Uncertainty Principle & Measuring Momentum: Is There a Confusion?

In summary: Summary:In summary, the relation between p and E is only valid for photons because of the uncertainty principle. It's generally difficult to determine position accurately, and measuring momentum doesn't always give you an accurate estimate of other observables.
  • #1
spidey
213
0
we have the relation p= E*C then why do we say that we cannot measure momentum accurately? if we know E then we can find p, and then we can find position at ease,whats more difficult here?
are we confusing with uncertainty principle? or is Uncertainty principle confusing us?
Or am i missing anything?
 
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  • #2
spidey said:
… we can find position at ease …

Hi spidey! :smile:

(that equation is for photons, of course …)

Nooo … finding position is actually quite difficult … the more you know about momentum, the less you can know about position. :smile:

You can get energy, and therefore momentum, as accurately as you like … but then you won't be sure about time or position! :cry:
 
  • #3
spidey said:
we have the relation p= E*C then why do we say that we cannot measure momentum accurately? if we know E then we can find p, and then we can find position at ease,whats more difficult here?
are we confusing with uncertainty principle? or is Uncertainty principle confusing us?
Or am i missing anything?

As has been pointed out, that relation only works for photons because it is for a massless particle.

But a more general question would be the relationship between "p" and "E". You will note that p and E (or to be accurate, H, the Hamiltonian) need not necessarily commute, except for a free particle. If they don't commute with each other, then measuring p will not tell you E with the same certainty. You'll have the same issue as p and x.

There's also a more common misunderstanding of the HUP here that I'm seeing very often in this forum. The HUP doesn't talk about the uncertainty in a single measurement. You can measure p and x as accurately as you want for a single particle. These accuracies depend on the instrumentation accuracy, i.e. how small is that spot made by that particle on the CCD. That isn't the HUP. The HUP comes in in 2 different ways:

1. If I have made a determination of x with an uncertainty of [itex]\Delta x[/itex], then how accurately can I predict [itex]p_x[/itex]?

2. I make many repeated measurement of x and many measurement of [itex]p_x[/itex], and look at the spread in values for those observables.

There's nothing in the above to prevent you from measuring x and [itex]p_x[/itex] as accurately as you want from each of the single measurement.

Zz.
 

1. What is the Uncertainty Principle?

The Uncertainty Principle, also known as the Heisenberg Uncertainty Principle, is a fundamental principle in quantum mechanics that states that it is impossible to simultaneously know the exact position and momentum of a particle. In other words, the more precisely we know the position of a particle, the less precisely we can know its momentum, and vice versa.

2. How does the Uncertainty Principle affect our ability to measure momentum?

The Uncertainty Principle affects our ability to measure momentum because it sets a limit on how precisely we can know both the position and momentum of a particle. This means that there will always be some uncertainty in our measurement of momentum, no matter how precise our instruments are.

3. Is there a confusion between uncertainty and measurement in the context of momentum?

Yes, there can be confusion between uncertainty and measurement when it comes to momentum. This is because the Uncertainty Principle states that the act of measuring one aspect (position or momentum) affects the other, leading to uncertainty in our measurement. This can be confusing for those who are used to classical mechanics, where precise measurements are possible.

4. How does the Uncertainty Principle impact scientific experiments and observations?

The Uncertainty Principle has a significant impact on scientific experiments and observations, especially in the field of quantum mechanics. It means that scientists must accept a certain level of uncertainty in their measurements and observations, and must carefully consider the effects of their measurements on the object being observed. It also means that certain experiments may be limited by the Uncertainty Principle, making it challenging to obtain precise data.

5. Is there any way to overcome the limitations imposed by the Uncertainty Principle?

There is no way to completely overcome the limitations imposed by the Uncertainty Principle. However, scientists have developed various techniques and theories to minimize the uncertainty in measurements and observations. These include using more precise instruments, performing multiple measurements, and employing mathematical techniques such as wavefunction collapse. Ultimately, the uncertainty in our measurements is a fundamental aspect of the quantum world and must be accepted in our scientific endeavors.

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