Instantaneous speed is the magnitude of the instantaneous velocity.Instantaneous velocity \(v\) is the velocity at a specific instant or the average velocity for an infinitesimal interval.Velocity is a vector and thus has a direction.But note that you can only deem one of the observers to be at rest if the other one does and out-and-back trip.\( \newcommand \nonumber.\] It takes more time than the observer at rest to measure the time interval of 5 sec? But we know about persepctive, so we don't shout woo, paradox! Nor should we when we're separated by relative motion and my time looks slower than yours and your time looks slower than mine. When we're separate by distance I look smaller than you and you look smaller than me. This is the "twins paradox" but it's nothing special. You see your clock light going like this ||, and my clock light going like this /\, and I do too. To appreciate what's going on here imagine we each have a parallel-mirror light clock. If you and I are two observers passing one another in space, we could each claim that the other guy is in motion, and that his clock is the one ticking slower. But note that time isn't "travelling", and motion is relative. You can write v²/c² because c=1, or you can write that as (v/c)², and we use a reciprocal to distinguish time dilation from length contraction.ĭoes this signify that as time is travelling slower for the observer in motion? The height gives the Lorentz factor, and it's $\sqrt$. The base represents your speed as a fraction of c. ![]() The hypotenuse of a right-angled triangle represents the light path where c=1 in natural units. Public domain image by Mdd4696, see Wikipedia Take a look at the simple inference of time dilation due to relative velocity on Wikipedia: The important point to appreciate is that the Lorentz factor is derived very simply from Pythagoras's theorem. Is the time taken by the observer in motion given by the equation Events that are simultaneous in one frame need not to be simultaneous in other and thus whatever is happening is perfectly okay and more like the only logical possibility of what can happen. Becuase the definition of simultaneity and invariance of the speed of light clearly dictates that simultaneity depends on the frame. Now is it a paradoxical or contradictory phenomenon? Not at all. They are running slow - Taking more time to show $5\ minutes$ elapsed. $B$ will observe that his ($B$'s) clock has shown $5\ minutes$ elapsed but $A$'s clocks have not. The relativity principle suggests that $B$ will also note similar about $A$! i.e. That is what Time Dilation says.īut the most interesting portion is not done yet. In other words, $A$ does note in his diary that $B$'s clocks were faulty and its hands took more time to show 5 minutes elapsed. ![]() Since the clock of B runs slower wrt $A$ this has to happen. ![]() So will it happen that Observer $A$ will never observe Observer $B$ to fire himself (because $B$'s clock is running slow wrt $A$)?Ī straight answer is 'Yes'. Now when any of the observers observes $5\ seconds$ elapsed in his own clock fires himself. They are at the same point in space at some instant and both of them start their clock precisely when they are at the same position in space. Let's say $B$ is moving wrt $A$ in the positive $X$ direction with speed $v$. But I am trying to answer it according to what I understand the question is and that is as follows:
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