Special Relativity Einstein's special theory of relativity

Special theory of relativity

The Special theory of Relativity (shortly, Special or Restricted Relativity, RE), first published by Albert Einstein in 1905, describes the physics of motion in the absence of gravitational fields.

Before it, most physicists believed that Isaac Newton’s classical mechanics, based on the so-called relativity of Galileo (origin of the mathematical equations known as Galileo transformations), described the concepts of speed and force for all observers ( or reference systems). 

Relativity: The Special and General Theory

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However, Hendrik Lorentz and others had found that Maxwell’s equations, which govern electromagnetism, did not behave according to Newton’s laws when the reference system changes (for example, when the same physical problem is considered from the point of view of two observers moving with respect to each other).

It is the notion of transformation of the laws of physics with respect to observers that gives the theory its name, which is adjusted with the qualification of special or restricted because it is limited to cases of systems in which gravitational fields are not taken into account. An extension of this theory is the general theory of relativity, also published by Einstein in 1916 and including these fields.

Motivation of the theory

Newton’s laws consider that time and space are the same for different observers of the same physical phenomenon. Before formulating the special theory of relativity, Hendrik Lorentz and others had already discovered that electromagnetism differed from Newtonian physics in that observations of a phenomenon could differ from person to person moving relatively early on at near speeds to those of light. 

Thus, one can observe the absence of a magnetic field while the other observes said field in the same physical space.

Lorentz suggested an ether theory in which objects and observers would travel through a stationary ether, undergoing physical shortening (Lorentz contraction hypothesis) and a change in the passage of time (time dilation). This provided a partial reconciliation between Newtonian physics and electromagnetism, which were combined by applying the Lorentz transformation, which would come to replace the Galilean transformation in force in the Newtonian system. 

When the speeds involved are much less than c (the speed of light), the resulting laws are in practice the same as in Newton’s theory, and the transformations are reduced to those of Galileo. In any case, the theory of the ether was criticized even by Lorentz himself due to this nature.

When Lorentz suggested his transformation as an accurate mathematical description of the results of the experiments, Einstein derived these equations from two fundamental hypotheses: the constancy of the speed of light, c, and the need for the laws of physics to be equal ( invariants in different inertial systems, that is, for different observers.From this idea came the original title of the theory, “Theory of invariants”. 

Read more: What came before the Big bang?

It was Max Planck who later suggested the term “relativity” to highlight the notion of transformation of laws of physics between observers moving relatively to each other.

Special relativity studies the behavior of objects and observers that remain at rest or move with uniform motion (ie, constant relative speed). In this case, the observer is in an inertial frame of reference. The comparison of spaces and times between inertial observers can be performed using the Lorentz transformations. The special theory of relativity can also predict the behavior of accelerated bodies when said acceleration does not imply gravitational forces, in which case general relativity is necessary.

Invariance of the speed of light

To support RE, Einstein postulated that the speed of light in a vacuum is the same for all inertial observers. Likewise, he stressed that all physical theory must be described by laws that have a similar mathematical form in any inertial reference system. 

The first postulate is in accordance with Maxwell’s equations of electromagnetism, and the second postulates a logical reasoning principle, in the form of the anthropic principle.

Einstein showed that the Lorentz equations are deduced from these principles, and, when applied under these concepts, the resulting mechanics have several interesting properties:

When the speeds of the objects considered are much less than the speed of light, the resulting laws are those described by Newton.

Likewise, electromagnetism is no longer a set of laws that requires a different transformation from that applied in mechanics.

Time and space are no longer invariant when changing the reference system, becoming dependent on the relative speeds of the observers’ reference systems: Two events that occur simultaneously in different places for a reference system, can occur in different times in another reference system (simultaneity is relative). Similarly, if they occur in the same place in one system, they can occur in different places in another.

The time intervals between events depend on the frame of reference in which they are measured (for example, the famous paradox of the twins). The first two properties were very attractive, since any new theory must explain the existing observations, and these indicated that Newton’s laws were very precise. The third conclusion was initially highly disputed, as it threw out many well-known and apparently obvious concepts, such as the concept of simultaneity.

Absence of an absolute reference system

Another consequence is the rejection of the notion of a single and absolute reference system. It was previously believed that the universe traveled through a substance known as ether (identifiable as absolute space) in relation to which speeds could be measured. 

The results of various experiments, however, resulting in the famous Michelson-Morley experiment, proposed that either the Earth had been stationary (which is absurd), or the notion of an absolute reference system was incorrect and should be discarded. Einstein concluded with the special theory of relativity that any movement is relative, there being no universal concept of “stationary”.

Equivalence of mass and energy

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famous formula on a german postage stamp

But perhaps much more important was the demonstration that energy and mass, previously considered differentiated measurable properties, were equivalent, and related through what is arguably the theory’s most famous equation:

E = m · c 2

where E is the energy, m is the mass and c is the speed of light in a vacuum. If the body is moving at speed v relative to the observer, the body’s total energy is:

E = gamma cdot m cdot c ^ 2


gamma = {1 over {sqrt {1- {v ^ 2 over c ^ 2}}}}

The term ? it is frequent in relativity. It is derived from the Lorentz transformation equations. When v is much less than c can the following approximation of? (obtained by Taylor’s serial development):

gamma = left ({1- {v ^ 2 over c ^ 2}} right) ^ {- {1 over 2}} = 1- left (- {1 over 2} right) cdot {v ^ 2 over c ^ 2 } + 0 cdot {v ^ 4 over c ^ 4} + ... approx 1 + {1 over 2} cdot {v ^ 2 over c ^ 2}


 gamma cdot m cdot c ^ 2 approx m cdot c ^ 2 + {1 over 2} cdot m cdot v ^ 2

which is precisely equal to the energy at rest , mc 2 , plus the Newtonian kinetic energy, ½ mv 2 . This is an example of how the two theories coincide when the speeds are small.

Furthermore, at the speed of light, the energy will be infinite, which prevents particles that have mass at rest from reaching the speed of light.

The most practical implication of the theory is that it places an upper limit on the laws of classical mechanics and gravity proposed by Isaac Newton when speeds approach those of light. Nothing that can transport mass or information can move faster than that speed. When an object approaches the speed of light (in any system) the amount of energy required to continue increasing its speed increases rapidly and asymptotically towards infinity, making it impossible to reach the speed of light. Only massless particles, such as photons, can reach that speed (and indeed must be translated in any reference system at that speed) which is approximately 300,000 kilometers per second (3 · 10 8 ms -1 ).

The name tachyon has been used to name hypothetical particles that could move faster than the speed of light. Currently, no experimental evidence of its existence has yet been found.

Special relativity also shows that the concept of simultaneity is relative to the observer: 

If matter can travel along a line (trajectory) in space-time without changing speed, the theory calls this line a time interval. Since an observer following said line could not feel movement (it would be at rest), but only travel in time according to its reference system. Similarly, a spatial interval means a straight line in space-time along which neither light nor any slower signal could travel. 

Events throughout a spatial interval cannot influence each other by transmitting light or matter, and may appear simultaneous to an observer in a suitable frame of reference. To observers in different reference systems, event A may appear to precede B or vice versa. This does not happen when we consider events separated by time intervals.

Special Relativity is universally accepted by the physical community today, unlike confirmed general relativity , but with experiences that might not exclude some alternative theory of gravitation. However, there is still a group of people opposed to SR in various fields, several alternatives having been proposed, such as the so-called Ether Theories.

Watch: Secrets of Quantum Physics

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The theory

RE uses turnbuckles or quadrivectors to define a non-Euclidean space. This space, however, is similar in many ways and easy to work with. The differential of the distance ( ds ) in a Euclidean space sees defined as:

ds 2 = dx 1 2 + dx 2 2 + dx 3 2

where dx 1 , dx 2 , dx 3 are differentials of the three spatial dimensions. In the geometry of special relativity, a fourth dimension, time, has been added, but it is treated as an imaginary quantity with units of c , leaving the equation for distance, differentially, as:

ds 2 = dx 1 2 + dx 2  + dx 3 2 -c 2 dt 2

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Dual cone.

If we reduce the spatial dimensions to 2, we can make a physical representation in a three-dimensional space,

ds 2 = dx 1 2 + dx 2 2 -c 2 dt 2

We can see that geodesics with zero measurement form a dual cone:

defined by the equation

ds 2 = 0 = dx 1 2 + dx 2 2 -c 2 dt 2

, or

dx 1 2 + dx 2 2 = c 2 dt 2

The previous equation is the circle equation with r = c * dt . If we extend the above to the three spatial dimensions, the null geodesics are concentric spheres, with radius = distance = c * (+ or -) time.

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ds 2 = 0 = dx 1 2 + dx 2 2 + dx 3 2 -c 2 dt 2

dx 1 2 + dx 2 2 + dx 3 2 = c 2 dt 2

This double cone of zero distances represents the “horizon of vision” of a point in space i.e., when we look at the stars and say “The star I am receiving light from is X years old.”, We are traveling through that line of sight: a geodesic of zero distance. We are seeing an event at d =? {x 1 2 + x 2 2 + x 3 2 } meters, and d / c seconds in the past. 

For this reason the double cone is also known as the light cone. (The bottom point on the left of the bottom diagram represents the star, the origin represents the observer, and the line represents the null geodesic, the “horizon of vision” or light cone .)

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Vision horizon.

Geometrically, all the “points” along the cone of light give information (represent) the same point in space-time (because the distance between them is 0). This can be thought of as a ‘point of neutralization’ of forces. (“The connection occurs when two movements, each of which exclusive of the other, come together in a moment.” – quote from James Morrison) 

It is where the events in space-time intersect, where space interacts with itself. It is like a point sees the rest of the universe and is seen. The cone in the -t region includes the information that the point receives, while the + t regionThe cone includes the information that the point sends. In this way, what we can envision is a space of horizons of vision and fall back on the concept of cellular automaton, applying it in a continuous space-time sequence.

Space of vision horizons.

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Inertial systems.

This also counts for points in uniform motion of relative inertial systems . This means that the geometry of the universe remains the same regardless of the speed ( ? X /? T ) ( inertial ) of the observer. Thus we fall back on Newton’s first law of motion: “An object in motion tends to remain in motion; an object at rest tends to remain at rest

Law of conservation of kinetic energy

However, the geometry does not remain constant when acceleration ( ? X 2 /? T 2 ) is involved, which implies an application of force ( F = ma ), and consequently a change in energy, which leads to general relativity, in which the intrinsic curvature of space-time is directly proportional to the energy density at that point.

Recommended Books:

Relativity: The Special and General Theory

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  1. Regardless if you believe in God or not, read this message!

    Throughout time, we can see how we have been strategically conditioned to come to this point where we are on the verge of a cashless society. Did you know that the Bible foretold of this event almost 2,000 years ago?

    In the book of Revelation 13:16-18, it states,

    “He (the false prophet who deceives many by his miracles–Revelation 19:20) causes all, both small and great, rich and poor, free and slave, to receive a mark on their right hand or on their foreheads, and that no one may buy or sell except one who has the mark or the name of the beast, or the number of his name.

    Here is wisdom. Let him who has understanding calculate the number of the beast, for it is the number of a man: His number is 666.”

    Speaking to the last generation, this could only be speaking of a cashless society. Why? Revelation 13:17 says that we cannot buy or sell unless we receive the mark of the beast. If physical money was still in use, we could buy or sell with one another without receiving the mark. This would contradict scripture that states we need the mark to buy or sell!

    These verses could not be referring to something purely spiritual as scripture references two physical locations (our right hand or forehead) stating the mark will be on one “OR” the other. If this mark was purely spiritual, it would indicate both places, or one–not one OR the other!

    This is where it comes together. It is incredible how accurate the Bible is concerning the implantable RFID microchip. These are notes from a man named Carl Sanders who worked with a team of engineers to help develop this RFID chip:

    “Carl Sanders sat in seventeen New World Order meetings with heads-of-state officials such as Henry Kissinger and Bob Gates of the C.I.A. to discuss plans on how to bring about this one-world system. The government commissioned Carl Sanders to design a microchip for identifying and controlling the peoples of the world—a microchip that could be inserted under the skin with a hypodermic needle (a quick, convenient method that would be gradually accepted by society).

    Carl Sanders, with a team of engineers behind him, with U.S. grant monies supplied by tax dollars, took on this project and designed a microchip that is powered by a lithium battery, rechargeable through the temperature changes in our skin. Without the knowledge of the Bible (Brother Sanders was not a Christian at the time), these engineers spent one-and-a-half-million dollars doing research on the best and most convenient place to have the microchip inserted.

    Guess what? These researchers found that the forehead and the back of the hand (the two places the Bible says the mark will go) are not just the most convenient places, but are also the only viable places for rapid, consistent temperature changes in the skin to recharge the lithium battery. The microchip is approximately seven millimeters in length, .75 millimeters in diameter, about the size of a grain of rice. It is capable of storing pages upon pages of information about you. All your general history, work history, criminal record, health history, and financial data can be stored on this chip.

    Brother Sanders believes that this microchip, which he regretfully helped design, is the “mark” spoken about in Revelation 13:16–18. The original Greek word for “mark” is “charagma,” which means a “scratch or etching.” It is also interesting to note that the number 666 is actually a word in the original Greek. The word is “chi xi stigma,” with the last part, “stigma,” also meaning “to stick or prick.” Carl believes this is referring to a hypodermic needle when they poke into the skin to inject the microchip.”

    Mr. Sanders asked a doctor what would happen if the lithium contained within the RFID microchip leaked into the body. The doctor replied by saying a terrible sore would appear in that location. This is what the book of Revelation says:

    “And the first (angel) went, and poured out his vial on the earth; and there fell a noisome and grievous sore on the men which had the mark of the beast, and on them which worshipped his image” (Revelation 16:2).

    You can read more about it here–and to also understand the mystery behind the number 666: [url=https://2ruth.org]HTTPS://2RUTH.ORG[/url]

    The third angel’s warning in Revelation 14:9-11 states,

    “Then a third angel followed them, saying with a loud voice, ‘If anyone worships the beast and his image, and receives his mark on his forehead or on his hand, he himself shall also drink of the wine of the wrath of God, which is poured out full strength into the cup of His indignation. He shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb. And the smoke of their torment ascends forever and ever; and they have no rest day or night, who worship the beast and his image, and whoever receives the mark of his name.'”

    Great hope is in our midst, and is coming in a mighty way–the greatest revival for Jesus in the history of the world where we will see the most souls come to Him of all tribes, tongues, nations, and peoples (Rev. 7:9-10); for we have this promise in God’s Word in the midst of these dark times:

    “Then I saw an angel coming down from heaven, having the key to the bottomless pit and a great chain in his hand. He laid hold of the dragon, that serpent of old, who is the Devil and Satan, and bound him for a thousand years (not literal–rather a spiritual label for time spent in eternity); and he cast him into the bottomless pit, and shut him up, and set a seal on him, so that he should deceive the nations no more till the thousand years were finished. But after these things he must be released for a little while (when the Antichrist and false prophet will rise up and God will test the world).” (Revelation 20:1-3)

    “The coming of the lawless one (the Antichrist) is according to the working of Satan, with all power, signs, and lying wonders, and with all unrighteous deception among those who perish, because they did not receive the love of the truth, that they might be saved. And for this reason God will send them strong delusion, that they should believe the lie, that they all may be condemned who did not believe the truth but had pleasure in unrighteousness.” (2 Thessalonians 2:9-12)”

    Who is Barack Obama, and why is he still around?

    So what’s in the name? The meaning of someone’s name can say a lot about a person. God throughout history has given names to people that have a specific meaning tied to their lives. How about the name Barack Obama? Let us take a look at what may be hiding beneath the surface.

    Jesus states in Luke 10:18, “…I saw Satan fall like lightning from heaven.”

    The Hebrew Strongs word (H1299) for “lightning”: “bârâq” (baw-rawk)

    In Isaiah chapter 14, verse 14, we read about Lucifer (Satan) saying in his heart:

    “I will ascend above the heights of the clouds, I will be like the Most High.”

    In the verses in Isaiah that refer directly to Lucifer, several times it mentions him falling from the heights or the heavens. The Hebrew word for the heights or heavens used here is Hebrew Strongs 1116: “bamah”–Pronounced (bam-maw’)

    In Hebrew, the letter “Waw” or “Vav” is often transliterated as a “U” or “O,” and it is primarily used as a conjunction to join concepts together. So to join in Hebrew poetry the concept of lightning (Baraq) and a high place like heaven or the heights of heaven (Bam-Maw), the letter “U” or “O” would be used. So, Baraq “O” Bam-Maw or Baraq “U” Bam-Maw in Hebrew poetry similar to the style written in Isaiah, would translate literally to “Lightning from the heights.” The word “Satan” in Hebrew is a direct translation, therefore “Satan.”

    So when Jesus told His disciples in Luke 10:18 that He beheld Satan fall as lightning from heaven, if this were to be declared by a Jewish Rabbi today influenced by the poetry in the book of Isaiah, he would say these words in Hebrew–the words of Jesus in Luke 10:18 as, and I saw Satan as Baraq O Bam-Maw.

    Malie and Natasha are the names of Obama’s daughters. If we write those names backward (the devil does things backwards) we would get “ailam ahsatan”. If we remove the letters that spell “Alah” (Allah being the false god of Islam), we would get “I am Satan”. Chance? I do not believe so!

    Obama’s campaign logo when he ran as President of the United States in 2008 was a sun over the horizon in the west, with the landscape as the flag of the United States. In Islam, they have their own messiah that they are waiting for called the 12th Imam, or the Mahdi (the Antichrist of the Bible), and one prophecy concerning this man’s appearance is the sun rising in the west.

    “Then I saw another angel flying in the midst of heaven, having the everlasting gospel to preach to those who dwell on the earth—to every nation, tribe, tongue, and people— saying with a loud voice, ‘Fear God and give glory to Him, for the hour of His judgment has come; and worship Him who made heaven and earth, the sea and springs of water.'” (Revelation 14:6-7)

    Why have the words of Jesus in His Gospel accounts regarding His death, burial, and resurrection, been translated into over 3,000 languages, and nothing comes close (the Quran about 110 languages)? Because the same Spirit of God (YHVH) who created all people likewise transcends all people; therefore the power of His Word is not limited by people; while all other religions are man-made, therefore they tend to primarily stay within their own culture. The same God who speaks to all people through His creation of the heavens and earth that draws all people around the world likewise has sent His Word to the ends of the earth so that we may come to personally know Him to be saved in spirit and in truth through His Son Jesus Christ.

    Jesus stands alone among the other religions that say to rightly weigh the scales of good and evil and to make sure you have done more good than bad in this life. Is this how we conduct ourselves justly in a court of law? Bearing the image of God, is this how we project this image into reality?

    Our good works cannot save us. If we step before a judge, being guilty of a crime, the judge will not judge us by the good we have done, but rather by the crimes we have committed. If we as fallen humanity, created in God’s image, pose this type of justice, how much more a perfect, righteous, and Holy God?

    God has brought down His moral laws through the 10 commandments given to Moses at Mt. Siani. These laws were not given so we may be justified, but rather that we may see the need for a savior. They are the mirror of God’s character of what He has written in our hearts, with our conscious bearing witness that we know that it is wrong to steal, lie, dishonor our parents, murder, and so forth.

    We can try and follow the moral laws of the 10 commandments, but we will never catch up to them to be justified before a Holy God. That same word of the law given to Moses became flesh about 2,000 years ago in the body of Jesus Christ. He came to be our justification by fulfilling the law, living a sinless perfect life that only God could fulfill.

    The gap between us and the law can never be reconciled by our own merit, but the arm of Jesus is stretched out by the grace and mercy of God. And if we are to grab on, through faith in Him, He will pull us up being the one to justify us. As in the court of law, if someone steps in and pays our fine, even though we are guilty, the judge can do what is legal and just and let us go free. That is what Jesus did almost 2,000 years ago on the cross. It was a legal transaction being fulfilled in the spiritual realm by the shedding of His blood with His last word’s on the cross crying out, “It is finished!” (John 19:30).

    For God takes no pleasure in the death of the wicked (Ezekiel 18:23). This is why in Isaiah chapter 53, where it speaks of the coming Messiah and His soul being a sacrifice for our sins, why it says it pleased God to crush His only begotten Son.

    This is because the wrath that we deserve was justified by being poured out upon His Son. If that wrath was poured out on us, we would all perish to hell forever. God created a way of escape by pouring it out on His Son whose soul could not be left in Hades but was raised and seated at the right hand of God in power.

    So now when we put on the Lord Jesus Christ (Romans 13:14), where God no longer sees the person who deserves His wrath, but rather the glorious image of His perfect Son dwelling in us, justifying us as if we received the wrath we deserve, making a way of escape from the curse of death; now being conformed into the image of the heavenly man walking in a new nature, and no longer in the image of the fallen man Adam.

    Now what we must do is repent and put our trust and faith in the savior, confessing and forsaking our sins, and to receive His Holy Spirit that we may be born again (for Jesus says we must be born again to see and enter the Kingdom of God in John chapter 3). This is not just head knowledge of believing in Jesus, but rather receiving His words, taking them to heart, so that we may truly be transformed into the image of God. Where we no longer live to practice sin, but rather turn from our sins and practice righteousness through faith in Him in obedience to His Word by reading the Bible.

    Our works cannot save us, but they can condemn us; it is not that we earn our way into everlasting life, but that we obey our Lord Jesus Christ:

    Jesus says,

    “Not everyone who says to Me, ‘Lord, Lord,’ shall enter the kingdom of heaven, but he who does the will of My Father in heaven. Many will say to Me in that day, ‘Lord, Lord, have we not prophesied in Your name, cast out demons in Your name, and done many wonders in Your name?’ And then I will declare to them, ‘I never knew you; depart from Me, you who practice lawlessness!’ (Matthew 7:21-23)

    “And having been perfected, He became the author of eternal salvation to all who obey Him.” (Hebrews 5:9)

    “Now I saw a new heaven and a new earth, for the first heaven and the first earth had passed away. Also there was no more sea. Then I, John, saw the holy city, New Jerusalem, coming down out of heaven from God, prepared as a bride adorned for her husband. And I heard a loud voice from heaven saying, ‘Behold, the tabernacle of God is with men, and He will dwell with them, and they shall be His people. God Himself will be with them and be their God. And God will wipe away every tear from their eyes; there shall be no more death, nor sorrow, nor crying. There shall be no more pain, for the former things have passed away.’

    Then He who sat on the throne said, ‘Behold, I make all things new.’ And He said to me, ‘Write, for these words are true and faithful.’

    And He said to me, ‘It is done! I am the Alpha and the Omega, the Beginning and the End. I will give of the fountain of the water of life freely to him who thirsts. He who overcomes shall inherit all things, and I will be his God and he shall be My son. But the cowardly, unbelieving, abominable, murderers, sexually immoral, sorcerers, idolaters, and all liars shall have their part in the lake which burns with fire and brimstone, which is the second death.'” (Revelation 21:1-8)

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