Author: Thomas Lee Abshier
Quantum Superposition Reframed
by Thomas Lee Abshier, ND
3/18/20205
The following is a list of experiments used as evidence for the phenomenon of quantum superposition of the quantum wave function.
1. Double-Slit Experiment
Overview:
The double-slit experiment is the most famous demonstration of quantum superposition.
- Setup: A coherent source of particles (photons, electrons, neutrons, etc.) is directed at a barrier with two slits, and a detector screen observes the pattern.
- Observation:
- When both slits are open, an interference pattern appears on the screen, which suggests the particles act as waves and pass through both slits simultaneously.
- If one slit is closed, the interference pattern disappears.
- If a detector is placed to observe “which slit” the particle goes through, the interference pattern is destroyed, and the particles behave like classical particles.
Significance:
- The interference pattern is evidence of the wavefunction’s superposition: the particle exists in a superposition of “going through slit A” and “going through slit B” until measured.
2. Stern-Gerlach Experiment
Overview:
The Stern-Gerlach experiment demonstrates superposition in the spin states of particles such as electrons.
- Setup: A beam of particles with spin (e.g., silver atoms) is passed through a non-uniform magnetic field.
- Observation:
- The beam splits into discrete components corresponding to the spin states $$(+ℏ/2+\hbar/2+ℏ/2 and −ℏ/2-\hbar/2−ℏ/2)$$
- If the particles are placed in a superposition of spin states before measurement, the measurement collapses the state into one of the possible outcomes.
Significance:
- The experiment shows that particles can exist in a superposition of spin states until a measurement collapses the wavefunction.
3. Bell’s Inequality Experiments
Overview:
Bell’s inequality tests confirm quantum entanglement, a phenomenon closely tied to superposition.
- Setup: Pairs of entangled particles are created, and their properties (e.g., spin or polarization) are measured at separate locations.
- Observation:
- The correlations between the measurements of entangled particles violate Bell’s inequality, a prediction of classical physics.
- These correlations can only be explained if the particles exist in a superposition of states until measured.
Significance:
- Bell’s experiments demonstrate that quantum superposition and entanglement are real phenomena, and no classical hidden variable theory can explain the results.
4. Quantum Interference with Large Molecules
Overview:
Experiments have extended the double-slit concept to large molecules such as buckyballs $$(C60\text{C}_{60}C60)$$ and even macromolecules.
- Setup: Molecules are sent through a double-slit apparatus, and their interference pattern is observed.
- Observation:
- Interference patterns appear, which suggests that even large molecules can exist in a superposition of quantum states.
Example:
- In 2019, experiments with molecules over 2,000 atomic mass units (amu) demonstrated interference, confirming superposition at the macroscopic molecular scale.
Significance:
- These experiments show that quantum superposition applies not only to small particles but also to larger systems.
5. Quantum State Tomography
Overview:
Quantum state tomography is a technique used to reconstruct the wavefunction of a quantum system.
- Setup: Repeated measurements are performed on identically prepared quantum systems, and the results are used to determine the probability amplitudes of the system’s wavefunction.
- Observation:
- The reconstructed wavefunctions confirm that quantum systems can exist in superpositions of states.
Significance:
- This provides direct evidence of the mathematical structure of quantum superposition.
6. Superposition in Superconducting Qubits
Overview:
Superconducting qubits used in quantum computers are engineered to exist in superpositions of quantum states.
- Setup: Qubits are prepared in superpositions of states $$∣0⟩|0\rangle∣0⟩$$ and $$∣1⟩|1\rangle∣1⟩$$ using precise microwave pulses.
- Observation:
- The qubit’s state is measured, and experiments confirm that it existed in a superposition before the measurement.
Example:
- Experiments in quantum computing, such as those performed by IBM and Google, routinely demonstrate superposition in qubits.
Significance:
- These experiments are practical applications of superposition in real-world quantum systems.
7. Quantum Interference in Mach-Zehnder Interferometer
Overview:
The Mach-Zehnder interferometer is a tool used to demonstrate superposition in photons or other particles.
- Setup: A photon is sent through a beam splitter, creating a superposition of two paths. These paths are then recombined at a second beam splitter before measurement.
- Observation:
- The photon exhibits interference effects, which confirm that it traveled both paths simultaneously in a superposition.
Significance:
- The experiment provides a direct demonstration of superposition in the spatial degrees of freedom of photons.
8. Delayed-Choice Quantum Eraser
Overview:
This is a variation of the double-slit experiment that explores whether “which-path” information can retroactively affect the interference pattern.
- Setup: A photon passes through a double-slit apparatus, and its entangled partner is used to determine “which slit” it went through. Crucially, the choice of whether to measure the path information is made after the photon has passed through the slits.
- Observation:
- If path information is erased, an interference pattern appears. If path information is retained, the interference pattern disappears.
- The results suggest that the photon existed in a superposition of paths until the measurement.
Significance:
- This experiment demonstrates the non-classical nature of superposition and challenges our notions of causality.
9. Quantum Superposition in Bose-Einstein Condensates
Overview:
Bose-Einstein condensates (BECs) are macroscopic quantum systems that exhibit superposition.
- Setup: At extremely low temperatures, atoms in a BEC occupy the same quantum state, forming a macroscopic quantum wavefunction.
- Observation:
- The BEC behaves as a single coherent quantum entity, demonstrating superposition at a macroscopic scale.
Significance:
- BECs provide evidence that quantum superposition can manifest in systems containing many particles.
10. Schrödinger’s Cat Experiments (Quantum Superposition of States)
Overview:
While Schrödinger’s cat is a thought experiment, analogous experiments have been performed.
- Setup: Systems like superconducting circuits or trapped ions are prepared in macroscopic superpositions (e.g., two distinct energy states).
- Observation:
- The system remains in a superposition until a measurement is made.
Example:
- In 2010, experiments with superconducting currents created macroscopic superpositions of current flowing clockwise and counterclockwise simultaneously.
Significance:
- These experiments demonstrate superposition at scales approaching macroscopic objects.
Summary
Experiments confirming quantum superposition include:
- Double-slit experiments (with photons, electrons, and even molecules).
- Stern-Gerlach experiments (spin superpositions).
- Bell’s inequality tests (entanglement and superposition).
- Quantum interference with large molecules (e.g., buckyballs).
- Quantum state tomography.
- Superposition in qubits (quantum computing experiments).
- Mach-Zehnder interferometers.
- Delayed-choice quantum erasers.
- Bose-Einstein condensates.
- Macroscopic superpositions (e.g., in superconducting circuits).
These experiments collectively confirm quantum superposition and demonstrate its validity across a wide range of systems, from individual particles to macroscopic states.
Thomas Question:
How does modern physics explain Quantum Superposition?
Quantum superposition is one of the most fundamental concepts in quantum mechanics, and its explanation lies at the heart of our understanding of the quantum world. While modern physics does not provide a fully intuitive, classical explanation for superposition, it offers a rigorous mathematical framework and several interpretations to describe and understand this phenomenon. Let’s explore how modern physics explains quantum superposition:
1. The Mathematical Framework
Quantum mechanics uses the formalism of Hilbert spaces and wavefunctions to describe the state of a quantum system. In this framework:
- A quantum state is represented by a vector $$∣ψ⟩|\psi\rangle∣ψ⟩$$ in a Hilbert space.
- The principle of superposition states that if $$∣ψ1⟩|\psi_1\rangle∣ψ1⟩$$ and $$∣ψ2⟩|\psi_2\rangle∣ψ2⟩$$ are two valid quantum states, then any linear combination of these states, $$∣ψ⟩=c1∣ψ1⟩+c2∣ψ2⟩|\psi\rangle = c_1|\psi_1\rangle + c_2|\psi_2\rangle∣ψ⟩=c1∣ψ1⟩+c2∣ψ2⟩$$ is also a valid quantum state, where $$c1c_1c1$$ and $$c2c_2c2$$ are complex numbers (probability amplitudes).
Wavefunction and Probabilities
- The wavefunction, $$ψ(x)\psi(x)ψ(x)$$ describes the quantum state in terms of spatial or other observables.
- The square of the wavefunction’s modulus, $$∣ψ(x)∣2|\psi(x)|^2∣ψ(x)∣2$$ gives the probability density of finding the particle in a particular state or position upon measurement.
Implications of Superposition
- A quantum system in a superposition state $$∣ψ⟩|\psi\rangle∣ψ⟩$$ does not have a definite value for the observable (e.g., position, momentum, spin) until a measurement is made.
- Instead, it exists in multiple possible states simultaneously, with probabilities given by the squared magnitudes of the coefficients $$∣c1∣2|c_1|^2∣c1∣2$$ and $$∣c2∣2|c_2|^2∣c2∣2$$
2. Experimental Evidence
The concept of superposition is supported by experiments such as:
- The double-slit experiment is where particles (e.g., electrons) interfere with themselves, behaving as if they pass through both slits simultaneously.
- Quantum entanglement experiments (e.g., Bell’s inequality tests) that show superposition and nonlocal correlations.
- Interference patterns are observed in macroscopic systems like Bose-Einstein condensates or large molecules.
These experiments confirm that superposition is real, even if counterintuitive.
3. Interpretations of Quantum Mechanics
The mathematical framework of quantum mechanics does not explicitly explain why superposition occurs or what it “means” in physical terms. Several interpretations aim to provide a conceptual understanding:
a. Copenhagen Interpretation
- In the Copenhagen interpretation, the wavefunction represents the probability amplitudes of all possible outcomes.
- Superposition is understood as a description of all possible states in which the system can exist until measurement.
- Upon measurement, the wavefunction “collapses” to a single state, and the system adopts a definite observable value.
Key Idea:
Superposition is a mathematical representation of potential outcomes, and it becomes “real” only upon measurement.
b. Many-Worlds Interpretation
- In the Many-Worlds interpretation, superposition is not just a mathematical abstraction but a physical reality.
- When a quantum system is in a superposition, and a measurement is made, the universe “branches” into multiple parallel worlds, each corresponding to one possible outcome.
- No wavefunction collapse occurs; instead, all possibilities coexist in separate worlds.
Key Idea:
Superposition represents the coexistence of multiple realities, with measurement splitting the universe into different branches.
c. Pilot Wave Theory (de Broglie-Bohm Interpretation)
- This interpretation introduces “hidden variables” to explain quantum phenomena.
- In this view, particles have definite positions and trajectories guided by a “pilot wave,” which evolves according to the Schrödinger equation.
- Superposition is explained as a property of the guiding wave, which influences the particle’s behavior.
Key Idea:
Superposition is a property of the pilot wave, not the particle itself, and the particle always has a definite position.
d. Quantum Bayesianism (QBism)
- QBism treats the wavefunction as a tool for encoding an observer’s subjective knowledge about the system, rather than an objective property of the system itself.
- Superposition reflects the observer’s uncertainty about the system until measurement.
Key Idea:
Superposition is an epistemic concept, representing the observer’s knowledge rather than an intrinsic property of the system.
e. Objective Collapse Theories
- These theories propose that superposition is a real physical phenomenon but that the wavefunction spontaneously collapses under certain conditions (e.g., interaction with the environment or when the system becomes sufficiently large).
- Examples include the GRW (Ghirardi-Rimini-Weber) and Penrose Objective Reduction models.
Key Idea:
Superposition is a real physical state that collapses due to intrinsic mechanisms or interaction with the environment.
4. Decoherence and Superposition
Decoherence is a key concept in modern physics that helps bridge the gap between quantum superposition and classical physics.
- What is Decoherence?
- Decoherence occurs when a quantum system interacts with its environment in such a way that the system’s superposition states become entangled with the environment.
- This process effectively “hides” the interference effects of superposition, making the system behave as if it has collapsed into a classical state.
- Does Decoherence Explain Collapse?
- Decoherence does not explain wavefunction collapse but shows how superposition states become unobservable in macroscopic systems due to environmental interactions.
Key Idea:
Decoherence explains why macroscopic objects appear classical even though they are composed of quantum systems.
5. Modern Physics and Superposition
Modern physics treats quantum superposition as a fundamental principle, with no need to “explain” it beyond the mathematical framework. However, ongoing research into the foundations of quantum mechanics aims to deepen our understanding:
Quantum Superposition and Quantum Field Theory
In quantum field theory (QFT), particles like electrons and photons are seen as excitations of quantum fields. Superposition applies to these fields as well:
- A quantum field can exist in a superposition of different states, leading to phenomena such as particle creation and annihilation.
- Superposition in QFT underpins many predictions of the Standard Model of particle physics.
Quantum Superposition in Quantum Computing
- Quantum superposition is exploited in quantum computing, where qubits can exist in a superposition of $$∣0⟩|0\rangle∣0⟩$$ and $$∣1⟩|1\rangle∣1⟩$$
- This allows quantum computers to perform many calculations simultaneously, with interference effects providing computational power.
6. Summary
- Quantum superposition is the principle that a quantum system can exist in multiple states simultaneously.
- The mathematical framework of quantum mechanics explains superposition using wavefunctions and probability amplitudes.
- Multiple interpretations of quantum mechanics (e.g., Copenhagen, Many-Worlds, Pilot Wave) offer conceptual explanations, but no single interpretation is universally accepted.
- Decoherence helps explain why superposition effects are not observed in macroscopic systems.
- Superposition is not fully understood on an intuitive level, but it is a mathematically and experimentally verified feature of quantum mechanics.
Superposition remains a cornerstone of quantum physics, driving advancements in quantum computing, quantum field theory, and our understanding of the universe.
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