Einstein mass energy relation discussion and derivation

Einstein’s mass energy relation:

You must have known the relation E = mc2. Let us derive it:

Derivation:

Consider an object of rest mass m’. If force is applied to the object such that it starts moving with relativistic velocity (that is comparable with the speed of light), then its mass will also vary with variation of mass with velocity relation

m = m’/(1-v2/c2)1/2 (1)

Now suppose that work dw will be done due to this force. If the object is displaced along x axis, then work will be:

dw = Fdx

or  dw = (dp/dt)dx      (because from Newton’s 2nd law F = dp/dt)

or  dw = [d(mv)/dt]dx   (because p =mv)

Differentiate R.H.S.

dw = (mdv/dt + vdm/dt)dx    (here m is also a variable quantity, thus m is also differentiated)

or dw = mdvdx/dt + vdmdx/dt

or dw = mvdv + v2dm                                       (2) Continue reading “Einstein mass energy relation discussion and derivation”

Time dilation in relativity derivation

Last time we have discussed and derive the length contraction in relativity, let us today discuss the concept of time dilation and derive the relation for time dilation.

Let us today discuss and derive an interesting concept in relativity called the time dilation. You must be astonished to know that when an object moves with a speed comparative to the speed of light, its time dilated or more appropriate term is that it is appeared to move slow. Continue reading “Time dilation in relativity derivation”

Length contraction in relativity derivation

Let us today discuss and derive an interesting concept in relativity called the length contraction. You must be astonished to know that when an object moves with a speed comparative to the speed of light, its length contracted or more appropriate term is that it is apparent length contraction in relativity.

Let us start to discuss and derive why the length contraction occur in relativity: Continue reading “Length contraction in relativity derivation”

Einstein postulates of theory of relativity

Explanation of the negative results of the Michelson-Morley experiment:

As the theoretical results of the M-M experiment did not match with the experimental results (Theoretically fringe shift result was not zero, it was about 0.4 but the experimentally it was 0). Even then the scientists of that time had conviction that ether exist and earth moves with respect to it. Thus there was lot of debate and discussion regarding this as why there were negative results (that is why the theory and experiment result did not match?).

Following are the reasons given by the scientists:

1.  Ether Drag Hypothesis: The then scientists assumed that ether exits and it is attached with the earth. Thus it will be dragged with the earth so the relative velocity of ether and earth will be zero. If this is taken then theory and experimental will get matched. But this hypothesis is discarded as there was no proof for this.

2. Lorentz-Fitzgerald Hypothesis: Lorentz told that the length of the arm (distance between the pale and the mirror M2) towards the transmitted side should be L(√1 – v2/c2) but not L. If this is taken then theory and experimental will get matched. But this hypothesis is discarded as there was no proof for this.

Einstein explanation of negative results of M-M experiment: Continue reading “Einstein postulates of theory of relativity”

Galilean transformation equations derivation

Let there are two inertial frames of references S and S’. S is the stationary frame of reference and S’ is the moving frame of reference. At time t=t’=0 that is in the start, they are at the same position that is Observers O and O’ coincides. After that S’ frame starts moving with a uniform velocity v along x axis.


Let an event happen at position P in the frame S’. The coordinate of the P will be x’ according to the observer in S’ and it will be x according to O in S. Continue reading “Galilean transformation equations derivation”

The concept of Relativity and frames of reference

The concept of Relativity and frames of reference:

The term relativity comes from the word “relative that is in relation”. In this universe, everything is relative, there is nothing like absolute rest. If you think that you are sitting somewhere and you are in the state of rest, then my dear you are wrong. You are also in the state of motion, because if someone is able to see you from outside the earth (suppose from moon), then you are also moving. Therefore, everything is relative.

Here question arises with respect to which we can study the motion of another object? This problem is solved with the concept of frame of reference.

Definition: The frame of reference is defined as any coordinate system with respect to which one can study the motion of the another object. For example, a bus can be a frame of reference with respect to which one can study the motion of another object.

Types of the frame of reference: Continue reading “The concept of Relativity and frames of reference”