I need someone who knows the math

That is correct A, B and C will have all aged the same and they will have aged less than the one that was left on earth.

I see no paradox at all. A, B, and C started in the same RF on earth. They all moved to another RF that was different than the earths RF. They all then returned to the same RF of earth. Of course they all agree that the same amount of time has passed. If they did NOT agree that would be a paradox.

Not understanding relativity does not mean it is paradoxical.

 

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No. Bound energy states (matter) persists and does not dissipate instantly precisely because in the rotational mode of propagation, time dilation occurs in the individual fundamental particles of which it is composed. This is the only reason geometry of any kind is possible, in your mind or in physical reality. Bound energy has some attributes of static Euclidean space. Good for doing statics and geometry; not relativity, and certainly not QM. Bound energy that possesses quantum spin and entanglement is the basis of physicality and of time itself. The particle of spin zero and the quantum field of which it is an excitation is the missing relativistic spin invariant. It belongs both to relativity (but not Minkowsi's) and QM.

Space, in every direction, is light travel time. Lorentz covariance (time vs space) is not necessary at all. Time is the ONLY physical dimension. It does not know complex numbers, quadratic inspired light cones (which are useless), quaternions, Pythagorus, Minkowski, or Hilbert. It knows Albert, but his relativistic description of the nature of time, entanglement and time dilation stopped far short of being complete.

Light cones are just another one of Minkowski's quadratic vanities. They do not explain entanglement, nor does the rest of his quadratic mathematical nonsense, and also Hilbert's, are what makes relativity inconsistent with QM AND EVEN THEIR OWN MATH. If they were consistent, a coordinate system with an origin that is anchored in inertialess relativistic space, agreed upon by all observers would be possible. It would be possible to specify whether objects contracted from one of the ends or the center, other than by mathematical convention. It would be possible to specify the coordinate that is the CENTER of Minkowski rotation, likewise agreed upon by all observers in any relative state of motion. Finally, it would be possible to describe simultanaeity in terms of ENTANGLEMENT. Since none of this is possible, the math that supports it must be rejected. Try again. This time, do it without an inconsistent and deranged affection for everything quadratic. Or even Greek static geometry. If something moves, time dilates. It is a scalar field for certain. Time is the only dimension, and it derives of quantum spin, the only arrow of which is the sense of its propagation. Linear propagation of light in the vacuum permeated by this quantum field cannot even occur without it.

 

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Your Post #81

Your Post # 79

If they see each other's clock time dilated, then how could they all have aged same ?

You are countering yourself just in 2 posts..

 

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Please don't post this pseudoscience gobbledygook in the science section.

 

Be more specific, or I will ignore you also.

 

It seems like countering to you because you do not understand SR.
They did see time dilation of each other. But they were always in the same inertial frame as each other so they all experienced the same time passage. You do realize that time diation is the same for both observers right. A is time dilated for B and B is time dilated the exact same amount for A.

 

I have a degree in physics. I know that you do also. As I said, if you believe that I am in substantial error about SR, in what way?

Your description matches that of Internet crazy John Doan, who swears the twin paradox is a hoax. Do you? The twin paradox is real. We see it happen every second of every day with GPS satellites. I have worked with this technology as it was being developed. The time dilation also works for circular paths, which those manifestly are.

 

Be more specific......

You say they will be time dilated, then you say still they will be aged same. So you are countering yourself ?

I will make it simple for you..

1. A moves with a speed of V in + x direction with respect to earth.
2 B moves with a speed of V in - x direction with respect to earth.

At any given instant during the journey (ignoring the turn around) the relative speed bewteen A and B shall be 2V, so there will be time dilation, meaning their clocks will read differently. But when they return to earth, they would have been time dilated with Earth RF by the same amount, then simple maths says that their clocks should match, but they are dilated.....

 

Exactly.

And, BTW, I'm also not claiming that length contraction isn't real; it most certainly is.

But the contraction is more akin to a sub-light Doppler shift than it is to a Minkowski rotation, a rotation in higher dimension Hilbert spaces, or a complex Pythagorean attempt at making the concept that much more mathematically and also physically incomprehensible. In a universe composed of energy transfer events, only excitations of a quantum field, entanglement and time are meaningful.

Otherwise, why does NIST use a wavelength as a universal standard of length? Because Einstein's SR informed them that at least the speed of light (if not the individual Doppler shifted wavelengths) could be relied upon to be invariant, that's why. I'm telling you that a quantum spin of zero is the at rest spin invariant that makes a wide range of physical parameters, including time itself and the speed of light, possible.

Does any science you know of even have a glimmering of an understanding of time itself? How about the 10^116 discrepancy in the VeV? How about the cause (not just the behavior) of gravity, or even just the derivation of the universal gravitational constant? How about that hierarchy problem? If you have no answers, you have no science.

 

That only happens if each has equivalent paths through space-time. Neglecting GR, in Earth-centered coordinates:

This is the time-dilation in Special Relativity:
\(\Delta \tau_A = \int_{start}^{finish} \sqrt{ 1 - c^{-2} \left( v_A(t) \right)^2 } dt \leq \int_{start}^{finish} 1 dt = t_{finish} - t_{start} = \Delta \tau_{Earth}\)
Since it is only dependent on a 1-parameter summary of the history of the magnitude of velocity relative to an inertially moving object, an alternate path through space-time may have the same elapsed proper time and thus same net time difference relative to clocks on Earth. The simplest family of similar space-time profiles are those generated by rotation, which looks like your cases B and C rotated by 180° and 90°, respectively.

Wrong. The closing speed in Earth-based coordinates is 2V, but the relative speed between A and B is initially \(\frac{2V}{1 + \frac{V^2}{c^2}}\).

The full analysis requires three inertial frames of reference: Earth, A outbound and A inbound since A has different states of inertial motion.
The full analysis requires four space-time events: O, departure; P, A's turnaround; Q, B's turnaround; R, return;

\(x_{outbound} = \frac{x_{Earth} - V t_{Earth}}{\sqrt{1 - c^{-2} V^2}} \\ t_{outbound} = \frac{t_{Earth} - c^{-2} V x_{Earth}}{\sqrt{1 - c^{-2} V^2}}\)

For the inbound trip we need to use an inhomogeneous Lorentz transform to avoid a discontinuity in the description of A's own position and time.
\(x_{inbound} = \frac{x_{Earth} + V t_{Earth} - 2VT}{\sqrt{1 - c^{-2} V^2}} \\ t_{inbound} = \frac{t_{Earth} + c^{-2} V x_{Earth} - 2 c^{-2} V^2 T}{\sqrt{1 - c^{-2} V^2}}\)


\( \begin{array}{c|ll|ll|ll} \textrm{Event} & x_{Earth} & t_{Earth} & x_{outbound} & t_{outbound} & x_{inbound} & t_{inbound} \\ O & 0 & 0 & 0 & 0 & - \frac{2VT}{\sqrt{1 - c^{-2} V^2}} & - \frac{2 c^{-2} V^2 T}{\sqrt{1 - c^{-2} V^2}} \\ P & VT & T & 0 & \sqrt{1 - c^{-2} V^2} T & 0 & \sqrt{1 - c^{-2} V^2} T \\ Q & -VT & T & -\frac{2VT}{\sqrt{1 - c^{-2} V^2}} & \frac{\left(1 + c^{-2} V^2 \right) T }{\sqrt{1 - c^{-2} V^2}} & -\frac{2VT}{\sqrt{1 - c^{-2} V^2}} & \frac{\left(1 - 3 c^{-2} V^2 \right) T}{\sqrt{1 - c^{-2} V^2}} \\ R & 0 & 2T & -\frac{2VT}{\sqrt{1 - c^{-2} V^2}} & \frac{2T}{\sqrt{1 - c^{-2} V^2}} & 0 & 2\sqrt{1 - c^{-2} V^2} T \end{array}\)

Now \(( t_R - t_O)^2 - c^{-2}(x_R-x_O)^2 = (2T)^2, ( t_P - t_O)^2 - c^{-2}(x_P-x_O)^2 = ( t_Q - t_O)^2 - c^{-2}(x_Q-x_O)^2 = (t_R - t_P)^2 - c^{-2}(x_R-x_P)^2 = (t_R - t_Q)^2 - c^{-2}(x_R-x_Q)^2 = (1 - c^{-2} V^2) T^2\) no matter which inertial coordinates one uses to compute.

Thus A & B each experience a total elapsed time of only \(2\sqrt{1 - c^{-2} V^2} T\) while Earth experiences \(2 T\).

 

OK, lets assume the relative velocity between the two is about 0.9c. It is important that both of our astronauts left from the same inertial frame. That means that A would saythat B's clock is running about 1/2 speed. However, that also means that B would say that A's clock is also running at about 1/2 speed. In other words they would BOTH say that their own clock was running at normal speed AND they would BOTH say that the each others clocks are running at about 1/2 speed. Therefore when they returned to earth and again are in the same inertial frame, they would find that both of there clocks agree. That is not a paradox, that is relativity. If this seems like a paradox then you are not taking relativity into account.

Do the math, it is only algebra, and convince yourself.

Edit to add: Never mind I see that Rpenner already did the math.

 

Actually, I think I recall chinglu [remember him?] proposing something similar as this nonsense....and as usual rpenner lead the way in refuting such nonsense.

 

Big Bang is God was looking for help SR and GR. Your post do not appear to be directed towards that end. I humbly suggest that it is the better part of wisdom and curtesy to keep the orginal purpose in mind when posting.

 

It appears that part of the problem is confusion over the meaning of time dilation. In one context it means the difference total elapsed time between a traveler who accelerated away, coasted, accelerated back, coasted again then accelerated a third and came to rest next to a someone who never accelerated or did so in a different direction. Another context is what each person see if he receives a time signal from the other(s). While moving away from each other the successive time signals will arrived late, when moving towards each other the successive times signals will arrive early (ie redshift and blueshift). As rpenner and others have pointed out these different contexts will give the same result when the math is done right (the tricky bit).

 

Different inertial or even accelerated frames of reference experience different time dilations. Only instantaneous velocity (if accelerated) makes any difference. This would include circular paths, and differences in time dilation effects would occur no matter how large or how small the radius of a circular path, analogous to time dilations for linear velocities <c.

The bound energy of fundamental particles experience infinite time dilations, the same as photons traveling a linear path at c. This is why they persist in the rest frame.

I'm talking about unconditionally stable particles of bound energy. Electrons never get old, nor do they decay until or unless they happen to meet a positron, which also never decays or gets old. This is why. It is most likely the same for protons, but not according to string theory, which insists they will decay with a half life many times the current age of the universe.

Science is supposed to provide answers to inquiries such as these. Why does it not?

 

In SR, it is immaterial in which direction spacecraft moves and returns, if the magnitude of velocity is same for all directions, they all will have same ageing with reference to earth guy, implying that there is no differential ageing between travelling crafts. But the paradox is any two crafts will have relative motion between them, suggesting differential ageing. This argument does not get countered by your response...

 

Some lolly polly stuff you can type.....tell me when you finally understand what you have typed.

 

When we have parties claiming such nonsensical stuff as GP-B was fraudulent, LIGO was fraudulent, BH's do not exist and that he is never wrong, it will need far more than maths, even from an expert like rpenner, to ever hope to convince him that SR/GR are both as near certain as anyone could hope, particularly in line with recent discoveries and confirmations.
http://mentalhealthdaily.com/2015/05/12/delusions-of-grandeur-causes-symptoms-treatment/

 

Show some mettle, and answer why there is no paradox...

 

There is no simple concept of differential aging relating to traveling crafts. That's the misconception of Relativity most famously associated with Herbert Dingle.

As demostrated in my previous post, the relation between +V and –V is the same as that between +2V/(1+V^2/c^2) and 0 or 0 and –2V/(1+V^2/c^2).

So rather than saying there is no relative time dilation, the inertial coordinate system where A is at rest sees B as time-dilated by the factor (c^2+V^2)/(c^2–V^2) and moving in the –x direction while the inertial coordinate system where B is at rest sees A as time-dilated by the same factor but moving in the +x direction.

So relative time-dilation is always associated with relative motion. And the Lorentz transformation is not one of time, but always one of time and space. Neglecting this aspect of special relativity was Dingle's failing.

Cutting through all of this malarkey is the concept of «proper time» which may be universally computed for any piecewise inertial path segment-by-segment as √[ (t_2-t_1)^2 -(x_2-x_1)^2/c^2 ] or by the equivalent integral formulation above.

The intuitive notion that some coordinate time has inherit physical meaning or commensurability with the proper time of space-time trajectories is not compatible with the physics of Special Relativity.

It's not an argument. It's a impediment to learning physics.