea13nqJ6242/ZxxxuVLmgbjZ/wnbh9CEbIY7IB8UY+IadMgSMZyTJWbTB0/HRzR+efTeJGUXR8dEGkenIlan9Ex3dQ93TPKZe77HB6fzZmuP6hlXO/pkwJ2hnQZAi5PWd2JQmib3eofbGO6gQxxugM8QP2dGm7YpcV7NXexMebEu92j8ljwum1x8GMx565M1kjGAAaoYTpWpyyLUD6tgxTkAq/Rojcv5vzrWkXdkSCzPf+2RFQFPlTKy7J9UZhRVUAP/mVNjPcpLZ0aVCbvmn7rzV9ZRK72vw9yO71XZ0nfpJPf8bGjxBLIsWaEMRY7MSuFdf3fe1bUKAVV+G21w5SbQLjn3OZGLrw82NewEIRsPU8BZUst1sSKiEe2tddkUmgPG8rZrhHk+Xs/z4Yr/2zjJi6sm7tr0YpI0xPi2YijAPZGZtrBLb0ZkZi5WoeQwgsHCkYwww2y8rKysrKypUkTu8V4u/d47SIXsZjvrPddD4yxsGiDq8wgONSefwx6uR1sclWH0faIjAoV3FH4YFElYT9q0Dq5fRRbjmQWZi75TP83dRODkBWF0EUNsj7F/6ugO8J/hiGlWffGrXp8UCdtfW2ECBrntkjRxVzEN25zAUhCvTRJ1meAORmGGJQReC5yfgjchtL9xmalrZZKEEBseAeEOAAWAhYSZBL9wKo7jQS3XAITDEsYEVpf1XsHzdYX/mG1NmFDnz2igeeql3i5OUf4TS0+Sv+5CBwI92hBQCgMHuKf8fVge5UWjgie4KOfSsA70pgxL7CVsK2/wy+9v8cY2fvC9WpEQAAAABJRU5ErkJggg==When we try to locate a moving electron via Bohr's microscope thought experiment which uses an apparatus,we transferred momentum via the photon that we send in order to measure the position or momentum of the electron.This gives rise to the position uncertainty Δx that is roughly equal to the width of the opening of the aperture and the uncertainty in momentum ΔPx due to the transfer of momentum.

2)The single slit experiment(diffraction pattern).This time,we again have uncertainty Δx roughly equal to the width of the slit and uncertainty in momentum ΔPy due to the wave diffraction(or you can also say because of photons hitting the edges of the slit).

The funny thing about these two examples is that they show you how the uncertainties in the experiment arise from the interaction of the particle that we want to observe with its surroundings(either due to the measurement or just passing through a slit).
So this brings me to my question,is Heisenberg's uncertainty principle something that rises ONLY from the measurement process(interaction)?Because if we don't interact with a particle,then there is no change/transfer of momentum so the particle has a definite momentum AND position(but this contradicts the fact that many claim to be truth-that the particle does not have an exact location until it is measured) but when we try to interact with it we "mess up" the situation in ways that are described by the two experiments that i aforementioned.Did i got something wrong here?

And if Heisenberg's uncertainty principle isn't something that rises ONLY from the measurement process(interaction) and it is something much more fundamental(i.e. it's not the interaction that causes there uncertainties),then how would you define the uncertainty principle in order for me to understand it more specifically(and what does a particle do when it does not interact with something?-details about position and momentum)?

The important part of the question is:In order to fully understand and answer my question just follow the my thinking as i present it.Follow the 2 examples that i showed above.They imply that its the interaction/measurement that make it impossible to know both momentum and position because you mess it all up(transfer of momentum and stuff).Keep this in mind while also having in mind the statement that "a particle does not have a position(it isn't anywhere) or momentum until measured" and you can see that what confuses me is that with these two in mind,my conclusion is that without )interacting with the particle,it does in fact have a certain momentum and position(not as the above statement says).
To clarify a bit more: Position and momentum do not HAVE values until measured,but HUP rises from the interaction with a particle.It interacts with a particle at a certain definite position and it transfers some momentum to the definite momentum that it already has(if it did not have a position,how could they interact,and if it did not have a momentum then how can we even talk about transfer of momentum?).

Note:Bear in mind that i don't want an explanation that is purely mathematical(like just saying that momentum is just the Fourier transform of position-which in my opinion is a RESULT of the principle and not the cause of it as someone might claim-again,correct me if i am wrong here).I am not saying that maths are not required in order to give me a complete explanation,just that i also want some kind of intuition and deeper understanding(because i think that most students take these fundamentals as granted and just proceed to solve exercises). Also, the pictures are from Eisberg and Resnick's book Quantum Physics.

 

[phinds]

The HUP is NOT a measurement problem, it is a fundamental limitation of nature. You will find conflicting reports on whether it means that it is always impossible to simultaneously measure, for example, the position and momentum of a quantum object to unlimited precision.

What everyone agrees on, however is that it is impossible to set up exactly the same starting conditions for making such a pair of measurements and get the same results every time. The results will have a statistical distribution.

Just in case that's not clear, let me try to be more specific. Let's say we have an apparatus that forces the position of an electron to be known more and more precisely and we can shoot electrons into that apparatus repeatedly with exactly the same velocity and position going in. When we measure the momentum of the electron, it will be different every time we measure it. and the degree of difference will grow as the position is more and more well known.

This is known as the "single slit experiment" which is shown in detail on the Internet.

EDIT: and by the way, even Heisenberg originally described the HUP as a measurement problem but that view has been discredited.

 

[Joker93]

The HUP is NOT a measurement problem, it is a fundamental limitation of nature. You will find conflicting reports on whether it means that it is always impossible to simultaneously measure, for example, the position and momentum of a quantum object to unlimited precision.

What everyone agrees on, however is that it is impossible to set up exactly the same starting conditions for making such a pair of measurements and get the same results every time. The results will have a statistical distribution.

Just in case that's not clear, let me try to be more specific. Let's say we have an apparatus that forces the position of an electron to be known more and more precisely and we can shoot electrons into that apparatus repeatedly with exactly the same velocity and position going in. When we measure the momentum of the electron, it will be different every time we measure it. and the degree of difference will grow as the position is more and more well known.

This is known as the "single slit experiment" which is shown in detail on the Internet.

EDIT: and by the way, even Heisenberg originally described the HUP as a measurement problem but that view has been discredited.

I know all these, but this is not what i am saying. What i am saying has to do with the nature of the momentum and position before we make a measurement or interact with the system. The statement a particle does not have a position(it isn't anywhere) or momentum until measured" is generally thought of being correct.But,when we do not interact with a particle(not transferring momentum etc),why don't we just say that a particle has definite momentum and position at each instance of time?I am asking this,because in my examples(and the single slit experiment) the uncertainties rise due to the measurement and/or interaction with the particle.The statistical interpretation has to do with the measurement of position and/or momentum.I am talking about BEFORE the measurement because some say that a particle does not have a position before the measurement while i am saying "why not"? because it is the act of measurement/interaction that gives rise to these uncertainties.

 

[phinds]

Yes, that is in fact what QM says ... certain things do not HAVE a value until measured. I'll have to leave it to the experts to explain that in more detail.

 

[Joker93]

Yes, that is in fact what QM says ... certain things do not HAVE a value until measured. I'll have to leave it to the experts to explain that in more detail.

And this is where my questiom come in.Position and momentum do not HAVE values until measured,but HUP rises from the interaction with a particle.It interacts with a particle at a certain definite position and it transfers some momentum to the definite momentum that it already has(if it did not have a position,how could they interact,and if it did not have a momentum then how can we even talk about transfer of momentum?).

 

[andresB]

And this is where my questiom come in.Position and momentum do not HAVE values until measured,but HUP rises from the interaction with a particle.It interacts with a particle at a certain definite position and it transfers some momentum to the definite momentum that it already has(if it did not have a position,how could they interact,and if it did not have a momentum then how can we even talk about transfer of momentum?).

it is not that way. Look at, for example, The Elitzur_vaidman bomb.

And for the why not to assign them definite position and momentum prior measurement look at for wheeler delayed choice experiment (or successive measurement of spin in different directions, like in the first chapter of Sakurai)

 

[bhobba]

then how would you define the uncertainty principle in order for me to understand it more specifically

Its a theorem about non commuting observables:
http://damtp.cam.ac.uk/user/eal40/teach/QM2012/7comm.pdf

Thanks
Bill