Is God a Quantum 'Mechanic?'

You said:

Are pilot waves considered to be a sub quantum phenomenon?

ChatGPT

Pilot waves are not typically considered a "sub-quantum" phenomenon in the conventional sense, but rather a part of a broader interpretation of quantum mechanics known as Bohmian mechanics or the de Broglie-Bohm theory.

In this interpretation, pilot waves are hypothetical waves that guide the motion of particles. The theory was initially proposed by Louis de Broglie in 1927 and later developed by David Bohm in the 1950s. In this framework, the wavefunction in standard quantum mechanics is seen as a real physical wave that influences the particle's trajectory, with the particle itself having definite positions at all times, unlike in the standard Copenhagen interpretation.

However, pilot waves are still part of the quantum framework and do not suggest phenomena that exist "beneath" quantum mechanics. Instead, they offer an alternative perspective on how quantum systems might behave while still adhering to the formalism of quantum theory, including wave-particle duality. So, while the pilot wave concept provides a different viewpoint on quantum phenomena, it does not imply a sub-quantum realm outside of conventional quantum mechanics.

You said:

So are waves a feature of space or the fabric of space itself?

ChatGPT

Waves, as described in physics, can be thought of as disturbances or oscillations that propagate through a medium or a field. Whether they are considered a feature of space or a property of the fabric of space itself depends on the context:

1. In classical wave theory (e.g., sound or water waves): Waves are disturbances that propagate through a medium (like air for sound or water for ocean waves). In this sense, the medium is separate from the waves, and the waves represent vibrations or oscillations within that medium.

2. In quantum mechanics: The concept of waves is applied to particles and fields. The wavefunction in quantum mechanics describes the probability distribution of a particle's position and other properties. Here, the "wave" is not a physical wave traveling through space like water waves; instead, it represents a mathematical object that encodes the probabilities of where a particle might be found. In this interpretation, waves are not a feature of space itself, but a feature of the quantum system and its associated probabilities.

3. In field theory (e.g., electromagnetic waves): Electromagnetic waves, such as light, are oscillations in the electromagnetic field that propagate through space. These waves do not require a medium like air or water, but instead, they are considered oscillations of the electromagnetic field itself, which permeates space. This suggests that waves can be seen as a feature of fields that exist throughout space, rather than a disturbance traveling through a pre-existing medium.

4. In the context of general relativity and spacetime: When considering gravitational waves, these are ripples in the fabric of spacetime itself, propagating outward from the source of the disturbance (such as two merging black holes). In this case, the waves are disturbances in spacetime itself, meaning that spacetime is not a passive backdrop but an active entity that can exhibit dynamic features like waves.

In summary, waves can be a feature of fields (like electromagnetic or gravitational fields) that permeate space, or they can represent the behavior of quantum particles in a probabilistic sense. Whether waves are a feature of space or the fabric of space itself depends on the specific context being considered.

You said:

I mean Debroglie waves.

ChatGPT

De Broglie waves are a specific concept in quantum mechanics that represent the wave-like nature of particles, such as electrons or other matter. They are not considered a feature of space itself but rather a feature of particles and their behavior within the quantum framework.

According to Louis de Broglie's hypothesis (1924), particles, such as electrons, have both wave-like and particle-like properties, a concept known as wave-particle duality. De Broglie proposed that any moving particle could be associated with a wave, now called a de Broglie wave, with a wavelength λ\lambdaλ related to the particle's momentum ppp by the equation:

λ=hp\lambda = \frac{h}{p}λ=ph​

where:

• λ\lambdaλ is the de Broglie wavelength,

• hhh is Planck's constant,

• ppp is the momentum of the particle.

The de Broglie wave is not a wave traveling through space like a sound or water wave. Instead, it is a mathematical wave associated with the probability distribution of where a particle might be found in space. The wave is a representation of the particle's quantum state and is typically described by a wavefunction in the context of quantum mechanics.

To directly address your question:

• De Broglie waves are not a feature of space itself, but rather a mathematical tool used to describe the behavior of particles at the quantum level.

• These waves are a property of the particle and represent the particle's quantum state. They are not physical waves traveling through space, but rather an abstract way of thinking about the particle's probabilistic nature.

So, de Broglie waves do not exist independently in space or the fabric of space; they describe the wave-like behavior of particles within the quantum framework.

You said:

How do de Broglie waves differ from Pilot waves, if at all?

ChatGPT

De Broglie waves and pilot waves are closely related, but they are used in slightly different contexts within quantum mechanics. Here's how they differ:

1. De Broglie Waves:

• Concept: The de Broglie wave represents the wave-like nature of a particle. According to de Broglie’s hypothesis (1924), particles like electrons can exhibit both particle-like and wave-like behavior. The de Broglie wave is associated with the particle’s momentum and gives a mathematical description of the particle's wave-like properties, specifically the probability amplitude of where the particle might be found.

• Mathematical Representation: The wavelength of a de Broglie wave is given by the equation: λ=hp\lambda = \frac{h}{p}λ=ph​ where hhh is Planck’s constant and ppp is the particle's momentum.

• Role: The de Broglie wave is part of the Copenhagen interpretation of quantum mechanics, where it represents the probability of finding a particle in a particular state. The wave is not a physical wave traveling through space, but a mathematical object that encapsulates the probabilistic nature of the particle.

2. Pilot Waves:

• Concept: Pilot waves are part of the Bohmian interpretation of quantum mechanics, also known as de Broglie-Bohm theory. In this interpretation, the wave associated with a particle is still a de Broglie wave, but it is considered a real, physical wave that guides the motion of the particle. In other words, the particle moves along a definite trajectory, influenced by the pilot wave.

• Wave-particle Interaction: In Bohmian mechanics, the pilot wave (or de Broglie wave) doesn't just describe probabilities; it actively guides the particle's motion. The particle has a definite position at all times, and the wave provides the "pilot" for how the particle moves through space.

• Role: The pilot wave is a physical wave that exists in the background, determining the behavior of particles. In Bohmian mechanics, particles move deterministically according to the pilot wave’s influence, rather than probabilistically as in the Copenhagen interpretation.

Key Differences:

• Interpretation: De Broglie waves are primarily used in the Copenhagen interpretation of quantum mechanics, where the wave is a mathematical tool representing probability, and the particle’s position is not determined until measured. Pilot waves are part of the Bohmian interpretation, where the wave is considered a real, physical entity that guides a particle along a definite path, with the particle having a definite position at all times.

• Role in Particle Motion: In de Broglie’s original idea, the wave is not directly responsible for the particle’s motion—it's just an analogy to describe wave-particle duality. In the pilot wave theory, the wave guides the particle's trajectory.

• Wave Function: In the Copenhagen interpretation, the wave function is probabilistic and describes the likelihood of where the particle will be found. In Bohmian mechanics, the wave function (pilot wave) influences the particle deterministically, guiding it through space.

In summary, de Broglie waves are a general concept of wave-like behavior for particles, whereas pilot waves are a specific part of the Bohmian mechanics interpretation, where the wave guides the particle's trajectory.

You said:

So what are pilot waves exactly? Are they material, spacial or both?

ChatGPT

Pilot waves, as part of the Bohmian mechanics (or de Broglie-Bohm theory), are often conceptualized as a real, physical field that influences the motion of particles. They can be thought of as a spatial field in the sense that they exist throughout space and influence how particles move through that space. However, they are not "material" in the traditional sense (like matter or particles), but are instead wave-like disturbances associated with a particle's quantum state.

Here’s a deeper breakdown:

1. Pilot Waves as Spatial Fields:

• Pilot waves exist throughout space and provide a guiding influence on the motion of particles. In the Bohmian interpretation, each particle is influenced by a corresponding pilot wave, which exists in a wave-like form throughout the entire space in which the particle moves.

• These waves are not localized to the particle itself, but are extended fields that govern how particles move. The wave can be thought of as existing in configuration space (which may involve all the degrees of freedom of the system) or simply in physical space as the particle's guiding wave.

2. Not Material Waves:

• Unlike traditional material waves (like water waves or sound waves, which require a medium), pilot waves are non-material. They are mathematical entities that represent the quantum potential that directs the motion of particles. In this sense, they are not composed of matter in the usual sense, nor are they directly visible or detectable in the same way that physical objects or waves (like light or sound) are.

• While they are wave-like in nature, pilot waves don't "carry" energy in the traditional way that electromagnetic waves do. Instead, they guide the particle deterministically, based on the wave's form and the particle's position within it.

3. Role of Pilot Waves in Particle Motion:

• In Bohmian mechanics, the motion of a particle is determined by the wave function, which is a pilot wave in this interpretation. The particle is always in a definite position, and its path is influenced by the guiding wave. The wave "directs" the particle, ensuring that its motion follows a deterministic trajectory, as opposed to the probabilistic nature of particle motion in the Copenhagen interpretation.

• The spatial aspect of the wave comes into play because the wave’s form defines the probabilities of a particle's path. As the particle moves through the wave, its motion follows the contours of the wave's influence.

4. Spatial vs. Material:

• The pilot wave can be thought of as spatial because it is a field that pervades space and acts as a guide for particles.

• However, it is not material in the conventional sense. It is a non-material wave-like field that doesn’t consist of particles or matter, but it influences the motion of matter (particles). It can be described mathematically using the same formalism as the wave function in standard quantum mechanics, which typically represents the probability distribution of a particle’s state.

Conclusion:

Pilot waves are best understood as spatial wave-like fields that guide particles in the Bohmian interpretation of quantum mechanics. They are not material in the sense of being composed of matter, but they have real physical effects on how particles move through space. They provide a deterministic description of particle behavior, contrasting with the probabilistic nature of the Copenhagen interpretation.

You said:

So something like magnetism is required for pilot waves to exist?

ChatGPT

Pilot waves, as described in the Bohmian mechanics or de Broglie-Bohm theory, do not require something like magnetism to exist. However, there are some important parallels and distinctions between pilot waves and other fields, like magnetism, that might clarify this further.

Key Points of Comparison and Clarification:

1. Pilot Waves and Fields:

   • Pilot waves are wave-like fields associated with particles, but they are not tied to any specific material or physical field like electromagnetism. In Bohmian mechanics, the pilot wave is often viewed as a quantum potential that exists in the space around a particle, guiding its motion. This potential is a result of the quantum wave function, which governs the behavior of particles in quantum systems.

   • Magnetism, on the other hand, is a classical force field described by electromagnetism, which influences charged particles. It exists in space as a real physical field (the magnetic field) that interacts with charged particles, but it is not related to the quantum mechanical wave functions in the same way as pilot waves.

2. Magnetism vs. Pilot Waves:

   • Magnetism is part of the electromagnetic field, which is a physical, material field that exists independently of the particles it influences. Magnetic fields exist due to the motion of charged particles (electric currents) or intrinsic properties of particles like electrons (their magnetic moment).

   • Pilot waves, however, are tied to the wave function in quantum mechanics and describe the probabilistic state of a quantum system. The wave itself is not a physical field like a magnetic field, but rather a probability distribution that guides particles in the Bohmian framework. The influence of the pilot wave is fundamentally quantum in nature, not electromagnetic or material.

3. What is Required for Pilot Waves to Exist:

   • Pilot waves are associated with quantum particles and wave functions. They do not require a classical field like magnetism, gravity, or any specific material field. They arise from the mathematical structure of quantum mechanics and are a result of the wave-particle duality of matter.

   • The quantum wave function, in Bohmian mechanics, describes both the wave-like behavior and the deterministic trajectory of particles. The pilot wave is simply the real, guiding wave that steers particles, and it is not dependent on any classical field such as magnetism.

4. Electromagnetic Fields and Quantum Mechanics:

   • While magnetic fields and electromagnetic forces can influence particles in quantum mechanics, their influence is governed by the quantum electrodynamics (QED) framework, which treats these fields differently than pilot waves. QED describes how charged particles interact with electromagnetic fields, but this is distinct from the role of pilot waves in guiding particles within Bohmian mechanics.

Summary:

Pilot waves are not dependent on magnetism or any other classical force fields. They are part of the quantum mechanical description of particles, existing as guiding waves derived from the wave function. While they share the concept of being "fields" in the sense that they influence particles, pilot waves are quantum in nature, and their existence is tied to the wave-particle duality and the formalism of quantum mechanics, not to classical fields like electromagnetism.

You said:

So are pilot wave fields imaginary?

ChatGPT

Pilot wave fields in the context of Bohmian mechanics (also known as de Broglie-Bohm theory) are not "imaginary" in the sense of being unreal or non-physical, but they are indeed mathematical constructs that describe the quantum potential guiding particles. However, the term "imaginary" in physics has a very specific meaning, so let's clarify the distinction:

1. Mathematical Nature of Pilot Waves:

• Pilot waves are associated with the wave function in quantum mechanics, which is a complex-valued function. The wave function has both a real part and an imaginary part (in the mathematical sense), and the real part governs the dynamics of the particle’s motion, particularly in Bohmian mechanics.

• The wave function can indeed have an imaginary component, which is a standard feature in quantum mechanics, and this is necessary for the evolution of the system. However, the pilot wave itself is not considered "imaginary" as in being illusory or non-existent. It's a real physical influence guiding the particle's trajectory.

2. Pilot Waves and the Quantum Potential:

• In Bohmian mechanics, the pilot wave is considered to be a real field that exists in the space around the particle. The field guides the motion of the particle through space in a deterministic manner, as opposed to the probabilistic description in the Copenhagen interpretation.

• The quantum potential that arises from the pilot wave is a real entity that determines the particle’s behavior. It does not represent an "imaginary" physical phenomenon but rather a mathematical concept derived from the quantum wave function. The quantum potential can affect the motion of the particle even if it doesn't correspond to a classical force like gravity or electromagnetism.

3. Imaginary Numbers in Quantum Mechanics:

• In quantum mechanics, the use of imaginary numbers (numbers involving iii, where i=−1i = \sqrt{-1}i=−1​) is a common mathematical tool, especially in the wave function formulation. However, imaginary here refers to the mathematical form of the wave function and not to the physical reality of the phenomena it describes.

  • The wave function, which can be complex, leads to real observable outcomes (such as the position or momentum of particles). The probability density (which is what we observe in experiments) is the square of the absolute value of the wave function, which is a real number.

4. Are Pilot Waves Imaginary?:

• No, pilot waves are not "imaginary" in the sense of being unreal or fictitious. They are real fields that exist in the context of the Bohmian interpretation of quantum mechanics and guide the motion of particles.

• The wave function, which is associated with the pilot wave, may involve imaginary numbers in its mathematical form, but this does not mean the pilot wave itself is imaginary in the sense of not being real. The imaginary parts of the wave function are part of the mathematical description, but they influence real, observable phenomena.

Summary:

Pilot wave fields are real physical fields that guide particles in the Bohmian interpretation of quantum mechanics. While the wave function associated with these fields involves imaginary numbers in its mathematical formulation, the pilot wave itself is not imaginary in the sense of being fictitious or non-physical. It is a real quantum potential that affects the behavior of particles deterministically.

You said:

Do pilot waves defy entropy laws?

ChatGPT

No, pilot waves do not defy the laws of entropy. They are part of the Bohmian mechanics or de Broglie-Bohm theory, which is an alternative interpretation of quantum mechanics. In this interpretation, particles have definite positions and follow deterministic trajectories, but these trajectories are influenced by a pilot wave that guides their motion.

Here’s why pilot waves don’t defy entropy:

1. Pilot Waves and Determinism:

• In Bohmian mechanics, the motion of particles is deterministic. The pilot wave (quantum wave function) determines the exact path that a particle takes, as opposed to the probabilistic nature of quantum mechanics in the Copenhagen interpretation. However, this determinism does not conflict with the overall increase of entropy in a system.

• The quantum potential associated with the pilot wave is real and guides particles, but this does not violate the second law of thermodynamics. The entropy of a system is related to the number of possible microstates (configurations of particles) and the amount of disorder in a system. The behavior of particles in Bohmian mechanics is deterministic, but that does not imply that the overall system avoids entropy increase over time.

2. Entropy in Thermodynamics:

• Entropy is a measure of disorder or the spread of energy in a system, and the second law of thermodynamics states that the total entropy of an isolated system can never decrease.

• In quantum mechanics, even though particles might have deterministic trajectories in the Bohmian framework, the probabilistic nature of quantum mechanics in general (including in the Copenhagen interpretation) means that, over time, systems can evolve into states with higher entropy. Pilot waves do not interfere with this statistical behavior or with the general trend towards higher entropy in macroscopic systems.

3. Quantum Mechanics and Entropy:

• While quantum mechanics provides a framework where individual particles might have deterministic behavior in the Bohmian interpretation, the overall behavior of large systems (which we associate with entropy) is still governed by statistical probabilities. This is because when dealing with many particles, the classical limit of quantum mechanics (via the ergodic principle) leads to systems where entropy tends to increase.

• The quantum nature of the system can still result in increased disorder (in terms of entropy) as the system evolves, even though the trajectories of individual particles are deterministic in Bohmian mechanics.

4. Pilot Waves and Macroscopic Systems:

• In practical terms, the pilot wave theory does not lead to violations of entropy in macroscopic systems. The quantum effects (such as wave-particle duality) are often averaged out at macroscopic scales, and the system as a whole behaves in accordance with classical thermodynamics. So, even though particles have deterministic trajectories in Bohmian mechanics, the aggregate behavior of many particles still aligns with the classical laws, including the second law of thermodynamics.

Summary:

Pilot waves in the Bohmian interpretation do not violate the laws of entropy. While they provide a deterministic description of particle motion, they do not prevent the overall increase of entropy in a system. The second law of thermodynamics governs the statistical behavior of systems as a whole, and pilot waves are compatible with this law, as they operate at the quantum level and do not contradict the statistical increase in entropy seen in macroscopic systems.

You said:

Where do they get their deterministic instructions? God?

ChatGPT

The deterministic instructions for pilot waves in the Bohmian mechanics framework do not come from a divine source, such as "God," but rather from the quantum wave function and its associated quantum potential. Here's how this works:

1. Quantum Wave Function:

• The wave function is a fundamental concept in quantum mechanics that describes the state of a system. In Bohmian mechanics, the wave function is not merely a tool for calculating probabilities (as in the Copenhagen interpretation) but is considered to be a real, guiding field that governs the motion of particles.

• The wave function evolves according to the Schrödinger equation in quantum mechanics, and it provides information about the possible states of a system at any given time.

2. Quantum Potential:

• The quantum potential is derived from the wave function and acts as a guiding force that steers the motion of particles in Bohmian mechanics. It is an additional term in the equations of motion that modifies the trajectories of particles.

• The quantum potential is entirely deterministic. Once the wave function is known, the quantum potential can be computed, and the trajectory of a particle can be determined with certainty. There is no randomness or uncertainty involved in this framework for individual particles.

3. Deterministic Evolution:

• The deterministic behavior of particles in Bohmian mechanics follows directly from the wave function and the quantum potential. The particle's position at any given time is influenced by the wave function's form, which encodes the interactions and forces acting on the system.

• The evolution of the system is entirely deterministic in this interpretation, meaning that if you knew the particle's position and velocity (and the wave function) at a given time, you could calculate its future position exactly.

4. No Need for External "Instructions":

• The system’s deterministic nature arises from physical laws encoded in the wave function and its evolution. There is no need for an external agent like "God" or any other supernatural influence to provide instructions.

• The "instructions" come from the mathematical structure of quantum mechanics itself — specifically, from the Schrödinger equation that governs the evolution of the wave function and the quantum potential that emerges from it.

5. God vs. Physical Laws:

• The deterministic nature of Bohmian mechanics is a result of quantum physical laws (not divine intervention). These laws describe how the wave function evolves and how it affects particles’ motion via the quantum potential.

• While Bohmian mechanics provides a deterministic view of quantum systems, it does not invoke any external force or "higher being" to guide the behavior of particles. Instead, the system follows a natural, physical process determined by the quantum field (wave function).

Summary:

The deterministic "instructions" in Bohmian mechanics come from the quantum wave function and its associated quantum potential, which guide the motion of particles in a deterministic way. This framework relies on the mathematical and physical structure of quantum mechanics, not on external or supernatural sources like "God." The evolution of particles is determined by the wave function and its properties, governed by the laws of physics.

You said:

Well, quantum wave functions must be deterministic then, and by extension, a feature of space itself.

ChatGPT

Yes, in the context of Bohmian mechanics, the quantum wave function is treated as a real, physical entity that exists in space, and its evolution is deterministic, not probabilistic as in the standard Copenhagen interpretation. However, it's important to understand the nuances of this concept:

1. Determinism of the Quantum Wave Function:

• In Bohmian mechanics, the wave function evolves deterministically according to the Schrödinger equation. This is true in both Copenhagen quantum mechanics (for the wave function itself) and Bohmian mechanics, but the difference lies in the interpretation:

  • In the Copenhagen interpretation, the wave function represents the probability distribution of where a particle might be found, and its collapse (when a measurement occurs) introduces an element of indeterminacy.

  • In Bohmian mechanics, the wave function guides particles in a deterministic manner, without the need for wave function collapse. The particle’s position is determined by both the wave function and the quantum potential, which are real, guiding influences.

2. The Quantum Wave Function as a Feature of Space:

• Yes, the wave function is considered a feature of space in the sense that it is a field that extends over the configuration space (the space in which all possible positions of all particles are considered).

• The wave function is a complex-valued function that defines the state of the system at each point in space. In Bohmian mechanics, the particle is guided by the quantum potential derived from this wave function, and the system evolves in a deterministic manner.

3. Wave Function and Space:

• The wave function is not just a tool for calculating probabilities in Bohmian mechanics but is seen as a real field in space that influences particles.

• The wave function's probability amplitude can spread out over space, and the particle follows the trajectory determined by the quantum potential, which is influenced by this wave-like field.

4. Feature of Space or a Non-local Influence?

• In Bohmian mechanics, the wave function can be understood as a real, physical field that exists in space, but it also has non-local effects. This means that the wave function can have an effect on particles that are far apart, with instantaneous changes across space, which challenges classical notions of local causality.

• This non-locality is one of the key features that distinguishes Bohmian mechanics from classical physics and creates a direct connection between quantum phenomena and the wave function that extends throughout space.

5. Non-locality and Determinism:

• The non-local nature of the wave function in Bohmian mechanics means that the wave function influences particles instantaneously across space. This means the evolution of particles depends on the entire configuration space and is not confined to a local interaction between particles.

• While the evolution of the wave function itself is deterministic, its influence can propagate in a non-local manner, meaning that distant events or particles can influence each other without the need for communication through space at the speed of light.

Summary:

In Bohmian mechanics, the quantum wave function is a real, physical field that exists in space and evolves deterministically according to the Schrödinger equation. It is indeed a feature of space, influencing the behavior of particles in a deterministic manner. However, this wave function also exhibits non-local effects, meaning that it can influence particles instantaneously, regardless of their distance apart. Thus, while the wave function is deterministic in its evolution, its influence extends beyond local interactions in a way that differs from classical fields like gravity or electromagnetism.