# Inherent impossibility of knowing both position and momentum

• Curious6
In summary: GR-QM unification.In summary, the conversation discusses the uncertainty principle in quantum mechanics, which states that the position and momentum of a particle cannot be simultaneously known. This is due to the fact that x and p do not commute, making it an intrinsic property of quantum particles. The conversation also touches on the concept of position in quantum mechanics, with some arguing that it is not a well-defined attribute of an electron, but rather an attribute of the interaction process between the electron and a measuring instrument. Overall, the conversation highlights the complexities and paradoxes of quantum mechanics and the ongoing search for a
Curious6
Hi, I'm writing just to clarify a question I have regarding quantum mechanics. Is the reason we cannot predict things on quantum scales due to the inherent impossibility of knowing both position and momentum or is it due to the fact that positions of particles are basically completely random (distributed along a Bell curve) until the moment of observation of the particle? Many thanks.

Also, isn't the position any particle can taken on not infinite, but limited by the speed of light, so that it can only assume a very large, but not infinite number of positions?

The uncertainty relation is due to the fact that x and p does not commute, that is all one needs to derive the HUP. So it is an intrinsic property of quantum particles.

The particle is not bounded by the speed of light, if you measure its momentum 100% here on earth, the particle have a non zero probability to be in say the andromeda galaxy. The reason for this is that only information must travel slower than light speed, QM is non local.

This was thought of by Einstein in the EPR paradox (http://en.wikipedia.org/wiki/EPR_paradox )

Thanks for your answer. So my question is, if particles can move around in seemingly random ways, are they maintained within an object or is there occasional 'jumping out' of particles from within that object? By an object I mean something like a table, a person's body, a rock...is it the case that at anyone time certain particles are moving out of the object and certain objects in? If anybody could give any insight on this it would be much appreciated!

The thing is that the particles in quantum world don't move randomly, their position is undetermined until it is measured.

That is an important concept in quantum mechanics.

OK, so here's a question for everyone. We are not able to determine the position AND the momentum of a particle at any given time, but however, that does not mean that the particle does not have position AND momentum at any given time. Is this right? If so, then, to find out if a particle was moving 'randomly' we'd have to know whether for any given momentum and position it would move to different positions at different times. However, this is impossible because of the uncertainty principle.

Experiments indicate that a particle does NOT have a "precise" position and momentum at a given time. Use wikipedia to learn about single electron double slit experiments and experiments in which Bell's inequalities are shown to fail.

OP started a new thread with this question and one more merged together. Not so cleaver done.

Curious6 said:
OK, so here's a question for everyone. We are not able to determine the position AND the momentum of a particle at any given time, but however, that does not mean that the particle does not have position AND momentum at any given time. Is this right?
No, it's even worse than that. At all times, the particle has neither a well-defined position nor a well-defined momentum. Even a measurement of position isn't enough to give the particle a well-defined position. The measurement is just an interaction that changes the state of the particle into one that's more sharply peaked around a particular position than before.

The word "uncertainty" is actually very misleading. It suggests that the particle has a position that we don't know, but that's not the case. It doesn't really have a position, ever.

Here's a quote from Rudolf Haag (Local quantum physics, page 2):

Take the example of a position measurement on an electron. It woud lead to a host of paradoxa if one wanted to assume that the electron has some position at a given time. "Position" is just not an attribute of an electron, it is an attribute of the "event" i.e. of the interaction process between the electron and an appropriately chosen measuring instrument (for instance a screen), not of the electron alone. The uncertainty about the position of the electron prior to the measurement is not due to our subjective ignorance. It arises from improperly attributing the concept of position to the electron instead of reserving it for the event.

right the whole thing QM asks that you reconsider is your notions of a particle.

Rather than being surrounded by particles, at the QM level certainty becomes only of interactions between systems - so if we measure a property of an electron we can only say that the result is created between the interaction of macro and micro systems rather than simply 'revealing a result' via measurement.

Fredrik said:
Here's a quote from Rudolf Haag (Local quantum physics, page 2):

Take the example of a position measurement on an electron. It woud lead to a host of paradoxa if one wanted to assume that the electron has some position at a given time. "Position" is just not an attribute of an electron, it is an attribute of the "event" i.e. of the interaction process between the electron and an appropriately chosen measuring instrument (for instance a screen), not of the electron alone. The uncertainty about the position of the electron prior to the measurement is not due to our subjective ignorance. It arises from improperly attributing the concept of position to the electron instead of reserving it for the event.
He would deserve a monument just for this passage.

malawi_glenn said:
The uncertainty relation is due to the fact that x and p does not commute, that is all one needs to derive the HUP. So it is an intrinsic property of quantum particles.

The uncertainty relation in QM is due to the fact that x and p does not commute. So it is an intrinsic property of quantum mechanics. It also is reflected/observed in certain types of measurements but also violated in other types of measurements such as photon emission for orbital transitions requiring an alternate explanation, the "colapse of the wave function".

The experimental and QM electron behaviors require conflicting physics views (spread out over all of space that collides like a point particle with a non-point psuedo vector field) and dual state inter changes (spread out over space to colapse to respread out over space) whenever it is required to make the mathematics and experiments coherent.

Thus one might question if these are actually properties of the particle itself (rather than properties of QM, the interaction behavior, e.g the rotational wave function is symptomatic of the inter-particle interaction uncertainty of a rotational pulsed [wave like] inter-particle interaction behavior).

Curious6 said:
is it due to the fact that positions of particles are basically completely random (distributed along a Bell curve) until the moment of observation of the particle?

QM (by which I mean the mathematical formalism that we use to calculate predictions with) simply does not address the questions, "what is the precise position or motion of a particle before it is observed?" or "what is the particle 'really doing' before it is observed?" All it can do is predict the probabilities of getting various values for position or momentum, etc. when we do observe it.

As of now, the answers to these questions fall in the realm of interpretations of QM, of which there are several. There is no general agreement on which interpretation is correct, because (so far) they all make the same predictions for the results of experiments. Different people prefer different interpretations, but as of now the choice is a matter of personal philosophical preference.

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## 1. What is the Heisenberg Uncertainty Principle?

The Heisenberg Uncertainty Principle is a fundamental principle in quantum mechanics which states that it is impossible to know both the exact position and momentum of a particle at the same time. This is due to the wave-particle duality of matter, where particles can exhibit both wave-like and particle-like behavior.

## 2. Why is it impossible to know both position and momentum?

This is because measuring the position of a particle requires interacting with it, which in turn changes its momentum. Similarly, measuring the momentum of a particle also changes its position. Therefore, it is impossible to know both parameters with absolute certainty at the same time.

## 3. How does the Heisenberg Uncertainty Principle affect scientific research?

The Heisenberg Uncertainty Principle has significant implications for scientific research, particularly in the field of quantum mechanics. It limits our ability to make precise measurements and has implications for the accuracy of our predictions and models. It also highlights the limitations of our understanding of the behavior of particles at the quantum level.

## 4. Is there any way to overcome the Heisenberg Uncertainty Principle?

No, the Heisenberg Uncertainty Principle is a fundamental law of nature and cannot be overcome. However, scientists have developed techniques such as the use of entangled particles and quantum entanglement to make increasingly precise measurements of particles' positions and momenta, although these measurements are still subject to uncertainty.

## 5. How does the Heisenberg Uncertainty Principle relate to other scientific principles?

The Heisenberg Uncertainty Principle is closely related to other principles in quantum mechanics, such as the principle of complementarity and the Copenhagen interpretation. It also has implications for other scientific principles, such as the conservation of energy and the conservation of momentum, as it limits our ability to make precise measurements of these quantities.

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