The Twin Paradox: Mainstream Rejection of Critical Thinking
David De Hilster, in his 12/19/15 CNPS videoconference, laid out the opportunity or really the pressing need for the CNPS community to use social media to promote itself. The first step in a social media campaign is to establish a positive image. David recommended that instead of the terms “dissident views” and “dissidents”, we adopt the more positive and more accurate terms “critical thinking” and “critical thinkers.”
For 50 years, I have focused on the Twin Paradox and Special Relativity’s time dilation. So I reflected on how mainstream relativists responded to critical thinking on that topic.
Twin Paradox Problem – Background
In 1905, Einstein wrote a paper that became the definition for Special Relativity. After deriving the time dilation equation, Einstein wrote “From this”, referring to the time dilation equation, it follows that a clock making a round trip will accumulate less proper time than a clock that remained at rest at the starting point of the round trip.
However, one can define a Twin Paradox scenario where both clocks are at rest in an inertial frame for 99.999999999999% of the scenario. Further, the time dilation equation effect is defined solely in terms of velocity. And, finally, Special Relativity was built on the Principle that the laws of physics are the same for all inertial frames. Using those facts, there were immediate objections from the physics community that there was an inherent contradiction in Einstein’s Special Relativity. Those objections noted that from the point of view of the “traveling” clock’s outbound and inbound frames, it should be the so called “stay-at-home” clock that accumulates less proper time because from those two frames’ views, the “stay-at-home” clock would have relative velocity v. Further, all agreed that proper times by definition were absolute and frame independent and proper times for a clock between any two pairs of events could be added.
Mainstream Solution – Abandon Logic Analysis
So the proponents of relativity argued that since the “traveling clock” accelerated (or changed frames), Special Relativity could not be used from the “traveling clock” frame(s). The relativists were claiming that Special Relativity could not be used by an observer or clock if the observer or clock had accelerated in the past or would accelerate in the future. However, this desperate “defense” of Special Relativity was at least equally condemning of Special Relativity as all microscopic and all macroscopic entities have accelerated in the past and would accelerate in the future.
Similarly, some proponents of relativity argued that Special Relativity could only be used for inertial frames. However, since virtually everything in the real world is accelerating (including orbiting and rotating) that again would mean that desperate “defense” of Special Relativity would be equally condemning of Special Relativity.
So that raises the question, “Why would relativist physicists who have very high aptitudes for logical analysis choose to totally ignore logical analysis when their belief system was challenged?” The answer is simple, namely, “Because they are human.” In fact, even “critical thinkers” who have developed their own “pet theory” individually exhibit the same behavior. It is in fact the behavior of a group of critical thinkers that distinguishes itself from a group of physicists who are committed to a single, shared view and require that all criticism be censored.
Other Examples
There actually is some implied dissent of currently accepted views on Special Relativity in the mainstream as long as it’s explicitly cast as support for currently accepted views. Fourteen different Special Relativistic causes for the accumulated proper time difference in a Twin Paradox scenario (and seven General Relativistic causes) have been published (see section “3 Accepted Resolutions” on the Report Page at http://TwinParadox.net). Presumably, this indicates that some relativists reject “time dilation” as cause. However, if one reviews the mainstream literature on the Twin Paradox, it would seem that all 14 different arguments attempting to reconcile Special Relativity with the Twin Paradox are tacitly accepted as valid defenses of Special Relativity as none are explicitly rejected.
At http://TwinParadox.net, an Open Letter and petition to critically analyze the Twin Paradox was signed by over 150 professors, Ph’D’s, Dipl. Ing.’s (the European equivalent to a Ph’D) and independent researchers from all over the world. This was quite an ad hoc response! However, the core of mainstream remained unmoved and all mainstream physics journals refuse to publish articles claiming there is a Twin Paradox problem or other criticisms of Special Relativity.
Prof. Herbert Dingle was one of the most respected physicists of his era and an acknowledged expert on Special Relativity. He was respected by his peers until he began to analyze the Twin Paradox and concluded that there was indeed a paradox/problem and further that the currently accepted interpretation of Special Relativity’s time dilation equation was invalid. He started the great Twin Paradox Debate with his relativist colleagues. They labelled his Twin Paradox thesis as quackery while worshipping Einstein as the infallible god of physics. However, Einstein had preceded Dingle by a couple of decades in coming to the exact same conclusion as Dingle regarding the Twin Paradox (see section “1a Einstein’s Changing Views” on the Report page at http://TwinParadox.net) – although Einstein continued to accept a modified version of Special Relativity. Despite Einstein’s openness to criticism, critical thinking on Special Relativity was not held in high regard by academia.
For another powerful example of the core of mainstream physics unwillingness to apply logical analysis to the Twin Paradox issue, see the Mainstream Response page of http://TwinParadox.net.
At least partially to address the problem raised by the Twin Paradox, relativist physics professors have used several different and contradictory interpretations of Special Relativity’s time dilation equation. Despite formal requests to define the currently accepted meaning of Special Relativity’s time dilation equation, the entire mainstream refuses to do so. In Germany, the Albert Einstein Institute (AEI) has been designated by law to answer all such questions about relativity. When asked repeatedly to define the meaning of time dilation, the AEI professors have strangely been most reluctant to do so even though several of those requests have come from German scientists.
Speaking of the AEI, Professor Bernard Schutz writes in his textbook “A First Course in General Relativity”, “Unfortunately, the careless student (or the student of a careless teacher) often comes away with the idea that SR does in fact lead to paradoxes. This is pure nonsense.” This technique is aimed at intimidating the young student from exercising critical thinking especially for such vulnerable areas as the Twin Paradox. Sometimes if one asks the AEI what the physical meaning of the SR time dilation equation is, the reply says to read Chapter 2 of Schutz’s above referenced book. This is a standard dodge to avoid answering specific questions about one’s theory.
In addition, to logic problems, Special Relativity now faces irrefutable evidence that the empirical data does not fit any interpretation of Special Relativity’s time dilation equation (see the Home Page at http://TwinParadox.net).
Future Consequences
The core mainstream now ignores both logic and data. What are the consequences? See my prior blog entry entitled “Sweeping Implications For Spacetime Physics And Cosmology”.
Is there any hope for a return to critical thinking in “spacetime” physics? In the past couple of years, I’ve started to debate several alleged proponents of Special Relativity. However, all have basically stated that Special Relativity is correct, but that their colleagues in the mainstream have “misinterpreted” Special Relativity whereas they have developed the correct interpretation. In other words, many relativists agree, albeit it tacitly or unconsciously, with many critical thinkers that the currently accepted interpretation of Special Relativity is seriously flawed. They claim they haven’t rejected Special Relativity, but they may have entered into the 1st stage of critical thinking. There may be hope.
Written by Nick Percival
The problem with this assessment is that there is no logical refutation of Special Relativity in conjunction with the twin paradox, if SR is interpreted and applied correctly. According to SR more time will elapse on a clock that is at rest in a Lorentz frame, than on any clocks moving with respect to that frame. The problem is that the traveling twin is not at rest in a Lorentz frame. It is important to note that a Lorentz frame is moving with a constant velocity 100% of the time, not just 99.999999999999%, for the entire duration needed to properly cover all events that are described within that frame (ignoring for example any setup required like clock synchronization that is assumed to have happened far enough in the past). It is assumed above that it should not matter if a velocity change occurs within an ever so small time window. That assumption is simply not correct. Thus, the supposed problem with the twin paradox is not based on correct logic. Correct logic has to stick to the premises, without any additional assumptions, and saying that it does not make a difference if the velocity is constant for only 99.999999999999% is an additional assumption.
In essence the quick velocity change that happens during the 0.000000000001% of the time corresponds to a switch of Lorentz frames, one corresponding to the outgoing velocity of the traveling twin, the other to the returning velocity of that twin. This does not make any difference for time keeping at the position of the traveling twin. However, a Lorentz frame keeps track of time by a system of clocks that have been carefully put in a very particular state of synchronization, which differs between Lorentz frames. Switching Lorentz frames means suddenly switching clocks. This does have an impact when describing events away from the position of the traveling twin, and it does have an impact for time keeping at the position of the stay at home twin. This has to be taken carefully into account to make a correct assessment, which is not done in the incorrect argument that less time should have elapsed for the stay at home twin.
It can be shown that there is no logical contradiction when describing the twin paradox within the Special Theory of Relativity. It is tricky and involves some subtleties, but it all works out consistently.
The basis of Special Theory of Relativity is clock synchronization.
Such synchronization appeared in Einstein’s paper “ON THE ELECTRODYNAMICS OF MOVING
BODIES” (§1).
The formula for synchronization: Tb – Ta = T’a – Tb, where Ta is time of light emission from system A, T’a is time of light arrival back to system A and Tb is time of light reflection in system B.
Even first look at formula telling us that something is wrong here. Indeed, the synchronization of two clocks is only possible when the rates of the clocks are the same. The “rate” is something very similar to velocity and required two points for definition. There are two times from system A, but only one for system B in Einstein’s formula, which makes synchronization not possible.
I will give you an example of “synchronized” clocks. Let’s assume the rate of the clock in system B is twice bigger compare to clock in system A. Two non-parallel lines are crossing at some points. Two clocks with different rates should show exactly same time once in a lifetime. Imagine that our clocks show same time at 7 o’clock. We could also assume that clock in system B was started when clock in system A showed 3.5 o’clock.
Let light travelling time from system A to B be one hour. We are emitting light at 6 o’clock from system A. Light reflected at 7 o’clock and returned back to system A at 8 o’clock.
Let’s put numbers in Einstein’s formula: 8 – 7 = 7 – 6.
And clock A is “synchronous” with clock B, which has double rate.
All other formulas in Einstein’s paper were derived in the same manner and, moreover they are based on clock synchronization!
It looks like the foundation of SRT is rotten and it is not even correct to discuss paradoxes raised from incorrect formulas.
Nikolai, you wrote, “Even first look at formula telling us that something is wrong here.” I agree with that sentiment, but not with your logic as to why it’s wrong. A and B are not two different systems, they’re two different clocks at rest in the same inertial system. However, there are many valid criticisms of that formula.
The reason why the formula is wrong is that it’s based on an assumption about the physical world that’s been proven to be invalid, namely, that the speed of light in all directions in all inertial frames is c relative to the observer and his clocks. Even if physics tries to make this valid by definition by defining time and space in terms of light speed, it’s wrong as it gives an erroneous view of the physical world including “spacetime” and simultaneity.
Response To Matthias’ Response
First, Tangential Thoughts On Critical Thinking
Matthias has responded above as a representative of the relativist position. Fortunately, Matthias is an “internet/email” friend and I know that he is quite knowledgeable and while his response below is somewhat automatic and reflexive, I know Matthias will not be dismissive and will give a serious effort to provide a physics analysis of points raised. Hence, this blog thread has the potential for being a most interesting example of “critical thinking” or, at the very least, an example of the challenges for “critical thinking”.
First, I will digress a bit and make some general comments about “critical thinking” that may provide an overall context for our exchanges, but then I will try to be very specific and very focused on the essence of the Twin Paradox.
Despite, my complimentary comments about Matthias above, I contend that because he is human and has adopted Special Relativity as a strongly held belief system, that will be an obstacle to accepting or even seeing valid arguments against his currently accepted belief system – again a standard human characteristic. Since I am also human and have adopted a strongly held belief system, I share the same obstacle. So, as is so often the case, “critical thinking”, or lack thereof, will depend on the interaction between two people, with opposite polarizations, who are individually closed minded on the topic being discussed. Fortunately, we will listen to the other, think about the essence of the logic presented and try to rebut the essence of that logic.
“Critical thinking” might be thought of as the ability to objectively analyze logic or data even if that logic or data argues against what one has been taught and against one’s currently held belief system. However, since for humans there is tremendous tenacity for currently held belief systems, a powerful agent is often needed to counteract that inertia. An “opponent”, acting in good faith, is often required as a catalyst for “critical thinking” to emerge.
Since we think of science and particularly physics as a cut and dried matter subject primarily to objective logic, it might help to realize that analyzing a paradigm change is more like a discussion between, for example, a Christian and a Muslim. They are both convinced that their religion is correct and consistent if correctly interpreted. They might decide to focus on a specific topic such as “Was Jesus the Son of God (per the Christian view)?” or “Was Jesus ‘just’ a great prophet (per the Muslim view)?” However, since all the pro arguments will draw upon a broad cross section of the respective set of Scriptures, the debate really becomes “Which is true, Christianity or Islam?” So we begin to see the difficulties. Those difficulties are compounded if the two are officials of their faith (e.g., minister, priest, Iman or professor) and compounded further if they are public proponents (e.g., authors) and compounded still further if their discussion is public.
Hence, we face formidable obstacles, but since we both can go beyond the reflexive dismissal of counterarguments, we are better off than the vast majority of exchanges on this topic.
Since I have thought, studied, analyzed and debated about the Twin Paradox and time dilation for 50+ years and my primary interest has been narrowly focused on that topic and my views have been published by papers and website and many think of me in terms of those positions, and this exchange will be public, those tendencies for inertia will be intensified. The same can be said for Matthias.
Hence, many of the key influences in terms of accepting ideas are outside of physics and logic, but are very common human psychological and emotional characteristics as has been shown by the history of science including physics. Academic experts seem to be better at extending currently accepted paradigms whereas outsiders have an advantage for changing accepted paradigms.
As a further aside, the Twin Paradox can be used by educators to teach physics students, before they become fully indoctrinated, how to “think physics” or to do “critical thinking”. This is a good topic even for gifted high school students as it does not require advanced courses in math, but instead requires objective logic and the ability to think in terms of physics models. Even the most biased relativist can use it because 21 physics causes have been published in top physics journals to explain the Twin Paradox so physics needs to decide which is the “real” physics cause and which of the other physics causes are invalid or logically equivalent to the “real” physics cause.
To do the above or almost anything else on this topic in the context of science, physics needs to give a specific, detailed interpretation of Special Relativity – something every mainstream journal, mainstream physics department and mainstream physics organization has avoided doing.
Having debated this topic for 50+ years with all comers, I have not only become familiar with most every technical (i.e., math, physics, logic) nuance, but also with the inner workings of the relativist’s mind. I learned that the most common error in reconciliation arguments is mixing proper time with “just observed” time. I learned that one cannot influence the relativist by means of one’s own “brilliant” arguments, but instead the relativist has to convince himself by finding the flaw in his beliefs himself. Using that insight, several debates with relativist professors have led to their admitting that their reconciliation argument for the Twin Paradox is wrong, but they have not been willing to go public with that admission. One representative of a 2nd group had insisted that, at the conclusion of our debate, the results were to be published in Physics Essays. This professor was as deeply committed to relativity as any. I asked him a series of questions. He confidently answered. I came to the denouement and asked a two part question – one part for each twin. He then said that he had to stop and do his taxes, but he never returned to complete our online exchange. Relativists will think that it’s likely he did that because he realized how dumb I was and excused himself. However, we had spent a great deal of time in our exchanges and this was the final question which would take approximately one minute to answer and the professor was most anxious to publish the exchange if he won, but if he answered the final simple, easy question, it would shown that his stated views led to a contradiction.
Admittedly, most relativists reflexively reply to my argument with “You don’t understand Special Relativity!” I agree, at least on this topic, and contend that was my primary advantage to gaining greater insight on this topic. I was able to admit that the professed mainstream reconciliation of the Twin Paradox didn’t make sense to me – that was key to making progress. Many students accept what they are taught and if they feel a twinge of “this doesn’t make sense”, they are not able to live with that because that seems to imply they aren’t as smart as everyone else, or it goes against physics authority or against group think, etc. In my initial search for an answer that made sense to me, I was quite relieved when I first encountered an alternative reconciliation argument, which seems to be somewhat along the lines of the solution given above by Matthias, as at first it seemed to make sense, but deeper analysis revealed flaws in that approach as well.
Twin Paradox Specifics
What Are We Talking About???
Hasok Chang, then of Harvard, did a comprehensive analysis of Herbert Dingle’s great debate on the Twin Paradox with the mainstream (H. Chang, Stud. Hist. Phil. Sci. 24(5), 741 (1993)). He concluded that while the mainstream professors all claimed victory, none actually addressed the issues that Dingle raised. It is typical that Twin Paradox debaters will “talk at cross purposes”.
For example, Matthias makes a number of assertions, such as “It can be shown that there is no logical contradiction when describing the twin paradox within the Special Theory of Relativity.” I won’t know if I agree or not until I know for sure what Matthias’ interpretation of “Twin Paradox” and “Special Theory of Relativity” is. His reconciliation argument suggests to me that his understanding of the Twin Paradox claim is non-standard. So I will try to clearly state my interpretation of the Twin Paradox claim so we can know if we’re in sync or not on that.
The Twin Paradox Claim
In Einstein’s 1905 paper, “On the Electrodynamics of Moving Bodies”, he drives Special Relativity’s time dilation equation and then writes “From this …”, with the “this” referring to the time dilation equation, and goes on to make his Clock Paradox claim which eventually, in 1911, became known as the Twin Paradox claim. The claim is generally interpreted, including by me, as asserting that if there are two clocks at rest in an inertial frame and one clock makes a round trip back to its twin clock, then the traveling clock will have accumulated less proper time than the “stay-at-home” clock and that net proper time difference will be due to the aforementioned time dilation and is a function of the clock’s relative velocity.
It is this interpretation that I was discussing. I’m examining the claim that the accumulated proper time for the “traveling” clock between the start event and the midpoint event plus its accumulated proper time between the midpoint event and the end event will be less than the accumulated proper time for the “stay-at-home” clock between the start and end events.
Further, this interpretation of the Twin Paradox claim implies that the physics meaning of Special Relativity’s time dilation equation is that it describes a physical slowing of proper time accumulation rates as a function of relative velocity. And, in fact, this interpretation of Special Relativity’s time dilation equation has been used in many papers published in mainstream physics journals and textbooks, etc.
In contrast, it seems to me that Matthias is, quite astutely, claiming a non-standard interpretation of the Twin Paradox claim. On the one hand, this non-standard interpretation of the Twin Paradox claim saves Matthias from a logic contradiction, but it does so at a cost which I will discuss if indeed my view of his position is correct.
Mathias seems to be claiming that there is no net proper time difference, but instead just a difference in clock readings due to some effect (perhaps relative simultaneity?). If I’m correct, then Matthias is implying that the physics meaning of Special Relativity’s time dilation equation is that it describes a “just observed” (i.e., no actual or physical) slowing of proper time accumulation rates as a function of relative velocity. Matthias, let me know if that’s your interpretation of the Twin Paradox claim and of Special Relativity’s time dilation equation.
When I first read Matthias’ response, I thought that he was claiming that when the “traveling” clock made its turnaround, then due to relative simultaneity, somehow the traveling clock lost time. This is a popular alternative reconciliation argument as it avoids the pitfalls of the original and standard interpretation, but it has its own problems. However, upon re-reading, I’m not sure what cause Matthias claims affects what clock so I’m requesting more detail and more specifics on this. Matthias’ reconciliation argument seems new to me and I’ve seen about more than 20 over the decades.
I know Einstein has defined a synchronization procedure for clocks in defining Special Relativity. I realize that when the “traveling” clock changes frames, it becomes out of synchronization with clocks synchronized for its new frame. Again, I know that some use that to claim that somehow the traveling clock loses time or needs to be manually adjusted.
However, Matthias writes, “This does not make any difference for time keeping at the position of the traveling twin. However, a Lorentz frame keeps track of time by a system of clocks that have been carefully put in a very particular state of synchronization, which differs between Lorentz frames. Switching Lorentz frames means suddenly switching clocks. This does have an impact when describing events away from the position of the traveling twin, and it does have an impact for time keeping at the position of the stay at home twin.” [Emphasis added]
This seems to be a different conclusion so I don’t know what Matthias’ conclusion/argument is. So I ask him to please elaborate.
“I learned that the most common error in reconciliation arguments is mixing proper time with ‘just observed’ time.”
Maybe I’m not the only one who detected this trouble:
One cannot measure the time from the distance and make this measure the distant time.
Therefore x’=ct’ is wrong ab origine.
https://bornmax.wordpress.com/2015/08/10/einstein-wo-habe-ich-mich-geirrt/
The appearantly innocent naive ideas of Einstein created his image to be the son of Dalai Lama.
The papers are online “Einstein preoperational”
An automatic and reflexive response can be good if it is correct. I will add that I was thinking very carefully through my response before posting it, and very clearly this was not a case of me not “accepting or even seeing valid arguments against my currently accepted belief system”. It was about an argument made in Nick’s original post not being valid, and I tried to give a clear reason why that is the case. Certainly, I was trying to keep this within a few paragraphs of a blog comment, and it is somewhat of a summary that can benefit from being elaborated. I have already started to do exactly that before Nick posted his response. I hope to run it by Nick first and discuss it, and maybe it can be put in a form that makes it appropriate for publishing it after we discuss it in private.
As far as my own position about the time dilation and the twin paradox is concerned, I see it a bit differently from Nick. From what I can see Nick believes that a contradiction arises in relativity that needs to be resolved. My angle on it is somewhat different. I will claim that no contradiction arises around the twin paradox in the first place if we carefully and precisely sort out what conclusions can be logically made from premises of the special theory of relativity. In other words, the question is how the theory of relativity is to be interpreted correctly. In general, I don’t even see myself so much as being an ardent supporter of relativity, but rather as somebody being critical and speaking out about what I recognize as unfounded and incorrect criticism against that theory. When it comes to that I am open to engage in discussions, not being afraid that these discussions turn out to be long and at time frustrating.
I would agree with the assessment made by many mainstream physicists that “relativity dissidents” very often simply don’t understand relativity. The question is though, do supporters of relativity understand the theory to the fullest extent? If so, one would think they should be able to easily answer Nick’s questions about the twin paradox, and come up with clear, logical and convincing answers. For my part, I believe I have a good understanding of relativity, and this is to a large part a result of engaging in discussions with dissidents, thinking through how to correctly assess different scenarios in the context of relativity. Part of that were some rather fruitful discussions I had with Nick in the past. But if Nick had the experience that relativity supporters were withdrawing from the discussion, I had the opposite experience that Nick sometimes asked to postpone our discussions – which is understandable as we all have other things going on in our lives that need attending.
Specifically about time dilation, my viewpoint is the following. I consider it a misunderstanding to say that time dilation is a statement about the rate difference of two clocks based on their speeds relative to each other. That would of course result in a contradiction, as it would imply that clock A has to run faster than clock B at the same time that clock B runs faster than clock A. Very carefully reading through Einstein’s 1905 paper I come to the interpretation that time dilation is not a statement about the rate of a clock B relative to an individual clock A, but rather a statement about the clock readings of clock B moving on an arbitrary trajectory, compared to an entire system of clocks of a Lorentz frame, at rest in that frame at various positions. If a segment of clock B’s trajectory starts out at the same position as a clock A of the Lorentz frame, and ends up at the position of another clock A’ of the Lorentz frame, the time tB(A’)-tB(A) elapsed on B is less than the difference of clock readings tA’-tA of the clocks it encounters, tA’ and tA taken when B is at the position of the respective clocks, and tB(A’) and tB(A) being the B clock readings at those encounters. The twin paradox scenario results for A’=A, when B returns to the same clock A. In this case time dilation states that more time will have elapsed on a clock that moves between two points with constant velocity (as is required if A is at rest in some Lorentz frame) than on a clock B that has moved on an accelerated trajectory. In all this, the statement of time dilation as a relation between specific clock readings, and and its special form for the twin paradox scenario can be considered physical facts, not something that is “just observed”.
Einstein discusses time dilation and the twin paradox with A’s Lorentz frame being the “stationary frame”, but because of the relativity principle this must be true for any Lorentz frame.
The supposed contradiction in the twin paradox as I understand it is based on a symmetry argument. The claim is that if it is from the viewpoint of A that B runs slow, the viewpoint of B should also show that A runs slow. No such symmetry argument can apply for two clocks that are separating and reuniting, as the conclusion about elapsed clock times was based on the assumption that clock A was moving at constant velocity, meaning that it was at rest in one and the same Lorentz frame for the entire time. Symmetry would only apply if clock B was also at rest in some Lorentz frame, but if that was the case no reunification would occur once the clocks have separated. In order to use time dilation to conclude that less time has elapsed on clock A than on clock B it is necessary that B remains in one and the same Lorentz frame, not just that it is at rest in some Lorentz frame for 99.999999999999% of the time.
One can still ask if there is any contradiction if both A and B move with constant but different velocities and are thus both at rest in their respective Lorentz frames. We have a time dilation statement about clock B with respect to A’s Lorentz frame, and a time dilation statement about clock A with respect to B’s Lorentz frame. But we have to keep in mind that this involves different sets of clocks. In one case it involves clock comparisons between clock B and two clocks A and A’, in the other a comparison of clock A with two clocks B and B’ of the other Lorentz frame. The fact that tB(A’)-tB(A) < tA'-tA and also tA(B')-tA(B) < tB'-tB is not a contradiction. The relation tB(A')-tB(A) < tA'-tA is not a direct statement about B running slower than A. Such a statement would require that the clock reading of B is compared to that of A at least twice, but according to our assumptions B and A are separating from each other and moving on with constant velocities and therefore will never be in the same place again where they could be directly compared.
According to Einstein the clocks of a Lorentz frame can be used to establish a "time" reference within that frame. Comparing the clock readings of B to the readings of the clocks in A's frame then does mean B's elapsed time is smaller compared to that time reference. According to that B is running slow as assessed according to the time reference of A's frame, whereas any clock in A is running at a normal rate by construction, thus B is running slower than A in that sense. I might call this "just assessed" rather than "just observed", a term Nick likes to use. At least, we have to keep in mind that such an assessment is not based on direct observation that can be instantly made. For example, at the position of A we cannot instantly what B's clock reading is "at the same frame time". We may have to collect data at various positions in the Lorentz frame and evaluate the data later, or we may wait for light signals from other positions to arrive before making the assessment. "Just observed" is perhaps too much of a suggestion that we can actually see what is occurring at other places "now".
According to the previous paragraph we can say it is just assessed that B is running slower than A according to to A's Lorentz frame, and it is also just assessed that A is running slower than B according to B's Lorentz frame. If we remember the full meaning of "just assessed", being based on clock comparisons between different clocks, it should be clear that there is no contradiction in this.
In summary, I do not see any contradictions arising related to time dilation or the twin paradox, based on strictly logical and correct arguments based on the premises of the special theory of relativity. Much of the above I had discussed with Nick before, and I believe we had basically been in agreement about it. It seems we had not discussed the "99.999999999999% argument" in sufficient detail. To my mind it is very clear that it is incorrect, and I am willing to engage in further discussion about it if necessary.
Nick's consideration go beyond what was discussed above, he has asked questions about how the difference of clock readings between the two twins develops during the twin paradox scenario. My answer to that is that relativity does not answer that question, beyond giving differing statements that can be considered "just assessed". That does not establish a contradiction. From how I understand Nick's position he considers that a deficiency of relativity and he expects a good theory to be able to give a concrete answer about the detailed development of time differences. Supporters of relativity do not share this opinion, considering it sufficient that it can be determined how proper time accumulates on an individual clock along its trajectory, without the ability to specify in a frame independent way how the difference of elapsed times of two clocks develops over time. This seems like a point where it can be agreed to disagree. However, if there is a way to determine how the time difference develops, it implies that we can say how much proper time tauA has elapsed on clock A when tauB has elapsed on B, and with that it establishes a way to compare the clock readings of distant clocks. It would also allow to objectively determine the rate difference as dtauB/dtauA. This is clearly not within the framework of special relativity, according to which distant clocks cannot be compared in a frame independent way that is not "just assessed".
From discussions with Nick I know that he favors a preferred frame theory. It is similar to relativity, but whereas relativity assumes that all frames are equal, preferred frame theory instead singles out one frame as giving the correct physical picture. In other words, any assessment made within the preferred frame can be considered as being an objective statement. However, some practical form of relativity arises if we don't know which of the possible Lorentz frames is the preferred frame. All frames are then equal in the sense that they could be the preferred frame. This is different from proper relativity that assumes that all frames are fundamentally equal, but still, in both cases we can use the laws of physics we know from relativity to determine the dynamic evolution of physical systems, and in both cases there are certain questions that cannot be answered – for example about the details of how proper time difference develops in the twin paradox. Importantly, if we can treat preferred frame theory without knowledge of the preferred frame within the framework of the resulting practical relativity in a way that is entirely free of contradictions, the same should be true for proper relativity if it follows the same rules. I therefore challenge Nick to find a contradiction in proper relativity that is not also a contradiction in preferred frame theory.
SRT is completely erroneous since it is based on the wrong kind of transformations: they have lost the scale factor characterizing the Doppler effect. First, Lorentz considered a more general form of transformations (with a scale factor), but then he, and also Poincare and Einstein equated it 1 without proper grounds. Their form was artificially narrowed, the formulas became incorrect. This led to a logical contradiction of the theory, to unsolvable paradoxes. Accordingly, GRT is also incorrect.
For more details, see my brochure “Memoir on the Theory of Relativity and Unified Field Theory” (2000):
http://vixra.org/abs/1802.0136
The classic twin paradox is “explained” because there is acceleration, but in the following version of the twin paradox there is no acceleration and I do not see how the dilation of time could be explained.
A version of the twin paradox without accelerations
Bob is standing on Earth and Alice is on a distant planet at a constant distance from Earth. Their watches are already synchronized in the following sense: Suppose Alice’s planet is a light-year away from Earth. Bob emits a light signal to Alice at time t = 0 according to Bob’s watch. When Alice catches the signal, she sets her watch to position t = 0. Bob sets his watch to t = 0 one year after the signal is sent. Now Bob and Alice’s watches are synchronized.
Alex stands behind Bob, then accelerates and the moment he overtakes Bob his speed stabilizes. At that moment they are synchronizing their watches, and this marks the beginning of the experiment. It does not matter what Alex did before the clocks were synchronized, so his acceleration does not count in the experiment.
Alex continues his journey until he gets too close to Alice. At that moment, Alex photographs his watch and Alice’s watch at the same time, and immediately after that, he slows down and stops. If at that moment Alex compares his watch with Alice’s watch, he should not find a significant difference from the difference between the photographed watches. Because Alice and Bob’s watches are synchronized, it is not necessary for Alex to return to Earth to compare his watch with Bob’s watch.
In this experiment we can assume that Alex is motionless while Bob and Alice are on the move. However, both alternative reporting systems are different aspects of the same events. This means that the photographed watches will have the same difference in both reference systems. But these reference systems are equivalent, as there is no acceleration. Without acceleration we cannot justify the dilation of time for any observer of the experiment. So I conclude the photographed watches should not be different, ie they do not record any dilation of time. But despite these objections,
the question is
Comparing the photographed watches, did Alex’s watch gain or lose time compared to Alice’s watch?