The Basics of Special Relativity

Albert Einstein is probably the most popular scientific figurehead in modern culture with his iconic messy hair and white lab coat. His image has been deemed by many people to be the stereotypical scientist. He is one of the favourite picks by young children to dress up for Halloween and his name is also a synonym of words such as “genius”. Additionally the very recent announcement of the detection of gravitational waves once again awakened people’s admiration for , however despite his immense popularity, most of the public have no idea what pioneering contributions he had made in the field of physics. Einstein’s breakthrough came from his work on Gravitation through his developments of two successful theories: Special and General theory of Relativity, with General Relativity becoming one of the two great pillars of modern physics, the other being Quantum Theory. In this post I will attempt to cover the basic concepts of Special Relativity.

What is special relativity?

To understand the theory it is necessary to keep clear in mind of the “absolutes”, to dismiss velocity and time as “absolutes” and comprehend that these values are independent to the specific observer. A simple example could be that a child standing on a football field is stationary in his own perspective, but to a space craft close to the Sun he is zooming past at thirty thousand kilometres per second with the Earth. It is important to notice that nothing in the Universe could be described as in absolute rest or absolute motion, everything is relative.

The Special Theory of Relativity combines the concepts Space and Time into one, Space-time and it is based upon two postulates.

  1. The laws of physics are identical for all observers/objects in an inertial (constant speed) reference frame.
  2. The speed of light is constant through a vacuum, no matter the observer’s relative motion to it.

Special Relativity is “special” in the sense of it only applying to objects moving in uniform motion, thus at a constant speed in a straight line. Relativistic effects are only apparent with objects that travel at extremely high velocities which means close to the speed of light – c.

Time and length

We are all familiar with the equation: Speed=Distance/Time. One of the postulates of Special Relativity is that light speed is a constant, which gives an indication that either Time or Distance must alter, and in this case changes are noticed in the values for both Distance and Time to account for the consistency of c for all observers.

Time Dilation

050318mathew_time_dilation
Formula used in calculations of time dilation where t=”proper” time and t’=dilated time
When an object is travelling at close to light speed, relativistic effects come into play and time dilation is one aspect. Consider a clock on a spaceship travelling at 0.9c. The “clock” is in fact a “light clock” and is hypothetical. It consists of two parallel facing mirrors separated by half the distance light travels in a second, so one second passes each time a light pulse is sent out from one mirror, strikes the opposite mirror and returns back. Let’s imagine this clock is replicated on Earth and synced beforehand. When comparing the two clocks, something odd is seen and that is the time it takes for the light pulse to make a round trip on the spaceship clock is much slower than for Earth.

time-dilation-002-mod-svg

Because of the high-speed motion of the spaceship, the light beam must travel a significantly greater distance in order to also keep up with the velocity of the spaceship itself, and from previous knowledge, light speed must always be the same consistent value, time has slowed down for everything on board the spaceship.

Length Contraction

lengthcontraction1
Formula used in calculations of length contraction where l=”proper” length and l’=contracted length
Another effect that would be perceived is length contraction. Length contraction is simply the difference in the length of an object as measured by a stationary and moving observer. Let’s bring back the Light Clock. When the light pulse makes a round trip on the clock it travels about 300 thousand kilometres when stationary on Earth. However at very high speeds, like 0.9c not only does time slow down, but the lengths of the moving objects also decrease, thus in this case the distance between the mirrors become a lot less than 150 thousand kilometres to account for the consistency of the speed of light.

The Twin Paradox

twin_paradox

Perhaps the most well-known thought experiment regarding Special Relativity is the Twin Paradox. It proposes the idea that one twin stays on Earth while the other flies off into space on a powerful rocket at close to light speed. The crux of the paradox is the difference in ages when the twin in the rocket returns. The twin on Earth sees the rocket fly past at close to light speed, and the clock hand on the rocket tick slower. The other twin sees the Earth fly past at close to light speed, the clock hand on her twin’s watch on Earth tick slower. Both perspectives are equally as valid as both are inertial reference frames and the laws of physics remain the same. Due to time dilation, when the twin returns to Earth she will believe her sister is younger than her, but her sister will believe the opposite, and that cannot happen. Solving the paradox requires knowledge from another closely related theory also developed by Einstein: General Relativity. When the twin on the rocket turns around to return to Earth, she must accelerate which means she would no longer stay in uniform motion and thus Special Relativity no longer applies to the situation. General Relativity states that time runs slower in an accelerated reference frame, therefore we can conclude that the twin on the rocket will in fact be younger than her twin when she returns home to Earth.

Special Relativity is difficult to imagine on a day to day practical level and many people struggle to think of any use of this theory, but there are many applications that have been revealed through its study. The development of GPS requires both Special and General Relativity to pin point our exact location on Earth. Theories such as Quantum Field Theory successfully blend together Special Relativity and Quantum Mechanics and is essential to understanding the nature of underlying constituents of the Universe. The famous mass and energy equivalence equation also arose from Special Relativity and yielded countless of substantial applications from nuclear reactors to PET scanning.

Author – Susan Chen

Susan is a 5th year high school student currently studying three STEM subjects at Scottish Higher level-Mathematics, Physics and Chemistry (Crash Course). She particularly loves ideas in cosmology and hopes to embark on an academic journey in the area of theoretical physics.

42 thoughts on “The Basics of Special Relativity

  1. Hiroji kurihara June 24, 2020 / 9:11 pm

    Perihelion shift of Mercury

    Let’s reconsider the main cause of perihelion shift again. On Mercury or Venus, main cause will be the size of sphere. On Earth or Mars, effect of satellite is added. On asteroids each, effects of size is negligible. On Jupiter or Saturn each, the powerful and unstable effect of the other will act. On Uranus or Neptune each, slight and unstable effect of the other all planets will act. Anyway, common view on Mercury is wrong.

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  2. Hiroji kurihara June 14, 2020 / 11:36 pm

    Perihelion shift of Mercury

    The perihelion shift of the earth is 11.45 arcsec / year. Main cause will be its size (size of sphere). It is the same to Mercury. In addition, the earth has a moon as a satellite that Mercury does not have. The inertial force of the moon and gravity of the sun acting on the moon are also considerable. And like Mercury, effect of other planets must be slight and unstable.

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  3. Hiroji kurihara June 13, 2020 / 11:25 pm

    Perihelion shift of Mercury

    There is a model of Mercury. A long lod penetrates a true sphere and at the both ends of the lod, weights are set. This model is rotating horizontally and is moving on the orbit of Mercury (two planes fall on). Main forces acting on the weights are gravity of the sun and inertial force (centrifugal force). And each force acting on the outside weight and inside weight is different.

    Inertial force pulls the orbit to the outside. But actual orbit of Mercury is pulled to the inside. Gravity of the sun acting on the two weights is inversely proportional to the square of the distance (not come out even. not plus minus zero). In Mercury, the action of gravity will be superior.

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  4. Hiroji kurihara June 11, 2020 / 2:54 am

    Perihelion shift of Mercury

    Value 5.75 arcsec/year seems to be an observed value. In a website, contribution of other planets to this value is shown. These are added simply !! And value 5.75 arcsec (and contributions) seems to be constant every year !! On these problems, further explanation seems not to be done.

    I say again, other planets will not be main cause of this value 5.75 arcsec.

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  5. Hiroji kurihara June 10, 2020 / 10:01 pm

    Perihelion shift of Mercury

    A model of Mercury is shown previously. Now, there are plural models. Length of lods and mass of weight each is different. These are revoleved around separately on the real orbit of Mercury. Maybe, all will be explained by Newton’s theory (including 575 arcsec).

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  6. Hiroji kurihara June 3, 2020 / 9:43 pm

    Perihelion shift of Mercury

    “It can be safely said that gravity of other planets has no effect on the perihelion shift of Mercury”. It’s in a website.

    Imagine that with long radius of orbit of Mercury, the space of the solar system is divided into left and right. The probability that other planets exist on the two is equal. There will be no shift of perihelion in one direction at constant speed (common view is wrong).

    But main cause of perihelion shift of Jupiter and Saturn will be mutual effect of gravity. Each perihelion is shifted every moment.

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  7. Hiroji kurihara June 3, 2020 / 12:39 am

    Is speed of light constant !?

    To the upper right at 45 degrees in still water, plane waves of light is propagated. Above the water surface is vacuum. Value of inclination of waves in vacuum can be determined. And also speed of light waves relative to moving observer who moves in vacuum horizontally or vertically can be determined.

    How about when there is air above the water surface ? When air is stationary relative to the water, apparent difference in looks will not be found.

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  8. Hiroji kurihara May 12, 2020 / 1:12 am

    Time dilation

    Two passenger cars are passing each other. At the front of side wall of each car, the same light source (frequency is the same also) is settled and light ray is emitted backward at 45 degrees. Each ray is reflected by mirror sticked on the side wall wholely and is coming back. Time dilation is impossible.

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  9. Hiroji kurihara May 1, 2020 / 11:23 pm

    Time dilation

    In outer space ahead, two space ships are receding to the right and the left (at the same speed : aether is invalid). On the outside of each ship, the same light source is shining and this light is observed by facing ship. Time dilation (twin paradox also) will be impossible.

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  10. Hiroji kurihara March 14, 2020 / 12:40 am

    Accelerated motion of a light source

    Light emitted from an accelerated source will follow instantaneous speed of the source. In short, light will scceed the motion vector of the instantaneous speed of the source. The emission theory imply the above.

    I say again, the emission theory will be valid for a few seconds only after the emission. After this, light follows aether.

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  11. Hiroji kurihara February 14, 2020 / 7:51 pm

    Aether

    Speed of light relative to medium (water or air) is constant. Speed of light relative to aether (physical substance) is constant also. Aberrations show this.

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  12. Hiroji kurihara December 21, 2019 / 12:37 am

    No one realizes

    In air, all the effect of aether is excluded. No one seems to realize this simple picture. Like Michelson.

    Whether the result of Fizeau measurement (on light speed : with gear) veries in the direction of the optical axis relative to the celestial sphere ? And how about when it is done on the moon’s surface ?

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  13. Hiroji kurihara November 23, 2019 / 4:00 am

    Acceleration ( I say again)

    On a plane, a straight line is drawn. On this line, two bodies are receding. One is at a standstill, the other is accelerating uniformly. In space, there seems to exist uniform isotropic rest frame that distinguish acceleration qualitatively and quantitatively.

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  14. Hiroji kurihara November 15, 2019 / 10:58 am

    Reexamination of propagation of light (I say again)

    In outer space, a mirror is reflecting star light ray. Speed of reflected light relative to the mirror is constant. Speed of incident light relative to the mirror is not constant (the latter is constant relative to aether).

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  15. Hiroji kurihara November 8, 2019 / 6:31 am

    Constancy of c is nonsense (I say again)

    1) There seems not to be reliable basis of constancy of c.
    2) It is easy to disprove constancy of c. And many easy ways are possible.

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  16. Hiroji kurihara November 2, 2019 / 5:39 am

    Constancy of speed of light

    In an area where propagation of light follows the emission theory, it is constant relative to the light source. In an area where propagation of light follows aether, it is constant relative to aether. So, it cannot be constant relative to moving observers.

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  17. Hiroji kurihara September 25, 2019 / 4:18 am

    Horizontal Doppler effect

    On a plane, pararell lines are drawn. On each line, light sources (frequency is the same) are moving in the opposite direction. Imagine light sources form japanese letter エ. Phenomenon horizontal Doppler effect will not be.

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  18. Hiroji kurihara September 25, 2019 / 2:01 am

    Lorentz contraction

    In a moving passenger car, MM experiment is being done. There is a considerable difference in length between two light paths diverged by half mirror. Lorentz contraction will not stand up.

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  19. Hiroji kurihara September 25, 2019 / 1:44 am

    Speed of light

    To an observer floating in outer space, speed of light of a star is depending on the position on celestial sphere. And when the source is not distant, speed of light is depending on the motion of the source (according to the emission theory). In addition, by the motion of an observer.

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  20. Hiroji Kurihara July 20, 2019 / 1:51 am

    Constancy of speed of light

    They say, it stands up on an observer in every inertial frame. Yes, when the light source shines in that frame, it is true.

    Some man mistook this fact natural for a great discovery. And it is believed widely.

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  21. Hiroji kurihara May 5, 2019 / 10:12 pm

    Time dilation

    A light source is shinning (frequency is constant). Two observers are receding from the light source at the same speed (in the opposite direction). Two observers receive the same frequency. Whete is time dilation ?

    Below is new URL of my web site. Yahoo’s service ends on Mar 2019.
    http://lifeafterdeath.vip/eng.html

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  22. Hiroji kurihara April 30, 2019 / 12:53 am

    Lorentz contraction

    Plain waves of light (wavelength is constant) are coming from the upper right 45 degrees. Two bars of the same length are moving to the right and the left at the same speed. The number of waves hitting the bars is the same. Lorentz contraction is unthinkable.

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  23. hiroji kurihara October 17, 2018 / 3:39 am

    Light Clock

    A light clock is working in a moving train. Light path of light clock is illustrated vertically (in books). But this light clock leans somewhat to the right (or to the left). So, to an observer who stands on the ground, zigzag of the light path (saw-tooth like) warps. Two kinds of dilation ? And if two clocks work, and if these lean differs ?

    http://www.geocities.co.jp/Technopolis/2561/eng.html

    Sorry, I cannot receive E-mail. I do not have PC.

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  24. hiroji kurihara October 17, 2018 / 3:24 am

    Light Clock

    A light clock is working in a moving train. Light path of light clock is illustrated vertically (in books). But this light clock leans somewhat to the right (or to the left). So, to an observer who stands on the ground, zigzag of the light path (saw-tooth like) warps. Two kinds of dilation ? And if two clocks work, and if these lean differs ?

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    • Susan Chen January 30, 2017 / 10:18 pm

      Thank you for sharing this! The subject of your paper is a really interesting and intriguing hypothesis. I’m having a little trouble comprehending the mathematics due to my lack of mathematical knowledge (senior high school) haha

      Like

      • gregoriobaquero January 30, 2017 / 10:38 pm

        What is important is understanding the phenomenon. It is similar to how relativity explains electromagnetism Veritasium has a good video explaining it. Thank you for reading it and do not get scared with the embedded calculus. I am putting a short video to explain it in a more intuitive way.

        Liked by 1 person

      • Susan Chen January 30, 2017 / 11:27 pm

        Great, cool! Haha, I’m enjoying calculus classes in school actually, so I cannot wait until I can apply it to more physics related problems 🙂

        Liked by 1 person

  25. Jiangmin Hou January 3, 2017 / 9:17 am

    Still can’t get over your amazing writing style, your article sums up what we are doing in class nicely!

    Liked by 2 people

    • Susan Chen January 3, 2017 / 9:45 am

      Thanks a lot my friend, even though I believe your writing skills are heck of a lot better than mine! And yes this article is based on content in the Higher Physics course and I intended on writing it for a friend who told me had difficulties understanding S.R. 🙂

      Liked by 1 person

      • Jiangmin Hou January 3, 2017 / 9:48 am

        Yeah I remember you mentioning, I am sure with a post as good as yours, she will have no problem understanding it!

        Liked by 1 person

  26. Isaac Gendler January 2, 2017 / 7:47 pm

    Astounding article! Takes me back to when I was first learning about the paradoxical nature of nature. I await to see any papers you do on relativity (I would not be surprised if it’s quality matches the work you are doing right now).

    Liked by 1 person

    • Susan Chen January 2, 2017 / 7:56 pm

      Thank you very much Isaac! I’m glad it made you feel nostalgic in a sense, and haha I feel so flattered. I really do hope my future work lives up to the standard of your expectations 🙂

      Liked by 1 person

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