Monday, February 28, 2011
www.google.co.inShrinkage of time:-
In previous post, i mentioned about this phenomena. Let discuss it. Will try to find, how your watch goes behind to some given conditions. Behind not 'slow', the word slow means moving ahead at a minimal speed.Here it means going behind,but not in terms of length in terms of time. So using the word slow might not be appropriate.
Imagine to your limit to some colossal rather astronomic figures.Did?Thanks,now let's start ,though it needs some calculations,but if i do that most of my readers may get bored with it,even annoyed also.So allow me to put the results only. Suppose you're riding an Einstein train along an endless railway track,at a speed of 240,000km/sec,setting your wrist watch(that designer one) with the clock of the boarding station.your destination? Let 864000,000km. away.The clock of that station shows same time with the boarding one. How much time it will take to reach the destination, relative to the station clock? Simple 864,000,000/240,000= 1hour= 60 minutes.Remember not relative to your wrist watch.Why? Because it will differ,no i am not puzzling you. Come see how?
Here i have to introduce another character an observer,who is watching you travelling from a stationery platform. Now,travelling at that astronomical speed you're requested to lit an electric torch placed on the floor of that train,focusing to the ceiling of that train,where a mirror is fitted. What will be the path of the focused beam, to you? Vertically up to the mirror,reflected and vertically down to the source, the torch. Yes the mirror assumed to be a plain one,not concave or convex. For the observer standing motionless compared to the platform is completely different. Here i will request you again, forget our every day standards,experiences. Stay in that astronomic imaginary state of standards.For the observer the time it takes the beam to travel from the source to mirror, the mirrors shifts towards the motion of the train:again the time it takes from mirror back to the source,the source(torch) shifts the same distance i.e. the distance the beam traveled from source to the shifted mirror(an angular distance).Remember light travels @300,000km/sec. What we derive from here? Is for the observer the path of that torch beam forms an isosceles triangle.What was your's? A vertical straight line. So your path is smaller than the observer.What you say? Am i correct? In other words you may say the time interval at the station is greater than your's on board. If i take the time interval of the beam from source to mirror and back to source as 10(ten) minutes,its easy to calculate the height of the train,will be an astronomical figure, no matter with that kind of speed.Now from laws of triangles you can easily calculate the relation of the time interval in between you and the observer.I am avoiding all those calculations here.The results of the calculation shows,what? An unbelievable one. That while 10(ten) minutes has passed in the station clock,only 6(six) minutes has passed in your clock.Why?As your beam path is lesser than that of the observer.So the ratio is 6:10 or 6/10.
Now you can easily find out what it will be for an one hour journey? 60 minutes (one hour) for the station clocks and 60x6/10= 36 minutes for your watch i.e. 24 minutes behind the station clock or the time lag is 24 minutes.Amazing isn't it? The greater the speed of the train the bigger the time lag. If we continue to accelerate the speed of the train up to the 0.9999 part of the light speed(i.e.3000,000km/sec),only one minute will pass in your watch against 60 minutes of the station clock.............. ridiculous? boring?pardon but bear with me up to the next post
Posted by NIRUPAM GHOSH at 12:32 AM