Can the Twin Paradox be simplified?

[OnlyMe]

This is about you explaining (or, even better) admitting your gross fumbles. Once you do that we can discuss more advanced subjects.

Tach, that was a question that could be answered "yes" or "no" and then an explanation why...

You do a great deal of deflecting and pointing behind curtains. I am beginning to wonder if you have some deeper issues. I think I am beginning to feel genuinely sorry for you.

Is there some reason why you cannot answer direct questions?

 

[RJBeery]

Please do so. I will be very curious how you explain away this monumental fumble:

You obviously seem to believe that T = T''' . Even worse, you conclude that 1.25=2.08.

I'm not avoiding your questions because I cannot answer them, I'm avoiding a waste of my time because I suspect that as I continue to explain my math you'll make sure to have those casters upon which your goalpost resides nicely oiled and ready to be moved again.

For example, T = T''' = 1.25 by definition because Tripleprime syncs his watch as he passes Unprime. Also, T' = 2.08 is the relative time of simultaneity of the co-location event of Unprime and Tripleprime, from Prime's point of view. T' = 2.08 <===> T = T''' = 1.25. Poorly presented, perhaps, but not wrong. Also, all times given on the graph are what the respective local watches would read.

As I said, I'll move through your entire critique but the fact that you aren't reaffirming our agreement is indicative of the fact that you already have your hands on that goalpost, ready to run around the field. Now, would you please answer the question:

Are you going to claim that, with proper calculations, the conclusions drawn by Unprime and Doubleprime will be in agreement with those drawn by Prime and Tripleprime? If so, what conclusions would those be, specifically?

 

[Neddy Bate]

The traditional Twin Paradox offers [apparently] contradictory observations in that each twin claims that the other's clock is running slow. The paradox is resolved when they meet up again due to acceleration.

Yes, acceleration certainly takes the ambiguity out of the problem.

The "Third Twin" was introduced (certainly by Tach in this thread and perhaps by the original author as well) in an attempt to prove that there can be an absolute determination made devoid of acceleration regarding which twin is actually aging slower.

Introducing the third twin does not tell you which twin is "actually" aging slower. What it does is let you determine what would happen if one of the twins were to accelerate, without introducing acceleration to the problem.

For example, for the case of two inertial travelers A and B getting further and further apart: You could introduce a third inertial traveler C who happens to be in motion from A back toward B. By letting C reset his clock to match A's clock as they pass each other, this arrangement gives you the same results as if A had accelerated. This would reveal A to be younger than B.

On the other hand, you could have chosen C to be in motion from B back toward A. By letting C reset his clock to match B's clock as they pass each other, this arrangement gives you the same results as if B had accelerated. This would reveal B to be younger than A.

So the time dilation is still reciprocal between A and B no matter what C does.

I've shown that the information gained in the Third Twin scenario offers no more information than the original Twin Paradox. In other words, we again have apparently contradictory observations that can only be resolved with acceleration. Under the presumption that the Third Twin scenario offers more information than the original Twin Paradox, I have generated actual contradictory observations which prove that presumption false. Make sense?

Yes, that makes sense. So you have shown that time dilation will always be reciprocal until someone actually accelerates. But what if no one ever accelerates? Does that mean all of the elapsed times measured by all of the inertial observers are useless? They are still real measurements aren't they?

 

[RJBeery]

Yes, that makes sense. So you have shown that time dilation will always be reciprocal until someone actually accelerates. But what if no one ever accelerates? Does that mean all of the elapsed times measured by all of the inertial observers are useless? They are still real measurements aren't they?

I don't really know; perhaps if no acceleration ever takes place then very little can be said about the system in any absolutely meaningful way.

 

[Tach]

For example, T = T''' = 1.25 by definition because Tripleprime syncs his watch as he passes Unprime. Also, T' = 2.08 is the relative time of simultaneity of the co-location event of Unprime and Tripleprime, from Prime's point of view. T' = 2.08 <===> T = T''' = 1.25. Poorly presented, perhaps, but not wrong. Also, all times given on the graph are what the respective local watches would read.

Why are you digging yourself deeper and deeper? It is not (only) "poorly presented", it is downright wrong. You arrive to the ridiculous conclusion that "1.25=2.08". This is no longer about your misunderstandings about simple physics, this has become a discussion about your grasp of first grade arithmetic.
I have taken the time to derive T>T'>T"' for you. The derivation is in line with what textbooks and mainstream physics say.
So, why don't you admit that you are wrong as you promised and move on?

 

[RJBeery]

Why are you digging yourself deeper and deeper? It is not (only) "poorly presented", it is downright wrong. You arrive to the ridiculous conclusion that "1.25=2.08".

I thank-you for pointing out what you believe to be a mathematical error on my part. As I don't consider it to be an error, could you please correct it for me? I feel I've explained my intentions clearly enough that you should be able to do this. The line of simultaneity (from Prime's frame) connects Unprime and Tripleprime's passing event to what point on Prime's timeline? I claim it is T' = 2.08.

Also, please answer the following:

Are you going to claim that, with proper calculations, the conclusions drawn by Unprime and Doubleprime will be in agreement with those drawn by Prime and Tripleprime? If so, what conclusions would those be, specifically?

 

[Tach]

I thank-you for pointing out what you believe to be a mathematical error on my part. As I don't consider it to be an error,

Of course not, in your concept of arithmetic "1.25=2.08" :

This allows us to calculate the Prime's simultaneity of the meeting of Unprime, Tripleprime and himself as
T = T''' = 1.25 yr = T'$$\sqrt{1-(.8)^2} $$ = 2.08 yr, with Tripleprime reaching Prime in another 2.08 yrs for a co-location time of T' = 4.166 yrs and T''' = 2.5 yrs.

I notice that you tried to cover up some of your errors by editing your post AFTER I posted my corrections at 12:00 AM:

"Last edited by RJBeery; Today at 01:40 AM.. " For example, your original formula was even more hilarious:

T = T''' = 1.25 yr = T$$\sqrt{1-(.8)^2} $$ = 2.08 yr

You tried covering up by replacing T' instead of T but you didn't manage to cover everything. There are too many errors to cover up everything.

could you please correct it for me?

I already corrected your errors. All your calculations (T,T',T"') are wrong. I posted the correct calculations and the correct values for you. All that is left is for you to admit that you were wrong in contradicting the mainstream view and to move on.

 

[RJBeery]

Of course not, in your concept of arithmetic "1.25=2.08" :

Unprime's watch would read 1.25 when Prime's watch would read 2.08 from Prime's POV. If you think these values are wrong please correct them but stop playing stupid like you don't understand what I've written.

I notice that you tried to cover up some of your errors by editing your post AFTER I posted my corrections at 12:00 AM:

"Last edited by RJBeery; Today at 01:40 AM.. " For example, your original formula was even more hilarious:



You tried covering up by replacing T' instead of T but you didn't manage to cover everything. There are too many errors to cover up everything.

None of this is true. I don't know why you think this but I ask any mods here to verify what I say. I would never, ever pull that kind of crap. The only change I made to my original post was a single typo (I had .6c instead of .8c for one of the velocities). Also, on my screen my post says "last edited at 11:40 PM" which was approximately 17 1/2 hours ago. Perhaps there's a timezone issue or something.

I already corrected your errors. All your calculations (T,T',T"') are wrong. I posted the correct calculations and the correct values for you. All that is left is for you to admit that you were wrong in contradicting the mainstream view and to move on.

No, you didn't. Please give me what you believe to be the proper value for T', if it is not 2.08 in the context of my reference. Also, please answer the following:

Are you going to claim that, with proper calculations, the conclusions drawn by Unprime and Doubleprime will be in agreement with those drawn by Prime and Tripleprime? If so, what conclusions would those be, specifically?

 

[Janus58]

*Despite Janus' claim that moving twice the speed of .8c = 1.6c and a "cute trick" (therefore implying impossible), relativistic addition of velocities would make it V = (.8 + .8)/(1 + .8*.8) = .9756c.

No, you cannot justify your claim that Tripleprime is traveling twice as fast as Prime that way. Relativistic addition of velocities is used for adding velocities in one as measured in one frame to find relative velocity for another. For instance if Prime was heading at 0.8c in one direction relative to Unprime and Tripleprime was moving at 0.8c in the othe relative to Unprime, then you can use it to find Tripleprime's relative velocity to prime (0.9756) as measured by either Prime or Tripleprime.

On the other hand, if you say that Tripleprime is moving twice as fast as prime, then unless you specifically state otherwise, this means "as measured in the same frame" and of the frames discussed in this scenario, the Unprime frame, being the frame in which prime is initially stated to be moving relative to, is the frame to which this statement would be applied.

And as stated, Tripleprime cannot travel twice as fast as prime as measured from the Unprime frame, as this would require Tripleprime to travel at greater than c relative to the Unprime frame.

The only way to make your use of the Relativistic addition of velocities work would have been if you had said something to the effect of:
"Tripleprime is moving at a speed such that its relative speed with respect to Prime as measured by Prime is equal to Prime's relative speed to Unprime as measured by Prime ."
This way you can add the relative velocities of Tripleprime and Unprime in the Prime frame to get the Relative velocity of Tripleprime relative to Unprime in the Unprime frame.

But this is in no way the equivalent of saying that Tripleprime is moving twice as fast as Prime. (Though if you tried, you could find a frame to which Tripleprime's relative velocity would be twice that of Prime's, but this would require introducing a whole new frame for no purpose.)

So rather than owning up to an minor oversight (Not realizing that prime's velocity relative to Unprime was already greater than 1/2c), You tried to hide behind a misapplication of the Relativistic Addition of velocities.

This strikes me as being the actions of a person who is more concerned about being seen as being right, than actually being right.

 

[Tach]

Unprime's watch would read 1.25 when Prime's watch would read 2.08 from Prime's POV. If you think these values are wrong please correct them but stop playing stupid like you don't understand what I've written.

I have corrected all your incorrect values. All your calculations are incorrect.

None of this is true. I don't know why you think this but I ask any mods here to verify what I say. I would never, ever pull that kind of crap.

The website shows the opposite. You edited your post at 1:40 AM AFTER my corrections at 12:00 AM. Unfortunately for you the errors were already captured.

The only change I made to my original post was a single typo (I had .6c instead of .8c for one of the velocities). Also, on my screen my post says "last edited at 11:40 PM" which was approximately 17 1/2 hours ago. Perhaps there's a timezone issue or something.

The website says "Last edited by RJBeery; Today at 01:40 AM. ". As far as we all know, 1:40 AM comes AFTER 12:00 AM, so I do not understand why you cling to this silly lie.
No matter, you left plenty of errors in your post.

No, you didn't. Please give me what you believe to be the proper value for T', if it is not 2.08 in the context of my reference. Also, please answer the following:

Says very clearly $$T'=3.412$$

How long do u plan to keep playing this game? I notice that Janus58 came back as well to point out some other errors in your thinking.

 

[Neddy Bate]

I don't really know; perhaps if no acceleration ever takes place then very little can be said about the system in any absolutely meaningful way.

If you consider my "two armies" arrangement, you will see that reciprocal time dilation can be measured and documented. This makes it absolutely real, even in the absence of any acceleration. The resulting time logs might look something like this:


__________



These would be the times the Blue army would record from Red clocks passing left-to-right very close to them:

Red                           0.000    -1.500    -3.000  -->
Blue                          0.000     0.000     0.000

Red                                     0.500    -1.000    -2.500  -->
Blue                          1.000     1.000     1.000

Red                                               1.000    -0.500   -2.000  -->
Blue                          2.000     2.000     2.000

__________



And these would be the times the Red army would record from Blue clocks passing right-to-left very close to them:

Red                          0.000     0.000     0.000
Blue                    <--  0.000     0.750     1.500

Red                          0.500     0.500     0.500
Blue          <--  0.250     1.000     1.750

Red                          1.000     1.000     1.000
Blue<--  0.500     1.250     2.000

__________



If you study these, you'll notice that each frame can legitimately claim that the other frame's clocks tick slower than their own, and no contradictions arise. Acceleration is not involved, only relative motion.

 

[RJBeery]

So rather than owning up to an minor oversight (Not realizing that prime's velocity relative to Unprime was already greater than 1/2c), You tried to hide behind a misapplication of the Relativistic Addition of velocities.

This strikes me as being the actions of a person who is more concerned about being seen as being right, than actually being right.

This is interesting Janus. What I had intended was for the velocity of Unprime to be equal in magnitude and opposite in direction of Tripleprime from Prime's point of view, which then allowed me to consider a simple "reflection" of the Third Twin scenario from another perspective. You are correct that saying "twice the speed" probably defaults to a Newtonian interpretation, however had my hackles not already been up I would've explained that I did not intend for a Newtonian interpretation because the math won't work even if the velocities were less than c/2 (unless we keep the entire exercise within the Newtonian framework).

Regardless, if this is really what you think then I completely admit my poorly chosen wording and I apologize.

 

[RJBeery]

Tach, I don't know what the hell you're looking at, but my main post was made YESTERDAY at 10:41 PM, and edited an hour later for a minor typo. 11 minutes after that, Neddy Bate asked me to define "contradictory observations". TEN HOURS LATER, you made your first response. What the hell do you want me to say? I did not and would not do the thing you are accusing me of, the very thing that you've been caught doing a couple dozen times. Let it go, man, it's a non-issue.

Perhaps a moderator could verify what I say?

 

[Tach]

Tach, I don't know what the hell you're looking at, but my main post was made YESTERDAY at 10:41 PM, and edited an hour later for a minor typo. 11 minutes after that, Neddy Bate asked me to define "contradictory observations". TEN HOURS LATER, you made your first response. What the hell do you want me to say? I did not and would not do the thing you are accusing me of, the very thing that you've been caught doing a couple dozen times. Let it go, man, it's a non-issue.

Perhaps a moderator could verify what I say?

Well, the time stamp says the opposite.
Your altered formula also says the opposite.

In addition to the above, you have enough errors to contend with, so why do you keep this up?

 

[RJBeery]

If you consider my "two armies" arrangement, you will see that reciprocal time dilation can be measured and documented. This makes it absolutely real, even in the absence of any acceleration.

If you study these, you'll notice that each frame can legitimately claim that the other frame's clocks tick slower than their own, and no contradictions arise. Acceleration is not involved, only relative motion.

Yes, I like it, and I agree that each army will reach the respective conclusions that you claim. They happen to reach the same conclusions as the army line leaders would if they were merely logging what they observed of the other army line leader, moving in the other direction. My issue then is perhaps a semantic one, because I have defined "absolute time dilation" earlier:

Absolute time dilation refers to that which cannot be denied by a change in measuring frame.

Because the time dilation you are referring to for each army is relative to that army, it doesn't fall under my definition of absolute; although I will grant you that it can certainly be measured and documented locally.

 

[Tach]

Because the time dilation you are referring to for each army is relative to that army, it doesn't fall under my definition of absolute; although I will grant you that it can certainly be measured and documented locally.

You still don't understand the difference between "time dilation" and "elapsed proper time", so how can you expect to have a meaningful discussion about the subject?

 

[RJBeery]

Tripleprime moves at the speed 0.9756 in the same direction as Prime (who moves at 0.8). According to you , Prime has a head start wrt Tripleprime of 1.25, so , the correct equation that you should be using in order to find out when Tripleprime catches Prime is:

$$v""T=v'T+v'.1.25$$

$$T=\frac{1.25v'}{v"'-v'}=5.69$$

all measured in Unprime's frame of reference.

This is again incorrect. You can't solve for T in this manner, you're using Newtonian velocity subtraction and then relativistic frame shifting. My calculations were and are correct. When Prime and Tripleprime meet up, Prime's watch reads 4.166 yr and Tripleprime's reads 2.5 yr. Tripleprime and Prime conclude that Unprime is aging more slowly than Prime, while Unprime and Doubleprime conclude that Prime is aging more slowly than Unprime.

Conflicting conclusions means no absolute statement can be made. Q.E.D.

 

[Tach]

This is again incorrect. You can't solve for T in this manner, you're using Newtonian velocity subtraction and then relativistic frame shifting.

Nope, these are the equations for "closing speed", i.e. two objects (Prime and Tripleprime) covering a common distance. They are the same in Galilean and in SR kinematics. I suggest you study them.

 

[AlexG]

Without acceleration, how can the two intertial frames be brought together to compare clocks? One frame or the other (or both) must undergo acceleration, or there will never be a frame in which both the original frames may be compared. To compare clocks, the relative velocity of the two frames must be zero, and without acceleration, this can't happen.

If you can't compare, there's no way to determine who is older. Therefore, without acceleration, the twin paradox is indeterminate.

 

[Tach]

Without acceleration, how can the two intertial frames be brought together to compare clocks? One frame or the other (or both) must undergo acceleration, or there will never be a frame in which both the original frames may be compared.

If you can't compare, there's no way to determine who is older. Therefore, without acceleration, the twin paradox is indeterminate.

That is not true, please check out the mainstream page on the "Three twins", the very clever and simple section entitled "Twin Paradox Without Accelerations ".