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We all know that if we consider the assumption of Einstein that is no material object can travel faster than light to be true then two effects that are Length Contraction And Time Dilation seem to be protuding out of this idea. But why this effects were necessary to come into picture? And how this (time dilation and length contraction) even related with the assumption of our impossiblity to travel faster than light?

Qmechanic
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CHAITANYA PARATE
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    This question is pretty broad. I'd recommend a textbook on special relativity. – Allure Oct 12 '21 at 02:25
  • There is nothing to stop an object from traveling faster than light. However, there is an asymptote at the speed of light that prevents objects from crossing from the "slower than light" realm to the "faster than light" realm, and vice versa. – David White Oct 12 '21 at 02:36
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    Time dilation & length contraction come from the Lorentz transformation. We have many existing questions on this topic. This answer https://physics.stackexchange.com/a/79892/123208 explains how the Lorentz transformation is connected to the finite speed of light. – PM 2Ring Oct 12 '21 at 03:02
  • These phenomenon occur due to fact to prevent the violation of laws of physics. – Anomalous Oct 12 '21 at 02:45
  • If this happening due to fact that nothing can travel faster than light then don't this apply to tachyon's? – CHAITANYA PARATE Oct 12 '21 at 14:50
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    I'm a bit surprised at all the downvotes as all three of time dilation, length contraction and the upper limit to the speed of light are derived from the invariance of the line interval. Chaitanya's question makes perfect sense when viewed in this light. – John Rennie Oct 12 '21 at 17:20
  • @CHAITANYAPARATE the more accurate statement is what David White wrote - you can have something that moves faster than light (tachyons), but they would not be able to slow down; they will always move faster than light. – Allure Oct 13 '21 at 08:33

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Length contraction and time dilation are a consequence of the speed of light being the same for everyone.

Imagine standing with a friend who sends out a pulse of light to their left and right. If you decide to walk in the direction of the right hand pulse then at any given instant it will seem to your friend that the pulse has travelled slightly further than it seems to have travelled from your perspective. Likewise, the left hand pulse, which you are walking away from, will seem at any instant to your friend to have travelled slightly less distance than it has travelled from your perspective. Since you both see the speed of light to be the same, the only way you can account for the fact that light has travelled different distances in the two directions is by disagreeing how much time has passed in each direction.

From your perspective, clocks in the frame of your friend are all running out of synch- the further away from your friend in your direction of travel, the more the clocks in your friend's frame are running ahead of time. Conversely, the further away from your friend in the opposite direction, the more the clocks in your friend's frame are running behind time.

The fact that you and your friend disagree on what time it is at any place along your direction of motion is the cause of both time dilation and length contraction. If your friend measures the length of an object in your frame, from your perspective she is measuring the position of the leading edge of the object before she measures the position of the trailing edge, which leads her to underestimate the length of the object. Likewise, if one of your clocks is compared against two clocks in your friends frame, it will seem to be running slow, because the second clock it passes is running ahead of the first.

Marco Ocram
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