Why the clock at rest runs faster, while another clock slows when moving?

Question

I have observed from my first question that it is hard for me to study the special relativity from every frame of reference. But, there is one most important question in my head right now that time runs slower for moving body if observe from rest and time runs faster in clock at rest if observe from that moving body. But, the rate at which the ticks slower for one and faster for another is different. Why it is not the same rate? Please answer in brief and simple language.

Answer 1

Please answer in brief and simple language.

If Alice and Bob are moving relative to each other with constant speed $v$, both of the following statements are true:

(1) Alice observes Bob's clock to run slow by a factor of $\frac{1}{\gamma_v}$

(2) Bob observes Alice's clock to run slow by a factor of $\frac{1}{\gamma_v}$

This is an elementary result of the Lorentz transformations that relate Alice's and Bob's spacetime coordinates. See, for example, this answer.

Answer 2

The situation is completely symmetric. Let the velocity of a frame A w.r.t another frame B is $\textbf{v}$. then from the perspective of A, the frame frame B has a relative velocity $-\textbf{v}$. From the perspective of A-observer, the clock of B-observer is slowed down and vice-versa. Note that the dialation factor depends upon the square of the relative velocity i.e., $\gamma(v)=1/\sqrt{1-v^2/c^2}$.

Answer 3

Time dilation of two clocks is related to a gravitational potential difference and to accelerations of the clocks. Moving two clocks in circles with the same diameter and th same speed (clockwise and anti-clockwise, their circle centres a little bit different not to have collision) they will show identical time during their meetings.

Not the same time one will get in the cases

• the clocks are on different high above the ground (in different gravitational potential)
• the clocks moving in circles with different diameters or different speed.

Answer 4

Einstein's postulates entail SYMMETRICAL time dilation - either clock is slow as judged from the other clock's system. Instead of honestly deriving this in 1905, Einstein derived, fraudulently and invalidly of course, ASYMMETRICAL time dilation - in his 1905 article the moving clock is slow and lags behind the stationary one which is, accordingly, FAST (this means that the moving clock and its owner travel into the future - if their speed is great enough, they can jump, within a minute of their experienced time, millions of years ahead):

http://www.fourmilab.ch/etexts/einstein/specrel/www/ ON THE ECTRODYNAMICS OF MOVING BODIES, A. Einstein, 1905: "From this there ensues the following peculiar consequence. If at the points A and B of K there are stationary clocks which, viewed in the stationary system, are synchronous; and if the clock at A is moved with the velocity v along the line AB to B, then on its arrival at B the two clocks no longer synchronize, but the clock moved from A to B lags behind the other which has remained at B by tv^2/2c^2 (up to magnitudes of fourth and higher order), t being the time occupied in the journey from A to B."

So even if Einstein's 1905 postulates were true (actually the second one is false), physics would still be dead by now, corrupted by the metastases of the asymmetrical time dilation (moving clocks run slower than stationary ones) invalidly deduced by Einstein in 1905.