Can the Twin Paradox be simplified?

[OnlyMe]

To tell you that I have already answered the question in detail and to get you go find the respective post.

Tach, that is an evasive and dishonest answer. This thread is now nearing 700 posts and is over 200 printed pages long.

If you know which post you are referring to just post the # or a link, or quote in a new post.

 

[OnlyMe]

The mid point of the trip.

This goes back to the ball analogy I raised with Tach.

If you consider the trip between the first and second turn around points, the ship is effectively behaving like a ball that has been thrown in the air. If it had a little lateral momentum it would describe a parabolic arc.

This however, implies that at a specific moment at the peak of the arc - the moment of the turn around in the original paradox, there is a moment where everything is at rest with regards to the stay at home twin - a moment of weightlesness which introduces a discontinuity in amongst all of this (even though the acceleration is equal in magnitude and direction on either side of this point).

I was aware of that issue and was waiting to see if you could get around it. The same thing comes up in spades for the canaval ride version of suspending the crews compartment that I suggested.

The only way I see to in any way address this, would be to discard the straight path out and back and essentially change the traveling twins path to a great loop. Even that would require that the clocks be synchronized and comparred for some orbital distance. Which might not even wind up with a twin in orbit on return.

This in many ways returns to a variation of the twin in orbit, that I believe Einstein had introduced at some point. Excluding the free fall conditions experienced in orbit. But I am unsure if that was even something considered in the original orbiting twin construction. I don't remember it in enough detail to know for certain and have been unable to locate a reference. Which means it is likely somewhere in the hard copy portion of my reference material and covered in dust.

 

[RJBeery]

For some reason, gentlemen, this topic has lost interest to me. I've laid out my reasoning many times over for many readers which, if not irrefutable, at least has logical merit.

I'll put together a sloppy summary before I bid you adieu, make some breakfast for my kids, and unsubscribe from this thread. To recap, I continue to make the claim that acceleration (and not relative velocity) is a necessary, causal component to absolute, unambiguous time dilation. Observations:

1) The usual counter-examples given to this stance are the Third Twin scenario and the Orbiting Muon. The time dilation in the Third Twin was proven to be ambiguous despite the usual misinterpretation. The experiment in which a muon under "magnetic orbital acceleration" is actually a misapplication of the EEP because, as we know, an object in free-fall does not experience acceleration as one does while resting on the ground, for example. Therefore, we should expect such a muon to possess the same lifetime as one which has been accelerated to that same linear velocity and energy (which is exactly what we find).

2) Clock A in the nose and clock B in the tail of a perpetually-accelerating rocket ship, OR clock A on a large non-rotating mass with clock B in the dead of space are two scenarios which would display unambiguous time dilation. In both scenarios we have acceleration (either direct or via EEP), yet we have no change in displacement over time between the clocks, hence no relative velocity.

3) If displacement is changing over time between two clocks (as is required for relative velocity to exist), two co-location events must occur in order to establish unambiguous time dilation. Two co-location events require acceleration for at least one of the clocks. Strictly speaking, this is sufficient to prove the necessary nature of acceleration but seems to get written off as a "technicality".​

In summary, we have no scenario in which unambiguous time dilation exists devoid of acceleration; we do have scenarios in which unambiguous time dilation exists devoid of relative velocity; lastly, we have that "last line of defense", even if it's a technicality, that says acceleration is required for there to be differing world line lengths between two co-location events...given all of this, I believe I can be forgiven for questioning the mainstream view on this subject. :shrug: Thanks

 

[OnlyMe]

To tell you that I have already answered the question in detail and to get you go find the respective post.

Tach, if this is the post you were referring to,

Post#564
Good , you corrected your errors. Now trouble is , the above problem statement doesn't help any with a twin paradox problem. Turns out that the traveling twin always returns younger, regardless of his acceleration. Which tells you what? That acceleration doesn't matter, only speed does. This also happens to be the standard view of mainstream physicists....
Correct application of the equations of accelerated motion in SR also teach you another fascinating thing, that the age differential between the two twins is:

$$\Delta \tau=\tau_h-\tau_r=\tau_h(1-\frac{arcsinh(\beta \gamma)}{\beta \gamma})$$

where

$$\tau_h$$ is the age of the "stay at home twin"
$$\tau_r$$ is the age of the "rocket twin"
$$\beta=\frac{v_1}{c}$$
$$v_1$$ is the cruising speed of the "rocket twin"
$$\gamma=\frac{1}{\sqrt{1-(v_1/c)^2}}$$

I did not make a response, because I read your introductory statements, as consistent with the intent of the post you were responding to, (which included the correction from its original form that both you and Trippy had pointed out.

I do not want to begin another debate involving the construction of a hypothetical, so if you are willing to stipulate to the ideal conditions and construction of Trippy's hypothetical, an answer can be derived without a lengthy debate on the practicality of the hypothetical.

Assuming:

• A stay at home observer, with a clock constantly located in a predefined position within a gravitational field, for our purposes assumed to be 1g and
• A traveling twin, who is always experiencing a constant and uniform acceleration and
• That Einstein's equivalence principle is valid and
• We assume no other external conditions or forces acting on any of the observer's clocks...

By application of the equivalence principle to the rate of acceleration of the traveling observer and his/her clock,

1. If the traveling twin's rate of acceleration is greater than 1g, his/her clock will run slow compared to the stay at home observer's clock and
2. If the traveling twin's rate of acceleration is less than 1g, his/her clock will run fast compared to the stay at home observer's clock.

I did not see where you transformed the constant acceleration to a cruising speed, ( $$v_1$$ is the cruising speed of the "rocket twin"), but other than that had no issues with the post.

As I have said before, it has been a long time since I claimed a working knowledge of the math and unless you fully define the terms, it takes me sometimes more effort that I believe is necessary to look up undefined mathematical symbols and their significance in a specific context.

Granted the way I constructed that post I did not mention the fact that a constantly accelerating spaceship, could have an rms velocity for the whole journey, that was greater than or less than, the rms velocity of any individual segment of the journey. I.e. the velocity of the traveling twin relative to the stay at home twin is not uniform throughout the hypothetical, even though the acceleration is assumed to be so. I thought that was obvious, to everyone.

If that was not the post you were referring to, please provide a link, as with well over 600 posts and >200 printed pages, I have no interest in spending the time it might take to find what ever post it might be.

 

[Tach]

For some reason, gentlemen, this topic has lost interest to me. I've laid out my reasoning many times over for many readers which, if not irrefutable, at least has logical merit.

Actually, your (very fringe) views have been refuted repeatedly.

To recap, I continue to make the claim that acceleration (and not relative velocity) is a necessary, causal component to absolute, unambiguous time dilation.

Repeating the same already refuted anti-mainstream ideas over and over does not constitute a proof.

The time dilation in the Third Twin was proven to be ambiguous despite the usual misinterpretation.

Nah, anyone with basic knowledge of SR understands it.

The experiment in which a muon under "magnetic orbital acceleration" is actually a misapplication of the EEP because, as we know, an object in free-fall does not experience acceleration as one does while resting on the ground, for example. Therefore, we should expect such a muon to possess the same lifetime as one which has been accelerated to that same linear velocity and energy (which is exactly what we find).

LOL.

2) Clock A in the nose and clock B in the tail of a perpetually-accelerating rocket ship, OR clock A on a large non-rotating mass with clock B in the dead of space are two scenarios which would display unambiguous time dilation. In both scenarios we have acceleration (either direct or via EEP), yet we have no change in displacement over time between the clocks, hence no relative velocity.

False, as explained to you countless times.

In summary, we have no scenario in which unambiguous time dilation exists devoid of acceleration; we do have scenarios in which unambiguous time dilation exists devoid of relative velocity; lastly, we have that "last line of defense", even if it's a technicality, that says acceleration is required for there to be differing world line lengths between two co-location events...given all of this, I believe I can be forgiven for questioning the mainstream view on this subject. :shrug: Thanks

LOL, mixing up physics with religion...

 

[OnlyMe]

You posted a bunch of new errors (see current page) in an attempt at covering older, already exposed errors. So, I pointed them out to you.

Tach, you do realize that the first link above is well described by the first sentence in that post, don't you?

You realize that you spent half a post attacking....

The second link is so flawed it is not worth, the space in this thread to address it!

While, you raise some issues which do have some merit, most of the time it seems to me, that setting aside the personal attacks embedded in most of your posts, you just jump into objections, to almost every aspect of the hypothetical under discussion, without first allowing it, the hypothetical, to be fully developed. There is nothing scientific about that. It is like reading the title of a peer reviewed paper and immediately beginning a rebuttal.

 

[Tach]

It is like reading the title of a pier reviewed paper

Poor English language......

and immediately beginning a rebuttal.

What can I do, the rebuttal starts rolling as soon as the errors start rolling.

 

[OnlyMe]

Poor English language......

What can I do, the rebuttal starts rolling as soon as the errors start rolling.

I corrected the misspelled word.

I have no control over when or how you arrive at what ever it is you think or interpret anything to be or to mean.

 

[RealityCheck]

...
...

On the other hand, using different acceleration profiles and observing no effect on the differential aging of the twins , mainstream scientists would correctly conclude that acceleration indeed doesn't play any role. This is very simple, basic experimental physics, I wonder how you could miss. On the other hand, I am not wondering anymore.



The solutions are of course, not equivalent. Only someone ignorant in experimental physics would claim such a thing. If you really and truly want to prove that acceleration has no role, you really need to impart non-equal accelerations to the twins. Get it yet? If you do what you did, any fool will point out that the equal accelerations cancel out, so you've proven nothing.

Hi Tach. Pleased to meet you.

You suggest differing accelerations of each up to the same velocity for both/all.

But that would merely introduce YET ANOTHER ASYMMETRY variable which cannot be 'teased' out in the final analysis of your scenario as described.

Can you (or anyone else) guess which asymmetry is involved in your suggestion? Hint: It is of a 'cumulative factor/effect'.

Back later to see the responses. Cheers.

.

 

[RealityCheck]

Actually, to no one person's versed in physics surprise, the clocks of the three twins all tick at the SAME exact rate, 1 second per second. The reason for the fact that the elapsed time shown on the clock of twin C when he meets twin A is less than twin A has absolutely nothing to do with clock rates. It has to do with something else.

Hi again, Tach.

Your statement seems trivially based on circuitous logic.

A 'second' is necessarily an 'agreed' duration against which a PARTICULAR tick rate FREQUENCY is 'agreed' to by all parties BEFORE an experiment starts.

Since the tick rate may vary according to further changes in frames (be these changes due to acceleration/velocity variations), then NO changed frame (which is now different from the 'starting frame (common to all before the experiment start) can claim that IT'S tick rate is STILL "one second per second" as you claim.

It can only claim that it has 'one TICK PER TICK' and nothing more. Trivial. Whether or not any particular frame's 'tick rate' REMAINED/VARIED during the experimental run is YET TO BE DETERMINED by comparing back to the COMMON STANDARD SECOND 'tick rate' applying BEFORE the start/change.

Think about it, mate. Your assumption about 'SECOND per SECOND' to describe frame-changed 'tick rates' is NOT valid.

Cheers.

.

 

[OnlyMe]

So... Has anyone come up with a flaw in the muon lifetime example I mentioned earlier? Does anyone care to dispute that the effects will be the same regardless of whether it's the muon source or the lab which initially accelerates?

First I am still thinking....

A question though, as QM was not an area I spent much time considering until relatively recently.

When muons are created in a particle accelerator, the muons are not theirselves accelerated right? The acceleration occurs for the proton (?) prior to the muon creation?

This may have no impact on your question. I am just trying to clarify things in my own mind.

Essentially all I know about QM is either from press releases over the years or from reading research papers and historical texts, on my own over the last few years. While I believe I have a fair understanding of the basics, I am no where near and expert and would describe myself in this area as an interested lay person.

 

[Tach]

Hi Tach. Pleased to meet you.

You suggest differing accelerations of each up to the same velocity for both/all.

No, you don't know what I suggest.

But that would merely introduce YET ANOTHER ASYMMETRY variable which cannot be 'teased' out in the final analysis of your scenario as described.

Nope, if you know how to write the formalism describing the motion, there is no problem in figuring out a very clear answer.
Based on your comments , I doubt that you have attempted writing any equations so you are just shooting from the hip.

Can you (or anyone else) guess which asymmetry is involved in your suggestion? Hint: It is of a 'cumulative factor/effect'.

Rubbish. This is a simple exercise in relativistic physics. Do you know how to write the formalism in terms of equations hyperbolic motion? No? Look up a few posts above yours, OnlyMe just cited the answer that disproves your anti-mainstream claims.

 

[Tach]

Hi again, Tach.

Your statement seems trivially based on circuitous logic.

You sound very much like OnlyMe, are you one of his sockpuppets? The logic I presented is basic, textbook stuff, if you want to brew your own anti-mainstream stuff, there is a special forum, called the Cesspool where you can post such ideas.

A 'second' is necessarily an 'agreed' duration against which a PARTICULAR tick rate FREQUENCY is 'agreed' to by all parties BEFORE an experiment starts.

Since the tick rate may vary according to further changes in frames (be these changes due to acceleration/velocity variations), then NO changed frame (which is now different from the 'starting frame (common to all before the experiment start) can claim that IT'S tick rate is STILL "one second per second" as you claim.

Mainstream physics says that you don't know what you are talking about.

It can only claim that it has 'one TICK PER TICK' and nothing more. Trivial. Whether or not any particular frame's 'tick rate' REMAINED/VARIED during the experimental run is YET TO BE DETERMINED by comparing back to the COMMON STANDARD SECOND 'tick rate' applying BEFORE the start/change.

Think about it, mate. Your assumption about 'SECOND per SECOND' to describe frame-changed 'tick rates' is NOT valid.

I thought about it, this is basic physics that you obviously know nothing about.

 

[OnlyMe]

Nope.

Rubbish. This is a simple exercise in relativistic physics.

You sound very much like OnlyMe, are you one of his sockpuppets? The logic I presented is basic, textbook stuff, if you want to brew your own anti-mainstream stuff, there is a special forum, called the Cesspool where you can post such ideas.

Mainstream physics says that you don't know what you are talking about.

I thought about it, this is basic physics that you obviously know nothing about.

Tach, where in these last two posts have you provided anything that is on topic?

And just so you don't waste more time on the issue, I don't even know who RealityCheck is. I have now, never have had, nor ever will have any sock puppet accounts.

If you disagree with a post. Provide some reasonable explanation as to why.

When I was trying to find "the" post, where you claimed you explained everything to me I scanned through at least half your posts in this thread. The way it appeared to me was that a large portion, approaching half if not more than half of what you post, has no on topic content and is either consistent with the above two posts or full of personal attacks on others.

BTW You never even confirmed whether the post I did respond to was the one you were referring to. Nor did you provide any further comment.

 

[Tach]

.

BTW You never even confirmed whether the post I did respond to was the one you were referring to. Nor did you provide any further comment.

No, it is not (though it is one of the posts where I corrected your misconceptions on the subject when acceleration is involved). It is the post where I explain why C (Tripleprime) shows a different elapsed time from A (Unprime) in the absence of any acceleration. Keep looking, you'll find it.

 

[OnlyMe]

No, it is not (though it is one of the posts where I corrected your misconceptions on the subject when acceleration is involved). It is the post where I explain why C (Tripleprime) shows a different elapsed time from A (Unprime) in the absence of any acceleration. Keep looking, you'll find it.

Typical! I am done looking thorugh your old posts.

Post a link, the post # or it's a dead issue. And by that I mean I will assume you concede what ever issue was involved.

 

[Tach]

Typical! I am done looking thorugh your old posts.

Post a link, the post # or it's a dead issue. And by that I mean I will assume you concede what ever issue was involved.

Too lazy to search, eh? Even after I explained what the post is all about?

 

[Tach]

First I am still thinking....

A question though, as QM was not an area I spent much time considering until relatively recently.

This isn't a QM issue, it is an issue of basic relativity.

Essentially all I know about QM is either from press releases over the years or from reading research papers and historical texts, on my own over the last few years. While I believe I have a fair understanding of the basics, I am no where near and expert and would describe myself in this area as an interested lay person.

Nothing to do with QM, you only need to know relativity to understand the post. So, why are you asking about QM?

 

[RealityCheck]

.
Hi Tach. Thanks for your reply.

no, you don't know what i suggest.



Nope, if you know how to write the formalism describing the motion, there is no problem in figuring out a very clear answer.
Based on your comments , i doubt that you have attempted writing any equations so you are just shooting from the hip.




Rubbish. This is a simple exercise in relativistic physics. Do you know how to write the formalism in terms of equations hyperbolic motion? No? Look up a few posts above yours, onlyme just cited the answer that disproves your anti-mainstream claims.

So, Tach, you COULDN"T guess what it was?

Why didn't you just say so? And why speak to me like that when I ONLY ASKED YOU TO GUESS what it was? And what is all that about 'formalism', when my challenge merely asked for the LOGICAL observation which YOU apparently missed in your own 'differing acceleration' suggestion/claims to Trippy....which SUGGESTION and CLAIMS were made perfectly clear by YOU in your OWN WORDS to Trippy, as quoted below in my relevant post which I ASKED you to 'guess' what you MISSED, as follows....?

...
...

On the other hand, using different acceleration profiles and observing no effect on the differential aging of the twins , mainstream scientists would correctly conclude that acceleration indeed doesn't play any role. This is very simple, basic experimental physics, I wonder how you could miss. On the other hand, I am not wondering anymore.



The solutions are of course, not equivalent. Only someone ignorant in experimental physics would claim such a thing. If you really and truly want to prove that acceleration has no role, you really need to impart non-equal accelerations to the twins. Get it yet? If you do what you did, any fool will point out that the equal accelerations cancel out, so you've proven nothing.

Hi Tach. Pleased to meet you.

You suggest differing accelerations of each up to the same velocity for both/all.

But that would merely introduce YET ANOTHER ASYMMETRY variable which cannot be 'teased' out in the final analysis of your scenario as described.

Can you (or anyone else) guess which asymmetry is involved in your suggestion? Hint: It is of a 'cumulative factor/effect'.

Back later to see the responses. Cheers.

So, how about just ADMITTING you DON"T know and CAN"T guess what you missed, and then I will tell you what it is and how it affects your OWN faulty 'corrections' to others?

Thanks.

.

 

[RealityCheck]

.

Hi Tach. You appear confused, evasive AND gratuitously insulting based only on your OWN FAULTY assumptions.

You sound very much like OnlyMe, are you one of his sockpuppets? The logic I presented is basic, textbook stuff, if you want to brew your own anti-mainstream stuff, there is a special forum, called the Cesspool where you can post such ideas.




Mainstream physics says that you don't know what you are talking about.



I thought about it, this is basic physics that you obviously know nothing about.

To correct your many and varied aspersions about me and another here, I would have you know that I have been a member at PhysForum for many years; and that I only registered here at SciForums a couple of days ago on the recommendation of a friend. So please stop your evasions and confusions using personal insults/disparagement/characterisation in order to deflect from YOUR OWN BAD BEHAVIOUR HERE.

Is your kind of senseless and foundationless behaviour-in-lieu-of-good-faith-discussion' accepted as the 'norm' here by the MODERATORS? If so, then perhaps the moderators are impotent to take you to task especially in this instance?


Anyhow, you AGAIN failed to respond to the point made about your OWN trivial/circuitous logic which INVALIDATES your claims about all frames having the SAME "second-per-second" tick rate, when it's obvious to all MAINSTREAM scientists that no such assumptions can be made IF frames change and their 'second' is DIFFERENT from the STANDARD 'second' DURATION which applied to ALL BEFORE the start of changes/experiment.

So please, Tach, for your own reputation, stop evading and insulting in lieu of honestly and in good faith responding to the points/questions made to you in my original posts. Then we can get on as scientists instead of like children, hmm?

Thanks.

.