B Identical devices in different places

[clickalot]

What I would like to know..., me and my friend, very good friend. Had an argument about time and relativity
What happens if I have 2 identical cassette players with each a tape of 30 minutes exactly!
I bring 1 player way up to uhm let's say Pluto for the greater distance..
Will the player on Pluto end exactly as the player on Earth ends
And let's asume they both are in a sealed box, no interference of the space and gravity

My opinion in this is, yes..if the conditions are exactly the same, then both players would end exact at the same time
Or can we hear the player runs faster on Pluto?

 

[russ_watters]

The way you have worded the question and answer shows a need to better define your reference frames to deal with relativity of simultenaity...setting aside how you'd know it ended.

So let's say the one sent to Pluto had a giant radio transmitter attached and you were listening from earth. You would hear it end about 4hrs after yours ended.

 

[Nugatory]

both players would end exact at the same time

What does it mean to say that they both end "at the same time"? Until you've clearly defined that, your question is itself not clearly defined, so has no straightforward answer.

One possible definition: Pluto is about five light-hours away, so it takes about five hours for light to get there from here. So we could say that if the guy on Pluto had been watching the earth-based cassette player through a telescope and saw it stop playing five hours after his own stopped playing... then the two stopped "at the same time" because it stopped five hours before the light reached him. In fact, it's hard to come up with any other intuitive definition of when things away from where you are right now happen - how can the starting time for a journey be anything other than the arrival time minus the travel time?

However, it turns out that by this definition of "at the same time", different observers will come up with different notions of what events happened "at the same time". Thus, there is no single right answer to your question. Some observers will find that the player on Pluto stopped first; others, moving at different speeds relative to the Earth and Pluto will just as correctly find that the player on Earth stopped first.

Google for "Einstein train simultaneity" to find the classic thought experiment that shows how this works in the simplest possible case... no gravity, no acceleration, no math beyond a smattering of high-school algebra needed.

 

[berkeman]

And let's asume they both are in a sealed box, no interference of the space and gravity

That's an impressive box!

 

[FactChecker]

Ok. I'll bite. You can correct any wrong assumptions that I make about your question.

Suppose we assume that you are talking about separation only in distance with no relative velocity or acceleration. When you say "no interference of the space and gravity" and "the conditions are exactly the same", I assume that you want to ignore General Relativity, which distorts space and time due to gravity.

Alternatively, we can assume that both boxes are in space at the same distance from the sun. That would produce the same time distortion for each. That only leaves Special Relativity where there is no relative velocity or acceleration. In that case, the answer is that the clocks in the two locations can be synchronized and will remain synchronized so that the tapes which begin at the same time will end at the same time. Separation in space does not, on its own, change space or time.

Suppose you are really asking about General Relativity. When you say "no interference of the space and gravity", you have to realize that the force of gravity is really a distortion of space and time. In that case, a tape on Earth and a tape on Pluto would appear to run for exactly the same time in each location's associated time. But those times are not the same. All physical processes look identical in each location's associated time, but the two location times can not remain synchronized, they will drift apart.

 

[pervect]

What I would like to know..., me and my friend, very good friend. Had an argument about time and relativity
What happens if I have 2 identical cassette players with each a tape of 30 minutes exactly!
I bring 1 player way up to uhm let's say Pluto for the greater distance..
Will the player on Pluto end exactly as the player on Earth ends
And let's asume they both are in a sealed box, no interference of the space and gravity

My opinion in this is, yes..if the conditions are exactly the same, then both players would end exact at the same time
Or can we hear the player runs faster on Pluto?

To answer this question properly, you need to specify how , operationally, you would determine if both players "ended at exactly the same time". This is not as trivial a question as it seems, due to the concept of the relativity of simultaneity. I would guess that you are perhaps not familiar with this concept. It's vital to your question as stated.

Rather than get into the details of the relativity of simultaneity, though, I'd like to propose a different experiment that avoids this. You have a tape player, and your friend goes out to pluto, and heads back. You can't get to pluto in 30 minutes, light speed forbids, so you'll need to change your figures a bit. The important thing is that you can compare both tape players at the same location in space so you don't need to worry about the relativity of simultaneity, and when you do this, you find that the tapes do not end at the same time.

This is called the "twin paradox".

If you want to get into the underlying issue about why simultaneity is relative, which is an important but tricky issue in its own right, you can try looking up the term "relativity of simultaneity" or "Einstein's train" on PF or on the www, though you'll have to be careful if you use the www, of course.