The Theory of Electrodynamics in the Framework of Relativity
Before Albert Einstein and before the theory of special relativity, electricity and magnetism appeared as if they were separate phenomena. But after Einstein introduced his theory and the Lorentz transformations, it was revealed that electricity and magnetism are two sides of the same coin, called electromagnetic fields.
Let us take an example to clarify the idea further:
Suppose you are an observer watching a wire with moving electrons. If you, the observer, are at rest relative to the wire, you will see a magnetic field around it.
However, if you move (run) at the same speed as the electrons, you will see the electrons as stationary and the positive ions moving (relative to you). In this case, you will observe an electric field.
In other words, depending on the reference frame, you observe something different.
But what does relativity have to do with all of this?
Relativity plays the fundamental role here because of Lorentz transformations, which showed the change in length measurements (contraction). This contraction alters the distribution of charges, and therefore, if an electric field appears in one frame of reference, it will appear as a magnetic field in another.
In summary, those who established and developed this theory were James Clerk Maxwell, Albert Einstein, and Hendrik Lorentz, and finally Hermann Minkowski, who expressed everything in the language of spacetime, making it simpler within relativity.
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Principle of Causality
The principle of causality states that in all reference frames, the cause must occur before the effect, and nothing can travel faster than the speed of light.
((It is the foundation of relativity))
In special relativity, spacetime and the constancy of the speed of light appear, and events are ordered here. Since the speed of light is the fastest speed in the universe and cannot be exceeded, the cause will occur before the effect. If this were violated (exceeding the speed of light), the effect would happen before the cause, which means a break of causality. This cannot happen (the light cone explains this matter in more detail).
In general relativity, some mathematical equations seem to allow causality to be violated. For example, some results of general relativity equations indicate that when an object approaches a region of very high spacetime curvature, like a black hole, it might return to the past. This breaks the principle of causality because the effect would occur before the cause. Many scientists rejected this result (such as Stephen Hawking) and pointed out that even if the mathematical equations give such results, they cannot happen in reality. It is only a theoretical matter on paper.
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Proper Time and Coordinate Time
First, let us define each concept, then take an example, and finally explain the main equation.
Proper Time:
Proper time is the time recorded by a clock that moves along with a specific object in space, or in any region with strong gravity and high velocity.
Coordinate Time (or Measured Time):
Coordinate time is the time recorded by a clock that is located at a fixed place relative to the observer (for example, a clock on Earth).
Each of these times will give different results, and they differ from one another.
Example:
Suppose there is an observer on a spaceship approaching a region with strong gravity, for example, a black hole. This observer has a clock.
Meanwhile, there is another observer on Earth, also with a clock, but in a fixed location (Earth).
Now, when the first observer on the spaceship looks at his clock, he will see time passing normally. But the second observer on Earth will see that many years have passed.
The time that passed for the person on Earth is called coordinate time, while the time that passed for the person in space is called proper time.
The Main Equation of Proper Time:
ΔT=Δt√1-v^2/c^2
ΔT= Proper time
Δt= Coordinate time
v = Velocity of the moving object
c = Speed of light
By applying the equation, we can determine how many years have passed on Earth and how much time has passed for the moving object.
This idea was introduced by Albert Einstein in 1905, and in 1908 the scientist Hermann Minkowski formulated the geometry of spacetime (Minkowski space), which further developed from the fundamental equation above.
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Tensors
Tensors are fundamental mathematical objects in General Relativity.
But what are they?
Tensors are quantities that remain unchanged no matter how the reference frames or coordinates are transformed.
They are often explained as if they were vectors. Normally,
a vector is a number plus a direction (for example,
a velocity
of
20 km/h
north
).
But tensors are more complex — they are a number plus multiple directions and more intricate relationships.
Example:
Imagine you have a grid, such as a soccer net. Any change happening in one part of the grid is recognized by the tensor, which can determine whether a certain point of the grid is flat or curved.
Now, going back to relativity, tensors measure every point in the universe in both space and time. They essentially define the
geometry
of
spacetime
at
a
specific point. From this, a tensor can determine whether that region of spacetime is curved (meaning there is mass, energy, or something like a black hole) or flat.
The first significant use of tensors was in Maxwell’s equations after the development of Special Relativity. However, these tensors are fundamentally different from those in General Relativity. In Maxwell’s formulation, tensors were used to combine the electric and magnetic fields. Previously, these equations were expressed only as differential equations.
One major reason for this shift was that the old formulation treated space and time as separate entities, and also considered the electric and magnetic fields as separate phenomena. The tensor formulation, however, unified them.
In General Relativity, tensors are entirely different in their role. They are used in objects such as the Ricci Tensor, the Riemann Curvature Tensor, and the Einstein Tensor, which describe the curvature of spacetime itself.
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Lorentz Transformations
Lorentz transformations are a set of equations upon which Special Relativity (by Albert Einstein) is based. They are used to transform coordinates between two observers moving at a constant velocity relative to each other. Lorentz transformations were originally introduced to explain electromagnetic phenomena, and their study revealed many important insights, including the fact that the speed of particles has a significant effect on measuring the physical dimensions of an object.
γ = 1 / √(1 - v²/c²)
Their equations show that both time and space vary depending on the observer’s velocity, meaning that time is relative. Time can dilate or contract (if it is close to the speed of light, then time contracts).
The reason for using Lorentz transformations is that Newtonian physics failed to explain velocities close to the speed of light, while Lorentz transformations succeeded in doing so.
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What is the Purpose of Lorentz Transformations and Why Did They Appear?
Let us go back in time to the era of Newton and after. At first, before the rise of relativity and modern physics, Newton’s laws governed physics.
Newton believed that time was absolute and unchangeable.
Moving forward a bit into the 17th century, the scientist Huygens proposed the existence of the ether.
The reason behind this assumption was that scientists thought light must propagate through a medium, so they imagined the ether: an invisible substance in space that carries light waves.
But in 1887, the scientists Michelson and Morley conducted their famous experiment, which disproved the existence of the ether. The experiment went as follows:
1_ They used a light source that emits a beam.
2_ The beam was split into two beams at a 90-degree angle.
3_ Each beam was reflected by a mirror and then returned to meet.
4_ The time difference taken by each beam to return had to be measured.
The expected result, if the ether existed, was that one beam should travel faster or slower than the other, producing an interference pattern.
The result: no difference was observed, and no interference pattern appeared. This meant that there was no ether, and that the speed of light is constant regardless of the motion of the source or the observer.
This experiment marked the beginning of the road to Special Relativity.
But now, what does the constancy of the speed of light have to do with making time and space relative?
First, let us recall the formula for speed:
Speed =Distance/Time
When the speed of light is constant, both distance and time must adjust to preserve that constancy. That is why space and time become relative.
For example, in General Relativity, why does time slow down near a massive object like a black hole?
The answer is that when light passes near a black hole, it travels through the curvature of its spacetime, taking longer because the path becomes stretched. Here, time must adjust: in order for the speed of light to remain constant (as dictated by the law above), a shift occurs in time. Meanwhile, distance is already altered due to the curvature of spacetime caused by the black hole’s mass.
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The Wave Function
A fundamental concept in quantum mechanics, the wave function is used to indicate the state of a quantum particle and determines the probability of its presence at a specific position and time. The particle’s existence is based on probability, not certainty as in classical physics. The wave function relies on the Schrödinger equation, which defines the evolution of the particle’s quantum state and describes how the wave function changes over time. The importance of the wave function lies in its ability to describe many quantum phenomena such as interference and quantum entanglement, where multiple particles have linked wave functions that can lead to their states being interconnected and dependent on each other.
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We always see this equation, but what is it? What does it state, and why is it important in physics?
Before this equation appeared, physics relied on classical physics (Newton’s laws), which stated that mass is constant, space and time are absolute (unchanging under any circumstance), and energy 1/2mv^2 is given by
However, with the advent of special relativity, these concepts changed, introducing more precise ideas that explained many phenomena Newton’s laws could not, the most important being the constancy of the speed of light. Among the concepts that changed are:
Spacetime (time and space) is relative.
Energy, motion, and mass are two sides of the same coin (the same thing).
Why did Einstein change these laws?
Because he observed that objects moving near the speed of light cannot have their kinetic energy correctly described by classical laws. Also, the mass of an object increases as its speed increases, meaning its energy increases.
Here, Einstein concluded that even stationary objects carry enormous energy, which he called “mass energy.”
An example in the universe:
When two atoms, such as helium and hydrogen, fuse in a reaction like those in stars, the mass after the reaction is less than the mass before. This shows that the lost mass has been converted into thermal energy. In other words, when mass loses energy, it also loses some of its mass, and vice versa.
In short: “mass = rest energy.”
Energy is also related to spacetime, meaning time and space determine the form of interaction between mass and energy (thermal, radiative,...).
As Einstein famously said:
“Spacetime tells energy how to move, and energy tells spacetime how to curve.”
Now the question arises: We can produce energy from mass, but can we convert energy into mass?
The answer is yes. This is what the principle of “pair production” states, where energy transforms into electrons and positrons.
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The Development of the Theory of Relativity: From Special to General Relativity
Albert Einstein arrived at the general theory of relativity through the concept of accelerated coordinates and their associated laws.
But what are accelerated coordinates?
Let us go back in time to the emergence of special relativity. This theory dealt only with inertial frames (where bodies move with constant velocity).
But in our reality, we do not deal only with inertial frames; we also deal with accelerated bodies (such as cars, rockets, and other objects with increasing velocity).
Therefore, the Rindler transformations appeared mathematically to describe accelerated coordinates. They revealed several results for the accelerated observer, which are:
Event Horizon (Rindler Horizon):
The accelerated observer does not see the light cone in the same way as the inertial observer. This means that there are events the accelerated observer cannot see and will never be able to see, no matter how long they wait or how hard they try (in other words, part of the light cone is hidden).
Accessible Region (Rindler Wedge):
These transformations also showed that the path of an accelerated body is not straight but curved. This makes the observer see only a portion of spacetime, which is the accessible region.
After the appearance of these transformations, and also with the equivalence principle, which states that:
“There is no local difference between uniform acceleration and the effect of gravity”
Albert Einstein concluded the following:
Since gravity is the acceleration of bodies toward the center of, for example, the Earth, then gravity is a geometric curvature in the fabric of spacetime.
And here he arrived at the general theory of relativity.
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Imagination will often carry us to worlds that never were. But without it, we go nowhere. Skepticism enables us to distinguish fancy from fact, to test our speculations. The Cosmos is rich beyond measure—in elegant facts, in exquisite interrelationships, in the subtle machinery of awe
-Carl Sagan
Cosmos
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The Principle of Equivalence
The Principle of Equivalence was established in 1907 by Albert Einstein and is considered one of the most fundamental pillars of General Relativity.
Its core idea states that:
“It is impossible to distinguish between the effects of gravity and the effects of acceleration.”
For example, if you were aboard a spaceship in outer space with no windows, and this spaceship had the same acceleration as Earth’s gravitational acceleration (9.8 m/s²), you would not be able to tell whether you were on Earth or in space.
The principle of equivalence is divided into several types:
1. The Weak Equivalence Principle (WEP):
All objects fall with the same acceleration in a gravitational field, regardless of their mass or composition.
Examples of this include Galileo’s experiment and the Apollo 15 experiment by astronaut David Scott. He repeated Galileo’s test under better conditions by dropping a feather and a hammer from the same height. On Earth, the feather falls slower due to air resistance. However, when he repeated the experiment on the Moon—where there is no atmosphere—both objects hit the surface at the same time, as shown on camera.
2. The Local Equivalence Principle:
This is the same example given above: if you are in a spaceship with no windows accelerating at 9.8 m/s², you cannot tell whether you are experiencing Earth’s gravity or acceleration in space.
3. The Strong Equivalence Principle (SEP):
This states that all the laws of physics hold true in the same way, whether in a gravitational field or in an accelerating frame of reference.
One of the most important consequences of this principle concerns light and gravity. For example, if a light beam is emitted on Earth, it bends when passing through a gravitational field. The same bending would occur if the light were in an accelerating frame (or even more if the acceleration were greater).
This led Einstein to predic
t the bending of starlight, which was later confirmed during the 1919 solar eclipse experiment.
This principle paved the way for General Relativity:
Einstein showed that gravity is not a force but rather the result of the curvature of spacetime. Objects move along geodesics in this curved spacetime, rather than being “pulled” as classical physics suggested.
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Hi
In principle, what you are going to read now is a personal confusion.
We all know that black holes, when they die through Hawking radiation and the other theories that modified this idea (such as Leonard Susskind’s theory) and the spreading of information into space, their spacetime returns to its natural state.
But, if we look at the matter from another perspective, such as wormholes connected to black holes,
if these wormholes are stable (supported by exotic matter), they will remain even after the disappearance of the black hole.
More clearly: the spacetime of the black hole (the wormhole) will remain even after the black hole disappears.
Therefore, this spacetime (since it is a curved spacetime) will generate gravity! but without energy or mass!
Only from the exotic matter.
In principle, what you are going to read now is a personal confusion.
We all know that black holes, when they die through Hawking radiation and the other theories that modified this idea (such as Leonard Susskind’s theory) and the spreading of information into space, their spacetime returns to its natural state.
But, if we look at the matter from another perspective, such as wormholes connected to black holes,
if these wormholes are stable (supported by exotic matter), they will remain even after the disappearance of the black hole.
More clearly: the spacetime of the black hole (the wormhole) will remain even after the black hole disappears.
Therefore, this spacetime (since it is a curved spacetime) will generate gravity! but without energy or mass!
Only from the exotic matter.
🆒2💘1