Why two mass attracts each other?

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Farsight said:
It isn't false at all, Tach. The twins "paradox" is where you and I are passing one another at some relativistic speed, and I say your parallel-mirror light-clock is going slower than mine because its light-path is zigzagging, and you say mine is going slower than yours and its light-path is zigzagging. People think this is amazing but it isn't. It's no more amazing than when we're separated by distance, and I say you look smaller than me whilst you say I look smaller than you.
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This couldn't possibly be any more wrong. The "twin paradox" is about differences in proper time between observers who experience acceleration, and observers who don't. In other words, it is about differences in proper times between asymmetric frames of reference. I will refrain from posting the maths here, since it is a waste of time.
 
Markus Hanke said:
This couldn't possibly be any more wrong. The "twin paradox" is about differences in proper time between observers who experience acceleration, and observers who don't. In other words, it is about differences in proper times between asymmetric frames of reference. I will refrain from posting the maths here, since it is a waste of time.
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So invariant proper time changes in space-time curvature?
 
Markus Hanke said:
As expected, the minute Farsight rejoins the discussion we are back to going in circles.
Petty, but hardly surprising. In any case, for those with an interest in what really goes on, refer here :

http://www.sciforums.com/showthread.php?134711-General-Relativity-Primer

Otherwise, there is nothing more to be gained from this thread.
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Yes.. i have read the thread.. Math makes understanding concepts very opaque.. I haven't studied them at all..

By the way.. i am working in basic mathematics.. I am 15 years old...
 
ash64449 said:
So invariant proper time changes in space-time curvature?
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I am not completely sure what you mean by this. The "invariant" here means that all observers agree on the proper time between the same two events, i.e. on the arc length of a given worldline connecting the two events. It does not mean that all possible worldlines between the events are of the same length, because clearly they aren't. Hence the "twin paradox" - an observer at rest and an accelerated observer trace out worldlines of different lengths, connecting the same two events. Physically that is because the accelerated observer's worldline possesses intrinsic curvature, whereas the stationary twin's worldline doesn't ( we assume he is not located in some gravitational field ).
 
ash64449 said:
Yes.. i have read the thread.. Math makes understanding concepts very opaque.. I haven't studied them at all..

By the way.. i am working in basic mathematics.. I am 15 years old...
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Ok, at that age no one will expect you to understand the maths required for GR; you would first have to study basic calculus before even standing a chance of tackling GR. But still, you can familiarize yourself with the concepts, if not the maths.
 
Markus Hanke said:
I am not completely sure what you mean by this. The "invariant" here means that all observers agree on the proper time between the same two events, i.e. on the arc length of a given worldline connecting the two events.
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I mean the same too.

Markus Hanke said:
It does not mean that all possible worldlines between the events are of the same length, because clearly they aren't. Hence the "twin paradox" - an observer at rest and an accelerated observer trace out worldlines of different lengths, connecting the same two events. Physically that is because the accelerated observer's worldlines possesses intrinsic curvature.
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I think people disagreed because one is accelerating frame as a result one takes different wordline. yeah.. You statement does makes sense to me.

But anyway for uniform frame of reference,i think everyone agrees with the invariant interval between the two events.

And i have understood that this is why we mean that space cannot be separated from time and as a result space-time.
 
Markus Hanke said:
Ok, at that age no one will expect you to understand the maths required for GR; you would first have to study basic calculus before even standing a chance of tackling GR. But still, you can familiarize yourself with the concepts, if not the maths.
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Yes. that is the one i will study next year.. Now i don't think i will understand GR.

I think when i talked to you in some other thread,you said i need to understand mathematics of GR to fully understand what GR means and it is tough to explain everything in terms of physical principle..

So i won't understand GR.. But SR seems to be very good.. i can understand them but i am sure that i don't understand it fully.. always i was corrected by someone..
 
ash64449 said:
But anyway for uniform frame of reference,i think everyone agrees with the invariant interval between the two events.
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Yes, precisely. If you eliminate the acceleration, you also eliminate any discrepancies in proper times. There can be no "twin paradox" for purely inertial observers.

you said i need to understand mathematics of GR to fully understand what GR means
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True, I did say that. However, the emphasise here is on fully; you can still get the basic principles without knowing any of the maths, that is definitely possible. The trick is to realize where the limitations of the popular "analogies" are. Some things can be explained in words, some things can't. A full grasp of GR is not possible without knowing the maths, but a basic understanding definitely is.
 
Markus Hanke said:
This couldn't possibly be any more wrong. The "twin paradox" is about differences in proper time between observers who experience acceleration, and observers who don't. In other words, it is about differences in proper times between asymmetric frames of reference. I will refrain from posting the maths here, since it is a waste of time.
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It isn't wrong.

Here's a webpage that explains the twins paradox fairly well: http://faraday.physics.utoronto.ca/PVB/Harrison/SpecRel/Flash/TwinParadox.html

Note this: "So in one frame of reference Sue ends up younger, while from the other viewpoint Lou ends up younger. This is the paradox".

Markus Hanke said:
There can be no "twin paradox" for purely inertial observers.
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The twins paradox has been simplified to "passing clocks", Markus. Both observers assert that the other observer's clock is running slower than his own.
 
Undefined said:
Please read my post to Tach regarding Farsight's post. It questions Tach's relevance when saying "false" re Farsight's statement. So your above personal comment seems premature and anyway is against site rules about flaming and trolling (especially in this instance). Please do this forum and yourself the favor of retracting or deleting your own objectionable science-empty and personal attack post. Thankyou.
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Relativity is not Newtonian mechanics.

Personal attacks, no. All I'm saying is that Farsight may suffer from Shell Shock and that could be the reason I don't understand him. I still try to see the good in everyone. But yes, maybe this is my failing.
 
Farsight said:
Here's a webpage that explains the twins paradox fairly well: http://faraday.physics.utoronto.ca/PVB/Harrison/SpecRel/Flash/TwinParadox.html
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That presentation confirms exactly what I explained - the difference in proper times arises due to the fact that the two frames aren't symmetric ( see slide 4 ). One of them experiences acceleration, the other one doesn't. Without acceleration there would be no differences in proper times. Time dilation between inertial frames in uniformly relative motion does not effect the proper times of the observers; they are invariant under Lorentz transformations. I explicitly quote the relevant section here for you, since you are so fond of quotes :

"We know that we can only do physics in inertial frames of reference. However, Sue is not in such a frame of reference. The Principle of Inertia is violated for her when she blasts off from Earth, again when she fires her thrusters to turn around, and once again when she lands on Earth."

So she experiences acceleration at three points during her journey, which is exactly what induces the differences in proper times between the observers. Note that this is all about proper times, not coordinate times. You simply do not get any paradoxes when working only in purely inertial frames - I can even prove this to you mathematically, for the general case. Would you like to see it ?
 
Undefined said:
Just to make it clear for my naive understanding of your position re handsa's "real time" conception/opinion, what do you, ash64449, mean when you say "Proper Time is invariant.. it can never change"? Are you referring to the rate of counting/ticking off increments of standard seconds etc, or do you refer to some "absolute universal" increment of time that does not vary according to what "standard increments" we human scientists choose and conventionally agree on to use for "timing" processes?
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Here "arrow of time" can be considered as invariant or uniform.

In the context of relativity for "proper time" see here.

In the context of relativity for "co-ordinate time" see here.
 
Farsight said:
The twins paradox has been simplified to "passing clocks", Markus. Both observers assert that the other observer's clock is running slower than his own.
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Another funny mistake, John, that illuminates your level of understanding, or lack of thereof. The twins paradox is all about elapsed proper time, not about clock rate. You are freely mixing up two different concepts.
Markus nailed you further on your lack of understanding of elapsed proper time as a function of path through spacetime.
 
Markus Hanke said:
That presentation confirms exactly what I explained - the difference in proper times arises due to the fact that the two frames aren't symmetric ( see slide 4 ). One of them experiences acceleration, the other one doesn't. Without acceleration there would be no differences in proper times. Time dilation between inertial frames in uniformly relative motion does not effect the proper times of the observers; they are invariant under Lorentz transformations. I explicitly quote the relevant section here for you, since you are so fond of quotes :

"We know that we can only do physics in inertial frames of reference. However, Sue is not in such a frame of reference. The Principle of Inertia is violated for her when she blasts off from Earth, again when she fires her thrusters to turn around, and once again when she lands on Earth."

So she experiences acceleration at three points during her journey, which is exactly what induces the differences in proper times between the observers. Note that this is all about proper times, not coordinate times. You simply do not get any paradoxes when working only in purely inertial frames - I can even prove this to you mathematically, for the general case. Would you like to see it ?
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So If the trip was symmetrical,when they reunite,what is the result? (just an assumption that "if the trip is symmetrical".Just wondering what would happen when they meet each other if the trip was symmetric)
 
ash64449 said:
Sorry, Your 'arrow of time' is not same as 'proper time'.
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"Arrow of Time" is the 'elapsed time' between two events. This time may not be measured by a clock. This time only can be known from sequence of events ie 'cause' and 'effect', where 'cause' precedes the 'effect'.

It seems "proper time" is dependent upon a clock.


So, "arrow of time" and "proper time" are not same.
 
hansda said:
"Arrow of Time" is the 'elapsed time' between two events. This time may not be measured by a clock. This time only can be known from sequence of events ie 'cause' and 'effect', where 'cause' precedes the 'effect'.

It seems "proper time" is dependent upon a clock.


So, "arrow of time" and "proper time" are not same.
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No. Proper time is not dependent on clocks at all.
 
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