![]() ![]() ![]() When negative and positive charges meet, it produces streaks of bright light and sound and the process is known as an electric discharge. The process of transferring of charge from a charged object to the earth is known as earthing. Some natural phenomena can cause large scale destruction of human life and property. When charges move, they constitute an electric current. ![]() When a plastic comb is rubbed with dry hair, it acquires some charge and the object is known as charged objects. are the natural phenomena.īenjamin Franklin, an American scientist, showed that the lightning and the spark from clothes are essentially the same phenomena. Physics Notes for UPSC IAS Prelims (Part I).This expression can be used to determine p*c, and that value can be compared to the original value of the momentum for one of the particles to determine the values of for β and γ necessary for the transformation. Where p*c has been used to represent the value of each momentum since they are constrained to be equal. Now evaluating the length of the momentum-energy 4-vector from the experimental information we have in the laboratory frame gives the quantity s above.Since s can be evaluated from laboratory information, we can concentrate on the expression for s in the zero-momentum frame. That's where the invariance of the length of the energy-momentum 4-vector is of value. While this gives the form of the necessary transformation, we don't know the values for β and γ necessary to achieve the zero-momentum condition. Transforming this to the zero-momentum frame One approach to this for a two particle system involves adding the momenta and energy for the two particles: The practical advantage of this for high energy collisions is that it allows you to calculate the momentum of each particle in the zero-momentum frame. For the two particles, you can determine the length of the momentum-energy 4-vector, which is an invariant under Lorentz transformation. The momenta of two particles in a collision can then be transformed into the zero-momentum frame for analysis, a significant advantage for high-energy collisions. The length of this four-vector is an invariant Two momentum-energy four-vectors can be summed to form a four-vector. The space-time Lorentz transformation produces the result:Īnd the energy-momentum 4-vector transforms as The Lorentz-transformation of both space-time and momentum-energy four-vectors can be expressed in matrix form. The invariance is associated with the fact that the rest mass is the same in any inertial frame of reference. The length of this 4-vector is the rest energy of the particle. The length of the energy-momentum 4-vector is given by This expression can be seen to be the equation of a sphere, with light propagating outward from the origin at speed c in all directions so that the radius of the sphere at time t is ct. This invariance is associated with the constancy of the speed of light. The length of a 4-vector is invariant, being the same in every inertial frame. The length of the space-time 4-vector squared is given by That minus sign is necessary for the property of invariance of the length of the 4-vectors. Note that this differs from the ordinary scalar product of vectors because of the minus sign. The scalar product of two space-time 4-vectors is defined byĪnd the scalar product of two energy-momentum 4-vectors by The energy-momentum 4-vector is defined by The invariance of the energy-momentum four-vector is associated with the fact that the rest mass of a particle is invariant under coordinate transformations. The invariance of the space-time four-vector is associated with the fact that the speed of light is a constant. This invariance is associated with physical ideas. They are defined so that the length of a four-vector is invariant under a coordinate transformation. In the literature of relativity, space-time coordinates and the energy/momentum of a particle are often expressed in four-vector form. Four-vectors in Relativity Four-vectors in Relativity ![]()
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