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Author Topic:   The Twins Paradox and the speed of light
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 147 of 230 (628924)
08-14-2011 7:14 AM
Reply to: Message 146 by Maartenn100
08-14-2011 5:29 AM


It's far more complex then you think.
Yes, it is. But also more complex than *you* think
If you want to talk about realistic situations with gravity, then we need to be thinking about General Relativity, not Special Relativity. Which means forgetting everything you think you know about the Twin's Paradox and starting from the beginning again.
The space-time we live in is four-dimensional and curved. Our lives are paths through space-time. The distance along a path represents how much time is experienced moving along that path.
The straightest paths are those followed by objects (spaceships, astronauts, planets) in free-fall - so falling freely or in orbit. In other words, those objects that have no forces exerted on them. So the Earth in orbit around the Sun is in free-fall, and its path through space-time is as straight as possible. Same with the Moon, and with an astronaut in the ISS.
Us, standing on the Earth, are experiencing an upward force from the surface of the Earth, preventing us from falling freely to the centre of the Earth. So our path through space-time is not so straight.
Here's the strange bit: in space-time, the straightest path between two points is the LONGEST PATH. Any path that is not straight must be shorter than the straight path. This is because in space-time has a different type of geometry (Pseudo-Riemannian) to our normal experience of the geometry of just space.
So: our path through space-time stood on the Earth is actually shorter than that of an astronaut orbiting in the ISS. Remember, length of space-time path equals time experienced. So, we experience less time stood on the Earth than we would orbiting. We usually think of this as gravitational time-dilation.
As your astronaut accelerates away from the Earth, his acceleration is forcing his space-time path to become much less straight. This makes his path shorter. When he returns to the Earth, his path will have been much shorter than the Earth's. The Earth was in free-fall all the time, and so followed the longest path possible. And so the Earth experiences much more time than the astronaut, and the astronaut appears young compared to his twin on the Earth.
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 146 by Maartenn100, posted 08-14-2011 5:29 AM Maartenn100 has replied

Replies to this message:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 164 of 230 (628985)
08-15-2011 3:32 AM
Reply to: Message 160 by Panda
08-14-2011 7:07 PM


Re: gravitational theory of relativity
And if there were 2 people on opposite sides of the black hole - would the black hole accelerate towards both of them at a high velocity?
Yes
Maartenn is actually just about correct here (or at least I know what he is saying), but he's mixing some very high level concepts with some rather low level, and with some tricky translations/language issues and a bunch of confusion, it's all coming out rather unintelligible. I may have time tonight to try to respond to him.

This message is a reply to:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 169 of 230 (629087)
08-15-2011 4:06 PM
Reply to: Message 168 by Maartenn100
08-15-2011 2:07 PM


Re: gravitational theory of relativity
ou as an observer, in reality, are always the reference point for movement, acceleration and weight.
No. Acceleration is not relative. Nor is rotation. Only velocity is relative. If you accelerate away from the Earth, you must experience a force. Although the Earth appears to be accelerating away from you, the Earth does not experience any force. This is the crucial break of symmetry that resolves the Twin's Paradox. The force that you experience is what takes you away from your free-fall path through space-time, and makes your space-time journey (i.e. time experienced) shorter.
Edited by cavediver, : Many typos cos I'm watching Falling Skies at the same time

This message is a reply to:
 Message 168 by Maartenn100, posted 08-15-2011 2:07 PM Maartenn100 has replied

Replies to this message:
 Message 170 by Maartenn100, posted 08-15-2011 4:12 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(2)
Message 171 of 230 (629095)
08-15-2011 4:40 PM
Reply to: Message 170 by Maartenn100
08-15-2011 4:12 PM


Re: gravitational theory of relativity
But Earth's rotation on its axis is an acceleration that is not been calculated in the twinparadox.
Ok, we are talking about General Relativity, so we should not be talking about "gravity".
The Earth orbiting the Earth-Moon system, which is orbiting the Sun, which is orbiting the centre of the Galaxy (with its supermassive black hole), which is orbiting in the Local Group, which is, etc, etc... all of this is free-fall - it is the closest you can get to "not accelerating". This is following the straightest path through space-time.
The only real acceleration is that of the twin stood on the Earth - accelerated upwards by the surface of the Earth, and accelerated around the Earth by friction and air resistance. All the other Newtonian motion and acceleration (around the Sun, Galaxy, etc) is free-fall (i.e. not acceleration) in General Relativity. And this slight acceleration from the Earth's surface is tiny compared to the relativistic acceleration of the twin's relativistic space-craft.
As the twin accelerates away from Earth, she sees her twin accelerate away, but this is not real. The Earth-bound twin still only experiences the 1G upward acceleration, no matter how much acceleration her twin thinks she must be experiencing. And if the twin in the space-ship uses her telescope to observer her twin on the Earth, she will see the force gauge proving that she is experiencing no greater acceleration.

This message is a reply to:
 Message 170 by Maartenn100, posted 08-15-2011 4:12 PM Maartenn100 has replied

Replies to this message:
 Message 172 by Maartenn100, posted 08-15-2011 5:05 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(2)
Message 173 of 230 (629098)
08-15-2011 5:26 PM
Reply to: Message 172 by Maartenn100
08-15-2011 5:05 PM


Re: gravitational theory of relativity
when you are in the vicinity of a heavy object, this object will begin to rotate (it's a bad ellips because of gravity) while you are moving away from it.
I'm sorry, I don't know what you are talking about. Why should a non-rotating object begin to rotate?
And this 'beginning to rotate' is an observation of movement of that body.
That rotation wasn't there before, given your reference point....
...But you will see path's curved who weren't curved before. And you will see things that followed a straight line, now following a curved path.
And you will see this whole object begin too move.
Here, you seem to be talking about simple coriolis motion. There is nothing relativistic about this. It is simple Gallilean Relativity, moving from a rotating frame to a non-rotating frame. These motions are negligible compared to an acceleration to relativistic speed of an astronaut moving away from the Earth.
Again, I repeat, the Earth remains in free-fall, where-as the astronaut accelerates on her journey. This means her journey must be shorter in time than the same interval measure on Earth by her twin. This is inevitable and vert simple to understand once you understand space-time. No arguing about apparent rotations of frames can ever change this.
And the rotation of the Eath *is* absolute in General Relativity. Rotation creates frame-dragging, and this is not a "relative" effect that can be transformed away simply by moving to a co-rotating frame.

This message is a reply to:
 Message 172 by Maartenn100, posted 08-15-2011 5:05 PM Maartenn100 has replied

Replies to this message:
 Message 174 by Maartenn100, posted 08-15-2011 5:53 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 177 of 230 (629164)
08-16-2011 8:15 AM
Reply to: Message 174 by Maartenn100
08-15-2011 5:53 PM


Re: gravitational theory of relativity
I'm sorry, I don't know what you are talking about. Why should a non-rotating object begin to rotate?
Euhm, are you from another world?
When you are leaving Earth and you are above Earth. Do you see the Earth rotation yes or no?
I said "non-rotating". The Earth is rotating. It does not matter what frame you or I are in, the Earth is rotating. While rotating with the Earth, we observe coriolis forces so we know that we are rotating.

This message is a reply to:
 Message 174 by Maartenn100, posted 08-15-2011 5:53 PM Maartenn100 has replied

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 Message 178 by Maartenn100, posted 08-16-2011 11:15 AM cavediver has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 187 of 230 (680160)
11-18-2012 5:14 AM
Reply to: Message 186 by Bolder-dash
11-18-2012 4:19 AM


Re: Twin paradox space time diagram
Nonukes, thanks for the attempt, but I am not sure you really read very clearly what I am questioning.
Yes he did.
Acceleration has nothing to do with it
No, it has everything to do with it.
From what I now understand, Einstein wasn't even able to answer the question of the twins paradox.
where do you get this crap? He answered it in multiple ways. Just as with many aspects of Relativity (General and Special), there are multiple answers,explanations, or analogies because our non-relativistic intuition sees relativistically unified concepts as distinct.
And as a side point, if all things are relative when considering speed, and one can always reverse which is the moving object
No, you can't. Not when acceleration is involved.
...why in my example can only one experience g force? In other words, if both are moving relative to the other, why does the twin circling feel g force, while the twin being circled feel nothing?
But that's impossible, because, as you have so correctly stated, acceleration has nothing to do with it... it's a mystery.
It seems only one can be said to be truly moving.
Oh my god, you mean you have found an asymetry between the two travellers???? But, but, this changes, like EVERYTHING. Who would have guessed?
If you are seriously interested in this stuff, why not stop reading crap from the internet such as that paper to which you linked, and treat yourself to a copy of Misner Thorne and Wheeler's "Gravitation". It is a graduate text, but much of their Track 1 material (minus the mathematics) can be understood by an interested reader with sufficient determination.
If nothing else, it will open your eyes to level of thought that has gone into 20th Century Relativistic physics, and hopefully convince you that an interested amateur has as much chance of critiquing the science as a paper plane maker has of finding the design flaws in an Airbus A380.

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 189 of 230 (680162)
11-18-2012 5:35 AM
Reply to: Message 188 by Bolder-dash
11-18-2012 5:18 AM


Re: Twin paradox space time diagram
What are the reality of physics that allows one inertial frame to cause a paradox of time, while a shifted inertial frame invalidates the outcome?
Space-time is four-dimensional. Points in space-time are called events. Let's say event A occurs before event B ("before" meaning that it is possible that a signal can be sent from A to B without exceeding the speed of light.) For example, event A is 4pm GMT 18/11/2012 on Earth, and event B is 4pm GMT 18/11/2013 also on Earth.
The 4-dimensional distance along the 4-d path taken through space-time from A and B is the time experienced. Because the distance measure on 4d space-time is not your simple Pythagoras but the more complex Minkowski metric , this means that the more curved the path through space-time, the *shorter" the distance (and hence time) between the two events.
To create a curved path through space-time, you will need to utilise non-inertial frames. i.e. you will need to accelerate / decelerate.
Thus, if non-inertial frames are involved in your path through space-time from A to B, you know that your path will be more curved than a path that does not involve non-inertial frames. And by simple 4d Minkowski geometry, your path will therefore be shorter, and you will experience less time on your path.

This message is a reply to:
 Message 188 by Bolder-dash, posted 11-18-2012 5:18 AM Bolder-dash has replied

Replies to this message:
 Message 190 by Bolder-dash, posted 11-18-2012 6:25 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 191 of 230 (680167)
11-18-2012 6:51 AM
Reply to: Message 190 by Bolder-dash
11-18-2012 6:25 AM


Re: Twin paradox space time diagram
Do you wish to make a wager as to whether or not Einstein believed he was able to satisfactorily answer the twins paradox problem?
Not sure exactly how we're going to prove that one without reanimating Albert, and last time I saw his brain, it had been thoroughly chopped up - so I wouldn't be entirely confident in what we'd get back.
Every attempt to show that Einstein was confused by the Twin's Paradox that I have seen was written by an idiot who while being thoroughly clueless of relativistic physics, was convinced that he understood it on a par with the rest of us professionals. So, bring it on...
Secondly, why does an accelerated-decelerated path necessary become a curved path?
Because that is what "curved" means... you know, 2nd derivatives and higher of displacement with respect to the time coordinate being non-zero, and all that?
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 190 by Bolder-dash, posted 11-18-2012 6:25 AM Bolder-dash has replied

Replies to this message:
 Message 192 by Bolder-dash, posted 11-18-2012 7:09 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(2)
Message 193 of 230 (680170)
11-18-2012 7:27 AM
Reply to: Message 192 by Bolder-dash
11-18-2012 7:09 AM


Re: Twin paradox space time diagram
First, I suppose we could use quotes by Einstein himself, that display his own doubts about solving the twins paradox
Well, you can try. Of course, there would by necessity be times when he would be unsure - sure as before he had even entertained Special Relativity, and around the time that the apparent clock paradox (as he termed it) first occured to him. But I'm sure you have something much more concrete than that...
Really, I thought you did this for a living
Not for the best part of 20 years. And then, history has never been my strong point.
I would hate to embarrass you by having an uneducated fop like me, show you the emptiness of your arrogance.
What part of "bring it on" did you not understand?
Secondly, so if we have acceleration and declaration as part of the equation of the paradox, then the paradox becomes invalid, because it no longer deals with Special Relativity?
Why does it not deal with Special Relativity? Special Relativity is essentially the physics of Minkowski spactime. You're not believing all that bullshit about acceleration not being part of Special Relativity are you?
And we can't accelerate and decelerate in a straight line, because by definition acceleration and deceleration is curved?
accelerating in a straight line in 3d, is creating a curve in 4d. Did you not look at time-distance graphs in school for uniform motion and accelerating motion? Can you not see the connection?
ABE:
I would hate to embarrass you by having an uneducated fop like me, show you the emptiness of your arrogance.
Arrogance?????
You mean something like:
Nonukes, thanks for the attempt, but I am not sure you really read very clearly what I am questioning.
Acceleration has nothing to do with it, it merely deals with the speed
Einstein wasn't even able to answer the question of the twins paradox.
It appears to just be a completely fabricated fun scientific exercise, with no basis in fact.
Just anther way of playing with numbers, to create false ideas.
You need to look into the mirror Bolder-dash, and perhaps you'll understand why I treat many of your comments with the contempt they deserve.
Edited by cavediver, : No reason given.
Edited by cavediver, : graph

This message is a reply to:
 Message 192 by Bolder-dash, posted 11-18-2012 7:09 AM Bolder-dash has replied

Replies to this message:
 Message 198 by Bolder-dash, posted 11-18-2012 10:48 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 197 of 230 (680182)
11-18-2012 10:33 AM
Reply to: Message 196 by Bolder-dash
11-18-2012 10:21 AM


Re: Twin paradox space time diagram
Cavediver is supposed to be an expert in this field, and he can't seem to even answer this in English, so maybe you can.
I'm sorry, was I pitching my explanations a bit too high for you? Just say the word and I'll dumb it down to your level. Now, you were going to bring me some Einstein quotes, I believe...?

This message is a reply to:
 Message 196 by Bolder-dash, posted 11-18-2012 10:21 AM Bolder-dash has replied

Replies to this message:
 Message 199 by Bolder-dash, posted 11-18-2012 10:51 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


(1)
Message 200 of 230 (680191)
11-18-2012 11:05 AM
Reply to: Message 198 by Bolder-dash
11-18-2012 10:48 AM


Re: Twin paradox space time diagram
At first you come out saying that it is crap to suggest that Einstein wasn't satisfied with answering this problem, and now you meekly assert that yes, he may have had doubts at times
oh dear, you really need to work on that English comprehension. I was simply and facetiously pointing out that of course Einstein would not have had an answer before the actual question had arisen, and in the minutes before he had managed to actually understand the issue. Do try to keep up.
when in fact you know full well he had doubts about this issue up until his deathbed.
Really? I know full well? Jesus, you must not only be a mind reader but you must be able to see deep into my subconscious mind, because my conscious mind has no such knoweldge and considers the idea that he had such doubts utterly laughable. See? -->
Einstein repeatedly stated that he wasn't sure that relativity could be applied to real life physical events.
No, he did not. Or certainly not that I have seen.
"The idea of the measuring rod and the idea of the clock coordinated with it in the theory of relativity do not find their exact correspondence in the real world. It is also clear that the solid body and the clock do not in the conceptual edifice of physics play the part of irreducible elements, but that of composite structures, which may not play any independent part in theoretical physics."
Are you really so stupid as to think that the above quote suggests that "he wasn't sure that relativity could be applied to real life physical events"? Does it not occur to you, even for the briefest of moments, that Einstein is here talking of the unphysicality of idealised measuring devices? Something that any of us who have actually taught Relativity have stressed ourselves to our students.
Jesus, Bolder-dash, if you are trying to convince us of your utter ineptitude, it is working wonderfully.
blah blah blah
Yep,. Bolder-dash, keep yapping... it is entertaining... for now.
Edited by cavediver, : No reason given.

This message is a reply to:
 Message 198 by Bolder-dash, posted 11-18-2012 10:48 AM Bolder-dash has replied

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 Message 201 by Bolder-dash, posted 11-18-2012 11:12 AM cavediver has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 202 of 230 (680194)
11-18-2012 11:13 AM
Reply to: Message 199 by Bolder-dash
11-18-2012 10:51 AM


Re: Twin paradox space time diagram
Your question is far too vague. State exactly what you mean. Constant speed does not mean the absence of acceleration; that would be constant velocity. If constant velocity, how are you bringing the two "twins" back into contact?

This message is a reply to:
 Message 199 by Bolder-dash, posted 11-18-2012 10:51 AM Bolder-dash has replied

Replies to this message:
 Message 203 by Bolder-dash, posted 11-18-2012 12:04 PM cavediver has replied
 Message 204 by Bolder-dash, posted 11-18-2012 12:09 PM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 206 of 230 (680208)
11-18-2012 1:12 PM
Reply to: Message 203 by Bolder-dash
11-18-2012 12:04 PM


Re: Twin paradox space time diagram
1) twin who stays home ages more
2) twin who stays home ages more
3) third party observer in the middle see both clocks running at same rate

This message is a reply to:
 Message 203 by Bolder-dash, posted 11-18-2012 12:04 PM Bolder-dash has not replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 207 of 230 (680209)
11-18-2012 1:16 PM
Reply to: Message 204 by Bolder-dash
11-18-2012 12:09 PM


Re: Twin paradox space time diagram
1) the travelling twin is younger

This message is a reply to:
 Message 204 by Bolder-dash, posted 11-18-2012 12:09 PM Bolder-dash has not replied

  
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