Question about Time Dilation

Question

I was studying about Time dilation and I wondered, does Time seem less for a moving body, or does it seem less for a resting body, both relative to each other, or does both occur at same time? Meaning if moving body experience 1s, does resting body experience lets say 0.5s? Or is it the other way around? Or does both happen?

Answer 1

Roughly speaking, it is the principle of relativity that each observer views nature as if he is stationary with all the other observers moving. Once people recover from the initial shock of time dilation, this is usually where they get tripped up. They think in terms of "A sees B with time slowed down, so B sees A with time sped up" or something like that. This is not correct. The time dilation is reciprocal.

FWIW, if you are serious about learning this and not just asking a random question, I always recommend people move on past "time dilation" and "length contraction" as soon as they are able and think in terms of Minkowski space and the Lorentz transform. While the math may seem harder, this is because it is more accurate. The "paradoxes" will all be much easier to resolve.

It is OK if you were just asking and are not intending on deep study too, of course.

Answer 2

Moving bodies experience less time in their reference frame compared to bodies at rest. This is what special relativity says , so for a given speed the moving body experiences 0.5 s where as the body at rest experiences 1s. If we increase the speed to speed of light then actually the body doesn't have a defined amount of time ( hence light doesn't experience time) because in the time dilation equation we usually compare the speeds to speed of light $$t^{'} = \frac{t}{\sqrt{1-v^2/c^2}}$$ t' is the new time experienced by the moving body c is the speed of light v is the velocity of body t is the time at rest . here $$\frac{1}{\sqrt{1-v^2/c^2}}$$ is known as the lorentz factor .

here as v is divided by c , so as speed increases the value of denominator also decreases and so the value of t' increases having more magnitude of time consumed so hence time experienced by the moving body is less!

Answer 3

The main problem here is where you say

Meaning if moving body experience 1s, does resting body experience lets say 0.5s?

The reason this is problematic is because, when you have two bodies that are not always in the same place, it is not clear how you are supposed to be comparing the time each one experiences. From a pre-relativistic perspective, this may seem confusing, as Newtonian physics admits a unique global time coordinate, allowing us to introduce a notion of "simultaneity" for this purpose. However, this is not the case in Einsteinian Relativity. Instead, if we want to compare the amount of time each body experiences, we must specify how the two bodies are communicating with each other (such as by sending each other light signals or by starting and ending in the same place), so that we can calculate the proper time of each path.

---

Note, some people like to talk about the notion of relativity of simultaneity in Special Relativity, in which there is a reference frame-dependent notion of simultaneity. However, I prefer not to think of things this way, since it does not naturally extend to General Relativity.

Answer 4

Unfortunately, the common perception of reciprocal time dilation is simply wrong. And it has nothing to do with acceleration, or turning around, or anything like that. The fact is that there IS a preferred frame of reference and this is proven every day with GPS satellites. Allow me to explain:

As you know, GPS satellites have their clocks adjusted for both special and general relativistic effects. So clocks on a GPS satellite run 45 microseconds per day faster than clocks on the ground. If this was not done then we would quickly drive off the road.

Other satellites (and intercontinental ballistic missiles) use GPS satellites to set their own navigation. Some of these satellites are following right behind the GPS satellite orbit, so they have no relative motion compared the GPS satellite. While other satellites are going in the exact opposite orbit, so they have extremely fast relative motion compared the GPS satellite. And others still are traveling at various cross angles to the GPS orbit, so they would have various relative motions.

If the concepts of special relativity were correct, then all of these other satellites would need to set their clocks and motion relative to the GPS satellite. But they DO NOT do this. They all set their clocks and motion relative to Earth. It is only in this way that the missiles reach their correct target.

Second, the wikipedia page referred to in another answer on reciprocity says that the reason the twin paradox is resolved is because the travelling twin must accelerate and turn around. This is also wrong. Lets imagine not twins, but quintuplets. Ann stays on Earth, Bob travels to star Beta and back; Charles to star Gama and back, Doris to Delta and back, Evelyn to star Epsilon and back. All of the travelling quints use exactly the same acceleration rate up to a top speed of .8c. They all turn around their star in exactly the same circle and they all decelerate at the same rate on return to Earth. The wiki article would imply that all the traveling quints age the same amount compared to Ann, because they all followed the same acceleration patterns. But this is not the case. The acceleration has absolutely nothing to do with this special relativistic effect. The only issue is how much time (or distance) they travelled at what speed. At the end of the experiment Ann will be oldest, Bob will be second oldest, Charles third oldest, Doris fourth oldest and Evelyn will be youngest.

These facts lead us to understand that while in theory there is no preferred frame of reference, in the real world there IS a preferred frame of reference.