Relativity Theory is THEORETICALLY wrong!

[przyk]

I haven't inserted any rule to STR.

Yes you have: that recprocity applies between all frames and not just inertial frames.

When analysing the ageing rate of the mothership observer as seen by one of the travelling twins, you keep imposing that what I call $$T_a$$ and $$T_a'$$ in post #75 are the same (or at least that the former is "negligible"). This is your own rule, not relativity's. Special relativity doesn't directly tell you what $$T_a$$ is.

There isn't a single Lorentz transformation that relates the travelling twin's and mothership observer's rest frames for the duration of the trip. If you use two transformations for the two inertial segments (before and after the acceleration), fine, but you can't simply assume whatever you like about what the accelerating twin sees as he switches from one inertial rest frame to another, then claim you've disproved a theory that doesn't make this assumption.

As far as General Relativity is concerned, your view is quite explicitly contradicted:

Gravitational time dilation is manifested in accelerated frames of reference or, by virtue of the equivalence principle, in the gravitational field of massive objects. In more simple terms, clocks which are far from massive bodies (or at higher gravitational potentials) run faster, and clocks close to massive bodies (or at lower gravitational potentials) run slower.

If you're in an accelerating reference frame, anything you are accelerating toward is at a higher gravitational potential than you.

 

[2inquisitive]

“ Originally Posted by 2inquisitive
The Earth also rotates faster than once per day (24 of the travelling twin's hours) as seen by the travelling twin during the travelling twin's inertial segments. ”

przyk,

How do you know this? The example you brought up only tells you what the average rotation rate of the Earth must be as seen by the travelling twin, and my point so far has been that relativity is perfectly compatible with this. Of course, there's still the seperate issue of how good a model of reality relativity is.

I can deduce my statement from experimental evidence + logic. First, experimental evidence confirms the fact that acceleration does not alter clock rates in excess of what velocity through spacetime predicts in the inertial observer's frame of reference. Your statements were as follows, quote:

On its own it says nothing about the rate of an inertial clock as seen by an accelerating observer.

GR predicts that the Earth will rotate faster than once per day (24 of the travelling twin's hours) as seen by the travelling twin only while he's accelerating toward Earth.

GR also predicts that the Earth will rotate slower than once per day as seen by the travelling twin while he is accelerating away from the Earth. These accelerating frames (away from and toward the Earth) should offset each other during the course of the entire trip, leaving the inertial frames as the frames where clock dilation would occur. Do you disagree with that assumption?

 

[przyk]

GR also predicts that the Earth will rotate slower than once per day as seen by the travelling twin while he is accelerating away from the Earth. These accelerating frames (away from and toward the Earth) should offset each other during the course of the entire trip, leaving the inertial frames as the frames where clock dilation would occur. Do you disagree with that assumption?

Yes. The gravitational time dilation is related to a gravitational potential difference. This means that, apart from the field strength, the effect will also increase with distance. The effect while the twin is turning around far from Earth will be much more significant than when he's taking off or landing.

 

[martillo]

przyk,

Whatever the effect on the intervals of accelerations of the twins can be you must consider:
1) The twins make a symmetrical travel and so the effect would be the same and will give exactly the same "Ta" for both and so this doesn't affects the problem.
2) I can choose the travel of the twins going so far as I want and the twins ageing so much as I want and the interval of acceleration so small as I want and so the effect of the acceleration can always be made neglihible.

We will ever find the same contradictions in the different observations seen from the different frames.

 

[przyk]

1) The twins make a symmetrical travel and so the effect would be the same and will give exactly the same "Ta" for both and so this doesn't affects the problem.

And the $$T_a$$'s each twin measures for the other couldn't possibly be such that the twins are the same age when they cross over?

2) I can choose the travel of the twins going so far as I want and the twins ageing so much as I want and the interval of acceleration so small as I want and so the effect of the acceleration can always be made neglihible.

If the gravitational time dilation effect increases with gravitational field strength (ie. acceleration) and distance, why should an infinite acceleration for an infinitely short duration be negligible? You keep claiming it is, but you can never justify this. A time interval approaching zero multiplied by an average ageing rate approaching infinity could quite easily yield a $$T_a$$ that approaches a finite, non-zero value.

 

[martillo]

przyk,

And the 's each twin measures for the other couldn't possibly be such that the twins are the same age when they cross over?

No, because of the symmetric travel the same "Ta" would be added to the relativistic predictions for both twins and the difference of the the different ages would remain the same.
Also note that "Ta" we can vary the time of the travel by varying arbitrary the travelling distance and so "Ta" would compensate the difference of age in a very particular case only not in the general case.

If the gravitational time dilation effect increases with gravitational field strength (ie. acceleration) and distance, why should an infinite acceleration for an infinitely short duration be negligible? You keep claiming it is, but you can never justify this. A time interval approaching zero multiplied by an average ageing rate approaching infinity could quite easily yield a that approaches a finite, non-zero value.

I agree that is my assumption that the travel could be made such a way that the accelerations in both twins would have neglihible effects but may be some calculations must be made to ensure if this is possible or not. Even if not we fall in the consideration 1) that both twins would have the same effect and the difference between the relativistic predictions between them remains the same.

So, even if a considerable "Ta" exist the thought experiment will give contradictory observations from the different frames.

 

[przyk]

No, because of the symmetric travel the same "Ta" would be added to the relativistic predictions for both twins and the difference of the the different ages would remain the same.

If we look at thing from, say, twin A's frame, then A's age by the time they meet up again is:

$$\text{A's age increase before accelerating} \; + \; \text{A's age increase after accelerating}$$​

B's age increase, as seen in A's frame is:

$$\text{B's age increase before A's acceleration} \; + \; T_a \; + \; \text{B's age increase after A's acceleration}$$​

With $$T_a$$ such that the twins are the same age when they cross over. The analysis will be completely symmetrical in B's frame.

Also note that "Ta" we can vary the time of the travel by varying arbitrary the travelling distance and so "Ta" would compensate the difference of age in a very particular case only not in the general case.

No, it would just mean that $$T_a$$ is a function of distance. The further an object is, the greater its jump in age for the same acceleration toward it.

I agree that is my assumption that the travel could be made such a way that the accelerations in both twins would have neglihible effects but may be some calculations must be made to ensure if this is possible or not.

Well STR only really gives you one way of calculating all these $$T_a$$'s: work out all the other terms, and there will only be one $$T_a$$ such that everyone agrees on all ages.

 

[martillo]

przyk,

That's the way what you believe it could work for both twins have the same age at the crossover point.
I don't think it works, I don't think it really happen that way.
I ask you now, if that were true why the traditional twin's paradox gives the travelling twin getting younger? Why your "Ta" is not considered in the traditional paradox? (The travelling twin has to accelerate to go away and to come back)
Following your reasoning there would be a "Ta" which make these both twins have the same age while the well known result is that the travelling one gets younger!
Sorry but your reasoning doesn't work.

I believe that acceleration effect could not be relevant to the final results of the problem.

 

[przyk]

Why your "Ta" is not considered in the traditional paradox? (The travelling twin has to accelerate to go away and to come back)

Because "STR doesn't apply in accelerating frames" is a much quicker rebuttal, also valid against your own version of the paradox. Rather than responding this way, though, I looked at the paradox in a bit more detail. (For the traditional paradox, your mothership observer is the equivalent of the Earth twin.)

Following your reasoning there would be a "Ta" which make these both twins have the same age while the well known result is that the travelling one gets younger!

The Earthbound observer doesn't accelerate in the traditional twin paradox. There's only one $$T_a$$: the jump in the stationary twin's age as seen by the accelerating twin. In your scenario each twin measures such an age jump for the other twin, as both accelerate.

I believe that acceleration effect could not be relevant to the final results of the problem.

Then relativity contradicts your personal belief - not itself.

 

[Singularity]

If relativity theory is anything then try answerin this http://sciforums.com/showthread.php?p=1387441#post1387441

 

[martillo]

przyk,

I will not discuss anymore.
I can only say that for me, as personal belief, your reasoning about the "Ta" has never been presented in any discussion about twin's paradoxes in forums and does not apply.

 

[przyk]

your reasoning about the "Ta" has never been presented in any discussion about twin's paradoxes in forums and does not apply.

Why? Because I demonstrated it to be a consequence of the Lorentz transformation? Because it shows how STR can be internally consistent? Honestly I don't know why you keep choosing to ignore something that is a prediction of General Relativity anyway.

 

[Rick]

Relativity is correct. Even if Einstein re-incarnates tommorrw (** I AM NOT DISCUSSING REINCARNATION PPL! ****) and says its incorrect i wont blv him.

Rick