Musing with GPT-4 on questions about electric current, all the way to string theory

gpt-4-electric-current-musing.txt

>> How come electricity signal goes to speed of light? What makes the electrons' wave transmit so
fast along a cable?

It's a common misconception that electricity or an electrical signal travels at the speed of light.
While it's true that electrical signals can travel very fast, they do not reach the speed of light.
The speed at which an electrical signal propagates through a conductor like a copper wire or an
optical fiber cable is influenced by various factors, such as the material's properties and the
surrounding medium.

When a voltage is applied to a conductor, the electric field created causes the electrons in the
conductor to move. However, the electrons themselves do not travel very fast. Instead, they drift at
a slow pace called the "drift velocity," typically much less than 1 mm/s. The reason an electrical
signal can travel much faster is that it is not the electrons themselves moving from one end of the
wire to the other, but rather the propagation of an electromagnetic wave.

This wave is formed by the interaction of the electric and magnetic fields. When a voltage is
applied to a conductor, it generates an electric field that in turn creates a magnetic field. These
fields interact with one another, forming an electromagnetic wave that propagates through the
conductor. This propagation is much faster than the drift velocity of the electrons and can approach
a significant fraction of the speed of light, depending on the material and surrounding medium.

In a vacuum, the speed of light is about 299,792 km/s (186,282 miles per second). In a typical
copper wire, the speed of an electrical signal can be roughly 50-99% of the speed of light,
depending on factors like wire composition, insulation, and temperature. In an optical fiber, the
signal speed can be even faster, at around 67% of the speed of light, as the signal is transmitted
as light rather than an electrical current.

So, while the electrical signal does not travel at the speed of light, it can travel very fast due
to the propagation of the electromagnetic wave through the conductor, not the movement of the
electrons themselves.


>> Why is there any drift velocity if the signal is transmitted by an electromagnetic wave?

Drift velocity and signal propagation are related but distinct phenomena in the context of electric
currents in conductors. Drift velocity is the average velocity at which free electrons in a
conductor move under the influence of an electric field. It is a measure of the actual movement of
the electrons themselves in response to an applied electric field.

When a voltage is applied across a conductor, the electric field created exerts a force on the free
electrons in the conductor. These electrons then start to move, colliding with atoms and other
electrons in the conductor. Due to these frequent collisions, the electrons move in a random and
somewhat slow manner, which results in the relatively low drift velocity.

On the other hand, signal propagation refers to the transmission of an electrical signal through a
conductor in the form of an electromagnetic wave. The wave is created by the interaction between the
electric field and the magnetic field that forms due to the movement of the electrons. This wave
travels much faster than the drift velocity of the electrons themselves.

So, why is there drift velocity if the signal is transmitted by an electromagnetic wave? The drift
velocity represents the actual movement of the electrons, which is necessary to create the
electrical current in the conductor. As the electrons move in response to the applied voltage, they
create a current that generates the electric and magnetic fields. These fields then interact and
propagate as an electromagnetic wave, carrying the electrical signal through the conductor.

In summary, drift velocity is related to the movement of electrons, which generates the current and
the associated electric and magnetic fields. These fields form an electromagnetic wave, which is
responsible for the fast propagation of the electrical signal through the conductor.


>> Is all the energy transmitted by an electrical current then coming from the electromagnetic wave?

Yes, the energy transmitted by an electrical current is carried by the electromagnetic wave. When an
electrical signal is transmitted through a conductor, the energy is conveyed through the interaction
between the electric and magnetic fields, which together form an electromagnetic wave.

When a voltage is applied across a conductor, the electric field created drives the electrons to
move, resulting in an electric current. This current generates a magnetic field, which is
perpendicular to the electric field. The two fields are interdependent and influence each other,
which creates the electromagnetic wave that propagates through the conductor.

The energy associated with this wave is given by the Poynting vector, which describes the flow of
electromagnetic energy in a given direction. The Poynting vector is the cross product of the
electric field and the magnetic field and is proportional to the product of the electric field
strength and the magnetic field strength.

The electromagnetic wave carries the energy that is transmitted by the electrical current. This
energy can be used to perform work, such as powering electrical devices or generating heat. When the
electromagnetic wave reaches the load (e.g., a resistor or an electrical device), the energy is
transferred from the wave to the load, which then dissipates the energy as heat or converts it into
other forms of energy (such as mechanical or light energy).

In summary, the energy transmitted by an electrical current is carried by the electromagnetic wave,
which is formed by the interaction between the electric and magnetic fields in the conductor. The
energy in the wave is then transferred to the load when the wave reaches it, allowing the load to
utilize the energy for various purposes.


>> How come then you need to have a closed circuit? What prevents the electromagnetic wave to form
if the circuit is open but a voltage is applied to one end?

When a voltage is applied to a closed circuit, the electric field generated by the voltage source
drives the electrons to move, creating an electric current. This current, in turn, generates a
magnetic field, and the interaction between the electric and magnetic fields forms an
electromagnetic wave that propagates through the circuit.

In an open circuit, however, there is no complete path for the electrons to flow through, which
means that no sustained electric current can be established. When a voltage is applied to one end of
an open circuit, an electric field is still created, but because the circuit is not closed, the
electrons have nowhere to go, and the flow of current is interrupted.

While the electric field still exists in the open circuit, the absence of a sustained current means
that a magnetic field does not develop as it would in a closed circuit. As a result, there is no
interaction between the electric and magnetic fields to form an electromagnetic wave, and thus, no
energy can be transmitted through the circuit.

In other words, a closed circuit is necessary for the formation of an electromagnetic wave because
the closed loop allows for the continuous flow of current, which generates the magnetic field
required for the wave to propagate. Without a closed loop, the energy transmission is interrupted
due to the lack of a sustained current and the associated magnetic field.


>> But since the drift velocity is so low how come the the current appears immediately as you close
the circuit

Although the drift velocity of electrons is very low, the current appears to flow almost
instantaneously when you close a circuit because of the way electric fields propagate through the
conductor.

When you close the circuit, the voltage applied to the conductor creates an electric field that
extends through the entire circuit. This electric field exerts a force on the free electrons in the
conductor, causing them to move. Although the actual movement of the electrons (drift velocity) is
slow, the electric field itself propagates through the conductor at a much faster speed, close to
the speed of light for the material.

As the electric field propagates, it influences the motion of electrons throughout the entire length
of the conductor. This means that electrons near the positive terminal of the voltage source start
moving almost at the same time as electrons near the negative terminal. The overall effect is that
when you close the circuit, the current appears to flow immediately, even though the electrons
themselves are moving at a relatively slow drift velocity.

In essence, the near-instantaneous appearance of the current is due to the fast propagation of the
electric field, which affects the motion of electrons throughout the conductor simultaneously. This
rapid propagation allows the current to be established quickly, even though the actual movement of
the electrons is much slower.


>> Okay. Now how come we can have an eletric field (since light is an electromagnetic wave as well)
in vacuum?

Electromagnetic waves, such as light, can indeed propagate through a vacuum. In contrast to electric
currents in a conductor, which rely on the flow of electrons, electromagnetic waves can travel
through empty space because they consist of oscillating electric and magnetic fields that are
self-sustaining and do not require a material medium to propagate.

An electromagnetic wave is formed by the interaction of an electric field and a magnetic field,
which are both perpendicular to each other and to the direction of wave propagation. These fields
continuously generate each other in a self-sustaining manner, allowing the wave to travel through
space.

The propagation of an electromagnetic wave through a vacuum can be understood using Maxwell's
equations, a set of four fundamental equations that describe the behavior of electric and magnetic
fields. Two key aspects of these equations explain why electromagnetic waves can propagate through a
vacuum:

- A changing electric field generates a magnetic field.
- A changing magnetic field generates an electric field.

As the electric field oscillates, it produces a changing magnetic field, which in turn generates a
changing electric field. This process repeats continuously as the electromagnetic wave propagates
through the vacuum. Since the electric and magnetic fields can create each other without the need
for a material medium, electromagnetic waves can travel through empty space.

This property of electromagnetic waves allows them to propagate across vast distances in space, such
as light from distant stars and galaxies reaching Earth or radio signals transmitted between
satellites and ground stations.

>> But what supports the eletric and magnetic fields if there is not matter. Is that a property of
space itself?

Yes, the ability of electromagnetic waves to propagate through a vacuum can be thought of as a
property of space itself. The electric and magnetic fields in an electromagnetic wave don't require
matter to exist and interact. They are self-sustaining and can propagate through empty space due to
the fundamental principles of electromagnetism described by Maxwell's equations.

In classical physics, empty space, or vacuum, is considered a stage or a backdrop where physical
processes and interactions occur. Although a vacuum is devoid of matter, it still allows for the
existence and propagation of electric and magnetic fields, which are intrinsic to the fabric of
spacetime itself.

The concept of fields is crucial in physics. Fields are mathematical constructs that represent the
distribution of certain quantities, such as electric or magnetic force, throughout space. They help
us understand how particles or objects interact with each other over distances without direct
contact.

In the case of electric and magnetic fields, they permeate and influence the vacuum of space,
enabling the propagation of electromagnetic waves. This is different from mechanical waves, like
sound waves, which require a material medium (air, water, or solid) to transmit energy through the
vibrations of particles in the medium.

In summary, the ability of electric and magnetic fields to exist and interact in a vacuum can be
considered a fundamental property of space itself. These fields do not require the presence of
matter to support their existence, and they allow electromagnetic waves to propagate through empty
space according to the principles of electromagnetism.


>> Are there generalization of general relativity theory to electric and magnetic field, that is,
framing them as a distortion of space time vs just a "force" ?

Yes, there have been attempts to generalize the concepts of general relativity to incorporate
electric and magnetic fields, often referred to as "electromagnetic gravity" theories. The aim of
these theories is to unify the description of electromagnetic fields and gravity within a single
geometric framework.

One such approach is the Kaluza-Klein theory, originally proposed by Theodor Kaluza in 1921 and
later extended by Oskar Klein. This theory suggests that the fundamental forces, including gravity
and electromagnetism, can be described within a higher-dimensional spacetime. In the case of
Kaluza-Klein theory, a 5-dimensional spacetime is considered, with one of the dimensions being
compactified or "curled up" at a very small scale. When this extra dimension is included, the
higher-dimensional version of Einstein's field equations can describe both gravity (in the form of
spacetime curvature) and electromagnetism.

Another approach involves the concept of "gauge fields" in particle physics. In this framework, the
electric and magnetic fields can be described as gauge fields associated with the electromagnetic
force, which is mediated by photons. These gauge fields are responsible for the interactions between
charged particles, much like the gravitational field is responsible for the interactions between
masses. In some theoretical models, the geometric description of gravity is extended to include
these gauge fields, potentially leading to a unified description of gravity and electromagnetism.

However, it is essential to note that these are theoretical attempts to find a unified description,
and none of them have been experimentally confirmed or widely accepted as a complete description of
the relationship between gravity and electromagnetism. The search for a consistent and
experimentally verifiable theory that unifies all fundamental forces, including gravity,
electromagnetism, the strong nuclear force, and the weak nuclear force, is still an active area of
research in theoretical physics.


>> Are these two theories kind of similar to string theory? Basically the premises being to add new
dimensions to extend Einstein's field equations to unify all forces we observe in nature?

Yes, the Kaluza-Klein theory and string theory share some similarities, as both approaches involve
adding extra dimensions to extend Einstein's field equations and attempt to unify the fundamental
forces of nature. While the Kaluza-Klein theory specifically focuses on unifying gravity and
electromagnetism in a 5-dimensional spacetime, string theory is a broader framework that attempts to
describe all fundamental forces and particles in terms of one-dimensional, vibrating strings.

String theory posits that all particles and forces, including gravity, electromagnetism, the strong
nuclear force, and the weak nuclear force, are manifestations of different vibrational modes of
these fundamental strings. To accommodate these vibrations and the interactions between strings,
string theory requires the existence of additional dimensions beyond the familiar four dimensions of
spacetime (three spatial dimensions and one time dimension).

Depending on the specific version of string theory, the number of dimensions can range from 10 to
26. The extra dimensions are often assumed to be compactified or "curled up" at extremely small
scales, making them undetectable in everyday experiences and experiments. The idea of compactified
dimensions in string theory is reminiscent of the extra dimension in the Kaluza-Klein theory.

The main difference between the Kaluza-Klein theory and string theory lies in the scope and the
underlying principles. The Kaluza-Klein theory is focused on unifying gravity and electromagnetism
in a higher-dimensional spacetime, whereas string theory is a more comprehensive framework that
attempts to describe all particles and forces in terms of vibrating strings in higher-dimensional
spacetimes.

Despite these similarities, it is important to note that string theory is still a theoretical
framework with no direct experimental confirmation. While it has produced some intriguing and
elegant mathematical results, the search for a consistent and experimentally verifiable theory that
unifies all fundamental forces remains an ongoing pursuit in theoretical physics.


>> Why does string theory require the introduction of the concept of strings? With a sufficient
number of dimensions can't we emulate any force field with Einstein's field equations?

The introduction of strings in string theory is not merely a consequence of adding extra dimensions
to spacetime. Instead, the concept of strings arises from the attempt to solve some inherent issues
in the existing theoretical frameworks, particularly the incompatibilities between general
relativity and quantum mechanics.

General relativity, which is based on Einstein's field equations, is a classical theory that
describes gravity as the curvature of spacetime caused by the presence of mass-energy. It has been
extremely successful in explaining gravitational phenomena at macroscopic scales. However, when
applied to extremely small scales or high-energy situations, general relativity is not compatible
with quantum mechanics, which governs the behavior of particles and forces at the subatomic level.

One of the primary issues in combining general relativity and quantum mechanics is the problem of
infinities that arise when trying to quantize the gravitational force. These infinities make it
difficult to develop a consistent quantum theory of gravity. String theory is an attempt to address
these problems by replacing point-like particles with one-dimensional, vibrating strings.

In string theory, the fundamental particles and forces are described as different vibrational modes
of these strings. The strings have a finite length, which helps to avoid the infinities that plague
the quantization of gravity in a point-particle framework. The introduction of extra dimensions in
string theory is necessary to accommodate the various vibrational modes and interactions between
strings.

While adding extra dimensions to spacetime can provide a unified description of gravity and
electromagnetism, as demonstrated by the Kaluza-Klein theory, it does not automatically resolve the
issues related to quantum mechanics and general relativity. The concept of strings in string theory
is a key element in addressing these issues and developing a consistent quantum theory of gravity
that incorporates all fundamental forces.

In summary, the introduction of strings in string theory is not just a byproduct of adding extra
dimensions, but a fundamental aspect of the theory that aims to resolve the incompatibilities
between general relativity and quantum mechanics.