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Twin paradox in a circle 
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#1
Nov1611, 10:23 AM

PF Gold
P: 6,120

There have been a couple of posts over the last few months that posit a relativisticspeed path in a circle around the earth and I want to make sure I correctly understand the ramifications. It's the twin paradox in a circle. SO ... here's a scenario that I think will solidify it for me:
This is a thought experiment, not something that would be practical, but it is remotely within the realm of physical possibility. Rocket achieves earth orbit and then with a massive waste of fuel accelerates in the circular orbit to very low relativistic speeds (say .001c), and then decelerates in the orbit and returns to earth. The person on the craft would be slightly younger than the one on earth, yes? I don't care if it's fractions of a second or what, just the absolute fact. That is, the end result is exactly the same as if the craft had accelerated away from earth and then it had turned around and came back (which is in essence what it IS doing). 


#2
Nov1611, 11:13 AM

P: 366

Thats entirely correct as I understand it.
My understanding is time dilation is directly related to curvature, curvature is intrinsically linked to gravity and geometry: acceleration can be used to "create" curvature and therefore time dilation. Any corrections to my understanding are welcome. 


#3
Nov1611, 06:20 PM

P: 1,414

Second, you can answer this by yourself by doing some simple calculations. 


#4
Nov1611, 06:45 PM

PF Gold
P: 6,120

Twin paradox in a circle



#5
Nov1611, 07:03 PM

P: 1,414

EDIT: Though you might have to look something up. Everybody has to do this from time to time. 


#6
Nov1611, 07:22 PM

PF Gold
P: 6,120

Oh, I might be able to do the math, but first I'd have to know what math to DO, and I don't.



#7
Nov1611, 07:24 PM

Mentor
P: 11,583

Phinds, that would only be correct if the velocity is high enough to offset the reduced effect of Earth's gravity on time dilation. GPS satellites are slower than Earth based clocks by 7 microseconds per day due to time dilation caused by their velocity, however they are FASTER by 45 microseconds per day due to being further away from Earth. Combined the two effects cause satellite clocks to be faster by 38 microseconds per day. AKA they age faster by 38 microseconds per day than those of us on Earth do.



#8
Nov1611, 07:25 PM

Mentor
P: 11,583




#9
Nov1611, 07:28 PM

P: 15,319




#11
Nov1611, 07:50 PM

P: 1,414

My point to Phinds was that by doing a few actual calculations, then he can answer lots of these sorts of questions for himself, more or less intuitively. As to the deeper question of what, physically, causes differential aging. Who knows? Superficially, it suggests that what we refer to as empty space isn't empty. And, as Cosmo Novice suggested, acceleration/deceleration seems to be affecting (producing changes in) the periods/frequencies of oscillators that are accelerating/decelerating. 


#12
Nov1611, 07:55 PM

P: 15,319




#14
Nov1611, 08:26 PM

PF Gold
P: 6,120




#15
Nov1611, 08:43 PM

PF Gold
P: 6,120




#16
Nov1611, 09:01 PM

P: 1,414

While I admire your defending him, I don't see any problem with requiring him to do a bit of homework. If you want some examples of extreme laziness, then just look at some of my posts. Anyway, bottom line, we all, including now Phinds I think, know the answer to his question. The really deep, intriguing question concerns, at least for me, the physical nature of relativistic differential aging. EDIT: And, thanks to George Jones for presenting a nice complication. 


#17
Nov1611, 09:16 PM

P: 1,414

Anyway, keep asking questions. I think we both find this stuff fascinating, and are thankful for the science advisors and mentors who donate their time to help us better understand what physics can tell us about our world. And, I apologize if I in any way offended you. My replies weren't meant to do that. As I mentioned, I've read many of your posts, and from those I think you are a thoughtful and intelligent person. 


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