EvC Forum: The Twins Paradox and the speed of light

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Topic: The Twins Paradox and the speed of light

onifre

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Message 13 of 230 (473628)
07-01-2008 1:00 PM

Reply to: Message 11 by cavediver
07-01-2008 12:43 PM

The GPS's atomic clock is affected by this also right?

All great truths begin as blasphemies

I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.

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onifre

Member (Idle past 2969 days)

Posts: 4854

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Message 27 of 230 (473723)
07-02-2008 11:52 AM

Reply to: Message 14 by NosyNed
07-01-2008 1:28 PM

Re: An alternate view??? (cavediver to check)

However, relativity theory has to transform between the different frames of reference and that produces different numerical values for a "tick" as you transform space and time variables. Neither clock (on earth or in the GPS satellites) are changed. But the calculations to compare them to one another (in whichever reference frame you pick) changes the numbers attached.

Thanks for the explanation, it made perfect sense.

All great truths begin as blasphemies

I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.

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	Message 14 by NosyNed, posted 07-01-2008 1:28 PM		NosyNed has not replied

onifre

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From: Dark Side of the Moon

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Message 40 of 230 (473863)
07-03-2008 10:26 AM

Reply to: Message 39 by New Cat's Eye
07-03-2008 10:09 AM

Re: Here is the simple explanation....maybe

As I understand it, if you're traveling between two points in spacetime, you have a time component and a space component. The total distance between the two points is the same whether you move in space or not (because they are the same points regardless). So therefore, if you don't move through space then all of the distance is from the time component. However, if you do move through space, then the time component of the total distance must be less because the total distance remains the same.

That makes sense to me. Is it accurate?

I hope its accurate too because your explanation cleared up for me perfectly.

Lets repet it over and over again like a chant, maybe it'll finally sink into my brain

All great truths begin as blasphemies

I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.

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	Message 39 by New Cat's Eye, posted 07-03-2008 10:09 AM		New Cat's Eye has not replied

onifre

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Message 48 of 230 (473926)
07-03-2008 6:10 PM

Reply to: Message 44 by New Cat's Eye
07-03-2008 11:30 AM

Re: Here is the simple explanation....maybe

But if experienced time, ds, is the same between the two spacetime coordinates regardless of the space component of the distance, then how can traveling through space affect the experienced time?

CS, in my attempt to understand it I'll try to answer you.

Experienced time is the same *at* the 2 space-time coordinates, not between them.

The affect of traveling is only relative to the one observing, to the one traveling the time hasn't been affected.

In the attempt to connect the traveler with the observer, given that the observers time is the one that we are going by, time dilation comes into play.

The way I understand it is that its *experienced* time, not an actual time change.

I think...

All great truths begin as blasphemies

I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.

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	Message 44 by New Cat's Eye, posted 07-03-2008 11:30 AM		New Cat's Eye has replied

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onifre

Member (Idle past 2969 days)

Posts: 4854

From: Dark Side of the Moon

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Message 50 of 230 (474307)
07-07-2008 2:22 PM

Reply to: Message 49 by New Cat's Eye
07-04-2008 1:35 PM

Re: Here is the simple explanation....maybe

So, its not that the traveling really affects the time experienced, its only that time dilation occurs to the stationary twin's observation because the other one is moving?

The time dilation would only exist if the clock for measuring time is at the observers end. The clock in the twins shuttle will not have slown down.

All great truths begin as blasphemies

I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth.

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	Message 49 by New Cat's Eye, posted 07-04-2008 1:35 PM		New Cat's Eye has replied

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	Message 66 by New Cat's Eye, posted 10-05-2008 12:49 PM		onifre has replied

onifre

Member (Idle past 2969 days)

Posts: 4854

From: Dark Side of the Moon

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Message 67 of 230 (485138)
10-05-2008 1:57 PM

Reply to: Message 66 by New Cat's Eye
10-05-2008 12:49 PM

Re: Here is the simple explanation....maybe

Slown...

Slowed...sorry about that. LOL, sometimes I throw shitty english out when I type quickly. Im the by-product of a text messaging world where spelling is optional.

Then why aren't the twins the same age?

What im explaining is that if you have a watch, and I have a watch, and they are synchronized, and you are traveling away form me in a rocket, in both frames of reference the watches are ticking normally. That is Einsteins elevator experiment,
Einstein's Relativity

The twins paradox deals with distance being reduced when traveling through space...as per Son Goku's equation. The stationary twin is traveling through more space, and time. The twin that is moving is traveling through less space, and time. So the stationary twin, having traveled more time is older than the twin who traveled for less time.

Edited by onifre, : No reason given.

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onifre

Member (Idle past 2969 days)

Posts: 4854

From: Dark Side of the Moon

Joined: 02-20-2008

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Message 69 of 230 (485222)
10-06-2008 12:35 PM

Reply to: Message 68 by New Cat's Eye
10-06-2008 10:03 AM

Re: Here is the simple explanation....maybe

The stationary twin is traveling through more less space so therefore more time and the moving twin is traveling through less more space so therefore less time.

Here's Son Goku's equation of the paradox'

Son Goku writes:

Stationary twin:
If one twin sits where they are for four seconds they end up with coordinates:
(1,200,000,000 ; 0) or t=1,200,000,000 and x=0.

Now I'll compute the spacetime distance. Since dx=0 (no difference or change in spatial coordinate) we just have ds^2 = dt^2.

dt = 1,200,000,000 - 0 = 1,200,000,000
dt^2 = 1,440,000,000,000,000,000
Hence ds^2 = 1,440,000,000,000,000,000 and taking the square root:
ds = 1,200,000,000 meters.

Moving twin:
The moon is roughly 384,000,000 meters from Earth. The second twin starts at Earth and travels to the moon in two seconds.
So they start at (0 ; 0) and end up at (600,000,000 ; 384,000,000).
The spatial difference is dx = 384,000,000 - 0 = 384,000,000
Similarly, dt = 600,000,000.
dx^2 = 147,456,000,000,000,000
dt^2 = 360,000,000,000,000,000

ds^2 = 360,000,000,000,000,000 - 147,456,000,000,000,000 = 212,544,000,000,000,000.

Taking the square root, ds = 461,024,945 meters.

Assuming the twin takes an exactly similar journey back to Earth, that is they return in two seconds, then the distance for the return journey is again ds = 461,024,945 meters.

Hence the total spacetime distance of the moving twin is
ds = 2 x 461,024,945 meters = 922,049,890 meters.

Which is significantly less than the 1,200,000,000 meters of the stationary twin. Hence spacetime distance is reduced by moving through space.

Which still gives us the end result of,

quote:
So the stationary twin, having traveled more time is older than the twin who traveled for less time.

CS writes:

because then, it make perfect sense to me

That's all I ever aim to do.

"All great truths begin as blasphemies"

"I smoke pot. If this bothers anyone, I suggest you look around at the world in which we live and shut your mouth."--Bill Hicks

"I never knew there was another option other than to question everything"--Noam Chomsky

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	Message 68 by New Cat's Eye, posted 10-06-2008 10:03 AM		New Cat's Eye has replied

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	Message 70 by New Cat's Eye, posted 10-06-2008 1:14 PM	onifre has replied
	Message 71 by cavediver, posted 10-06-2008 1:43 PM	onifre has replied

onifre

Member (Idle past 2969 days)

Posts: 4854

From: Dark Side of the Moon

Joined: 02-20-2008

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Message 72 of 230 (485272)
10-06-2008 5:47 PM

Reply to: Message 71 by cavediver
10-06-2008 1:43 PM

Re: Here is the simple explanation....maybe

Cavediver writes:

and the traveller's spacetime path (the time he experiences) is shorter than the static twin's spacetime path.

So it's in the spacetime interval that the experienced time is shorter. Is this only the case at speeds close to the SoL?

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	Message 71 by cavediver, posted 10-06-2008 1:43 PM		cavediver has replied

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	Message 73 by cavediver, posted 10-06-2008 6:27 PM		onifre has replied

onifre

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Posts: 4854

From: Dark Side of the Moon

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Message 74 of 230 (485280)
10-06-2008 6:38 PM

Reply to: Message 73 by cavediver
10-06-2008 6:27 PM

Re: Here is the simple explanation....maybe

The spacetime interval IS the experienced time - they are one and the same.

Right, I fudged up the way I tried to say it. Got it now.

And it will be shorter for all speeds - just reasonably measurable as the difference in speed approaches c.

Thanks again for the explanations cavediver.

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	Message 73 by cavediver, posted 10-06-2008 6:27 PM		cavediver has not replied

onifre

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Posts: 4854

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Message 75 of 230 (485293)
10-06-2008 11:41 PM

Reply to: Message 70 by New Cat's Eye
10-06-2008 1:14 PM

Re: Here is the simple explanation....maybe

CS writes:

That very honorable. I do too, but that's not all

sometimes its just too much fun to rile up the liberals

Yeah, but really, it fun to rile up anyone who's too far to either side.

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onifre

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Posts: 4854

From: Dark Side of the Moon

Joined: 02-20-2008

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Message 85 of 230 (511635)
06-10-2009 6:22 PM

Reply to: Message 84 by WaveDancer
06-10-2009 9:07 AM

Re: A twist

I guess this just goes to prove how difficult facts in cosmology are to pin down and how ambiguous the whole concept is.

There is one minor problem with this statement, the "twin paradox" wasn't actually a fact.

Source

quote:
While there are a variety of possible examples of the Twin Paradox in action, let's consider the following version. Prime and Unprime are twins; they say their farewells as Prime boards a train. Prime takes a trip on the train to a distant station (distance L), at uniform velocity v (a considerable fraction of the speed of light). Upon reaching the distant station, Prime takes a return train at the same speed, returning to meet Unprime at the original station. Unprime has been waiting patiently at the original station for the return of Prime. Upon arriving at the original station, Prime and Unprime discover that Unprime has aged considerably, yet Prime hasn't aged much at all.

The "paradox": Special relativity says that physics is the same in reference frames that move at a uniform velocity relative to one another. Observers in any two frames moving relative to one another should not be able to make any observation that indicates which one is "actually" in motion. So, how is it that one of the twins (Prime) is younger than the other? Does this mean one of the twins was "actually" in motion while the other was not?

Like all such paradoxes the paradox is only apparent. In this case, Prime has actually taken a trip. That is, Prime has left the Frame of Reference of Unprime (feeling an initial acceleration at the beginning of the trip), then, after some time, Prime again feels an acceleration as Prime slows to a halt and turns around (boards the return train), again accelerating up to speed, then finally halting back at the original station. Prime has felt lots of accelerations; Unprime has felt no accelerations. Therefore, Prime did actually do something "out of the ordinary" --- it might not be unreasonable to find that Prime and Unprime have had different experiences. Indeed, it appears that Prime has experienced less time duration during the separation of the twins than Unprime has experienced.

The key point is "acceleration". Further in the link you'll find the Twin Paradox without acceleration as well.

- Oni

Petition to Bailout Comedy The Laugh Factory is imploring Congress to immediately fund what owner Jamie Masada calls an "Economic Cheer-Up." If Congress fails to act quickly, the Laugh Factory comedians are planning to march to Washington and plea to President Obama.

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	Message 84 by WaveDancer, posted 06-10-2009 9:07 AM		WaveDancer has replied

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onifre

Member (Idle past 2969 days)

Posts: 4854

From: Dark Side of the Moon

Joined: 02-20-2008

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Message 89 of 230 (511720)
06-11-2009 12:21 PM

Reply to: Message 88 by cavediver
06-11-2009 11:38 AM

Re: A twist

Perhaps the confusion is that there is no paradox. The effect is real but there is nothing paradoxial about it...

Thanks, cavediver. That's what I meant.

I guess I should have expressed that better.

- Oni

This message is a reply to:
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