Relativity and Simultaneity: A Cosmic Perspective

[martinlodge1964]

Homework Statement

GOT IT? In Essential University Physics

Relevant Equations

Clocks running slow

Posed question is that a comment plunges into Jupiter. Same time as my physics class starts on Earth. My friend is traveling towards Jupiter at a significant percentage of c. Would the person in spaceship say that the comment collision occurred before, after or as class started?

My answer: same time - in the spaceship, my friend sees Earth receding but from Earth I see spaceship receding. We both say the others’ clock is running slow. Since both run slow by same amount, and our clocks are independent of what is happening on Jupiter, we see comet collision occurring at same time. Right?

 

[PeroK]

I don't agree with your answer. But, more important, I think you need to do some proper analysis based on events and their coordinates in different reference frames. You have put this post in advanced physics homework. Let's see some advanced physics!

 

[martinlodge1964]

Thanks. I am not a physicist, an engineer. Trying to understand. But okay - try this: my friend in spaceship thinks my clock runs slow so, as he approaches Jupiter and sees the collision, he assumes my clock is running slow and therefore comet has hit before my class starts?

 

[PeroK]

Thanks. I am not a physicist, an engineer.

That's no excuse! Seriously, you need to set up coordinates for these events, and transform those coordinates between the two reference frames.

You can't just say "the answer must be ..." without proper analysis.

 

[martinlodge1964]

Okay. Will do that. Appreciate the tough love!

 

[phinds]

Okay. Will do that. Appreciate the tough love!

We're very good at that here on PF

Also, if a comment plunges into Jupiter, you should say whether it's a good comment ("Jupiter, you're beautiful") or a nasty comment ("Jupiter, your gas smells awful").

 

[Office_Shredder]

Relativity of simultaneity kind of says that the answer cannot be at the same time, because two observers in different frames do not agree on what events occur at the same time.

The key to resolving a lot of these paradoxes is to remember that the situation is not symmetric despite your clock analogy - length dilation means your friend thinks they traverse the distance from Earth to Jupiter significantly faster than you think they traverse it. Obviously both frames agree on what the clock says at Jupiter when they reach Jupiter, and this has implications for what your friend thinks the clock says on Jupiter when they are passing you on earth.

 

[Orodruin]

Relativity of simultaneity kind of says that the answer cannot be at the same time, because two observers in different frames do not agree on what events occur at the same time.

Not really. Given two observers moving at a non-zero relative speed their simultaneities are three-dimensional non-parallel hyperplanes in Minkowski space. Consequently, they will intersect in two-dimensional hyperplanes. If the two events lie on the same such hypersurface (effectively, simultaneous in one frame and on a plane orthogonal to the relative velocity between the observers - ie, not the case here) then they are simultaneous in both frames. Hence, one cannot make the blanlet statement that two events cannot be simultaneos in two different frames.

 

[martinlodge1964]

We're very good at that here on PF

Also, if a comment plunges into Jupiter, you should say whether it's a good comment ("Jupiter, you're beautiful") or a nasty comment ("Jupiter, your gas smells awful").

Funny!

 

[martinlodge1964]

Relativity of simultaneity kind of says that the answer cannot be at the same time, because two observers in different frames do not agree on what events occur at the same time.

The key to resolving a lot of these paradoxes is to remember that the situation is not symmetric despite your clock analogy - length dilation means your friend thinks they traverse the distance from Earth to Jupiter significantly faster than you think they traverse it. Obviously both frames agree on what the clock says at Jupiter when they reach Jupiter, and this has implications for what your friend thinks the clock says on Jupiter when they are passing you on earth.

Thank you. Less brutal than some of other responses. I am working through the logic: not a field us civ engineers deal with too often!

 

[phinds]

Funny!

Just FYI, there's an icon that you can use that saves you the time of replying. Also, the "like" button gives you choices immediately.