Time dilation, Mechanical Engineering

Time Dilation

The measurement of time involves the concept of clocks attached at each position co-ordinate of a Lorentz frame. As a consequence of Lorentz transformations, it is said (though incorrectly) that a moving clock runs slower than a stationary one. Let us discuss this phenomenon, which is known as time dilation.

Consider two events occurring at same position x', at different times t1' and t2' as observed in a clock attached at x' in frame S'. When observed from stationary frame S, the two events are observed to occur at different space-time points (x1,t1) and (x2, t2). The time co-ordinates of the two events, according to clocks fixed in S at points x1 and x2, are related to S'. Hence, we get

t2 - t1 =  452_download (7).png  (t2' - t1') , (x2' = x1' = x')

or, Δ t' = 1/ 452_download (7).png   Δ t = Δ t (1 - v2/c2)1/2

That is, the time interval observed by the moving clock is less than the interval observed by stationary clocks. The time scale is apparently stretched out or dilated as observed by the moving clock. Hence the phrase, "the moving clock runs slower."

However, all clocks run at the same rate in all Lorentz frames.

For an infinitesimal time interval, we have

dt' = 1/ 452_download (7).png   dt

While dt' is the time interval according to (same) clock associated with moving position co-ordinate (or the moving object to which this clock is attached), dt is the time interval as observed by two neighbouring clocks associated with the stationary frame. Remember that t1 and t2 are the readings by clocks at x1 and x2 in frame S.

The time interval measured by the clock attached to a moving object is called proper or intrinsic time interval of the object. It is denoted by d τ; hence,

d τ = dt' = 1/ 452_download (7).png   dt

where dt is the corresponding interval recorded by a stationary observer.

Now, the space-time interval ds' for the object at rest in S' is,

ds'2 = c2 dt'2 - dl'2

= c2 dt'2 = c2 d τ2

Therefore, d τ =ds'/c

is an invariant of Lorentz transformations. That is, in a sense, is trivial because d τ is always the time interval measured in the frame attached to the object.

Posted Date: 9/18/2012 1:21:14 AM | Location : United States

Related Discussions:- Time dilation, Assignment Help, Ask Question on Time dilation, Get Answer, Expert's Help, Time dilation Discussions

Write discussion on Time dilation
Your posts are moderated
Related Questions
Find the twist of a circular hollow shaft: Discover the twist per metre length of a circular hollow shaft having 120 mm outer diameter and 90 mm inner diameter, respectively,

Following sets of the three forces act on a body,. In which case resultant cannot be zero? 1) 10N, 10N, 10N 2)10N, 10N, 20N 3)10N, 20N, 20N 4010N, 20N, 40N Ans)      In 4th

explain with suitable eg. static and dynamic force analysis

Stress in thin rotation rims

Carbon Dioxide (CO 2 ) Lasers   The CO 2 laser is a gas discharge device and it operates by electric excitation of an active medium that is a mixture of helium, nitrogen an

Q. How can you implement chemically coated sand? Chemically coated sand : Clean silica grains are sometimes coated with a non thermosetting hydrocarbon resin, which acts as a

Connecte d Rod: It is attached to piston at its small end by means of gudgeon pin. The big end bearing is connected to crank pin. It is made up of forged steel.

Illustrate throttling process and free expansion process in details? A fluid is confined in a cylinder by a spring loaded frictionless piston so that pressure in the fluid is a