Position Eigenstates Indeterminacy

In summary, the conversation discusses the indeterminacy of position eigenstates and whether they can be considered classical states when smeared by a certain length, such as 10 Planck lengths. The accuracy of devices in measuring such small lengths is also mentioned. The Heisenberg uncertainty equations are suggested as a potential source for answering these questions.
  • #1
Edward Wij
130
0
How large could position eigenstates indeterminacy be so as to be indistinguishable from classical state? For example. If a particle is smeared by 10 Planck length.. could we tell or could we consider it as classical state? What is the most accurate device that has probe the smallest region enough to say the smearing can be such and such length like 5 Planck length that we can still call classical state (assuming supposed there was no collapse and born rule not applied to the decoherence mixture of basis)?
 
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  • #2
I can't even read your last question clarified in quotes. However, the actual values of 10 Planck lengths or even 100 or 1000 (or even a Million) times 10 Planck lengths are so small as to be beyond our measurement NOW. We define this measurement, mathematically. Actually measuring this value is another matter.

Perhaps you should look into the Heisenberg uncertainty equations for an answer to your question.
 

Related to Position Eigenstates Indeterminacy

1. What is a position eigenstate?

A position eigenstate is a state of a quantum system in which the particle is localized at a specific point in space with a definite position. It is an eigenstate of the position operator, meaning that if a measurement is made on the system, the result will always be the same position value.

2. How is indeterminacy related to position eigenstates?

Indeterminacy, also known as uncertainty, is a fundamental principle in quantum mechanics that states that certain pairs of physical properties, such as position and momentum, cannot be simultaneously known with absolute certainty. In the case of position eigenstates, the particle's exact position is known, but its momentum and velocity are completely unknown.

3. What is the Heisenberg uncertainty principle?

The Heisenberg uncertainty principle is a fundamental principle in quantum mechanics that states that the more precisely one property of a particle is measured, the less precisely the other complementary property can be known. In the case of position eigenstates, knowing the exact position of a particle means that its momentum and velocity are completely uncertain.

4. Can a particle be in multiple position eigenstates at the same time?

No, according to the principles of quantum mechanics, a particle can only be in one position eigenstate at a time. This is known as the superposition principle, where a particle can exist in multiple states at the same time until a measurement is made, collapsing it into a single eigenstate.

5. How are position eigenstates used in quantum computing?

In quantum computing, position eigenstates are used as the basis for qubits, which are the building blocks of quantum computers. By manipulating and controlling the position eigenstates of qubits, quantum computers can perform complex calculations and algorithms that are impossible for classical computers to solve efficiently.

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