I Relative Motion vs Time: Paradox Explained

[EspressoDan]

Hi,

I'm reading a book explaining relativity. I previously understood the subject in layman's terms but am now confused.

The author has introduced relative motion in an invariant universe with the concept that motion through space is only relative to the observer.

Given this, I'm now struggling with the traditional 'man travels from Earth on spaceship and time slows for him relative to the observer on Earth' effect.

If motion is relative then why isn't the observer on Earth equally traveling away from the ship (ie ship is stationery relative to Earth in it's reference)? Why doesn't the man on the ship observe time passing more slowly on earth?

I realize that this is a paradox, but I can't figure it out. Confused.

 

[Nugatory]

If motion is relative then why isn't the observer on Earth equally travel away from the ship (ie ship is stationery relative to Earth in it's reference) and the man on the ship observe time passing more slowly on earth?

As long as the ship is just moving away from the earth, that is exactly what happens: The man on the ship finds that the moving earth-based clocks are running slow compared to his clock, while the people on Earth finds that the moving spaceship clock is running slow compared to their clock. This apparent paradox in time dilation is resolved by the relativity of simultaneity; we have many other threads here that discuss this. Here is one; post #10 of this thread is another; and we have many many more.

The Twin Paradox in which the spaceship turns around and returns to Earth is a completely different problem. The traveller will have experienced less time and aged less on the journey, even though at all times both stay-at-home and traveller agree that the other one is moving relative to them so has the "slow" clock. For a detailed explanation of this problem you should try the Twin Paradox FAQ.

 

[EspressoDan]

Thanks. You need to know what paradox you're worrying about to know what paradox you're worrying about!

The FAQ was useful, the Doppler-shift answer worked for me.

 

[PeroK]

Hi,

I'm reading a book explaining relativity. I previously understood the subject in layman's terms but am now confused.

If you are learning SR from a proper textbook, then it may be an idea to clear your mind of everything you thought you knew about the subject "in layman's terms". It's more than likely that anything you think you already know will turn out to be a hindrance to a proper understanding of the subject.

 

[Arkalius]

In my experience, layman's guides to special relativity rarely mention the concept of the relativity of simultaneity, or only in passing without much explanation. I personally find that this concept is actually quite integral to developing anything approaching an intuitive understanding of the subject. Without that understanding, everything you learn about relativity will either be understood incorrectly (ie not realizing that *both* sides of the twin paradox see the other's clock tick more slowly), or just sound completely contradictory or perplexing (ie how can they both see the other's clock ticking more slowly? that doesn't make sense!). It's also possibly the hardest concept to really internalize. The idea that there is a single moment that is "now" for everyone everywhere is so instinctually ingrained in us that it becomes very challenging to accept an idea that contradicts that.