- #1
Joker93
- 504
- 36
I found these two examples in a books which demonstrate Heiseberg's uncertainty relation:
1)http://data:image/png;base64,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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.
1)http://data:image/png;base64,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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.
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