- Einstein’s special theory of relativity is the basis for Doctrine of The Relativity of Simultaneity. That Doctrine is, according to knowledgeable authorities, an especially challenging concept to teach interested students. Rachel Scherr et al. published an article in 2001 which, IMO, “broke ground” then and now in teaching the Doctrine: Student understanding of time in special relativity: Simultaneity and reference frames.
- However, personally, I dare to find fault with the article although I found it to be very useful.
- Specifically, my objection is to the incomplete thought experiment employed to teach the Doctrine.
- The article’s Abstract reads as follows:
- This article reports on an investigation of student understanding of the concept of time in special relativity. A series of research tasks are discussed that illustrate, step-by-step, how student reasoning of fundamental concepts of relativity was probed. The results indicate that after standard instruction students at all academic levels have serious difficulties with the relativity of simultaneity and with the role of observers in inertial reference frames. Evidence is presented that suggests many students construct a conceptual framework in which the ideas of absolute simultaneity and the relativity of simultaneity harmoniously co-exist. © 2001 American Association of Physics Teachers. [DOI: 10.1119/1.1371254]
- Initially, the thought experiment posed in the article begins with a seismologist located halfway between two volcanoes when each volcano erupts. And the seismologist determines, scientifically that both volcanoes, identified as Mt. Hood and Mt. Rainier, erupted “at the same time”, i.e. simultaneously [Figure 1.]
- Next, assume that Event A is the eruption of Mt. Hood and that Event B is the eruption of Mt. Rainier; and assume that Spacecraft #1 flies at a relativistic velocity v, along a straight path over Mt. Hood, the seismologist, and Mt. Rainier while both volcanoes erupt.
- As the article explains, Spacecraft #1’s pilot will–based on relativistic principles–say that Mt. Rainier erupted before Mt. Hood. [This is the famous counter-intuitive “relativity of simultaneity” which causes students so much difficulty.]
- The article stops “explaining” there.
- In fact, if we assume that Spacecraft #2 flies at the same relativistic velocity v as Spacecraft #1, along a straight path over Mt. Rainier, the seismologist, and Mt. Hood while both volcanoes erupt, Spacecraft #2’s pilot will say that Mt. Hood erupted before Mt. Rainier.
- In summary, given the two volcanoes’ eruptions while both Spacecrafts fly over the volcanoes at the same velocity v, and the seismologist determines that both eruptions occurred simultaneously, one pilot would say that Mt. Rainer erupted before Mt. Hood while the other pilot would say that Mt. Hood erupted before Mt. Rainier.
- The three different claims of the seismologist and pilots give rise to a conundrum which troubled Einstein himself and that he expressed to Rudolf Carnap–as reported by Carnap. The theoretical physicist Lee Smolin called the conundrum: "the problem of the Now.
- My personal fascination with “the relativity of simultaneity” and discovery of “the Problem of the Now” led me to propose a solution to “the Problem” offered here: The Problem of “the Now”.
- Head’s up! I expect my “solution” will evoke howls of dismay or more. I offer no defense if it does.
Hello @Terry_Sampson, and welcome to Peaceful Science. 
I read your mini-bio, but can you tell us a bit more about yourself?
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The X-rated version, or “just the facts, sir, just the facts”? 
Welcome to the forum, @Terry_Sampson. Relativistic physics is a subject that’s been discussed here a couple of times in the past - and when it is I usually poke my head in, haha. I wouldn’t say your “solution” is evoking any howls of dismay from me, though I must admit to shaking my head a little bit.
I may go into specific criticisms when I have more time, but first I’m curious to know just how familiar you are with relativity theory (have you studied it formally or are you self-taught, where did you learn it from, that sort of thing) - and also if you’ve read John Bell’s paper “How to teach special relativity”. I ask specifically about that paper both because it addresses the pedagogical angle that you started your post with, and because it is suggestive of one way the “conundrum” might be resolved, namely, by taking a neo-Lorentzian interpretation of relativity.
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- Thanks for the welcome, @structureoftruth and @Dan_Eastwood
- In answer to your curiosity regarding “who I am”:
- I’m nobody worth arm-wrestling with.
- At the age of 74, I’m too old to call “Sir”.
- Being retired and child-free,piddling around on the computer between naps and meals keeps me entertained.
- Officially, I’m a Crank; I don’t ask for respect, and am never disappointed when I don’t get it.
- B.A. Accounting; M.S. School Psychology
- Retired I.R.S Revenue Agent; too old to hire as a School Psychologist
- Undergraduate Math Skills once upon a time: up to Precalculus; current retention: Beginning Algebra
- No formal Physics education beyond Freshman General Science
- Learned the rudiments of SR watching competent Relativists correct novices and studying books and on-line
- Prefer diagrams to formulas and Loedel Diagram to Minkowski Diagrams; and I have a really neat one that I composed myself
- I have one unresolved question about SR and no interest in explaining every experiment cited in favor of SR using Neo-lorentzian or Non-Mainstream Science.
- Re: Bell’s paper; no, I hadn’t seen it until today. Having now “seen” it, I can honestly say, I’m not impressed, but in all fairness, I’m just too ignorant for it to hold my attention.
- Re: your mention of "a neo-Lorentzian interpretation of relativity; I was surprised. Years ago, I had some limited communications with the Frenchman, Joseph Levy, before and after getting banned permanently from two preeminent Physics forums for posing a hypothetical thought-experiment which cannot be performed which distinguishes neo-Lorentzian relativity from SR. I think I still have a copy of Levy’s email confirming that my thought-experiment diagram was useful for conveying the distinction between his theory and SR.
P.S. Pet Peeve: although I am an unchurched Eclectic Christian, as a rule churched Christians who think SR is the greatest thing since sliced bread and I have irreconcilable differences. Unfortunately, they seem to have difficulty in “moving on” from those differences.
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Note: Link edited to enable viewing by anyone with the link. T.S. 3/21/2023, 7:21 AM (PST)
We’ve seen worse. Another 15 years and I might be you! 
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-
Brief Instruction on the construction of a simple Loedel Diagram:
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Brief Loedel Diagram of The Double Triplet Scenario:
Black dots where events occur identifying encounters between each of the Triplets in one frame with each of the Triplets in the other frame. -
Loedel Diagram with label change of Worldlines and all Lines of Simultaneity:
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Partial Loedel Diagram of Triplets’ Worldlines:
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Partial Loedel Diagram of all relevant Lines of Simultaneity:
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Partial Loedel Diagram of all events on Lines of Simultaneity from one Point of View:
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Partial Loedel Diagram of all events on Lines of Simultaneity from the other Point of View:
- My "Hypothetical “Thought Experiment” which I shared with Joseph Levy.
Note: The Neo-Lorentzian Theory (NLT) is, as I understand it, another name for the Lorentz Ether Theor [LET].
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Nifty.
I learned Newtonian physics at undergrad level as part of my formal education, but beyond that (i.e., for relativity and quantum theory) I am also self-taught. (I have acquired enough familiarity with spacetime digrams that I can roughly visualize Lorentz transformations on simple figures, so I can’t say I have a preference between Minkowski vs. Loedel diagrams; both have their uses.)
How did you make these diagrams? I think I could cobble something like them together in Desmos (online graphing calculator), but it would be a bit cumbersome. Maybe I should try asking ChatGPT to write me a script for plotting worldlines and doing Lorentz transformations on spacetime diagrams.
Your “double triplet” scenario seems conceptually similar to a “speeding rulers” scenario, or the “pole vaulter running through a barn” one - in each there are two systems which each appear shorter than the other depending on which reference frame they are being viewed from. I’m afraid to say you draw the wrong conclusion, though. A Lorentzian interpretation of SR does not predict that the triplets on spaceship B will agree about the order of events with the triplets on spaceship A - not unless they happen to know their velocity relative to the privileged frame and deliberately adjust all their measurements accordingly. If they measure things in the usual way, without that knowledge (knowledge which is inaccessible as a consequence of the theory!) they will perceive the same order of events that is predicted by orthodox SR.
What question is that?
Well, no problem there: given the explanation in orthodox SR, it is a trivial task to generate the explanation in the Lorentzian interpretation. Simply transform everything to the perspective of the privileged frame, and there you go, renowned hypothetical experimentalists Alice and Bob are your aunt and uncle.
To be clear, what I mean by a “neo-Lorentzian interpretation of relativity” is simply a theory which postulates a) there is a privileged inertial reference frame describing things in 3D space changing over time, and b) in this frame, the laws of physics have Lorentz symmetry. (These are in place of the usual postulates of relativity, which are a) that the laws of physics are the same in every inertial reference frame, and b) there is an invariant speed.) Any mention of an aether is superfluous.
(That being said, I’m sympathetic to the claim that there is something aether-like permeating all of space, on account of there needing to be something to bear properties that the physical vacuum seems to have, e.g., metric properties in GR, or quantum mechanical properties in QFT. And it may be that the old philosophical arguments against the possibility of a true void are sound after all.)
I don’t know who Joseph Levy is, but he is wrong about the theoretical prediction of Lorentzian relativity for your thought experiment (which I found rather clever, by the way - it draws out an interesting implication of relativity). The reason is that your assumption #1 fails - for a moving mirror, the angle of incidence is not always equal to the angle of reflection. From what I’ve read, this has to do with the fact that there is both a longitudinal and a transverse Doppler shift in relativity, so the different components of the wave-vector get affected differently, which can affect the direction of the light beam. The net result is that the velocity of the system relative to the privileged frame is as undetectable as ever, and the Lorentzian interpretation makes the same prediction as orthodox SR.
(Edit: after reading up on it a bit more I found that the relativistic reflection law requires that the change in momentum of the light ray is perpendicular to the surface of the mirror in all cases. When there is no Doppler shift, the magnitude of the momentum is the same before and after, and the angle of reflection equals the angle of incidence. But when there is a Doppler shift, which happens whenever there is some component of the velocity of the mirror perpendicular to its surface, the magnitude of the momentum changes, and the angle of reflection is different from the angle of incidence.)
For my own part, I think there is a philosophical and even a scientific case to be made against orthodox SR’s rejection of absolute simultaneity, hence my interest in the Lorentzian interpretation. But I don’t have time to get into that at the moment, I’m afraid.
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- By tedious manipulation of “shapes” in MS doc’s word processing software and using a polar graph to set the angles of the worldlines relative to each other. And using the “Brief Instruction” that I pasted in the same post. I assumed the two frames relative velocity v = 0.8667 which results in 50% Length contraction and Time dilation.
I’ve long marveled that no one ever came up (or revealed to me that there is already) a simple plug-in and generate software program for creating Minkowskis or Loedels. One guy I knew was either very skilled or had some tool at hand. He always seemed to be able to post a Minkowski for any relative velocity very quickly. But he never explained how he did it.
- Nuts! Shortly after I saw your post, something happened or I did something on my PC as a result of which I have no cursor and my mouse is completely non-functional. This response has been typed on my iPad. Up to this point in the response I have managed to hunt and peck this much of a reply, but it has been tedious to write this much. So I’m going to postpone a fuller response until I have identied the cause of the missing cursor and the dead mouse and get the first back and get rid of the second.
Till then, don’t hold your breath.
- I’m uncertain what it is that you’re objecting to. In Section III. I present what I believe is the standard/mainstream science/SR version of my Double Triplet Scenario ending with Table I on page 5. And in Section IV. I present what I believed is the Neo-Lorentzian version of the my Double Triplet Scenario ending with Table II on page 8.
- My understanding of SR is that the occupants of one spaceship and the occupants of the of the other spaceship will not agree on the chronology of “the events”.
- And my understanding of the Neo-Lorentzian Theory has been that the occupants of both spaceships will agree on the chronology, i.e. the order, of the events. If you’re referring to Table II, which events do you believe Neo-Lorentzian theorists will not agree with?
- Note: To be sure, the occupants of both spaceships will not agree on the “times” of the events, but they should, IMO, agree on the order of all events. Correct me where I am wrong.
- BTW: There is a bigger “defect” in my Neo-Lorentzian version of the Scenario, which you did not bring up. But I won’t bring it up until someone else does.
- All in good time. I think I/we need to clear up what it is that we don’t seem to agree on up above, in this message.
- Beg your pardon? If I were to explain every experiment cited in favor of SR using a Neo-Lorentzian privileged frame I would end up with the same interpretation? How does that work? What am I missing?
- While it is true that the Neo-Lorentzians are relativists, I call them “quasi-relativists” to distinguish them from mainstream “Einsteinian relativists”. If you’re suggesting that “relativists are relativists” and there are no distinctions between any of them, that’s new news to me. In my experience, there are knowledgeable and competent mainstream relativists, knowledgeable and competent Neo-Lorentzian relativists (the ones I call “quasi-relativists”), and a bunch of folks I call “pseudo-relativists”, who usually get their butts kicked by the knowledgeable and competent mainstream relativists. Now I don’t speak or read French, but Joseph Levy’s English–spoken and written–seemed pretty good to me, and I’m sure that he distinguished between his version of relativity and mainstream science’s view of relativity commonly known as SR.
- In fact, I have a signed copy of his book From Galileo to Lorentz… and beyond Paperback – June 1, 2003 by Joseph Lévy (Author)
- And from https://arxiv.org/, I got the following papers by the same Jospeph Levy:
- Is the aether entrained by the motion of celestial bodies? What do the experiments tell us?
- Phase tuning in Michelson-Morley experiments performed in vacuum, assuming length contraction
- General Transformations of Space and Time according to Aether Theory
- Aether Theory Clock Retardation vs. Special Relativity Time Dilation
- Relativity and Aether Theory, a Crucial Distinction
- Aether Theory and the Principle of Relativity
- Basic Concepts for a Fundamental Aether Theory
- Two-way speed of light and Lorentz-FitzGerald’s contraction in aether theory
- To be clear, this is the Joseph Levy that I am personally acquainted, have corresponded with on-line and by email, and to whom I have referred in this or previous posts above, to wit: Joseph Levy
- From the Wikipedia article cited:
- After graduate studies in physics at the university of Paris, J. Levy did his military service at the Centre of Nuclear Studies of Fontenay aux roses where he has been in charge of a work dedicated to electron spin resonance. He then continued his studies at the University of Paris obtaining a diploma of in-depth study of theoretical physics. Pursuing research at the Centre de mecanique ondulatoire appliqu (CNRS) he earned a Ph.D in physics entitled “Interaction spin reseau et tenseur spectroscopique de l’lectron”, with honours. Meanwhile he trained as a radioisotopist and earned a degree awarded by the National Institute of Nuclear Science and Technology of Saclay. Following the work undertaken he has published several articles in peer reviewed journals. Although his previous work dealt with different issues more related to quantum physics, he has long been interested by the theory of relativity from a critical point of view. Since 1990 he has attended numerous international conferences devoted to this topic, including ?Physical interpretations of relativity theory? (PIRT) sponsored by the British society for the philosophy of science and has given several lectures. He has since published 3 books and numerous articles in the proceedings of the conferences and in peer reviewed journals and he wrote chapters for two collective books. He was also a member of the editorial board of congress Geometrisation of physics held in Kazan state University Russia.
- J. Levy is convinced that, contrary to what is generally believed, the experiment in physics does not give an exact description of reality and must be reinterpreted, and this even if it is made with the maximum accuracy. Rods and clocks as well as masses in a state of absolute motion are modified and therefore the measurement of physical data concerning them is altered and depends on the absolute speed of the frame where it is made. A part of his work consists in determining the real values of the physical data behind the apparent ones. The divergences between physicists often arise more or less consciously from the credit which they give to the result of the experiments prior to any interpretation.
- J. Levy is now in charge as co-Editor and author of a scientific program entitled Ether space-time and cosmology, which will result in the publication of several volumes in collaboration with Michael C. Duffy (who is the chairman of PIRT) and Volodymyr Krasnoholovets. The program is dedicated to the exploration of the modern ether concept, evidence of its existence and implications for modern physics The introduction of the ether as a main actor in physical processes, will resolve a number of paradoxes in 20th century physics which arose because of its dismissal. (Volume 1 and 2 are now available and can be ordered at Apeiron, Target.com or Amazon.com).
- Not a problem, I’m not planning on going anywhere. Of course, I am 74, so I could disappear long-term. In that case, we’ll have to continue this exchange elsewhere and in person, I suppose.
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- Warning: The next Loedel Diagram pretty much contains the features of the SR version of my “Double Triplet Scenario” on one page. IMO, it’s a very busy diagram which required some serious attention to detail to draw and requires equally serious attention to understand. I don’t recommend trying to make sense of it if you’ve other, more important things to do. In other words, take a bathroom break, get your "refreshments, and put a “Do not disturb” sign on your door.
- Here it is:
In orthodox SR there is relative simultaneity. In Lorentzian SR there is absolute simultaneity, but there is also apparent simultaneity which coincides with the relative simultaneity of orthodox SR, and fundamental limits on our ability to determine which distant events are simultaneous, i.e., to determine our state of motion with respect to the privileged reference frame. Namely, we can’t determine our state of motion with respect to the privileged frame, so all we’re left to work with is apparent simultaneity.
We can know that the apparent order of timeline-separated events corresponds to the absolute order, but we can’t know whether the apparent order of spacelike-separated events corresponds to the absolute order. In your double triplet scenario, this means that everything looks the same whether orthodox SR or Lorentzian SR is true (with the results you encapsulate in Table I); the theories are empirically equivalent.
Please do bring it up, I’m curious.
The theories are empirically equivalent - they make the same predictions about what we can observe - but they still say different things about the underlying structure of reality.
I briefly skimmed the works from Levy that you provided, and don’t have much to comment other than to note that differences between what he is saying and what I am saying seem to be mostly a difference of emphasis. Levy seems to be quite insistent that we should be working in the privileged frame, or at least working with that frame’s time coordinate, whereas I don’t see any need for that. I think Lorentzians can affirm the reality of change (which, to me, requires the affirmation of absolute simultaneity) without requiring a frame-independent time coordinate or specific knowledge of the privileged frame.
I did find one thing I disagreed with him on when skimming his papers - he claims that in SR the fact that two observers in relative motion each observe the other to be undergoing length contraction and time dilation is paradoxical. But that is only the case if you impute the Lorentzian’s “changing 3-dimensional view” to the orthodox relativist, instead of the “4 dimensional view” they are likely to actually hold.
And as for his claim that your experiment could distinguish orthodox and Lorentzian relativity, his being competent and knowledgeable doesn’t mean he can’t get things wrong sometimes. 
He is wrong in this case; it is a postulate of Lorentzian relativity that the laws of physics have Lorentz symmetry, and an implication of that postulate is that no experiment can determine one’s state of motion relative to the privileged frame. (And the particular way it fails to do so in this case is through the failure of the familiar law of reflection for moving mirrors.)
Edit: okay, reading Levy a bit more here and there, I think I may have understated the degree of my disagreement with him. In some places he seems to think of the aether as a material medium that can potentially be entrained by other matter or have motion of its own? This is very much in the spirit of the pre-relativistic aether theories and is not at all what I have in mind by a “neo-Lorentzian interpretation” of relativity, which only postulates a privileged frame (no mention of an aether as a material medium) and Lorentz symmetry. He also asserts in several places that some experiments could distinguish absolute motion relative to the privileged frame, which is just not if Lorentz symmetry holds.
- Someone could have chided me for limiting my Figures in Section V. of my paper, for drawing a contracted Red Frame but not repeating the events from the POV of the contracted Red space vehicle.
- If I fly by your house in a contracted spacehip and try to measure its side parallel to my flight, will my measurement be larger, smaller, or the same as your measurement of your house?
I think my measurement of your house will be larger than your measure of it, no?
- If I fly by your house in a contracted spacehip and try to measure its side parallel to my flight, will my measurement be larger, smaller, or the same as your measurement of your house?
- So neither is falsifiable?
- For the record: for all my talk about Neo-Lorentzians and Joseph Levy, I’m not a Neo-Lorentzian, either. I may be surprised that you don’t agree with his assessment of my Hypothetical Experiment, but I’m not dismayed.
- Three message back, I posted a Loedel Diagram of The Double Triplet Scenario.
- Coincidentally, it “corresponds” somewhat to my conclusion of " ‘The Two Erupting Volcanoes’ conundrum" which I began this thread with. That conclusion ended with three reference frames in motion relative to each other: the seismologist’s and the two spacecrafts’. In my Loedel diagram there are three reference frames: A privileged frame and one each for the two spacecrafts. It is strictly an SR-based diagram and I can barely imagine a contorted Loedel diagram based on Neo-Lorentzian Relativity. I’d welcome anybody’s more creative attempt to draw a Loedel diagram of a Neo-Lorentzion version of “The Double Triplet Scenario”.
- That said, I mention here a brief answer given by a reputable SR-Relativist regarding “the solution” to the question: “How can we tell which of two twins, in the Twin Paradox is younger, the one who stayed at home or the one who flew away and returned?” My source’s answer was, simply, the one with the shortest worldline.
- So here’s the question that I postponed earlier, “Which of the worlldlines in my Loedel diagram is the shortest?”
- Not long after coming up with “The Doublle Triplet Scenario” and drawing the Loedel Diagram of it that I posted in my post #14 above, I realized that it was possible to assume that:
- both the Blue and Red space vehicles started from positions at rest with respect to each other,
- accelerated off in space in opposite directions,
- circling the same central point,
- passing each other halfway around a circle in a manner that corresponds to their journey past each other in The Double Triplet Scenario,
- continuing to complete their circular flights,
- decelerating to their positions, once again, at rest but on opposite sides of each other, having traveled from 0 miles per second.
- accelerating to 0.8667c, and
- decelerating to 0 miles per second again.
- That’s when I set myself to drawing the following diagram which, IMO, I think I managed to do successfully.
- Now, which Triplets have the shortest worldlines?
No, since my house is in relative motion to you, from your perspective it will be length contracted, and you will measure it to be shorter than I do.
The key thing to remember in these scenarios is that measurements of length depend on one’s judgement of simultaneity. You want to know the distance between the front and back end of the thing you’re measuring at the same point in time. That is how both parties can measure each other’s spaceships to be shorter - the events of “the front end of your spaceship is here” and “the back end of your spaceship is here”, and thus yea distance apart, are simultaneous from my perspective but not from yours.
They are falsifiable - for instance, demonstrating a violation of Lorentz symmetry would falsify both Lorentzian SR and orthodox SR.
(But one can envision falsifications that would fit more comfortably with the Lorentzian paradigm; for example, one might say that quantum non-locality conflicts with Lorentz symmetry, but it’s fits well with the postulate of absolute simultaneity, and still allows Lorentz symmetry to appear at the macroscopic or statistical level.)
All of their worldlines are the same length in your scenario. Your scenario is asking a different question than the twin paradox, so it has a different answer. (Namely: measurements of length presuppose a judgement of simultaneity.)
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