What is the theory of relativity?

Published by Rahul Aggrawal on

albert einstein's theory of relativity

What is the theory of relativity?

Let us start with a simple example. Abhi and Rama decide to meet at a candy store. Abhi approaches the candy store from one end and Rama approaches the candy store from the other end of the straight road. Abhi says the candy store is to his left and Rama says it is to his right. Who is correct? Both.

From the above example, it is clear that we need to define something called an ‘observer’. Abhi and Rama here were our two observers. Each of them was right from his own perspective. They do not agree with each other about ‘left’ and ‘right’ but both would agree that it is a candy store!
Observer along with a measuring stick to measure lengths and clock to measure time constitutes a frame of reference.
Law of addition of velocities
Consider three observers A, B and C. A is riding a motorcycle, B is sitting inside a train and C is standing on a footpath. As a simple case let us take this to be a 1-D problem. Velocity of A cannot be specified unless you mention the observer who is measuring the velocity of A. Let us say velocity of A with respect to C= v and velocity of B with respect to C=u. Then the law of addition of velocities says that =-.
means velocity of A with respect to B or velocity of A as seen from B.
This law of addition holds for accelerations as well.

Inertial frames of reference in the theory of relativity:
Newton’s first law states that a body continues to be in its state of rest or of uniform motion unless an external force acts on it. This is valid only in the case of inertial observers or other word for it, inertial frames.
In a moving train, sometimes you notice trees on the ground moving backwards. If the train is moving with constant velocity ‘v’ with respect to the ground then the trees appear to move with a constant velocity v backwards. No external force acts on the trees backwards, hence they will continue to move with same velocity v backwards as seen from the train. Hence this does not violate Newton’s first law.
However let us say the train is accelerating forward, then as seen from the train the tree appears to accelerate backward. No external force acts on the tree in opposite direction, yet it appears to accelerate (not uniform motion). This implies that Newton’s laws hold good only in inertial frames or frames which move with constant velocity.
The train observer in the first case was inertial while in the second case was non-inertial.
Galilean Relativity
Abhi and Rama are playing tennis on stationary ground. Now if they play tennis on a ship moving smoothly (i.e. with constant velocity) then they will not be able to tell whether the ship is moving or it is stationary on condition that they are not looking outside the ship.
This can be commonly seen in train journeys. When all the windows are closed, we can hardly make out sitting in the train whether the train is at rest or it is moving. (moving with constant velocity).
However, if the train or ship accelerates or takes a turn we can feel it without having to look outside, like we feel extra pressure on the seat etc.
Principle of relativity as stated by Galileo states that all inertial frames are equivalent and Laws of mechanics hold good equally in all inertial frames.
In Galilean relativity mass, length and time are invariant from one frame to another. Velocities, accelerations etc. depend on frames of reference.
Einstein’s theory of relativity
Einstein observed that principle or the theory of relativity could be extended to laws of electromagnetism.
Speed of light ‘c’ in vacuum is a fundamental constant which depends on properties of vacuum space and not on any velocity. Speed of any wave (light or sound) does not depend on the speed of source of the observer, it only depends on the medium.
Combining these two facts and the principle of relativity as extended by Einstein, we can say that speed of light in vacuum is constant with respect to any inertial frame of reference.
In Einstein’s framework length, mass, time also change depending on the observer.

The frame of Einstein

-Balaji Dodda


Rahul Aggrawal

I am a teacher and a theoretical physicist. Physics gives me pleasure and teaching physics gives me stable happiness. For More info visit www.rahulaggrawalphysics.blogspot.com

58 Comments

hiroji kurihara · October 5, 2018 at 11:42 pm

External Force (reexamination)

The core will be not external force but accelerated motion and inertial force (e.g. in F = ma). Vector of accelerated motion and inertial force are corresponding qualitatively and quantitatively (without exception). On the other hand, how about external force ? Imagine balanced plural external forces. Imagine rotating disk. External force seems not to be core.

And inertial force (caused by motion relative to aether frame) must not be fictitious force.

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Hiroji Kurihara · March 17, 2019 at 1:04 am

Gravitational acceleration

Who started to say gravitational acceleration ? Is it a technical term really ? It seems to be an adjective.

Is there a difference between an acceleration caused by an ordinal force ? If there is not a difference, a thing called gravitational acceleration will not exist.

Hiroji Kurihara · April 2, 2019 at 3:13 am

Turn your eyes to accelerated motion and inertial force. It does not matter what gravity is.

Hiroji kurihara · April 30, 2019 at 5:33 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.

Hiroji kurihara · May 26, 2019 at 5:57 am

Reconsideration of space-time

Our motion will not affect space-time. Our motion is various and space-time is one and only. And every relative speed will follow Galilean transformation. Including speed of light.

Hiroji kurihara · May 27, 2019 at 3:34 am

Speed of light

Plane waves of light (frequency 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. In the formula lightspeed=wavelength x frequency, wavelength is the same (number of waves hitting the bars is the same) and the two will not be the same.

Hiroji kurihara · May 30, 2019 at 12:53 am

Free fall

Are the two indistinguishable? Vector of the two are opposite.

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Hiroji kurihara · May 31, 2019 at 1:47 am

Equivalence principle

In space, there are two gravitational sources (point source). In the middle of the two, a small area is selected. This area will be weightlessness (not zero gravity). Like an elevator in free fall.

Hiroji kurihara · June 4, 2019 at 2:08 am

Bremsstrahlung

A website says, “A charged particle is decelerated. And energy of motion is emitted as electro magnetic waves”. But difference between deceleration and acceleration will be relative seen from inertial frames. Or, phenomenon bremsstrahlung depends on the absolute rest frame?

Hiroji kurihara · July 2, 2019 at 7:10 am

Free fall

Vector of gravity and vector of inertial force are said to be indistinguishable. But direction of the two is opposite.

Vector of gravity and vector of inertial force are ubiquitous around us. And resultant forces are the same also. Why they make a big fuss on an elevator in free fall ?

Inertial force ma is said to be a virtual. If so, mg in free fall will be the same. And normal force will be virtual.

Hiroji Kurihara · July 20, 2019 at 1:25 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.

Hiroji kurihara · September 23, 2019 at 10:54 pm

Difference of motion

Difference of inetrial motion and accelerated motion will be the difference of the motion relative to aether frame. And accelerated motion and inertial force are the front and back of a fact. Inertial force is not fictitious.

Hiroji kurihara · September 24, 2019 at 1:45 am

Free fall

There are inumerable vectors of inertial forces and gravity everywhere. On an elevator cabin, why they are making a big fuss ?

Hiroji kurihara · September 24, 2019 at 8:50 am

Free fall and non free fall

Imagine various density of air. An elevator cabin is falling (in non free fall). On a desk, all will be clarified by hydrodynamics. Data will deny the equivalence principle.

Hiroji kurihara · September 25, 2019 at 5:01 am

Speed of light

To an observer floating in outer space, speed of light of a star is depending on the position of the celestial sphere. And when the light 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.

Hiroji kurihara · October 15, 2019 at 1:50 am

Equivalence principle
The two forces the same strength are acting on a particle from the opposite. The two are inertial force, tension and gravity. Different combinations are three. Forget the equivalence principle.

Hiroji kurihara · November 2, 2019 at 11:29 pm

Is speed of light constant (uniform) ?

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.

Hiroji kurihara · November 3, 2019 at 2:16 am

A web site on anti relativity

A site above written by member voluntees of Japan science council is now being published (in Japanese). Below is URL.
http://reriron.kage-tora.com

Hiroji kurihara · November 4, 2019 at 4:48 am

Basis of special relativity

We seem to measure c only by the light source situated on the same inertial frame. A web site says, reasonable basis of constancy of c cannot be found in web ( with three words).

Hiroji kurihara · November 8, 2019 at 6:10 am

Constancy of c is nonsense (I say again)

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

Hiroji kurihara · November 15, 2019 at 10:40 am

Reexamination of propagation of light (I say again)

In outer space, a mirror is reflecting a 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).

Hiroji kurihara · November 17, 2019 at 12:33 am

Inertial force is not fictitious

On a plane, there are two bodies. One is at a standstill, the other is accelerating. Acceleration (a) and inertial force (ma) both are not fictitious.

There are two disks. One is not rotating, the other is rotating. Acceleration and inertial force both are not fictitious.

Hiroji kurihara · November 19, 2019 at 5:50 am

Acceleration

From nothing, a seems not to emerge. By acceleration of body relative to aether, am will emerge. Qualitatively and quantitatively.

Hiroji kurihara · December 8, 2019 at 12:55 am

Elf fires

Are there still berievers of relativity ? Elf fires. It is not a things of this world.

Hiroji kurihara · December 20, 2019 at 2:45 am

No one realizes

In air, all effect of aether is excluded. No one seems to realize this simple picture. Not only Michelson.

Whether the result of Fizeau measurement (on light speed ; with gear) varies in the direction of optical axis relative to the celestial sphere ? And how about when it is done in vacuum ?!

Hiroji kurihara · December 23, 2019 at 8:48 am

Glass and light (I say again)

From the right, star light is coming. Two cubes of glass are moving toward the star at different speed. In the glass, speed of light is c/n : the same. Because in the glass, light emitted from particles follows the emission theory. By the way, let’s see the light before arriving (from the glass). Wavelength is the same. Frequency and lightspeed are not the same.

Hiroji kurihara · January 6, 2020 at 1:50 am

Equivalence principle (I say again)

Vector of inertial force is shown by an arrow. Vector of gravity cannot be shown by an arrow generally. These are different as physical facts.

Hiroji kurihara · January 12, 2020 at 4:19 am

Accelerated frame and non-accelerated frame

There are plural accelerated frames and plural non-accelerated frames. The two will not be relative.

Hiroji kurihara · February 14, 2020 at 2:59 am

Aether

Speed of light relative to mediums (water and air) is constant. Speed of light relative to aether (physical substance will be) will be constant also. Aberrations show this.

Hiroji kurihara · March 7, 2020 at 4:53 am

About inertial force (I say again)

On a plane, there are two passenger cars. One is accelerating and the other is at a standstill. Difference of the motion of the two is not relative but absolute.

On a plane, a passenger car is accelerating. On the floor (no frection), a body is put. This body is not accelerated (to everyone). In physics of 20th century, nonsenses overflow.

Hiroji kurihara · March 11, 2020 at 7:56 am

Sagnac effect

Let’s try to explain Sagnac effect by the emission theory. There is a picture of light pathes (a light source and two mirrors form equilateral triangle). On this triangle, there are three emission points (different inertial frames). It will be a cause of this effect.

Hiroji kurihara · March 13, 2020 at 9:56 pm

Accelerated motion of light source

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

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

Hiroji kurihara · March 21, 2020 at 10:51 pm

Propagation of light (I say again)

Light is propagated in three ways (as follows).
1 In mediums, speed of light is c/n. M M experiment will be invalid.
2 In outer space, star light is reflected by a mirror. Speed of incident light is constant relative to aether.
3 In outer space, star light is reflected by a mirror. Speed of reflected light is constant relative to the mirror.

In three pictures above each, speed of light to a moving observer follows Galilean transformation.!

Hiroji kurihara · March 28, 2020 at 11:51 pm

Aether

Aether exists undoubtedly. However, in loboratories on the earth, no effect caused by aether drift seems to be observed (on such as particles). Aether (absolute space) is mysterious yet.

Hiroji kurihara · March 31, 2020 at 2:09 am

All of light speed (I say again)

All of light speed is shown in aberration. One is that in outer space, speed of light is constant relative to aether. Every motion of the light source is cancelled. The other is that light speed is not constant relative to moving earth.

Hiroji kurihara · April 13, 2020 at 12:20 am

On acceleration, there is a web site.

“Orders of magnitude (acceleration) – Wikipedia”

Hiroji kurihara · April 17, 2020 at 1:29 am

Acceleration and nonacceleration

A passenger car is accelerating (uniformly). A body is hung from the roof, a body is placed on the floor ( no friction) and a station building. Physics seems not to distinguish the three.

Hiroji kurihara · April 27, 2020 at 3:55 am

Time dilation

Ahead of us, a light source is shining. On the left space, two space ships are passing each other (horizontally : at the same speed). How is difference of frequency of light observed by space ships explained ?

Hiroji kurihara · May 1, 2020 at 9:44 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 outside of the ship, the same light source is shining and this light is observed by facing ship. Time dilation (twin paradox also) will be impossible.

Hiroji kurihara · May 3, 2020 at 3:30 am

Perihelion shit of Mercury

Mercury revolving is devided in two (hemisphere facing the sun A and the other B). Inertial force is A<B and gravity is A>B (center of gravity is not on the orbit).

Hiroji kurihara · May 4, 2020 at 1:14 am

Perihelion shift of Mercury

Yesterday’s post must be the most natural explanation of perihelion shift of Mercury. Because the value of perigee movement of the moon is remarkable (around 8.85 years). On the other hand, value of asteroids will not be found. Common explanation is not acceptable.

Hiroji kurihara · May 6, 2020 at 4:31 am

Perihelion shift of Mercury

Perihelion shift moves forward constantly. It cannot be explained by gravity of other planets.

On asteroids, no perihelion shift will be observed. Some size will be needed.

Cause of perigee movement of the moon is written to be the sun. Not understandable. Because it will be the same phenomenon to perihelion shift of planets.

Hiroji kurihara · May 19, 2020 at 8:42 pm

Equivalence principle (I say again)

An elevator cabin is accelerating horizontally (no friction : at 2g). At every mass point (at every infinite small area), acceleration is 2g.

Hiroji kurihara · June 3, 2020 at 6:07 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.

Hiroji kurihara · June 4, 2020 at 3:11 am

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.

Hiroji kurihara · June 7, 2020 at 6:00 am

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.

Hiroji kurihara · June 11, 2020 at 8:12 am

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).

Hiroji kurihara · June 11, 2020 at 8:18 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.

Hiroji kurihara · June 15, 2020 at 5:08 am

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.

Hiroji kurihara · June 16, 2020 at 4:07 am

Perihelion shift of Mercury

This is the top of tall tower. Two rods of equal mass and different length are arranged vertically (heigth of center of gravity is the same). Now, two rods start to fall at the same time. The fall of center of gravity will not be the same. Because the strength of gravity is inversely proportional to the square of the distance. This will be the main cause for perihelion shift of Mercury.

Hiroji kurihara · June 20, 2020 at 10:33 am

Perihelion shift of Mercury

Mercury has an own size as a sphere. Therefore, the sun’s gravity will have a different effect on Mercury than it does on the center of gravity. Strength of gravity is inversely proportional to the square of the distance. Actual orbit will be different from that the center of gravity must follow. On Mercury, it will be the main cause of the perihelion shift.

Hiroji kurihara · June 24, 2020 at 9:53 am

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.

Hiroji kurihara · June 26, 2020 at 6:55 am

Perihelion shift of Mercury

In an binary system (formed by main star and companion star), periapis is shifted also. Motion of companion star (apsidal shift) will be depending considerably on its size. Common view (says main cause is pertubation of other planets) will be invalid.

Main cause of perihelion shift of Mercury is said to be gravity of the other planets. But position of other planets move (also position of perihelion of Mercury moves). If so, values 5.75 secarc/year is unthinkable. Main cause lwill be in Mercury itself. And also it will be the same on values of perihelion shift of the other planets.

Hiroji kurihara · July 8, 2020 at 5:25 am

Perihelion shift of Mercury (the truth)

In Mercury (in terms of Mercury’s size), the non-uniformity of the Sun’s gravity may be the main cause of perihelion shift. In artificial satellites, the effects of non-uniformity of the Earth’s gravity (the position of the center of mass and the center of gravity are different) are also mentioned.

Hiroji kurihara · July 10, 2020 at 6:12 am

Perihelion shift of Mercury (rewritten)

Mercury is moving on the revolution orbit. The sun’s gravity is equal to the centrifugal force. Because the two are action and reaction. Following are some explanations. Centrifugal force follows Mercury’s mass. But in addition, gravity is affected by the size of Mercury (and acting position of gravity is different). These are caused by the non-uniformity of gravity (in the space occupied by Mercury). And after perihelion passage, orbit will be pulled inward (from its original orbit).

High tide level twice a day is the same. Gravity and centrifugal force caused by the moon will be action and reaction. Centrifugal force is not fictitious.

Hiroji kurihara · July 19, 2020 at 4:33 am

Moon and Earth (additional)

Suppose the moon and the earth is two-body problem. And imagine, the earth is revolving (not rotating) around the common center of gravity with the moon. The orbit is a perfect circle. If lunar attractive force acting on the center of gravity of the earth is action, the centrifugal force of the earth is a reaction. And the strength of the two will be equal. This will be also true for the earth as a whole.

In an illustration, the earth is drawn next to moon. Imagine two points on the surface of the earth closest to the moon and farthest from the moon. The difference between lunar attractive force and the centrifugal force of the earth at above two points will be almost equal and therefore the resultant force will also be almost equal. This will explain that the level of high tides twice a day are almost equal.

Note: Is the law of action and reaction valid for celestial bodies on elliptical orbits?

Hiroji kurihara · August 21, 2020 at 5:59 am

Perihelion shift of Mercury (again)

The main forces acting on Mercury are attractive force of sun and centrifugal force only. Hemisphere of Mercury facing sun is supposed to be A and the other hemisphere is B. The attractive force of the sun acting on the two will be A>B, and the centrifugal force will be B>A. From the look of the perihelion shift, the attractive force acting on Mercury as a whole will be slightly stronger.

Hiroji kurihara · August 29, 2020 at 11:19 pm

Perihelion shift of Mercury (an essay)

A celestial body called Vulcan is revolving on orbit of Mercury. It has the same mass and revolution cycle as Mercury. And diameter is twohold (the both stars are uniform in density). Since the sun’s gravitational field is non-uniform, the sun’s gravity acting on both stars will be slightly larger in Vulcan and smaller in Mercury. The value of perihelion shift also likely will be similar. In short, the size of the celestial body (close to the gravitational source like Mercury) will be the main reason for the perihelion shift.

Imagine a cone with evenly spaced concentric circles on its surface. The non-uniformity of gravity will be exponential non-uniformity.

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