1. Origins and significance

Special relativity has a wide range of consequences, which have been experimentally verified.
They include the relativity of simultaneity, length contraction, time dilation, the relativistic velocity addition formula, the relativistic Doppler effect, relativistic mass, a universal speed limit, mass–energy equivalence, the speed of causality and the Thomas precession.

First you have to describe and demonstrate, by means of experiments what all these physical subjects are, and then you have to explain them in relation to Special relativity.
The tricky part is Special relativity has a lot to do with Electrodynamics, Light, The speed of light and observers. The issue is what has that to do with all the physical processes we experience with every day life?

A defining feature of special relativity is the replacement of the Galilean transformations of Newtonian mechanics with the Lorentz transformations.

That belongs to mathematics.

Time and space cannot be defined separately from each other (as was previously thought to be the case).

What is the meaning of space ? What is the meaning of time?

Rather, space and time are interwoven into a single continuum known as "spacetime".

What does the word interwoven mean? What means spacetime?

Events that occur at the same time for one observer can occur at different times for another.

This sentence becomes easier to dicuss when the word "Events" is replaced by "Two events".
As such the sentence is true, but that is physical not important. The problem is if an observer observes two events at the same time there is no guarantee that they actual happened at the same time.
What is of uttermost importance is when an observer establises that two events did not occur at the same time that it is physical possible that they actually occured simultaneous (some where in space). This sentence chalenges the importance of observers. . The importance is that two events with happen at the same time i.e. simultaneous, can not physical influence each other!

2. Traditional "two postulates" approach to special relativity

3 Principle of relativity

3.1 Reference frames and relative motion

Reference frames play a crucial role in relativity theory.

Reference frames play a crucial role in any theory.
At the same time it also raises a serious question: Why do you need reference frames? plural?

The term reference frame as used here is an observational perspective in space that is not undergoing any change in motion (acceleration), from which a position can be measured along 3 spatial axes (so, at rest or constant velocity)

In addition, a reference frame has the ability to determine measurements of the time of events using a 'clock' (any reference device with uniform periodicity).

It is very important to describe what a clock is. A simple definition is a device which emits light flashes between two parallel mirrors.
From a physical point of view, to understand the evolution of the universe, of almost any process, a clock is not required. What is importance is the concept universal time, which is the time at any point, every where in the universe.

Since the speed of light is constant in relativity in each and every reference frame, pulses of light can be used to unambiguously measure distances and refer back the times that events occurred to the clock, even though light takes time to reach the clock after the event has transpired.

The problem is that the path of a light ray is (normally) straight, but the path of a clock, using light signals can be bended. This is the case when you place a clock on the surface of the earth. This makes the use of such a clock tricky.
A different problem is that the path of a light signal is not always straight. This is the case when the clock is placed in outer space.

In relativity theory, we often want to calculate the coordinates of an event from differing reference frames. The equations that relate measurements made in different frames are called transformation equations.

What is the reason to use different reference frames? IMO this is only confusing.

3.2 Standard configuration

3.3 Lack of an absolute reference frame

The principle of relativity, which states that physical laws have the same form in each inertial reference frame, dates back to Galileo, and was incorporated into Newtonian physics.

This sentence seems to indicate as it is wrong when you try to understand the processes that take place in the Universe when you only use one reference frame.
This question raises one basic question: why do you need different reference frames in order to understand the laws of physics?

But in the late 19th century the existence of electromagnetic waves led some physicists to suggest that the universe was filled with a substance they called "aether", which, they postulated, would act as the medium through which these waves, or vibrations, propagated.

The aether was thought to be an absolute reference frame against which speeds could be measured, and could be considered fixed and motionless relative to Earth or some other fixed reference point.

This sentence is a typical case which is not clear based on wrong assumptions.

Einstein's solution was to discard the notion of an aether and the absolute state of rest.

How can you discard an aether and an absolute state of rest when both concepts are not clear.

In relativity, any reference frame moving with uniform motion will observe the same laws of physics.

The first question to answer is which "laws of physics" are considered?
In many cases these laws are studied in a laboratorium, considerd at rest.
It is not clear to me, what is the sense to study the same laws in a different laboratorium moving with uniform motion with the first.
What makes sense is to study the differences between a laboratorium at earth compared to a laboratorium at the moon. But that is outside the scope of Special Relativity.

In particular, the speed of light in vacuum is always measured to be c, even when measured by multiple systems that are moving at different (but constant) velocities.

The whole issue is how the speed of light is measured.
Consider an observer who emits a flash of light at t0. This flash is supposed to propagate in a sphere, centered around a source p0. How is this measured?
Consider a second observer which at the same time t0, when the first observer emits his flash at p0, passes p0 with a speed v and emits a second flash around the source p0. How does this observer measures the speed of light?

3.4 Relativity without the second postulate

4 Lorentz invariance as the essential core of special relativity

4.1 Alternative approaches to special relativity

4.2 Lorentz transformation and its inverse

4.3 Graphical representation of the Lorentz transformation

5. Consequences derived from the Lorentz transformation

5.1 Invariant interval

5.2 Relativity of simultaneity

Two events happening in two different locations that occur simultaneously in the reference frame of one inertial observer, may occur non-simultaneously in the reference frame of another inertial observer (lack of absolute simultaneity).

How do you know that those events happened/occured simultaneous? The fact that an observer observes two events simultaneous is no prove that these events actual happened simultaneous.
The same is true when an observer observes two events not simultaneous.
The most important issue is if the two events happened or not, and secondly when. Not what the observer sees. The first issue is that two simultaneous events can influence each other. That is no prove if they either physical happened simultaneous or not simultaneous.
The issue is how are simultaneous events defined? Does it make sense to define simultaneous events?
Simultaneous events, my understanding, should be defined as physical events which cannot influence each other.
To define differently: Simulataneous events have the same Universal Time.

5.3 Time dilation

The time lapse between two events is not invariant from one observer to another, but is dependent on the relative speeds of the observers' reference frames.

That sentence is very difficult to understand.
If you want to have any reasonable or sensible discussion you first must have an agreement about the definition of the concepts: Time, space, objects and the universe. See also proper science or scientific method. See: https://en.wikipedia.org/wiki/Scientific_method
The main problem with Time dilation (moving clocks) is that all moving clocks behave physical differently.

Time dilation explains a number of physical phenomena; for example, the lifetime of muons produced by cosmic rays impinging on the Earth's atmosphere is measured to be greater than the lifetimes of muons measured in the laboratory.

The cause that these processes behave different is not Time dilation. The only thing that you can say is that Time dilation describes this behaviour (i.e follows the same logic). To find the cause you have to investigate the process itself in more detail.

5.4 Length contraction

The dimensions (e.g., length) of an object as measured by one observer may be smaller than the results of measurements of the same object made by another observer (e.g., the ladder paradox involves a long ladder traveling near the speed of light and being contained within a smaller garage).

The most important issue is how is this length measured. In fact it should be measured in the same reference frame.

5.5 Lorentz transformation of velocities

5.6 Thomas rotation

5.7 Causality and prohibition of motion faster than light

6 Optical effects

6.1 Dragging effects

6.2 Relativistic aberration of light

6.3 Relativistic Doppler effect

6.4 Measurement versus visual appearance

Time dilation and length contraction are not optical illusions, but genuine effects.

Both subjects should always be discussed separatly. Time dilation has to do with the behaviour of moving physical clocks (using light signals). This definitly involves physical changes.
Length contraction is much more difficult to demonstrate and maybe is a total illusion.
IMO this discussion should be based on what is physical real and what is physical not real. Real implies physical changes of the measurable parameters of objects. You can also call them genuine.
All what is physical not real are illusions. For example the length (observed) of a train of a moving train.

Measurements of these effects are not an artifact of Doppler shift, nor are they the result of neglecting to take into account the time it takes light to travel from an event to an observer.

Mesurements etc. How?
Physical effects have nothing to do with an observer. They constitute internal changes in the process itself and should be measured indepently of view point of any observer.

Scientists make a fundamental distinction between measurement or observation on the one hand, versus visual appearance, or what one sees.

The problem is in many experiments observers are involved. There is nothing wrong with this in principle.
If you measure the water temperature with a thermometer, the water temperature changes. That is part of the game.
An observer can make observations with his eyes, that is okay. Better is which type of instruments he uses.
What is important that all observations from something at a distance, show something in the past.
If you see a flash, the flash happened in the past as a function of distance.
If you see a flash and this reflash is reflected by a mirror and caused by you, than the vent of the flash happened twice this distance.

Another example where visual appearance is at odds with measurement comes from the observation of apparent superluminal motion in various radio galaxies, BL Lac objects, quasars, and other astronomical objects that eject

Another example where visual observations are at odds with the physical reality and create a sort of illusion comes from the observation of apparent superluminal motion in various radio galaxies etc

This is the effect when a train approaches an observer and shows length expansion, but this length expansion is an illusion See: Length Contraction: A visible illusion ?

7 Dynamics

7.1 Equivalence of mass and energy

7.2 How far can one travel from the Earth?

8. Beyond the basics

8.1 Rapidity

8.2 4-vectors

8.2.1 Definition of 4-vectors

8.2.2 Properties of 4-vectors

8.2.3 Examples of 4-vectors

8.2.4 4-vectors and physical law

8.3 Acceleration

8.3.1 Dewan–Beran–Bell spaceship paradox

8.3.2 Accelerated observer with horizon

9 Relativity and unifying electromagnetism

10 Theories of relativity and quantum mechanics

11 Status

12 Technical discussion of spacetime

12.1 Geometry of spacetime

12.2 Physics in spacetime

13. See also

Following is a list with "Comments in Wikipedia" about related subjects

• Length contraction Comments
• Mass Gravitational Mass & Inertial Mass Comments
• Mass-energy equivalence Comments
• Mass in special relativity Comments
• Quantum entanglement
• Relativity of Simultaneity Comments
• Scientific law Comments
• Scientific method Comments
• Scientific theory Comments
• Shape of the universe Comments
• Space and time Comments
• Spacetime Comments
• Terrell rotation
• Time dilation Comments

Reflection 0 - What is the position of general relativity in relation to the laws of physics.

My definition of the laws of physics is the collection of all the laws physics which are each used to describe a specific physical process. Together they describe all physical processes.

Reflection 1 - Length contraction

Consider two long horizontal railways. Both railways are identified by the tracks AB.
On both railways is a train. Each train with the lines LR. Each train can drive in both directions, and can be controlled from both points L and R. At both L and R is an (emergency) stop Button.
The train T1 at the bottom drives towards the right. The train T2 at top drives towards the left.
There are two observers: O1 at the left and O2 at the right.
The questions are:

1. what does O1 observes when both trains moves towards point X.

2. what happens when the point L on both trains are direct opposite each other and when on each train the stop Button is pressed.

3. Are there any differences between what O1 and O2 observe.

The train T3 is a special case.

<-- L---T2---R ----A----------------------------------------------------------------------B---- O1 X O2 L---T1---R --> ----A----------------------------------------------------------------------B---- <-- L---T3---R ----A----------------------------------------------------------------------B---- Fig 1

Fig 1 shows 2 moving trains T1 and T2, at the same instant that the back L of train T1 is at the same position as O1 and that the back R of train T2 is at the same position as O2, which coincide with the positions A and B.
That means at that same instant observer O1 sees the back L of train T1 and O2 sees of the back R of train T2.
But what happens at that same moment with the front R of Train T1?
Fig 1 shows the actual position R of the train T1. But that is not what O1 observes, because light from that position still has to travel from point R to point O1 and will reach point O1 later. That means what O1 sees is light from an earlier position of the front R of the train T1, closer to point O1, because T1 travels away from O1. That means the length of the train T1 seems shorter.
But what does O1 sees from the approaching train T2? To get an impression, train T3 is used, which travels towards Observer O1.
At the moment discussed the physical positions L and R of both trians T1 and T3 are identical, the difference are the directions. Fig 1 shows the actual position R of the train T3. But that is not what O1 observes, because light from that position still has to travel from point R to point O1 and will reach point O1 later. That means what O1 sees is light from an earlier position of the back R of the train T3, further away to point O1, because T3 travels towards O1. That means the length of the train T1 seems longer.

What observes O1 when T1 moves towards point X and T2, from opposite direction also towards point X?
If O1 is capable to observe both the points L and R of train T1 than O1 will conclude that there is constant length contraction involved
If O1 is capable to observe both the points L and R of train T2 than O1 will conclude that there is constant length expansion involved

What happens when point L of T1 coincide with point L of T2, identified as point X? Each train stops 'immediate' and there is no collision. In reality each train will not stop immediate, but glide forward and then stop. (May be to use a parachute is the solution). How ever if you are capable to remove this extra distance from the positions R observed you will see:

That the position of R of T1 will move away and the train will become longer (length contraction disappears).

That the position of R of T2 will move forward and the train will become shorter (length expansion disappears).

A different complication is that when the average speed of the moving away train is calculated this is slower than the expected speed. The opposite is true for the approaching train, the average speed is higher.

The most important lesson is, that vissible observations of moving objects are tricky. The reality is not what you see.
Length contraction and length expansion are illusions.

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Reflection 2 - What is the purpose of a reference frame?

A reference frame is a virtual grid with a each grid point a virtual clock. The definition of a virtual grid is that the distance between the 6 nearest grid points in the x,y,z direction is identical. The definition of a virtual clock is that all virtual clocks are identical and all virtual clocks show the same time. The purpose of a reference frame is to measure the position of an object.
The trajectory of an object can be described as a sequence of points (x,t) = (0,0),(1,1),(2,2),(3,3) What that shows is that the object moves in a straight line (in the x direction) with a constant speed.
The trajectory of a different object can be described as: (x,t) = (6,0),(5,1),(4,2),(3,3) This shows is that this second object moves in a straight line (in the -x direction) with a constant speed.
What this shows that there is a collision between the two objects at (x,t)=(3,3)

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Reflection 3 - The Definition of Time, Space, Objects and the Universe.

There does not exist a clear definition of the Universe, it is more or less a concept we all agree about.
It is important to make a distinction about two different concepts: The physical universe and the observable universe.
The physical universe is a certain area filled with objects called galaxies, stars, and Black holes. It is assumed that the size is expanding. It is also assumed that the universe had a beginning and started with wath we call the Big Bang. The age of the physical universe is called Universal time. The universal time any where in the physical universe, at of this moment, is the same.
The observable universe is a part of the Physical universe going backwards in universal time. It is that part of the universe we can observe. Going back ward in time in principle we can observe the Big Bang. The current main stream opinion is that the earliest events we can observe happend 300000 years after the Big Bang.
The concept time also has two definitions: Universal time and clock time. Universal time defines the age of the universe. Clock time is the time measured with a clock.
The concept of Universal time is that at any moment the time in the universe is every where the same. The consequence is, that two events with happen simultaneous can not influence each other. Think about two collisions between two stars which happen simultaneous. Consider each collisions results in a shock wave. The event that these shock waves can meet each other, is always later as the two original collisions. The concept of clock time, i.e. the time measured by a clock is tricky. The problem is that a clock is a physical object and its behaviour is (gravitational) influenced in the same manner as all object are influenced by all objects and influences all other objects.

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Reflection 4 - Is the universe relative or absolute.

The distinction between absolute and relative only makes sense if both concepts have a clear definition.
To understand the Universe implies to understand the details of the evolution of the Universe.
My definition of the Universe is: An area in space filled with small and large objects. The position and composition of these objects continuously changes, influenced by forces.
To understand the Universe is a human activity. The main tool to understand the evolution of universe we use light. With the aid of light humans can observe the shapes and sizes of objects in the Universe which emit light. At the same time there also exist a large number of objects which don't emit light. These objects also have to be included if we want to understand the evolution of the universe, because all (baryonic) mass in the universe influences each other. The definition of the Universe also includes that at any moment all the objects in the universe have a certain position. It also includes the concept that at any moment all the events that happen in the universe, happen simultaneous. Events can be collisions between two objects or elementary particles. These events are vissible if they emit light i.e. photons. By comparing the positions of an object at two specific moments, based on the distance between the positions (in one frame) the velocity of a specific object can be calculated.

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Created: 21 October 2024

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