Martillo talks about the twin paradox

[przyk]

Yes I responded. I said that due to the nature of the perfectly symmetrical travles of the twins the situation of the twins is exactly the same at ny point of the travels but you don't understand or refuse to accept it.

I don't accept this because not only have you not supported it, but I have specifically explained why your reasoning is wrong. The description of how the twins travel is not symmetric in either of the twins' frames. That's obvious just by definition, because when you look at one twin's perspective you are by definition attaching a reference frame to one of the twins but not the other. Worse, it's an accelerating frame part of the time, so (in GR parlance) it effectively has an (anisotropic) gravitational field in it, which has its own bag of additional effects.

Your argument is correct in the "rest" frame, and only in that frame, where you have the two twins following symmetric trajectories in an inertial (so isotropic) frame and they indeed always remain synchronised in that frame. But only in that one frame, where both twins are simultaneously described in a truly symmetric way.

If I'm failing to respond is because I don't know what to say anymore because seems you just don't understand what I'm saying.

I understand perfectly what you are saying. It rather seems like you haven't understood, or simply refuse to accept, my refutation of what you are saying. You argued something, I explained exactly what was wrong with it, and so far your only response has been to repeat your original (shown flawed) argument with no modification whatsoever.

 

[eram]

I don't accept this because not only have you not supported it, but I have specifically explained why your reasoning is wrong. The description of how the twins travel is not symmetric in either of the twins' frames. That's obvious just by definition, because when you look at one twin's perspective you are by definition attaching a reference frame to one of the twins but not the other. Worse, it's an accelerating frame part of the time, so (in GR parlance) it effectively has an (anisotropic) gravitational field in it, which has its own bag of additional effects.

Your argument is correct in the "rest" frame, and only in that frame, where you have the two twins following symmetric trajectories in an inertial (so isotropic) frame and they indeed always remain synchronised in that frame.

I think what Martillo is trying to say is that your argument is simply invalid.

Martillo, just because there's symmetry in one frame doesn't mean that its eternally, omnisciently, universally symmetrical.

 

[martillo]

In post #209 the mod prometheus asked for me to not post more in this thread and I will not do it.
He said he will split the thread probably separating the posts relating to my postings. This part then could appear as other thread and may be in the "Alternatives Theories" forums, I don't know. Anyway seems useless continue discussing. Seems we can't understand each others may be due to a too different background. emil only seemd interested in my point of view but if I'm not wrong he is also a fifty old engineer...

 

[przyk]

In post #209 the mod prometheus asked for me to not post more in this thread and I will not do it.

I'd assume he meant after he split the thread you shouldn't post here and instead post in the new thread dedicated to the sub-discussion you effectively started.

 

[Aqueous Id]

Martillo: You could get around that by trying to analyze GPS. Prometheus will only cull out the pseudoscience. Real science is always welcome. I'm willing to walk through it with you if you want to know how it works and how it proves relativity is true and correct.

 

[martillo]

I will continue posting assuming przyk right when he says:

I'd assume he meant after he split the thread you shouldn't post here and instead post in the new thread dedicated to the sub-discussion you effectively started.

Hope this would not bring more problems for me to post at sciforums...

Martillo: You could get around that by trying to analyze GPS. Prometheus will only cull out the pseudoscience. Real science is always welcome. I'm willing to walk through it with you if you want to know how it works and how it proves relativity is true and correct.

If you mean GPS satelittes system I think it could not bring too much about the validity of Relativity because in spite of the probable relativistic treatment of timing in them as an engineer I'm quite sure the engineers should have added a continuos correction in the synchronization of the clocks of the sattelites with some clock at Earth ground to prevent many type of errors or disturbances in the electronics of them like thermal noise, signals interference, etc. So the relativistic timing formulation in the satellites would be "masked" by the synchronization's correction control. Am I wrong?

 

[przyk]

I think what Martillo is trying to say is that your argument is simply invalid.

I'm not sure what that would mean, since I am not so much making an argument as explaining why martillo's argument fails.

Like I've explained, martillo's general line of argument could also be used to "prove" that classical physics is "self-contradictory", because each travelling twin sees the other Doppler shifted while not seeing himself Doppler shifted, despite them both experiencing the "same physical effects".

Martillo, just because there's symmetry in one frame doesn't mean that its eternally, omnisciently, universally symmetrical.

Just to elaborate, there's a real symmetry between left-twin and right-twin in martillo's version of the twin paradox. It's just not as strong as he says it is and it doesn't imply what he's saying it does. It doesn't imply both twins are always the same age in either twin's frame, just like it doesn't imply they both have the same Doppler shifts or are moving with the same coordinate velocity in either frame.

Basically, the only use of the symmetry is that if you calculate everything in left-twin's frame, you know the same results apply in right-twin's frame with left- and right-twins interchanged. As I put it before, there is a symmetry between the frames but not within each frame.

 

[Tach]

Am I wrong?

Yes.

 

[martillo]

Basically, the only use of the symmetry is that if you calculate everything in left-twin's frame, you know the same results apply in right-twin's frame with left- and right-twins interchanged. As I put it before, there is a symmetry between the frames but not within each frame.

I don't understand that difference you talk about about symmetry between and within frames.

 

[przyk]

If you mean GPS satelittes system I think it could not bring too much about the validity of Relativity because in spite of the probable relativistic treatment of timing in them as an engineer I'm quite sure the engineers should have added a continuos correction in the synchronization of the clocks of the sattelites with some clock at Earth ground to prevent many type of errors or disturbances in the electronics of them like thermal noise, signals interference, etc. So the relativistic timing formulation in the satellites would be "masked" by the synchronization's correction control. Am I wrong?

My understanding is that what you're saying is true now, so the GPS system isn't a good test of relativity while it's in operation. But before GPS was put into operation the first satellite was allowed to orbit "uncorrected" just to see what would happen:

At the time of launch of the first NTS-2 satellite (June 1977), which contained the first Cesium clock to be placed in orbit, there were some who doubted that relativistic effects were real. A frequency synthesizer was built into the satellite clock system so that after launch, if in fact the rate of the clock in its final orbit was that predicted by GR, then the synthesizer could be turned on bringing the clock to the coordinate rate necessary for operation. The atomic clock was first operated for about 20 days to measure its clock rate before turning on the synthesizer. The frequency measured during that interval was +442.5 parts in 10[sup]12[/sup] faster than clocks on the ground; if left uncorrected this would have resulted in timing errors of about 38,000 nanoseconds per day. The difference between predicted and measured values of the frequency shift was only 3.97 parts in 10[sup]12[/sup], well, within the accuracy capabilities of the orbiting clock. This then gave about a 1% validation of the combined motional and gravitational shifts for a clock at 4.2 earth radii.

Source: http://www.phys.lsu.edu/mog/mog9/node9.html.

From memory, relativity predicts that a GPS clock would lose about 7 microseconds a day from SR-type time dilation but gain about 45 microseconds a day from gravitational time dilation. The net result is the 38 microsecond/day gain reported in the quote above.

 

[martillo]

My understanding is that what you're saying is true now, so the GPS system isn't a good test of relativity while it's in operation. But before GPS was put into operation the first satellite was allowed to orbit "uncorrected" just to see what would happen:



Source: http://www.phys.lsu.edu/mog/mog9/node9.html.

From memory, relativity predicts that a GPS clock would lose about 7 microseconds a day from SR-type time dilation but gain about 45 microseconds a day from gravitational time dilation. The net result is the 38 microsecond/day gain reported in the quote above.

Well, the problem now is that in the proposed new theories clocks also can exhibit differences in their readings if working at differences velcities but because the proposed electric and magnetic fields (which also governs atomic scale phenomena) have a new factor in their definitions which is velocity dependent. It is proposed that this is the cause of the experimentally verified variations in timings with particles, atoms and clocks currently called "relativistic time dilations" (briefly presented in Appendix B of the manuscript). So Relativity can explain those variations in timing but also the proposed new theories although in a different way. Then, as a possible new interpretation is possible to explain the timing variation it cannot be considered a proof anymore.
By the way, there, in Appendix B, is presented other interpretations possible for Mercury's precession and the bending of light by massive objects like the Sun.
Other interpretations for other phenomena and experiments are even described within the text.
Then many considered experimental tests in favor of Relativity could not be considered totally valid evidence in favor of Relativity only anymore. They are also compatible with the new theory.

 

[Emil]

In SRT physical quantities involved are time, distance (length) and speed, their derived.
Involvement of any other physical quantity is not allowed.

 

[przyk]

I don't understand that difference you talk about about symmetry between and within frames.

Symmetry "between" the frames means that there is a symmetry in when you switch from say, left-twin's frame to right-twin's frame.

To clarify, suppose your two twins accelerated at different rates up to different velocities, so the situation is not symmetrical any more. If you wanted to know what was happening from both twin's points of view, then you would have to work out what was happening in left-twin's frame and then you would separately have to work out what was happening in right-twin's frame. In your scenario, because the accelerations and velocities are symmetric, you only need to do the calculation once: you can work out what's happening in left-twin's frame, and then transpose the results to right-twin's frame just by exchanging the roles of left-twin and right-twin.

Example: just after left-twin has accelerated, he finds his clock still reads $$t_{\mathrm{L}} = 0$$ while in his frame right-twin's clock reads some time $$t_{\mathrm{R}} = T$$, which in principle we can calculate from relativity (from the relativity of simultaneity effect). Then from symmetry, without calculating anything further, you know that just after right-twin has accelerated, he'll find his clock reads $$t_{\mathrm{R}} = 0$$ and that left-twin's clock reads $$t_{\mathrm{L}} = T$$ in his frame, with the same $$T$$ as before.

Symmetry "within" a frame means that both twins are described in a symmetrical way in just one frame. This is only the case in your "rest" frame, and in the "rest" frame you can safely conclude that you will always have $$t_{\mathrm{L}} = t_{\mathrm{R}}$$, but it's not true in any other frame. If you look at left-twin's frame for example, he describes himself as just sitting still at the origin of his frame, while right-twin is moving in some nontrivial way. Not only that, but if left-twin is accelerating, then the fact that left-twin and right-twin aren't in the same place also makes a difference (from GR, left-twin would say that right-twin is at a higher gravitational potential for example). So there is no symmetry in that sense and you can't conclude that $$t_{\mathrm{L}}$$ always equals $$t_{\mathrm{R}}$$ in left-twin's frame. In fact, if you work out the relationship between $$t_{\mathrm{L}}$$ and $$t_{\mathrm{R}}$$ in left-twin's frame using relativity, you will specifically get something very different.

 

[Emil]

przyk, can you answer this question?

scenario 1:
a and b in the same place at rest. (a and b have equal masses)
A force acting upon b during one month, which finally lead to a speed V.
After a month, the force acting on b reverses the direction ,
during two months.
Then the force changes direction again for a month and now b is found at original place together with a.
(b always had an accelerated motion)

scenario 2:
Same as scenario 1 with the difference:
after a month of acceleration, for one year does not act upon b any force, so there is a movement with a constant speed relative to b, during one year.
Same difference when b returns.
(So b had a motion relative to a with constant speed V, during two years.)

scenario 3:
a and b in the same place at rest. (a and b have equal masses)
Two forces F / 2 but with opposite directions, one acting on a, and the other acting on b,during one month.
After a month, the forces disappears and a and b are moving with constant speed V relative to each other during one year.
Now the two forces (F/2) start reverse acting upon a and b, during two months.
Same on the way back, they move with constant speed during a year, but now is approaching, then reduce speed during one month and they meet each other.

scenario 4:
Like scenario 3), but the two forces are not equal, but their sum is still F.
For instance 2F / 3 and F / 3.

Every scenario has a single question. When a and b are meeting again who is "the older" and who is "the younger".

 

[martillo]

Symmetry "between" the frames means that there is a symmetry in when you switch from say, left-twin's frame to right-twin's frame.

To clarify, suppose your two twins accelerated at different rates up to different velocities, so the situation is not symmetrical any more. If you wanted to know what was happening from both twin's points of view, then you would have to work out what was happening in left-twin's frame and then you would separately have to work out what was happening in right-twin's frame. In your scenario, because the accelerations and velocities are symmetric, you only need to do the calculation once: you can work out what's happening in left-twin's frame, and then transpose the results to right-twin's frame just by exchanging the roles of left-twin and right-twin.

Example: just after left-twin has accelerated, he finds his clock still reads $$t_{\mathrm{L}} = 0$$ while in his frame right-twin's clock reads some time $$t_{\mathrm{R}} = T$$, which in principle we can calculate from relativity (from the relativity of simultaneity effect). Then from symmetry, without calculating anything further, you know that just after right-twin has accelerated, he'll find his clock reads $$t_{\mathrm{R}} = 0$$ and that left-twin's clock reads $$t_{\mathrm{L}} = T$$ in his frame, with the same $$T$$ as before.

I agree.

Symmetry "within" a frame means that both twins are described in a symmetrical way in just one frame. This is only the case in your "rest" frame, and in the "rest" frame you can safely conclude that you will always have $$t_{\mathrm{L}} = t_{\mathrm{R}}$$, but it's not true in any other frame. If you look at left-twin's frame for example, he describes himself as just sitting still at the origin of his frame, while right-twin is moving in some nontrivial way. Not only that, but if left-twin is accelerating, then the fact that left-twin and right-twin aren't in the same place also makes a difference (from GR, left-twin would say that right-twin is at a higher gravitational potential for example). So there is no symmetry in that sense and you can't conclude that $$t_{\mathrm{L}}$$ always equals $$t_{\mathrm{R}}$$ in left-twin's frame. In fact, if you work out the relationship between $$t_{\mathrm{L}}$$ and $$t_{\mathrm{R}}$$ in left-twin's frame using relativity, you will specifically get something very different.

Seems I also agree. To not complicate things let assume there's no external different influence on the twins (like gravitation of external bdies,etc). What you are saying then is that what one twin observes about himself at his "rest" frame is different than what he observes (the relativistic prediction) of the other twin, am I right?
If so I also agree with this. I don't understand then how we can have different conclusions.
My conclusion is that as they make a perfect symmetrical travel the observation of each twin from his own "rest" frame on the other twin (his relativistic prediction on this other twin) are exactly the same and here the paradox arise. If one twin observes the other aging less then this otherone will see the first one aging less and so contradictory observations.
Please explain your conclusion on this scenario.

 

[brucep]

Well, the problem now is that in the proposed new theories clocks also can exhibit differences in their readings if working at differences velcities but because the proposed electric and magnetic fields (which also governs atomic scale phenomena) have a new factor in their definitions which is velocity dependent. It is proposed that this is the cause of the experimentally verified variations in timings with particles, atoms and clocks currently called "relativistic time dilations" (briefly presented in Appendix B of the manuscript). So Relativity can explain those variations in timing but also the proposed new theories although in a different way. Then, as a possible new interpretation is possible to explain the timing variation it cannot be considered a proof anymore.
By the way, there, in Appendix B, is presented other interpretations possible for Mercury's precession and the bending of light by massive objects like the Sun.
Other interpretations for other phenomena and experiments are even described within the text.
Then many considered experimental tests in favor of Relativity could not be considered totally valid evidence in favor of Relativity only anymore. They are also compatible with the new theory.

You're completely wrong. Show us any derivation you have that could be substituted for the GR predictions for the natural precession of the perihelion of Mercury's orbit and the GPS. You should be able to write it out in detail in this thread.

 

[martillo]

You're completely wrong. Show us any derivation you have that could be substituted for the GR predictions for the natural precession of the perihelion of Mercury's orbit and the GPS. You should be able to write it out in detail in this thread.

I don't have a detailed alternative explanation about the GPS, I only thought what I posted. For the Mercury precession alternative interpretation you can find it in Appendix B of the manuscript but prometheus forbidded me to post any link for now and so you should look in my profile the link to the website in the "About Me"/interests section and look for the Appendix B in the Content at the main page.
Too extense and include graphics so I don't want to try to repeat that posting it in the thread.

 

[brucep]

I don't have a detailed alternative explanation about the GPS, I only thought what I posted. For the Mercury precession alternative interpretation you can find it in Appendix B of the manuscript but prometheus forbidded me to post any link for now and so you should look in my profile the link to the website in the "About Me"/interests section and look for the Appendix B in the Content at the main page.
Too extense and include graphics so I don't want to try to repeat that posting it in the thread.

You can't do it so you post an excuse and ask me to read your bullshit. What you're trying to say is space and time intervals are absolute rather than relative as any intellectually honest person would conclude from the empirical evidence supporting scientific predictions. Third time I've posted this in the last several days. A simple derivation for the natural precession of the perihelion of Mercury's orbit.

Start with the Schwarzschild metric [geometric units] setting theta at 0.

dTau^2 = (1-2M/r)dt^2 - dr^2/(1-2M/r) - r^2(dphi)^2

Substituting constants of geodesic motion E/m and L/m for dt and dphi

dt = [(E/m)/(1-2M/r)]dTau

dphi = [(L/m)/r^2]dTau

solving for this expression which relates squared values for radial motion (dr/dTau)^2, energy per unit mass (E/m)^2, and the effective potential per unit mass (V/m)^2 = (1-2M/r)(1+[(L/m)^2/r^2]).

(dr/dTau)^2 = +/- (E/m)^2 - (1-2M/r)(1+[(L/m)^2/r^2])

Taking some license for the weak field and multiplying through by 1/2 after multiplying out the squared effective potential

1/2(dr/dTau)^2 = 1/2(E/m)^2 - [1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3]

setting (V/m)^2 = U/m

U/m = 1/2 - M/r + (L/m)^2/2r^2 - M(L/m)^2/r^3

1st derivative

d(U/m)/dr = M/r^2 - (L/m)^2/r^3 + 3M(L/m)^2/r^4

2nd derivative d'2(U/m)/dr'2 = rate of radial oscillation = w^2_r

w^2_r = M(r-6M)/r^3(r-3M]

without writing down details the rate of angular velocity becomes

w^2_phi ~ (dphi/dTau)^2 = M/r^2(r-3M}

Both are really close in the weak field. We could approximate a large value for r and we would have Newton's result M/r^3 for both radial rate of oscillation and rate of angular velocity but we would end up with a wrong answer that GR orbits and Newton orbits are the same.

So here it comes

w^2_phi - w^2_r = 6M^2/r^3(r-3M)

This is the difference so we can find a factor x M/r^3 which closely approximates 6M^2/r^3(r-3M)

That factor is 6M/r

(6M/r)(M/r^3} = 6M^2/r^4

The last step is further license for the weak field taking the root of the factor and doing the approximation

(6M/r)^1/2 ~ 1/2(6M/r) = 3M/r

So a very close approximation for the rate of orbital precession, in the weak field [our solar system] is 3M/r. You can plug in numbers for and get the right answer.

3M_Sun = 4431m
r_mean Mercury = 5.8x10^10 meters
415.1539069 revolutions in 100 Earth years
360 degrees per year
3600 arcseconds per degree
etc...

 

[przyk]

Well, the problem now is that in the proposed new theories clocks also can exhibit differences in their readings if working at differences velcities but because the proposed electric and magnetic fields (which also governs atomic scale phenomena) have a new factor in their definitions which is velocity dependent.

If you are talking about SR time dilation then you need no such factors. Electromagnetism, as Maxwell finally formulated it, already predicts that moving systems held together by electromagnetic interactions will experience time dilation (and length contraction, for that matter). This was noticed by the likes of Lorentz and Larmor in the last years of the 19[sup]th[/sup] century, several years before Einstein's 1905 paper.

The whole point of relativity is that we know what the time dilation factor will be from a symmetry argument, because electromagnetism is a relativistic theory, without having to do detailed electromagnetism calculations like Lorentz and Larmor originally did.

That said, the dominant effect reported for the GPS satellite was due to gravitational time dilation, which is dependent on altitude and the gravitational field, and not on velocity.

Then, as a possible new interpretation is possible to explain the timing variation it cannot be considered a proof anymore.

Your choice of language is strange because there is no such thing as a "proof" of anything in experimental physics. The scientific method implicitly recognises that just because a theory makes a correct prediction doesn't necessarily imply it is the only possible explanation of the result. So an experimental result is never a proof and that is not how we use evidence in science.

The way we use evidence in science is different: if a theory predicts result A, and the foundation of the theory is small and has nothing specifically to do with A, scientific policy is not to regard that as a coincidence. By making lots of measurements, we expect to filter out the right theory.

The reason we think general relativity is a "good" theory is not just because it manages to get the right results, but because it is a theory that depends on just two parameters (the gravitational constant G and the speed of light c, both of which were fixed beforehand), and the theory didn't need to be fiddled around with to get the right results. The bending of starlight is considered strong evidence for GR partly because it was observed after GR made the prediction. The same is true of gravitational time dilation and the rate of GPS satellite clocks: GR was formulated in 1915 and made correct predictions about experiments performed decades later, without any need for "interpretation". So when you say that other explanations might be possible, you are technically correct, but you are missing the point and not addressing why we consider these results good evidence for GR in the first place.

By the way, there, in Appendix B, is presented other interpretations possible for Mercury's precession and the bending of light by massive objects like the Sun.
Other interpretations for other phenomena and experiments are even described within the text.
Then many considered experimental tests in favor of Relativity could not be considered totally valid evidence in favor of Relativity only anymore. They are also compatible with the new theory.

I think the appendix you refer to is a perfect example of what's wrong with your approach to physics: you need to make up a new explanation for every effect you consider, and you never show that you can get the right numerical result. Regarding your attempt to explain Mercury's perihelion advance, I think it also doesn't help you that 19[sup]th[/sup] century astrophysicists weren't stupid, and if they knew how to account for perturbations of Mercury's orbit due to the other planets, they could certainly have dealt with an asymmetry in the mass distribution in the sun if they had expected that to be significant. It also doesn't help you that the sun is quite well studied and if there were a significant asymmetry in its matter distribution, I would expect we would know about it. You are doing nothing to establish that what you are saying is significant, hasn't been considered[sup]*[/sup], and is actually consistent with what is known about the sun.


[sup]*[/sup] a quick check at Wikipedia reveals that at least the oblateness of the sun, leading to a quadrupole moment in its mass distribution, was considered and accounts for 0.0254 arc seconds per century of Mercury's perihelion advance. Astronomers apparently also tried explaining the perihelion advance in terms of another as yet undiscovered planet, and had fun predicting where that planet might be.

 

[przyk]

To not complicate things let assume there's no external different influence on the twins (like gravitation of external bdies,etc).

For clarity, when I was talking about a "gravitational potential", I wasn't talking about external gravitational bodies. I was referring to GR's equivalence principle, which states that effects in an accelerating frame are (roughly) equivalent to effects in a gravitational field. In GR, if you have a clock higher up in a gravitational field, it advances faster due to gravitational time dilation. The equivalence principle says that we should expect the same thing in an accelerating frame: if you accelerate toward something, you expect it to age faster in your frame than if you were not accelerating.

Historically, by the way, the deduction was made the other way around. I think Einstein looked at accelerating frames in about 1907 and deduced the effect I've just described, and then concluded we should see the same thing in a gravitational field like the one on Earth. So we could almost say that looking at how the twin paradox is resolved in accelerating frames lead to the prediction of gravitational time dilation.

What you are saying then is that what one twin observes about himself at his "rest" frame is different than what he observes (the relativistic prediction) of the other twin, am I right?

I am saying that the whole situation as described in either twin's frame is not symmetric. So there is no principle that tells you that they should age at the same rate in either twin's frame, and the twin's ages and ageing rates aren't the only things that are different. Like I keep saying each twin sees the other twin Doppler shifted but not himself Doppler shifted for example. You get that even in classical physics.

I don't understand then how we can have different conclusions.

Put simply, you are drawing a much stronger conclusion than the symmetry in your scenario actually allows you to draw. There are a number of things you can deduce from the symmetry between the twins, but "they should be the same age in both twins' frames" is not one of them.