1. Derive the mathematical expression for the Lorentz transformation equation. relative orientation of the co-ordinate systems indicated in fig.2
A light-signal, which is proceeding along the positive axis of x, is transmitted according to the equation : x - ct = 0 _______ (1).
Since the same light-signal has to be transmitted relative to K1 with the velocity c, the propagation relative to the system K1 will be represented by the analogous formula x' - ct' = 0 _______(2) therefore: (x' - ct') = λ (x - ct) ______(3).
Here λ is constant
If we apply quite similar considerations to light rays which are being transmitted along the negative x-axis, we obtain the condition
(x' + ct') = µ(x + ct) __________ (4).
By adding …show more content…
Explain the phenomena of time dilation with the help of twin paradox.
Ans: In Einstein's special theory of relativity, there is no such thing as "time" in the singular. Time passes differently for different observers, depending on the observers' motion. The prime example is that of the two hypothetical twins: One of them stays at home, on Earth. The other journeys into space in an ultra-fast rocket, nearly as fast as the speed of light, before returning home.
Afterwards, when the twins are reunited on Earth, the travelling twin was marked younger when compared to her sibling. The exact age difference depends on the details of the journey. For example, it could be that, aboard the space-ship, two years of flight-time have passed - on-board clocks and calendars show that two years have elapsed, and both spaceship and travelling twin have aged by exactly that amount of time. On Earth, however, a whopping 30 years have passed between the spaceship's departure and its return. Just like all other humans on the planet, the twin on Earth has aged by 30 years during that time. Seeing the two (ex?) twins side by side, the difference is …show more content…
From the point of view of the twin on Earth, one can explain the age difference by appealing to Time Dilation. It involves an observer or more precisely an inertial observer, for instance an observer that lives on a space station floating through empty space. For such an observer, special relativity predicts that, for any moving clock, that observer will come to the conclusion that it is running slower than his own. Whether it is a clock on another space station floating past or a clock on an engine-driven rocket, in the time it takes for a second to elapse on the observer's own clocks, less than a second will have elapsed on the moving clock. This slowdown is true not only for clocks, but for everything that happens on the moving space station or in the flying rocket. All processes taking place on these moving objects will appear slowed down for our
A light-signal, which is proceeding along the positive axis of x, is transmitted according to the equation : x - ct = 0 _______ (1).
Since the same light-signal has to be transmitted relative to K1 with the velocity c, the propagation relative to the system K1 will be represented by the analogous formula x' - ct' = 0 _______(2) therefore: (x' - ct') = λ (x - ct) ______(3).
Here λ is constant
If we apply quite similar considerations to light rays which are being transmitted along the negative x-axis, we obtain the condition
(x' + ct') = µ(x + ct) __________ (4).
By adding …show more content…
Explain the phenomena of time dilation with the help of twin paradox.
Ans: In Einstein's special theory of relativity, there is no such thing as "time" in the singular. Time passes differently for different observers, depending on the observers' motion. The prime example is that of the two hypothetical twins: One of them stays at home, on Earth. The other journeys into space in an ultra-fast rocket, nearly as fast as the speed of light, before returning home.
Afterwards, when the twins are reunited on Earth, the travelling twin was marked younger when compared to her sibling. The exact age difference depends on the details of the journey. For example, it could be that, aboard the space-ship, two years of flight-time have passed - on-board clocks and calendars show that two years have elapsed, and both spaceship and travelling twin have aged by exactly that amount of time. On Earth, however, a whopping 30 years have passed between the spaceship's departure and its return. Just like all other humans on the planet, the twin on Earth has aged by 30 years during that time. Seeing the two (ex?) twins side by side, the difference is …show more content…
From the point of view of the twin on Earth, one can explain the age difference by appealing to Time Dilation. It involves an observer or more precisely an inertial observer, for instance an observer that lives on a space station floating through empty space. For such an observer, special relativity predicts that, for any moving clock, that observer will come to the conclusion that it is running slower than his own. Whether it is a clock on another space station floating past or a clock on an engine-driven rocket, in the time it takes for a second to elapse on the observer's own clocks, less than a second will have elapsed on the moving clock. This slowdown is true not only for clocks, but for everything that happens on the moving space station or in the flying rocket. All processes taking place on these moving objects will appear slowed down for our