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Chapter 6: Problem 96

In the television series Star Trek, the transporter beam is a device used to "beam down" people from the Starship Enterprise to another location, such as the surface of a planet. The writers of the show put a "Heisenberg compensator" into the transporter beam mechanism. Explain why such a compensator (which is entirely fictional) would be necessary to get around Heisenberg's uncertainty principle.

Short Answer

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The Heisenberg compensator is a fictional device in the Star Trek series that addresses the limitations posed by the Heisenberg's uncertainty principle in the transporter beam mechanism. According to the uncertainty principle, it is impossible to know the exact position and momentum of a particle simultaneously. The transporter beam, however, relies on scanning and recreating a person's complete quantum state, including their position and momentum. The Heisenberg compensator overcomes this limitation by rectifying the uncertainties in position and momentum, allowing the transporter beam to function without causing negative consequences for the person being transported.

Step by step solution

01

Understand Heisenberg's Uncertainty Principle

Heisenberg's 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. Mathematically, this is represented as: \[\Delta x \cdot \Delta p \geq \frac{\hbar}{2}\] Where \(\Delta x\) is the uncertainty in position, \(\Delta p\) is the uncertainty in momentum, and \(\hbar\) is the reduced Planck constant.
02

Explain the Function of a Transporter Beam

In Star Trek, the transporter beam is a device that allows people and objects to be teleported from one location to another, such as from the Starship Enterprise to the surface of a planet. This mechanism is based on the idea of scanning an object's complete quantum state (including its position and momentum), disassembling its particles, and then reassembling them at the destination.
03

Identify the Issue with the Transporter Beam Due to Heisenberg's Uncertainty Principle

The Heisenberg's uncertainty principle states that it is impossible to simultaneously know the exact position and momentum of a particle. Therefore, it would be impossible for the transporter beam to accurately scan and recreate a person's complete quantum state, which includes the precise position and momentum of every particle in their body, without causing significant alterations to the original state.
04

Explain the Role of the Heisenberg Compensator in the Transporter Beam Mechanism

The fictional Heisenberg compensator in Star Trek serves to overcome the limitations imposed by the Heisenberg's uncertainty principle. It allows the transporter beam to accurately scan and recreate a person's complete quantum state, including their exact position and momentum, without violating the uncertainty principle. In the Star Trek universe, the Heisenberg compensator rectifies the uncertainties in position and momentum, allowing the transporter beam to function without causing negative consequences for the person being transported. While the compensator is a fictional device, its inclusion highlights the writers' understanding of the fundamental principles governing the quantum world.

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Most popular questions from this chapter

What is the maximum number of electrons that can occupy each of the following subshells? (a) \(3 s,(\) b) \(2 p,(\mathbf{c}) 4 d\), (d) \(5 s\).

(a) What are the similarities of and differences between the \(1 s\) and \(2 s\) orbitals of the hydrogen atom? (b) In what sense does a \(2 p\) orbital have directional character? Compare the "directional" characteristics of the \(p_{x}\) and \(d_{x^{2}-y^{2}}\) orbitals. (That is, in what direction or region of space is the electron density concentrated?) (c) What can you say about the average distance from the nucleus of an electron in a \(2 s\) orbital as compared with a 3 s orbital? ( \(\mathbf{d}\) ) For the hydrogen atom, list the following orbitals in order of increasing energy (that is, most stable ones first): \(4 f, 6 s, 3 d, 1 s, 2 p\)

As discussed in the A Closer Look box on "Measurement and the Uncertainty Principle," the essence of the uncertainty principle is that we can't make a measurement without disturbing the system that we are measuring. (a) Why can't we measure the position of a subatomic particle without disturbing it? (b) How is this concept related to the paradox discussed in the Closer Look box on "Thought Experiments and Schrödinger's Cat"?

A stellar object is emitting radiation at \(3.0 \mathrm{~mm} .\) (a) What type of electromagnetic spectrum is this radiation? (b) If a detector is capturing \(3.0 \times 10^{8}\) photons per second at this wavelength, what is the total energy of the photons detected in 1 day?

Calculate the uncertainty in the position of (a) an electron moving at a speed of \((3.00 \pm 0.01) \times 10^{5} \mathrm{~m} / \mathrm{s},(\mathbf{b})\) a neutron moving at this same speed. (The masses of an electron and a neutron are given in the table of fundamental constants in the inside cover of the text.) (c) Based on your answers to parts (a) and (b), which can we know with greater precision, the position of the electron or of the neutron?
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