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LOLOLOL. First, you need to understand acceleration is absolute motion. Next, given d is absolute and SD is also, SD - d is the correct answer. Then, you can create length contraction as follows. ta = 2 * t + [ (SD-d)/v ] / γ ta - 2t = [ (SD-d)/v ] / γ (ta - 2t)v = (SD-d) / γ There are you happy now? What? If the relative motion period adjustment exceeds the acceleration adjustment, then the paradox exists regardless of mass. Do you have math to back up this assertion?

I am not going to do a homework problem. I will explain how it is done. a - acceleration in the accelerating frame. T - Time in the accelerating frame of the acceleration. t - Time in the inertial frame that corresponds to the T d - the distance traveled during acceleration. v - the resultant relative velocity v achieved by the acceleration. Earth frame proper time Acceleration phases Hence, t = 2 * (c/a) sinh(aT/c) for those phases Relative motion phase v = c tanh(aT/c) To calculate the distance traveled by the accelerating frame, it is d = 2 * (c²/a) (cosh(aT/c) - for both the accel and deccel phases. From the view of the earth, it will be the star distance - d. Hence, t = (SD-d)/v for the relative motion phase. Therefore, the earth clock will elapse (SD-d)/v + 2 * (c/a) sinh(aT/c) Accelerating frame.proper time T(total) = 2 * T d = 2 * (c²/a) (cosh(aT/c) - for both the accel and deccel phases. t = (SD-d)/v Elapsed time = 2 * T + (SD-d)/v Earth frame.view of the accelerating frame's elapsed time 2 * T + [ (SD-d)/v ] / γ Accelerating frame view of Earth's elapsed time 2 * t + [ (SD-d)/v ] / γ

OK, reciprocal time dilation for the frames for the 100 days, time dilation only for the accelerated frame when accelerating. GPS uses two adjustments, one for GR effects and one for velocity differentials. Now, let's assume a satellite is directly over a unit that is in open space and inertial. This means the unit has a y value only and x = 0. At that instant, the satellite emits a light pulse. The satellite will contend that light travels a distance √[(vt)² + y²] to meet the unit. The unit contends light only has a y component since it is at rest. Given the constancy of light for both frames, the clock of the unit must beat slower from the view of the satellite given the two different frame view on the distance light travels. Now, we put this same logic using the earth. Sure, there exists a gravity component, but there exists a competing SR time dilation component as verified by the logic of Neil Ashby as I posted. However, from the view of the satellite, it turns out to be false that the earth clock beats slower in this context. Only the gravity effects are valid. Hence, the light travel distance differential does not exist. Therefore, light is not behaving by experiment the way SR says it should. You see, this is not strictly are gravity differential issue. The satellite is not moving at the same speed as the earth unit. I've never disputed these results.

I want to make sure I understand you correctly. Are you claiming the accelerating frame beats faster in time? Next, I realize time dilation due to acceleration/gravity and time dilation due to frame speed differentials are different concepts. That has nothing to do with what we are talking about. We are strictly taking about the effect on time due to acceleration. You are now adding other variables that were not part of the acceleration/decceleration of the OP. The OP did not include a relative motion phase as the normal twins paradox would indicate. So, in the context of this thread, the time dilation is due to acceleration only. But, while we are on paradoxes and you want to talk about time dilation due to inertial velocity differentials in GPS, SR mandates reciprocal time dilation. Can you explain why GPS proves time dilation is not reciprocal. In other words, the GPS satellite does not view the earth clocks as time dilated as mandated and required by SR. Oh, I forgot to mention gravational mass and inertial mass are not distinguishable. This is why regardless of the mass, all objects move at the same acceleration when dropped toward the earth. Therefore, in GR, time dilation due to a gravitational differentials and time dilation due to acceleration differentials are the same. Further, I produced many papers proving the sin hyperbolic function is used to calculate the time dilation of uniform acceleration relative to an inertial frame. Do you dispute these mainstream calculations?

I have no ides what you are talking about. It is standard mainstream that the accelerating clock beats more slowly. Here is experimental proof. The effects are emphasized for several different orbit radii of particular interest. For a low earth orbiter such as the Space Shuttle, the velocity is so great that slowing due to time dilation is the dominant effect, while for a GPS satellite clock, the gravitational blueshift is greater. http://relativity.livingreviews.org/Articles/lrr-2003-1/ In the GPS experiment, the satellite is in a lower amount of gravity ie less acceleration and hence will beat faster for this GR effect or the more accelerated earth clock beats faster. Now, for the paper, you will see, t = c/g sinh(gT/c) Where g is the acceleration measured in the accelerated frame and T is the proper time in the context of the accelerated frame. t is the time in the inertial frame. If you plot the graph, you will find t > T or the accelerating frame is time dilated. Oh, and this is an absolute agreement between the frames. Here is a link that gives a simpler analysis. http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html In short, the paper I posted backs my position. The accelerating frame is time dilated. First the embankment frame is M'. Now, he said M and M' are co-located when the strikes occured simultaneously in the context of M'. That is exactly what I said. Now, I said if M' is co-located with M, then M is co-located with M'. How did I conclude this? Well, in Einstein's "claimed" proof of consistency, he said, At the time t = t' = 0, when the origin of the co-ordinates is common to the two systems http://www.fourmilab.ch/etexts/einstein/specrel/www/ Now, this implies co-location is part of the logic of SR since the origins are common. As such, it is not a theorem of SR that when M is co-located with M', M' is not co-located with M. Therefore, using the Einstein logic above, M and M' are mutually co-located. So, you are wrong. It is only a paradox in your mind because you are misinterpreting his meaning. I have no idea what you are talking about. You will note I quote Einstein for my positions. So, quote him for yours.

Yes. I mostly agree with you. But, with length contraction, it would be uniform for the A and B lightning strikes points and thus would sync at d'=ct'. So that does not present a problem, but your length contraction does. Let me introduce observers F and R and F' and R' where the primed frame is the embankment. Then, if F and F' are co-located when M and M' are co-located, in the frame of M', then F and F' will not be co-located from the view of M. However Einstein was clear, when a light is emitted, frames can set their clocks to 0 at the common emission point. This is also fundamental to the light cone. Also, Einstein said the strike were simultaneously emitted from the view of M' when M and M' are co-located. Clearly, this thought experiment is a paradox because we cannot perform all the actions Einstein said we are allowed to do.

The MMX experiment is used to measure whether light is measured c in two different directions at one place on the earth. If this is false, please specify. If a handheld unit is at that same location, it does not measure c in all locations. If this is false, please specify.

What? I thought you folks had the answers. Was I wrong? Source the photons. That is what I am looking for.

Is time dilation reciprocal?

So what. This is length contraction. You are having a problem not me. Einstein said M and M' are co-located. Yes or no. Then Einstein claimed for all light pulses, you can co-located the light pulses and set the clocks to zero. Yes or no? If no, then LT construction is impossible and so is his alleged proof of consistency. Now what? Here is the mainstream paper that supports this http://arxiv.org/abs/physics/0411233 Uniform acceleration under SR is absolute and both frames agree the accelerating frame beats more slowly.

Yea, this is hand waving. Source all the photons. No, I just want all the photons sourced. I would like to see an accounting.

MMX And The Earth's Rotational Sagnac MMX experiments are the cornerstone for proving the validity of special relativity. Tom Roberts specifies "The speed of light is said to be isotropic if it has the same value when measured in any/every direction." He then lists a large collection of MMX or round trip speed of light comparisons to prove the speed of light is isotropic or measured c in all directions. This is an alternative way of stating the light postulate of special relativity. However, the earth's rotational sagnac does not show up in MMX experiments. GPS on the other hand validates this rotational sagnac, in particular, Robert A. Nelson and Todd A. Ely, in RELATIVISTIC TRANSFORMATIONS FOR TIME SYNCHRONIZATION AND DISSEMINATION IN THE SOLAR SYSTEM noted: In the case of a receiver at rest on the Earth, an observer in the ECEF frame regards the receiver as stationary and applies the Sagnac correction. However, an observer in the ECI frame sees that the receiver has moved due to the Earths rotation during the signal time of flight and instead applies a propagation time correction due to the additional path length. The term Sagnac effect is part of the vocabulary of only the observer in the rotating reference frame. The corresponding correction applied by the inertial observer might be called a velocity correction. While the interpretation of the correction is different in the two frames, the numerical value is the same in either frame. http://tycho.usno.navy.mil/ptti/ptti2006/paper28.pdf This sagnac correction is also noted by Neil Ashby in http://relativity.livingreviews.org/Articles/lrr-2003-1/ Since MMX proves light is measured c in all directions on the earth and the earth's rotational sagnac at that same location uses a velocity correction to the speed of light, then the two results are inconsistent with each other. Curiously, even though both results are inconsistent with each other, both are used to claim SR is experimentally validated . Therefore, we should expect to find this velocity sagnac correction in MMX since the experiment is performed in the ECEF frame. The question is why not. Well, simple math explains this. The timing of roundtrip light travel using the sagnac correction is at most t = d /(c+v) + d/(c-v) = 2dc/( c² - v²) if you happen to be lucky and measuring in or against the direction of rotation. Otherwise it is less. So for one arm of MMX, the round trip timing for light travel is 2dc/( c² - v²) for the arm in the direction of rotation and at the 90 degree arm the round trip light travel is timed at 2d/c. For MMX to detect the difference between the two, the calculation is 2dc/( c² - v²) - 2d/c = 2d[ c/( c² - v²) - 1/c ]. So, in the lab we might have d = 1 meter = 0.001km c ≈ 300,000km/sec v ≈ 1669.8 km/hr ≈ 0.46383 km/sec for the speed of the earth's rotation. Then the timing differential is calculated. ∆t = 2d[ c/( c² - v²) - 1/c ] ∆t = 0.002 * [ 300000/(300000² - 0.46383²) - 1 / 300000 ] = 1.5936*10-20 seconds. No wonder MMX can't find the earth's rotational sagnac correction. This sensitivity requirements is well beyond anything available. Therefore, even though MMX has been used for years to experimentally validate SR, the sagnac correction picked up and proven by GPS is missing in MMX. But as shown by the math above, the two way light travel differential in MMX is invisible to modern experimental devices. Hence, the null results of MMX are not actually null but too small to detect. As such, MMX has been a false positive for SR. .

I would like to propose an experiment much like the GPS sagnac proves the earth is rotating. Can we do this for the earth's orbit around the sun since this is a sagnac path with the radius being from the earth to the sun? This would settle this problem. Is this correct?

OK, let's remove the term "simultaneous" because that is not really what I meant. I meant, when lightning strikes position A, two conditions are true. 1) Ma and M' are co-located. 2) At the position of the front lightning strike, I will call it A/A', both frames can sync t'=t=0 at that particular location. Make sense? So, when M and M' are co-located, neither frame can disagree t=t'=0 at the location of the lightning strke. Yea, you have a very good view of the embankment frame. However, we are taking the train as stationary. So, it does not travel toward the light. It this true, or does a rest frame travel toward a light pulse?

I read your proof and conclusions that your theoretical value is at the pobs. How does your value and the mainstream cause the universe to expand outwards. How do you create negative mass?

How is it science to claim the abstraction of energy converts into what you need for your theory? The photons need to be sourced.

Einstein said the following. At the time t'=t=0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then From the origin of system k let a ray be emitted at the time along the X-axis to x', http://www.fourmilab.ch/etexts/einstein/specrel/www/ I do not mind admitting I am confused. Can you explain in the two above why these statements of simultaneous emissions are false? Einstein required a simultaneous emission of light for LT construction and for his "proof" of the logical consistency of SR. If these are not simultaneous frame emissions as you say and they are stupid, then how can you agree with Einstein?

Yea, but this conversion requires an axiomatic method for the conversion. We do not have that. You cannot just use an absract term energy to create photons. They must be sourced.

We are talking about the light emission as being simultaneous. Let's see, if the light emission is not simultaneous between the frames, how would you possible do the original mirror experiment for LT construction? It assumes a common light emission where both clocks are set to 0. Furthermore, Einstein used a common light emission to prove the consistency, which he is wrong, of SR. So, you cannot say the light emission was not simultaneous to the frames at the front of the trains or your refute all of SR.

OK, how does the train frame conclude the front flash occurs before the back. We must remember, both flashes happen when M and M' are co-located. Hence, both are equidistant light flashes that occir to each frame when M and M' are co-located. How will you make the flahs in the front of the train emit before the back? That implies if and A and A' were co-located at the flash at the same place, one would have to claim light is speeding down the x-axis whereas the other at the same place claims light is not there. How do you work this out? Yes, we are tallking about light reception. Does each receive the signals differently. Let's stay on the M' train frame. Are they two flashes equidistant yes or no.

Yes, the lab sagnac is consistent with SR, the earth's rotational sagnac is consistent with SR and the lack of the orbital sagnac is consistent with SR. Also, MMX is consistent with SR. Can you expalin why MMX does not pick up the earth's rotational sagnac? Also, the null result of MMX proves SR and the earth's rotational sagnac proven by GPS proves SR and yet the two are inconsistent. Can you help me with this also?

OK, based on the link provided on this thread that supplies all the answers to the problem, The pp I branch 3 2He + 3 2He → 4 2He + 2 1 1H + 12.86 MeV http://en.wikipedia.org/wiki/Proton%E2%80%93proton_chain_reaction Now, where does the kinetic energy come from. Note, this branch does not offer particles to create this kinetic energy and thus black body radiation. It only offers the abstraction of 12.86 MeV which we have to conclude is radiation or photons without being sourced.

Well, when the front flash occurs, each observer are equidistant to the flash. That is a fact since both are co-located when the flash occurs. Same is true for the rear flash. So, we have a moving light source (which does not matter) with light flashes that are equidistant to the observer when they occur. Thus, the train as stationary will conclude the flashes are simultaneous whereas the embankment will conclude they are not for the train observer. the light simply flashes at 2 different times See, this is the problem. Let's just take the front flash. You are claiming when M and M' are co-located, the flash in the front occurs at a closer distant to M', the moving observer than M. Since the speed of light is a constant, this must be true. You see, you cannot claim lightning is at a location from one frame and not at that location in another. But if the lightning is closer, then both frame agree it strikes in 2 different locations. Your logic does not work. So, let's review, we have ONE lightning flash at ONE location that occurs when M and M' are co-located, ie at the same place.

The only thing that has been proven is that as gravity increases frequency reddens given a source. Now, we use clocks based on frequency. So, naturally as gravity increases these "clocks" beat slower. Your logic works iff time will only be measured by light frequency and all other measurements are false. I doubt all will agree in this.

We know the earth is rotating because of the GPS rotational sagnac. Any circular path is subject to sagnac. The earth's orbital path is circular and thus subject to sagnac. However, the orbital sagnac does not exist as proven by GPS. Oddly, this would appear that the earth is not revolving around the sun unless our theory of light is totally confused.