Calculating Time Dilation for Earth Signals at 0.600c

[overtak3n]

A person on Earth signals with a laser beam at 6 minute intervals. Another person on a rocket moving away from Earth at 0.600c detects the signals. At what time intervals does the person on the rocket receive the signals from the Earth.

The formula we use is:

Δt=Δto/sqrt((1-u²/c²))

u = 0.600c

I obtained two possible answers: 4.8 min and 7.5 min. However, I'm struggling to figure out which is the proper time and therefore cannot decide which answer is correct.

 

[Orodruin]

Which do you think is correct? Also, is it really the time when the signal is received?

 

[overtak3n]

I think 4.8 min is correct. Am I right?

 

[Orodruin]

And why do you think that? What is your reasoning? If you just give us your final answer, it is impossible to see where you go wrong/right and correct it.

 

[overtak3n]

The time in the rocket moves slower and I treat that as the proper time because it's the rocket that's moving. This resulted in 4.8 min.

 

[Orodruin]

The time in the rocket moves slower and I treat that as the proper time because it's the rocket that's moving. This resulted in 4.8 min.

You have to beware here and not simply try to apply formulae if you do not understand their meaning. First, select a reference frame in which to describe the events. Then think about what time the events occur at and what time this corresponds to for the rocket.

 

[overtak3n]

I'm a little confused. Instead of intervals I thought of a clock. When the person on Earth has a clock that shows 6 minutes, the person on the rocket has a clock that shows 4.8 minutes.

 

[Orodruin]

I'm a little confused. Instead of intervals I thought of a clock. When the person on Earth has a clock that shows 6 minutes, the person on the rocket has a clock that shows 4.8 minutes.

This is true in the Earth's rest frame. In the rocket rest frame, the rocket has a clock which shows 7.5 minutes when the Earth clock shows 6 minutes. This is the very essence of the relativity of simultaneity. What you have to ask yourself is "does either of these times represent the time you seek?"

 

[overtak3n]

This is true in the Earth's rest frame. In the rocket rest frame, the rocket has a clock which shows 7.5 minutes when the Earth clock shows 6 minutes. This is the very essence of the relativity of simultaneity. What you have to ask yourself is "does either of these times represent the time you seek?"

In the rocket rest frame, the proper time is 6 minutes? Is there an easy definition or trick for proper time that will help me apply it correctly next time? It's now my understanding that the proper time is in the moving frame that moves with respect to the rest frame that we use. So if the rocket is the rest frame, the Earth is the moving frame with respect to the rocket.

 

[Orodruin]

Proper time is the time experienced along a world line between two events, events are defined in time and space and proper time therefore is not tied to a particular frame. I suggest you try to answer this question:

does either of these times represent the time you seek?

 

[overtak3n]

I appreciate all the help.
The question is kind of difficult for me to answer. I'm not quite sure what it's asking. Which time are we seeking in the question in the OP?

If there was a clock on the Earth and one on a spaceship, and the question was "What would a person on the spaceship read on his clock?" Would the spaceship clock represent the proper time?
Suppose we reversed the question: "What would a person on the Earth read on his clock?" Would the Earth clock represent the proper time in this case?

 

[Orodruin]

If there was a clock on the Earth and one on a spaceship, and the question was "What would a person on the spaceship read on his clock?" Would the spaceship clock represent the proper time?

Yes, but to find the time you need to compute the time of the correct event. The question is "what time does the rocket read when the light reaches the rocket?" Is this the question you are answering?

 

[overtak3n]

Yes, but to find the time you need to compute the time of the correct event. The question is "what time does the rocket read when the light reaches the rocket?" Is this the question you are answering?

Is this suggesting that there is a delay for the light to reach the rocket because it's traveling?

 

[Orodruin]

Is this suggesting that there is a delay for the light to reach the rocket because it's traveling?

Yes.

 

[overtak3n]

Okay. Thank you. I'll think about this.