In fact, no such experiment to determine absolute velocity relative to space is possible. The speed of light is constant and we always obtain the same number when we try to measure it. The speed of light is determined by fundamental constants:and so is also constant.

]]>A

The waves move at a speed defined by the equationIf the source itself is moving at a speed close tothen it nearly keeps pace with its own spherical wave fronts as shown in the top diagram below.

In the second diagram the speed of the source is larger than the speed of the wave. When the source S was at positionit generated wavefrontand when it was at positionit generated wavefrontAll the spherical wavefronts expand at the speedand their boundaries move along the surface of a cone. In the case of a wave source in a fluid like water or air, the cone signifies a shock wave and is referred to as the Mach cone. The surface of this cone has half-angleand is tangent to all the wave fronts. A similar effect occurs for light when an electrically charged particle traverses a dielectric medium at speeds that are greater than those of light in that medium. In this case, the electric and magnetic fields associated with a rapidly moving charge excite the atoms of the medium. The excited atoms emit part of their light in the form of a coherent wavefront of radiation at fixed angle with respect to the trajectory of the charged particle as shown below.

To be precise, this radiation, named Cerenkov radiation after its discoverer, is produced whenever the velocity \beta c of the particle exceedswhereis the speed of light in a vacuum,is the refractive index of the medium traversed by the charge, andis the usual relativistic factor

ifis the velocity of the particle. For most cases, energies are high enough for us to assumeFrom the diagram above, we can see that the light cone formed in Cerenkov radiation has a valueThe radiation appears as a continuous spectrum. In a dispersive medium, bothandare functions of the frequency of radiation. The number of photons at a particular frequency or wavelength, as it turns out, is proportional to This means that, in the visible range, blue light predominates over all other colours. The blue glow that emanates from the water in which highly radioactive nuclear reactor fuel rods are stored is caused by the Cerenkov effect. For fuel rods, much of the radiation they emit is in the form of high energy electrons. The electrons travel through the water at a velocity greater than that of light in water and hence cause the characteristic ``Cerenkov glow''.

]]>The theory also predicts that moving bodies appear to be shorter. The faster a body moves, the shorter it appears to be. If the body is a spaceship with people on board, it will not appear to be shorter according to those people. It will appear to be the same length. In fact if the spaceship is moving with uniform velocity, they will not be able to determine if the outside world is stationary or the spaceship. If the velocity of the spaceship relative to the outside world is V, then the velocity of the world relative to the spaceship is -V. Velocity is truly relative, and if the spaceship appears to be shorter relative to an observer, then the observer appears to be shorter relative to the observers on the spaceship.

Time passes more slowly for moving objects. The faster a body moves, the more slowly time appears to pass. If the body is a spaceship with people on board, time will not appear to move slower according to those people. It will appear to be move at the same normal rate that time moves. It will only appear to move more slowly for those observers relative to whom the spaceship is moving. In fact if the spaceship is moving with uniform velocity, they will not be able to determine if the outside world is stationary or the spaceship. If the velocity of the spaceship relative to the outside world is V, then the velocity of the world relative to the spaceship is -V. Velocity is truly relative, and if the time on the spaceship appears to be move more slowly relative to an observer, then the time for the observer appears to be pass more slowly for the observers on the spaceship.

]]>The Universe is full of mass and energy, so of course the universe is curved on a large scale. A beam of light sent from a point might either keeps going forever, if space is flat or negatively curved, or travels in a large quasi – circular curve if space is positively curved.

]]>Our concept of mass also has to change. An object has a rest mass,the mass of an object when measured by someone at rest relative to the object. If the object is moving its mass increases asand so does its energy. The energy of an object is

Because the object is moving it has kinetic energy. The familiar equation of kinetic energyno longer applies. Instead we write kinetic energy as the difference between the energy a particle has when it is at rest and when it is moving.

(1)

Ifis much smaller thanas it is for most of us in our small lives here on Earth, then we can use the binomial expansion to rewrite (1) as

since v/c is small

]]>It is important to realise that most quantum mechanical calculation only use the principles and equations of quantum mechanics. Gravity is not taken into account because gravity is so weak compared to the other fundamental forces. Only in extreme situations such as in the interior of a neutron star, do we need to include gravity in some way because we must balance the neutron degeneracy which stops the star from collapsing with the force of gravity which stops the star exploding. In these situations the calculations are extremely complex and not the result of a single physical theory, but an approximation forced by the use of two fundamentally incomplete theories to model phenomena outside the range they may be used to model – scientists may be using extrapolation to expand the theories beyond the range at which they are valid. While not good practice, the limitations of the theories we have make this the best option.

]]>If two events 1 and 2 occur at the points in spacetime with coordinatesand and these are the measuring of the ends of a ruler which is stationary in O', and we assume that these events happen at the same time in O so thatthen the distance between the two events isin O'. We can use the Lorentz transformation to find the distance between the two events as measured in O.

(1)

(2)

(2)-(1) gives

Hence we can writewhereandare the lengths of the ruler in O and O' respectively. ]]>

In coordinate system O the event indicated has coordinates

In coordinate system O' the event indicated has coordinateswhere

The reverse transformation can be applied by replacingbyand interchangingandandandandand

]]>>

Each event P could be uniquely labelled by three space and one time coordinate,and all observers could agree on the coordinates of each event.

From antiquity into the eighteenth century, contrary views which denied that space and time are real entities maintained that the world is necessarily a material plenum. Concerning space, they held that the idea of empty space is a conceptual impossibility. Space is nothing but an abstraction we use to compare different arrangements of the bodies constituting the plenum. Concerning time, they insisted, there can be no lapse of time without change occurring somewhere. Time is merely a measure of the cycles of change within the world.

Associated with these issues about the status of space and time was the question of the nature of true motion. Newton defined the true motion of a body to be its motion through absolute space. Those who, before or shortly after Newton, rejected the reality of space, did not necessarily deny that there is a fact of the matter as to the state true motion of any given body. They thought rather that the concept of true motion could be analyzed in terms of the specifics of the relative motions or the causes thereof. The difficulty (or, as Newton alleged, the impossibility) of so doing constituted for Newton a strong argument for the existence of absolute space.

]]>The observer on the right is stationary in his reference frame, and the observer on the left sees the other moving to the right with speed

The observer on the right bounces a light signal between the ceiling and the floor. It takes a timeto return to the floor, so that

The observer on the left sees the moving framer of reference moving to the right, and will see the ray of light travel a distancein a timewhereHe will observe the ray of light to take a timeto return to the floor, so that

Substituteandinto

Square both sides to give

hence

Move the last term to the left.

Divide byto give

Factorise withto give

Hence

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