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Assume O and O' are clocks are in relative motion in the standard configuration. Assume the stationary frame is O. According to SR, when the clock O elapses t, the clock in O' elapses t/γ, thus, when the clock in O elapses tγ, the clock in O elapses t. That is simple time dilation. By the measure at c logic of SR, if light is emitted when O and O' are co-located, light proceeds spherically from the origin of each. This website shows this. http://casa.colorado.edu/~ajsh/sr/paradox.html Now, considering O', when its clock elapses r/c, light proceeds a distance r in all directions. This is the SR measure at c logic. OK, now for the experiment, when the clocks O and O' are co-located, light is emitted at the co-location point by O'. Only the positive x-axis will be considered. Let r be a chosen distance. 1) Allow the time γr/c to elapse in O. 2) By SR, light proceeds a distance γr in O. 3) Since γr/c elapses in O, then r/c elapses on the clock of O'. 4) By SR logic, when r/c elapses in O', light proceeds r in all directions. Hence, the light is a distance r from O' along the positive x-axis. 5) When γr/c elapses in O, O' is located at a position vt or v(γr/c) in the coordinates of O. 6) But, since r/c elapsed in O', then light is a distance r from O'. Therefore, in O light is a distance vt + r/γ from O or v(γr/c) + r/γ = γr( v/c + 1/γ²) Hence, gathering all the SR logic, when the clock of O elapses γr/c, light is located at γr( v/c + 1/γ²) and γr which is a contradiction.

Yea, a theory that replaces SR would need to be consistent with current results. I just do not think any science theory is at the point of being a fact. And, you cannot say SR cannot contradict itself. That is similar to the halting problem. It may simply be the case the contradiction has not been thought up or the like. Merged post follows: Consecutive posts merged Now, see, sure the apple will fall. But, there have been and currently are disputed explanations with GR being the most used. But, it is not the final answer. Improving a theory does not imply the apple does not fall, but that it falls and everything else is also explained.

I can't tell. He seems to be trying to prove light speed is not a constant. But, I do not knows what he means by this. If he is trying to claim it is not a constant in the vacuum of space, then that would go against many experiments and he would need to explain why these experiments are wrong. Merged post follows: Consecutive posts merged I am not sure about your thought exeriment idea. After all, one day SR will be replaced as a theory in which case someone will think up a thought experiment against it and then possibly peform it. Othewise, it is a fact. A fact to me is a theory perfectly models reality and therefore cannot ever be disproven. I do not think humans are there yet, if ever. Nothing will beat a proper calculation apart from experimental evidence. I agree on a proper calculation. I have a question, assume light is emitted at t=0 and a frame clock elapses r/c, how far has light traveled in the frame?

You misunderstood me. This was the statement I was talking about. SR follows directly from the postulate of invariant speed of light, and if a thought experiment shows a contradiction, it is because of an error in the thought experiment. I do not agree with it and it implies SR is a fact and can never be refuted by any thought experiment ever. Is this your position also regarding SR? Merged post follows: Consecutive posts merged You fail to understand what I am saying. I DID NOT say Ritz/s theory is true. I have NEVER indicated that I believe in Ritz's theory. In fact, I wrote: There are tests from moving light sources that demonstrate light moves through space at one speed. http://math.ucr.edu/home/baez/physic...g-source_tests It is clear this is inconsistent with Ritz's ballistic theory. I only pointed out the fact that MMX cannot disprove Ritz's theory. In Ritz's theory of light, light is always measured c between the emission point in the frame and the reception point because the light speed matches the uniform motion of the frame. The velocity v_ is the velocity of the source and v_(t − r/c) is the velocity of the source at the moment of emission. Equation (10) describes an expanding sphere whose center is no longer at rest in the coordinate system; if the source were to continue to move uniformly with velocity v_, it would remain the center of the sphere. This geometrical description was favored by Ritz. http://www.pitt.edu/~jdnorton/papers/Einstein1905.pdf Here check it out. SR also says the moving frame will remain the center of the light sphere. That is interesting. Anyway, as to the OP, I was simply pointing out he will get nowhere trying to disprove anything about SR using MMX. That was my whole point.

Wow, this means SR is a fact of nature and not a theory. Merged post follows: Consecutive posts merged MMX is consistent with Ritz's theory of light. It is a common misconception that it proves the light postulate that light moves through the vacuum of space at one speed. Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment, not requiring aether. The theory postulates that light has always the same velocity in respect to the source.[6] However it also led to several "obvious" optical effects that were not seen in astronomical photographs, notably in observations of binary stars in which the light from the two stars could be measured in an interferometer. If this was correct, the light from the stars should cause fringe shifting due to the velocity of the stars being added to the speed of the light, but again, no such effect could be seen. http://en.wikipedia.org/wiki/Michelson-Morley_experiment One such attempt is known as the Emission Hypothesis (or the ballistic theory of light), and was developed partly by Walther Ritz (C&N p.353). According to this theory, light behaves like bullets shot from a gun, its speed with respect to the source being a universal constant and independent of any ether. This idea is consistent with the null results of the Michelson-Morley experiment and many others. http://laser.phys.ualberta.ca/~egerton/specrel3.htm Modern Physics/Michelson-Morley Experiment Walter Ritz's emitter theory (or ballistic theory), was also consistent with the results of the experiment http://en.wikibooks.org/wiki/Modern_Physics:Michelson-Morley_Experiment This rules out any conceptually coherent ballistic theory of light propagation, according to which the speed of light is the vector sum of the velocity of the source plus a vector of magnitude c. Ironically, the original Michelson-Morley experiment was consistent with the ballistic theory, but inconsistent with the naïve ether theory, whereas the Sagnac effect is consistent with the naïve ether theory but inconsistent with the ballistic theory. Of course, both results are consistent with fully relativistic theories of Lorentz and Einstein, since according to both theories light is propagated at a speed independent of the state of motion of the source. http://www.mathpages.com/rr/s2-07/2-07.htm This paper shows emission theory is consistent with SR.* http://arxiv.org/PS_cache/physics/pdf/0512/0512036v1.pdf There are tests from moving light sources that demonstrate light moves through space at one speed. http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html#moving-source_tests So, are you trying to prove light is not measured c in a frame between the emission point and the reception point or are you trying to prove c is not an absolute contant speed in the vacuum of space? One last comment, if your proposal is correct, you should be able to force LT into a contradiction using it. Hence, if your thought experiment really does prove the inconsistancy of SR, you should be able to translate it into some kind of mathematical contradiction within the theory.

No, I think I need to use the x and y in the equations for the composition. He has a wξ and a wη in chapter 5. http://www.fourmilab.ch/etexts/einstein/specrel/www/ I guess this is the x component speed and the y component speed of the second moving object in the moving frame coords where the moving frame has v along the positive x-axis of the stationary frame. This is what I am not sure about but I cannot ses it any other way.

No, it is not that simple. Normally, it would be atan2(y/x). I do not have the correct y and x. They are not simply wt and vt. A veclocity magnitude as produced by the equations can be satisfied by an infinite number of directions.

Wow!. How exactly does dark matter and dark energy fit into GR?

Can anyone tell me the direction of the resiltant velocity vector for the composition of velocities equations of SR? Thanks

Clock synchronization is relative to each frame using 2-way light signals. hmmmmmm. Einstein’s proclaimed the clock synchronization method is “free from contradictions”. http://www.fourmilab.ch/etexts/einstein/specrel/www/ This means the clock synchronization method is a logical truth and not a "relative truth". Now, if there exists multiple light emission points under SR, this means SR cannot logically decide the origin of the light path. Yet, SR claims the light path distance and thus the light emission point to the receiver is "free from contradictions". As such, SR is a failed theory.

Interesting. Velocity is also a state as compared to light. Light travel is more primitive than clocks as distance and light travel are used to sync clocks under SR. Hence, while light moves d, an object moves d(v/c). Note, clocks are a human thing. Clocks do not control nor alter this relationship.

Insufficient. Your model declares LT results are not logically decidable and other methods must be used to decide the problem like light transfer. I can prove to you frame to frame clock synchronization is not logically decidable. This is all over the literature. As such, frame to frame light signal transfer cannot decide the logic of this problem. I should not need to come behind LT with light signals to proclaim the logical consistency of SR. If you propose this, you are proclaiming LT is not sufficient to solve this problem correctly. With that, you and I are in agreement.

Let's just get to the point. The following is not disputable. O stationary O concludes the one light beam is a distance vd/c + d from the burn mark. O concludes O’ will measure this distance as (vd/c + d)/λ. O’ stationary O' concludes the one light beam is a distance d/λ from the burn mark. O' concludes O will measure this distance as d/λ2. Now you claimed I am hitting boundary conditions or some such thing. Specify these boundary conditions to support this claim. What is clear is is O concludes the one light beam is a distance vd/c + d from the burn mark. O' concludes the one light beam is a distance d/λ from the burn mark. These cannot be refuted or explained by length contraction. And no, I do not need a target. Math is sufficient to demonstrate the contradiction in the theory. If you have an alternative explanation, then list it. What is above is a logical thought experiment within the domain of SR. The conclusions of the thought experiment are derived based on the logic of SR. There is nothing wrong with anything above.

Hey thanks for the lesson. Your world diagram needs clock differentials to resolve and explain the light distances. We are not using clocks only distances. Note your t-axis. This does not resolve the below. when the burn mark and O’ are co-located. O stationary O concludes the one light beam is a distance vd/c + d from the burn mark. O concludes O’ will measure this distance as (vd/c + d)/λ. O’ stationary O’ concludes the one light beam is a distance d/λ from the burn mark. O’ concludes O will measure this distance as d/λ2. Hence, an observer at the burn mark from O' claims the light stretches down the x-axis by a distance d/λ in its measurements. A co-located observer from the O' frame at the burn mark claims light stretches down the x-axis a distance of vd/c + d in its measurements. Since we are not using clocks and all we have is length contraction as a frame to frame differential, there is no explanation for this immense light path length differential for co-located observers. Merged post follows: Consecutive posts merged Also, just a comment about this "paradox". No solution resolves the fact that the origin of the two light spheres are separated in space by vt after any time t. I can do sphere to sphere mapping using LT and convert the points of the light sphere from one to the other and back. Note, this translation must be done point by point to work correctly. That is all fine and good except the two light spheres have two distinct origins in the space of either frame. That is a physical impossibility. There is no resolution to this problem anywhere in the literature for the origins and LT dioes not address diverging origins. However, here is a point I developed for you to play with. x = vtλ /(1+λ) You will find this is on both light spheres at any time t and further, t' = t using LT.

OK, I will apply it. I thought it obvious it was insufficient to resolve it. When the burn mark and O’ are co-located. O stationary O concludes the one light beam is a distance vd/c + d from the burn mark. O concludes O’ will measure this distance as (vd/c + d)/λ. O’ stationary O' concludes the one light beam is a distance d/λ from the burn mark. O' concludes O will measure this distance as d/λ2. Obviously, sans length contraction, frames cannot disagree on the length, from a co-located point, of a single light beam. So, where is the flaw? Looking above, the term vd/c actually represents the distance between the two light emission points. Each frame believes its own emission point is the correct one.

Actually, let's remove the target. When O' and the burn mark are co-located, O contends the light beam is vd/c + d from the burn mark O' contends the light beam is d from the burn mark. Since this is one light beam, it cannot travel two different distances from a co-located point of measure between two frames. Length contraction/expansion does not resolve this problem. Oh, simultaneity does not resolve the twins contradition I proposed.

You are making good points. Yes, but I am not using any clocks. It is temporal logic and nothing more. Further a light ray moves. You must conclude in O when the burn mark is hit by O', T is hit by the one light beam. So, when O' is co-located with ther burn mark, light is no where near T in the frame of O'. The connection between the frames is the one light beam. Frames cannot control it. Hence, if the frame of O' had a co-located observer at T, that observer would conclude T is not hit while a correspnding observer at T in O would conclude T is hit. BM and T are simultaneous for O and O' is moving toward BM then O' must expect BM to happen before T. That is consistent with relativity. It is actually demanded by it. The order of events is relative in relativity, so I don't think there is any contradiction. Yes, it is the case that BM is moving toward O'. But, the issue here is that it is one rod for O and length contracted in O'. So, BM moving toward O' has no impact on what light does or how it moves. There is no provision in SR where relative motion of the light emission points have any impact on the travel of light. O and O' are light emission points for each frame. It is the receiver T that would normally be at issue under SR. SR never discusses the divergence of the light emission points in each frame.

Yes, but this is not about clocks.and simultaneity. It is about light distance travel. The two frames without any clock measurements contradict each other on the physical distance travel of one light ray. Light moves the same way regardless of clocks.

Here is an interesting problem. Please break it. The Burn Mark Problem The below experiment will avoid clocks and use light distance travel and frame distance travel. Since the SR clock synchronization method uses distance and light travel for its implementation, then distance and light travel are more fundamental than clocks. Assume a stationary light source O and target T at a distance d and a moving frame O’ moving at v in the direction of the negative x-axis. When O and O’ are co-located, O emits a light pulse. O concludes when light moves a distance d to hit the target T, the observer O’ moves to the x coordinate –vd/c. O decides to place a burn mark at that x location. Then O tells O’, when O’ is co-located with the burn mark, light moved a distance necessary to strike the target T. Since it is supposed to be one light ray, this is legitimate logic. BM |----O-----------------------------------T v<-O' On the other hand, when O’ is co-located with the burn mark, O’ concludes its distance to T is (vd/c + d)/λ. Also, when O’ sees the burn mark, O’ concludes O is located a distance (vd/c)/λ. Further, in O’, light travels a distance d/λ when O travels a distance (vd/c)/λ. Now, it is supposed to be a fact when O’ sees the burn mark, light has traveled a sufficient distance to hit the target T. Obviously, in the real external world, either light hit the target or it did not. However, when O’ sees the burn mark, it concludes light traveled a distance d/λ since the O frame traveled (vd/c)/λ. But the target is a distance (vd/c + d)/λ from O’ which is further away than the distance light traveled. Therefore, in the frame of O, when O’ is co-located with the burn mark, O contends T has been hit with the light. However, in the frame of O’, when O’ is co-located with the burn mark, O’ contends T has not been hit with the light. This is a contradiction. [Change the above] [Edit based on comments from Iggy: Therefore, in the frame of O, when O’ is co-located with the burn mark, O contends T light has traveled a sufficient distance to strike T. However, in the frame of O’, when O’ is co-located with the burn mark, O’ contends light has not traveled a sufficient distance to strike T. This is a contradiction.]

The axiom of infinity and then the axiom of the power set applied to the set of natural numbers generated by the axiom of infinity acquires the cardinality of continuity. So, Aristotelean logic is insufficient to generate the real numbers.

Correction, Compton scattering In physics, Compton scattering is a type of scattering that X-rays and gamma rays undergo in matter. The inelastic scattering off electrons in matter results in a decrease in energy (increase in wavelength) of an X-ray or gamma ray photon, called the Compton effect. Part of the energy of the X/gamma ray is transferred to a scattering electron, which recoils and is ejected from its atom, and the rest of the energy is taken by the scattered, "degraded" photon. http://en.wikipedia.org/wiki/Compton_scattering

The end of the experiment brings both twins back into the same frame. Each can perform clock synching to decide the age ordinality or one can transmit the answer to the other. It doesn't matter, each will know one answer. And, if the clock sync method is not realiable, meaning produces incorrect results or multiple results, then LT is immediately false since it is based on the clock sync method. This is not a basis for ruling out reciprocal*time dilation. Further, to support this claim, one would need to prove a rotating referencing frame proves absolute time dilation, meaning one way. There is no such proof. I suppose labels matter, but what I am doing is not connected to labels. I am assuming one frame as stationary and calulating the results. This is normal. Therefore, the frame will have a view of its proper time and also a view of the proper time of the other frame. This is all I did. I am not assuming anything. I bring clocks together in one frame. I check their clock values and report the results while they are in the same frame. There can only be only answer. Specifically, what do you find wrong or assumed here? I do not really know if they will have the same clock values (simultaneity). What I do know is there is one and only one answer. Do you dispute this?

It does not. The thought experiment is a step by step procedure which terminates at the clock sync. Each step is well defined. The clock sync produces one answer. Therefore, this is a recursive procedure. As such, the problem is logically decidable. Other the other hand, LT produces two different answers. Therefore, the problem is not logically decidable. This is a contradiction. Assume GPS and the satellite frame as stationary. The earth clocks do not run slower as they should since that would be the moving frame. Hence there is comething absolute about time dilation and not relative. Sort of. It means the order in terms of time. a < b, a > b or a = b. It would establish which one of these is true. Agreed, but that is not frame mixing. I call one frame stationary and do the calculations. Then, I call one the other frame stationary and do the calculations. Well, not exactly about relative. Free from contradiction means there is only one answer. It means they are in sync or not in sync and not both. The clock sync is more fundamental than LT also. In fact, it is the basis of LT construction. So, since the clock sync can be performed and the answer is trusted, this proves this experiment concludes with one viable answer only and not two as suggested by LT.

Uhhh, no. Each step of this experment can be performed in physical reality. In other words, it is algorithmic. So, LT is supposed to calculate the proper time of a moving frame. It is supposed to model physical reality. Now, if you have a theory that provably decides one twin will be older while at the same time the other twin will be older in the same set of circumstances, then you have a theory that cannot correctly model physical reality because from experience we know this cannot happen. I am sure you are aware that the experiment can be performed in reality. Now, if I needed infinite sets or something that are not available in the real world, the above comments would hold as valid. Further, you cannot prove the clocks will be in sync or not in sync. That is a failure of LT. But, since they are in the same frame, we can establish the ordinality of the clocks by using the clock sync method. Can we trust this method when they are in the same frame? Einstein wrote: We assume that this definition of synchronism is free from contradictions, http://www.fourmilab.ch/etexts/einstein/specrel/www/ Yes, so we use the method to see if they are in sync and if not, we can determine the ordinality. Now, once this answer is provided, we find LT supplying two different answers for the same problem. Thus, in SR, we have one answer that is free from contradictions and two answers from LT that contradict each other.

1) Technically, I have to say endpoint because it is a piecewise integral. 2) The reason burntime is used rather than instant acceleration instead is to keep the experiment a posteriori. 3) It needs to be a posteriori is to compare the results at the end because that is needed to produce the contradiction. The purpose of the above is to show LT cannot possibly calculate the proper time of a moving frame correctly since it provably calculates two different answers. The significance is not that they disagree as much as it indicates one or both are wrong. In particular, the above experiment gives physical evidence by the final clock sync so we are no longer in the realm of different points of view since this sync gives verificable evidence on whether LT correctly models reality. The above shows LT does not model reality because the physical evidence proves both cannot be younger.