Why two mass attracts each other?

[ash64449]

Which equivalence principle, you are following? There are many equivalence principles. Give the specific statements of the principle you are following or give reference.

Einstein's Equivalence principle.. Don't know?

Give reference.

Take a copy of the pdf book : Theory Of Relativity or go to wikipedia

That is Newtonian concept. Einstein's concept is different.

Gravity is still attractive in Einstein's concept. Oh.. so you are saying gravity is repulsive too?

You are following 'Newtonian model' or 'Einstein's model' or mixing both the models?

Always following Einstein's model

NO. Energy is more fundamental than mass.

Ok. there is nothing fundamental than the other.. haven't you studied the 7 important fundamental quantities.. i mean that one.. and don't think i think mass is the source of gravity.. i know energy is the one..you misunderstood me.. you should have not asked why two "masses" attract each other at all.

Are you referring Newtonian model?

Yes.. i said 'earlier' People thought mass is the reason for gravitational force...

I think here you are considering 'Einstein's model'.


I think perhaps you are mixing up the 'two models of gravity'. Consider any one model and try to explain.

Not at all.. you haven't understood anything from my statement at all..

 

[hansda]

invariant means dosen't change

Is a clock 'invariant'?

 

[OnlyMe]

So once again - what is called the "twin paradox" in physics literature is not just any old gedanken experiment, but a very specific set of circumstances, namely the comparison between an inertial and a non-inertial frome of reference in terms of the proper times they measure. That is how "twin paradox" is defined :

Since I have not been following the whole discussion, the following is only intended to question the above statement. I am reasonably sure none of this is news to you, and that the above quote was intended in the greater context of the larger disscussion.

Some of the earliest examples did not include acceleration. They assumed instantaneous inertial but relativistic velocity and were intended only to address time dilation associated with relative velocity. Acceleration was added, as it is required for the twins to begin and end in a common frame, and yet still have experienced a period of time dilation associated with a difference in their relative velocity.., which as the hypothetical is generally set up is the result of only one twin changing frames.

The main point here is that there is no, "one very specific set of circumstances", that can be said to be "the" twin paradox. The original began as a comparrison of two inertial frames in relative motion with respect to one another, and since then there have been many variations, most of which have included acceleration. The inclusion of acceleration is only required as a practical explanation (or solution), of how the twins begin in a common frame, experience a period of time in relative motion with respect to each other and then return to a common frame to compare clocks.

Einstein's earliest references did not include twins or acceleration. It was the lack of acceleration that leads to an apparent paradox and the inclusion that leads to a solution without paradox.

 

[hansda]

In mathematical terms, the "stay at home" twin measures

$$T=1yr$$ on his clock

while the "traveling twin" measures

$$\tau=\int_0^T{\sqrt{1-(v/c)^2}dt}<T$$



Wrong: $$\tau=\int_0^T{\sqrt{1-(v/c)^2}dt}<T$$

$$\tau=11mo$$ and $$T=1yr$$

This is freshman physics , John, when will you ever learn?

Have you read this paper on time.


This paper suggests there is no "time reversal".


That means "time" is invariant.

 

[OnlyMe]

Have you read this paper on time.


This paper suggests there is no "time reversal".


That means "time" is invariant.

It doesn't mean time is invariant. It only means it does not run backwards. Time dilation does not cause clocks to run backward, IE time reversal. It just affects the rate at which clocks record change or time.

 

[hansda]

It doesn't mean time is invariant. It only means it does not run backwards. Time dilation does not cause clocks to run backward, IE time reversal. It just affects the rate at which clocks record change or time.

"Time Dilation" is 'slowing down of time' or 'slowing down of clock'?

 

[rpenner]

OnlyMe -- I disagree. I think it is a statement of hyperbolic geometry.

If $$t_2 > t_1$$ and $$c^2 (t_2 - t_1)^2 > (x_2 - x_1)^2$$ then it follows that of all possible time-like paths that the inertial path: $$x - x_1 = \frac{x_2 - x_1}{t_2 - t_1} ( t - t_1 ) $$ is the path with the longest proper time. (The same holds if the x symbols is everywhere replaced by a 3-vector.) (Proof: pick any point that is both in the future light cone of $$(t_1,x_1)$$ and in the past light cone of $$(t_2,x_2)$$, and show that the sum of the proper times from start to this point to the end is bounded above by the original proper time and this is only an equality when the point is on the original inertial path.) And this is true if the other path is differentiable so one may speak of finite acceleration or piecewise differentiable so that one may speak of finite velocity changes. Because the Lorentz transform preserves proper times, one can fairly Lorentz transform to coordinates where the inertial path is motionless; that obscures the geometry because "at rest" seems more special than inertial but in Relativity they are the same.

The other path is not-inertial which is more important to the geometry than descriptions like "traveling", "accelerating" or "making a round trip".

 

[quantum_wave]

OnlyMe -- I disagree. I think it is a statement of hyperbolic geometry.

If $$t_2 > t_1$$ and $$c^2 (t_2 - t_1)^2 > (x_2 - x_1)^2$$ then it follows that of all possible time-like paths that the inertial path: $$x - x_1 = \frac{x_2 - x_1}{t_2 - t_1} ( t - t_1 ) $$ is the path with the longest proper time. (The same holds if the x symbols is everywhere replaced by a 3-vector.) (Proof: pick any point that is both in the future light cone of $$(t_1,x_1)$$ and in the past light cone of $$(t_2,x_2)$$, and show that the sum of the proper times from start to this point to the end is bounded above by the original proper time and this is only an equality when the point is on the original inertial path.) And this is true if the other path is differentiable so one may speak of finite acceleration or piecewise differentiable so that one may speak of finite velocity changes. Because the Lorentz transform preserves proper times, one can fairly Lorentz transform to coordinates where the inertial path is motionless; that obscures the geometry because "at rest" seems more special than inertial but in Relativity they are the same.

The other path is not-inertial which is more important to the geometry than descriptions like "traveling", "accelerating" or "making a round trip".

Darn it, I was following the concept of time and agreeing that it appears to be variable when being measured but cannot run backwards. Are you disagreeing with that, and do your equations present a case to support any disagreement?

 

[OnlyMe]

OnlyMe -- I disagree. I think it is a statement of hyperbolic geometry.

If $$t_2 > t_1$$ and $$c^2 (t_2 - t_1)^2 > (x_2 - x_1)^2$$ then it follows that of all possible time-like paths that the inertial path: $$x - x_1 = \frac{x_2 - x_1}{t_2 - t_1} ( t - t_1 ) $$ is the path with the longest proper time. (The same holds if the x symbols is everywhere replaced by a 3-vector.) (Proof: pick any point that is both in the future light cone of $$(t_1,x_1)$$ and in the past light cone of $$(t_2,x_2)$$, and show that the sum of the proper times from start to this point to the end is bounded above by the original proper time and this is only an equality when the point is on the original inertial path.) And this is true if the other path is differentiable so one may speak of finite acceleration or piecewise differentiable so that one may speak of finite velocity changes. Because the Lorentz transform preserves proper times, one can fairly Lorentz transform to coordinates where the inertial path is motionless; that obscures the geometry because "at rest" seems more special than inertial but in Relativity they are the same.

The other path is not-inertial which is more important to the geometry than descriptions like "traveling", "accelerating" or "making a round trip".

Admittedly, I over talk things which confuses my intent as often as not. I was not trying to address the current discussion or any definitive resolution/solution to the twin paradox.

I was really only commenting on the statement that, "sounded" like there was only one construction, and that it included acceleration. There was an apparent paradox in Einstein's initial construction(?), which did not include any mention of acceleration or twins. The phrase, "what is called the "twin paradox" in physics literature is not just any old gedanken experiment, but a very specific set of circumstances".., is really all I was commenting on. I don't believe the twin paradox can be constrained to any specific construction...

Your post goes way beyond anything I intended to be addressing.

 

[OnlyMe]

Darn it, I was following the concept of time and agreeing that it appears to be variable when being measured but cannot run backwards. Are you disagreeing with that, and do your equations present a case to support any disagreement?

I am pretty sure rpenner was commenting on my post re: the twin paradox, rather the one on time reversal.., unless he was somehow merging the two. My initial intent in the two posts did not overlap.

My post on time reversal was also, limited in intended scope. It was only meant to say that time dilation is not the same as time reversal, which I read to mean time going backwards.

 

[OnlyMe]

"Time Dilation" is 'slowing down of time' or 'slowing down of clock'?

Hansda, time dilation is not something that is measured in the same frame that the clock is in. You won't see a clock you are holding speed up or slow down, as a function of time dilation.

Time dilation is measured when comparing clocks that are in different frames, which may be frames moving at different velocities or at different distances from a significant gravitational source.

In either case time dilation does not ever result in time going backwards. Which is what I understood your reference to time reversal to mean.

 

[Tach]

I am pretty sure rpenner was commenting on my post re: the twin paradox,

He's pointing out the mistakes in your posts. Like these:

and yet still have experienced a period of time dilation associated with a difference in their relative velocity.., which as the hypothetical is generally set up is the result of only one twin changing frames.

The twins paradox has nothing to do with time dilation, nor with "difference in their relative velocity". As an aside, are you writing in a non-English language and are you using an automatic language translator? I am asking because many of your sentences cannot be parsed.

 

[OnlyMe]

He's pointing out the mistakes in your posts.

Tach, my whole post bills down to two things...

First, I said it was not a statement on the discussion.., or as the quote I referred to, related to that discussion.

Second, the twin paradox has been constructed in a variety of ways.., even in the early years, each attempting to address some issue someone had at the time. There is generally no "ONE" correct way to construct the hypothetical. I generalized the statement I was commenting on as, extending beyond the basic twin paradox and its solution.

I was reading that post out of the context of the discussion and admitted that up front.., and that, in the context of the thread discussion what I was pointing out, may not be applicable.

He's pointing out the mistakes in your posts.

And his (rpenner's) post was on the science, not a simple you're wrong type statement like yours.

 

[OnlyMe]

The twins paradox has nothing to do with time dilation, nor with "difference in their relative velocity". As an aside, are you writing in a non-English language and are you using an automatic language translator? I am asking because many of your sentences cannot be parsed.

Explain how one twin aging faster than the other has nothing to do with time dilation

And no I am not using a translator and the root causes for any difficulties you are seeing in my posts are a lack of proof reading and other issues not related to any discussion on these forums.

 

[Undefined]

See my last post. What is called the "twin paradox" is a very specific scenario that involves the comparison between two frames, one of which is inertial and the other one is not. Your argument is therefore meaningless in this context, because we are not comparing two symmetric frames in relative motion, that is why acceleration is important "all of a sudden".

Btw, if you compare two purely inertial frames, then obviously the acceleration history has no impact on time dilation between the frames, simply because there is no acceleration, otherwise the frames wouldn't be inertial ! The kind of time dilation you find between purely inertial frames if symmetrical, i.e. you can freely interchange the frames without changing the physical outcome. Not so in the "twin paradox" scenario - you cannot interchange the frames, because they are physically distinguishable due to the presence of acceleration in one of them. That is the whole point.

So, to sum up :

1. Time dilation between inertial frames is a function of their relative velocity only, and has nothing to do with acceleration. Proper time between two given events A and B is an invariant, so all observers will agree on it, regardless of their state of relative motion.
2. Time dilation between inertial and non-inertial frames does depend on acceleration history, and the proper times here are no longer the same for all observers. That is why the travelling twin measures a shorter proper time than the stationary twin.

Also, acceleration and the presence of a gravitational field are physically indistinguishable as per the equivalence principle; "non-gravitational acceleration" is a term that makes little physical sense.

With all due respect, Markus Hanke, I ask you naively: How do you think differing "inertial frames" got to be differing motion states? Their precursor acceleration history, that's how? You conveniently leave out acceleration when it suits, but then include it when it suits the opposite view? That is called "wanting it both ways", isn't it? Either acceleration history is automatically involved in all "differing inertial motion scenarios", or it isn't? You can't select the instances when it is included/excluded just for your convenient ignoring of that aspect when making "explanations" which "want it both ways"? So if your argument invalidates the twin experiment validity, it automatically invalidates ALL such experimental/theoretical "explanation scenarios" you use as well, yes?

Edit/: I expressly included the qualifier "non gravitational" acceleration to forestall Tach chiming in with another diversion saying "there is no gravitational acceleration in the twin scenario!" or some such evading tactic to distract from his failures. Tach is good at that pettiness tactic, as has been observed objectively by practically all here, yes?

 

[Tach]

Explain how one twin aging faster than the other has nothing to do with time dilation

Post 595.

And no I am not using a translator and the root causes for any difficulties you are seeing in my posts are a lack of proof reading and other issues not related to any discussion on these forums.

But most of them make no sense whatsoever in terms of physics or they are outright mistakes. I think that doesn't come from lack of proofreading.

 

[OnlyMe]

Post 595.

From post 595 for the traveling twins measurement of time: $$\tau=\int_0^T{\sqrt{1-(v/c)^2}dt}<T$$

Two references from Wiki - Time Dilation and The Twin Paradox (respectively)

In the theory of relativity, time dilation is an actual difference of elapsed time between two events as measured by observers either moving relative to each other or differently situated from gravitational masses.

If twins are born on the day the ship leaves, and one goes on the journey while the other stays on Earth, they will meet again when the traveler is 6 years old and the stay-at-home twin is 10 years old. The calculation illustrates the usage of the phenomenon of length contraction and the experimentally verified phenomenon of time dilation to describe and calculate consequences and predictions of Einstein's special theory of relativity.​

​

You used a Lorentz transform to determine the time dilation between the stay at home twin's measurement of the passage of time and that of the traveling twin.

Wiki resources both define time dilation relative to velocity (the traveling twin) and time dilation directly in the twin paradox.

I wasn't saying that time dilation is what the solution to the apparent paradox is about, but it does play into the age difference experienced by the two twins.

But most of them make no sense whatsoever in terms of physics or they are outright mistakes. I think that doesn't come from lack of proofreading.

You could always just ask for clarification, when you don't understand something, but that would be a first.

 

[Tach]

From post 595 for the traveling twins measurement of time: $$\tau=\int_0^T{\sqrt{1-(v/c)^2}dt}<T$$

Two references from Wiki - Time Dilation and The Twin Paradox (respectively)

Wiki is not the standard for doing physics and cherry picking quotes from wiki is even less. Total elapsed proper time and time dilation are two different concepts, the twins paradox uses the former and not the latter.

 

[OnlyMe]

Wiki is not the standard for doing physics and cherry picking quotes from wiki is even less. Total elapsed proper time and time dilation are two different concepts, the twins paradox uses the former and not the latter.

You are twisting and turning here Tach, but you are right. Each twin measure the total elapsed time in their own frame of reference... And the difference in the two total proper times, is the result of time dilation....

BTW remember that bit about Wiki quotes, next time you toss one out there.

 

[Tach]

You are twisting and turning here Tach, but you are right. Each twin measure the total elapsed time in their own frame of reference... And the difference in the two total proper times, is the result of time dilation....

No, it isn't, obviously you don't know the difference. The former is accumulated time, the latter is time ratios.

BTW remember that bit about Wiki quotes, next time you toss one out there.

I don't do physics via wiki cherry picking.