User:DhawanRohit/sandbox

As the Figures for the work are not being uploaded so for clarity about the concept with figures and equation I am giving a link where the same work is published properly.

'''https://mecsci.blogspot.com/2018/06/modification-to-time-dilation-formula.html '''

Tilting the Einstein’s Clock  Rohit Dhawan'''

(Ph.D. scholar)

Department of Mechanical Engineering, D.C.R.U.S.T Murthal, Sonepat, Haryana, India

Email: - rohitdhawan28@gmail.com

Abstract''': - This work is just a simple extension to Einstein’s Time dilation theory. But the outcomes of the work are quite interesting and tells a bit more about the way the Time behaves with the addition of motion. Till now we are only aware about the fact that the time is not absolute and is different for different observers according to their reference frame works. The current work focuses about the rate at which time flows in different directions. The findings of the work reveals that, in the same reference frame work, time varies at a different flow rate in different directions. Key words: - Time dilation, theory of relativity, time flow rate.

I.INTRODUCTION: - Time theory dates back to the revolutionary theory put forth by Sir Albert Einstein in 1905 widely known as the “Theory of Relativity”. Let us traverse through this theory of time. The foundations for the time dilation were established by the renowned work of Einstein’s special relativity. The theory follow the concepts of constant speed of light and the other one is that observers moving at same speed follows the similar laws of the physics. The time dilation theory uses the thought experiments of light bearm traversing along a vertical direction in a horizontally moving object. To understand the concept of time dilation assume a light clock with a light source (at the bottom) and the reflector (at the top) as shown in the Figure.1. This light clock along with observer A is placed on a moving object such as an aeroplane or train etc. A similar light clock is also available in stationary reference frame of the observer B. The light is emitted from source L and it reaches the reflector R and bounces back to source L. This one cycle of light beam corresponds to one tick of the light clock. Suppose the distance between L and R is ‘D’. Both of the clocks are well synchronized. In a situation when moving clock is in rest position, then both of the clocks will tick simultaneously. But as soon as the train starts to move, the situation starts to change and some different phenomenon comes in to existence. The phenomenon is going

Figure 1 Light clock to be named as time dilation after a few lines. Now for observer A of the moving train the clock 1 (moving clock) will tick at a normal rate. For observer A light is travelling the distance 2*D in one tick of the clock. As we know that speed = distance / time so time is equal to distance/speed., Time in moving train = 2D / C where C – speed of light. Or  T = 2D / C        							                       -                  (1) But for the stationary observer B, the scenario is somewhat different. What he observes regarding the moving clock is a different issue. According to observer B, the light beam of moving clock is not traversing a distance of 2 D but a somewhat greater distance as shown in Figure. 2

Figure 2  Moving light clock Now as speed of light is constant for both the observers and for observer B the light beam of moving clock is travelling a greater distance so time for B = New_distance/speed. or T ’ = 2 L / C                                                                                                              -            (2) As New_distance > distance 2 D so New_time > time. Thus for observer B the moving clock is showing more time than the clock in his stationary reference framework, which ultimately means that according to observer B time is passing slowly on moving train. Suppose the train is moving with a velocity V, then (for stationary observer B) the distance travelled from L1 to L2 =  (1/2(V*T')), Distance from L2 to R2  =  D, Thus according to  Pythagoras theorem L=√((1/2(V*T'))^2+D^2 )                                                                                                                                          -                   (3) After eliminating L and D from equation 1, equation 2 and equation 3 the result is

T'=T/√(1-V^2/C^2 )                                                                                                                   -                  (4) II. TILTED LIGHT CLOCK: - Thus from equation (4) it is clear that time period for moving clock is greater than the time period for stationary clock. This is the main essence of the theory of relativity which depicts that the time in not absolute and it changes according to observer’s frame of reference. Till now it is all about the work for which train is moving horizontally and light beam of light clock is moving vertically. Now suppose that the Einstein’s clock is not positioned vertically but is tilted at an angle α with the horizontal direction as shown in Figure. 3.

Figure 3 Tilted light clock In the case train is stationary, the distance between light source and reflector = T * C, thus vertical distance between light source and reflector is T*C*Sinα. Now suppose that the train is moving with any velocity V, in that case the distance between light source and reflector is T*C but for stationary observer B, the distance travelled by light beam is T’*C as is shown in the Figure. 4. Now the horizontal distance travelled is equal to T’ * V and vertical distance is equal to                       T * C * sin α. Thus according to Pythagoras theorem 〖T'〗^(2 )=((T^2*C^2*sin^2 α)+(V^2*〖T'〗^2))/C^2                                                                      -                       (5)

Figure 4 Moving tilted light clock (only half cycle shown) T^2*sin^2 α=〖T^'〗^2-((V^2*〖T^'〗^2 ))/C^2                                                                                   -                      (6) =〖T^'〗^2 (1-V^2/C^2 )                                                                                     -                      (7) 〖T'〗^2=((T^2 * sin^2 α))/((1-V^2/C^2 ))                                                                                      -                      (8)

T^'=(T*sin⁡α)/√((1-V^2/C^2 ) )                                                                                                  -                     (9)

T’ = γ * (T *Sin α)		                          			                                               --	               (10) Thus whatever may be the speed of train, time in moving train varies according to ‘α’. Thus time becomes zero for α = 00 and α = 1800 i.e there is no existence of time in horizontal directions for this case (when train is moving horizontally and clock is also placed horizontally). Similarly time dilation will be maximum for α = 900 and it will start decreasing from α = 900 to α = 1800. Thus it can be concluded that on a moving object the rate of time flow is different for different directions. Hence we can say that rate of time flow is also not constant and it also varies according to direction or in other words time flows at different rates in different directions.

'''III. Conclusions:-'''

1.For calculating the time dilation the formula should be amended to T = γ * (T *Sin α) instead of T’ = γ * T.

2. Time dilation will be maximum for α = 900

3. In the same reference frame Time flows at different rates in direct directions

'''IV. References:-'''

1.  Einstein, A. (1905). "On the electrodynamics of moving bodies". Fourmilab.

2.  Mr.Vijay A. Kanade, International Journal of Scientific & Engineering Research, Volume 5,   Issue 7, (2014)   (published)

3. https://en.wikipedia.org/wiki/Time_dilation