# Wave-particle duality question

#### autonomous

i was wondering, what if you shined two parallel rays of light directly next to eachother and shot the particle throught them, one being a short wavelength and the other a long wavelength and measured each one. the first ray of light would find the momentum, so when u found the position you could already know its momentum. would this be accurate, considering the speed of the particle is constant?

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#### autonomous

if you untirely understand what im saying, its basically to help find a particles position and momentum, sense the whole wave-particle duality is about how its impossible to find both because once you find one you now no less of the other. a shorter wave length will help you find the position, and the longer wave length helps you find the momentum, or maybe its the other way around, but this is what i've read, and no one has ever tried doing both so i figured it may be possible. just read up on the 'wave-particle duality' and you will know more of what my earlier post is asking.

#### SeReNiTy

autonomous said:
if you untirely understand what im saying, its basically to help find a particles position and momentum, sense the whole wave-particle duality is about how its impossible to find both because once you find one you now no less of the other. a shorter wave length will help you find the position, and the longer wave length helps you find the momentum, or maybe its the other way around, but this is what i've read, and no one has ever tried doing both so i figured it may be possible. just read up on the 'wave-particle duality' and you will know more of what my earlier post is asking.
Search and read up on the EPR paradox, you might be enlightened to know that you weren't the first one to propose the collapse of the uncertainty principle.

#### CarlB

Homework Helper
autonomous said:
i was wondering, what if you shined two parallel rays of light directly next to each other and shot the particle through them, one being a short wavelength and the other a long wavelength and measured each one. the first ray of light would find the momentum, so when u found the position you could already know its momentum. would this be accurate, considering the speed of the particle is constant?
For your plan to work, you're going to have to measure momentum first, then position. Clearly if you reversed the order, you'd end up screwing up the momentum and get the Heisenberg limit.

So your question really comes down to this. When you make a measurement of momentum, does it also screw up later measurements of position?

The answer is that it does. In QM, to make an accurate measurement of momentum requires that the particle be placed in an approximate eigenstate of the momentum operator. The math then shows that its position cannot be accurately determined.

By the way, the EPR experiment involves correlated particles being measured, one for momentum, the other for position. In your case, you only have one particle, so the Heisenberg uncertainty principle does, in fact, apply.

Carl

#### Antiphon

The discussion here is quite complete.

In QM, to make an accurate measurement of momentum requires that the particle be placed in an approximate eigenstate of the momentum operator. The math then shows that its position cannot be accurately determined.
To be even clearer, it won't have a localised position in the classical sense
which is subject to discovery. But it will acquire one if and when a position

I use the funny verbiage "subject to discovery" because in english the
word "determine" has two meanings and is the source of much confusion
on this topic.

#### DaTario

It is interesting to note that if you perform one masurement you may find experimental results for position and momentum with as high precision as you want.
The HUP enters the discussion when you try to associate these values of position and momentum to a certain time, a certain initial state and a certain set of physical influences (Hamiltonian). By doing a set of identical experiments you will find statistical dispersion on these results, and it is exactly at this point that HUP appears, if I understood it well.

Best Regards

DaTario

"Wave-particle duality question"

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