Have you ever wondered what to do with your unused pet while on vacation? Do you feel bad about just dumping it in some airport pet kennel and showing up again four weeks later? Do you ever wonder how to keep your pet fresh longer instead of having it age uselessly? This is where Pet-O-Tel comes in, the new and convenient way of how to temporarily get rid of your beloved companion without it even knowing that you were gone for long: shoot it into space! Our modern mostly safe rockets will transport your pet around the galaxy at 0.9998c while you go skiing in the alpine mountains or golfing in St. Andrews. You are gone for four weeks, but for your pet, you are only gone for ... how long? Hint: you better ignore acceleration, even though it in fact is what makes this scenario asymmetric.

Question

Have you ever wondered what to do with your unused pet while on vacation? Do you feel bad about just dumping it in some airport pet kennel and showing up again four weeks later? Do you ever wonder how to keep your pet fresh longer instead of having it age uselessly? This is where Pet-O-Tel comes in, the new and convenient way of how to temporarily get rid of your beloved companion without it even knowing that you were gone for long: shoot it into space! Our modern mostly safe rockets will transport your pet around the galaxy at 0.9998c while you go skiing in the alpine mountains or golfing in St. Andrews. You are gone for four weeks, but for your pet, you are only gone for ... how long? Hint: you better ignore acceleration, even though it in fact is what makes this scenario asymmetric.

I don't know where to start. I plugged it in the lorentz factor and got 50.1 but it was wrong.

Answer 1

To determine the time experienced by the pet while you are away, we can use the concept of time dilation from special relativity. Time dilation occurs when an object is moving relative to an observer, causing time to pass differently for the moving object compared to the stationary observer.

In this scenario, your pet is travelling at a velocity of 0.9998 times the speed of light (c) relative to you. We can use the Lorentz factor to calculate the time dilation experienced by the pet.

The Lorentz factor (γ) is given by the formula:

γ = 1 / √(1 - v^2 / c^2)

where v is the velocity of the pet and c is the speed of light.

Plugging in the values, we have:

γ = 1 / √(1 - 0.9998^2)

Solving this equation will give us the correct Lorentz factor.

However, it is important to note that in this scenario, the acceleration involved in launching the pet into space is not taken into consideration. Properly accounting for acceleration would require using more complex calculations, such as integrating the Lorentz factor with respect to time.

If you would like to simplify the scenario and only focus on the time dilation due to constant velocity, you can use the Lorentz factor calculated above. Otherwise, a more comprehensive solution would require accounting for the effects of acceleration.