# Time Paradox: Calculating Time Dilation for Objects Moving at 90% Speed of Light

• Trojan666ru
In summary: The answer to that question is 1hr and 6 mts. The object is not moving inertially in your frame, so you cannot use the time dilation formula to find the time in your clock. Time dilation only applies in inertial frames, where the relative speed between two frames is constant.In summary, the question is posed about an object traveling towards the speaker at 90% speed of light, which is placed 1hr c away. The speaker initially calculated that it would take 1 hour and 6 minutes for the object to reach them. However, the speaker then mentions the concept of time dilation and how it may affect the travel time. The correct answer to the initial question is 1 hour and
Trojan666ru
Suppose an object "O" is traveling towards me at 90% speed of light which is placed at 1hr c away, then how much time in "MY Clock" would it take to reach me?
I calculated it to be 1hr and 6 mts, am i right?
But on the other hand I'm the one who is moving towards the object "O" so by time dilation I'll reach there in 26.16mts, which one is the correct answer?

Trojan666ru said:
Suppose an object "O" is traveling towards me at 90% speed of light which is placed at 1hr c away, then how much time in "MY Clock" would it take to reach me?
I calculated it to be 1hr and 6 mts, am i right?
Right. Assuming that the given distance the object had to travel is as measured by you.

Of course, as seen by an observer moving with the object, the distance you have to travel is shorter due to length contraction. Note also that that observer disagrees with how you measured the travel time, due to relativity of simultaneity.

Trojan666ru said:
Suppose an object "O" is traveling towards me at 90% speed of light which is placed at 1hr c away, then how much time in "MY Clock" would it take to reach me?
I calculated it to be 1hr and 6 mts, am i right?
But on the other hand I'm the one who is moving towards the object "O" so by time dilation I'll reach there in 26.16mts, which one is the correct answer?
The reason that there is any confusion is that you didn't clearly specify the problem. To fully specify the problem you should have said "Suppose an object 'O' is traveling towards me at 90% speed of light which is placed at 1hr c away in my frame, then how much time in 'MY Clock' would it take to reach me?"

I can confirm that both calculations are correct. However, they represent different perspectives and frames of reference. From the perspective of the object "O", it would take 1 hour and 6 minutes for it to reach you, as observed by an external observer. This is due to the time dilation effect, where time appears to slow down for objects moving at high speeds.

From your perspective, as the observer who is also moving towards the object "O", time would appear to pass faster for you due to the same time dilation effect. Therefore, you would reach the object in 26.16 minutes, as calculated.

Both answers are correct and valid, but they represent different viewpoints and frames of reference. This is a fundamental concept in the theory of relativity, where time and space are relative to the observer's frame of reference. Therefore, it is important to specify the frame of reference when discussing time dilation effects.

## 1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass at different rates for objects moving at different speeds. This is due to the principles of special relativity, which state that time and space are relative and can be affected by the speed and gravity of an object.

## 2. How does time dilation occur for objects moving at 90% the speed of light?

According to the theory of special relativity, as an object approaches the speed of light, time for that object will appear to slow down relative to an outside observer. This means that time will pass slower for an object moving at 90% the speed of light compared to a stationary observer.

## 3. How is time dilation calculated for objects moving at 90% the speed of light?

The formula for calculating time dilation at a velocity of 90% the speed of light is t = t0 / √(1 - v2/c2), where t is the time experienced by the moving object, t0 is the time experienced by the stationary observer, v is the velocity of the object, and c is the speed of light.

## 4. Can time dilation be observed in everyday life?

While time dilation is a well-established phenomenon in physics, it is not usually noticeable in everyday life. The effects of time dilation are only significant at extremely high speeds, such as those near the speed of light, which are not achievable by most objects in our daily lives.

## 5. How does time dilation affect space travel at high speeds?

Time dilation is a crucial factor to consider in space travel, especially at high speeds. As an object approaches the speed of light, time for that object will appear to slow down. This means that astronauts traveling at high speeds will experience time differently than those on Earth, leading to potential discrepancies in time between the two locations.

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