md65536

Because not all of the frames will agree on the simultaneity of events. You definitely can define a "now" and you can do it however you want to (a foliation of spacetime would make sensible instants of time throughout space, but the problem is you can foliate it in many different ways, so essentially your "now" would be completely arbitrary). To be useful, you would want to be able to say that all the events in your "now" are simultaneous. Someone in a different inertial frame would not agree that those events are simultaneous, and would have no reason to accept your personal definition of "now".

On second thought I think what I crossed out is true, and possibly equivalent to what I implemented.

I think I've solved it and the answer surprised me. I'll restate the puzzle as I solved it: There's some number with digits abcd, with 0<=d<=c<=b<=a<=9. Person P1 knows a and d. P2 knows a*b*c*d. P3 knows a+b+c+d. P1 says "A) I don't know the digits but B) neither does P2". P2 says "C) I don't know the digits but D) neither does P3." P2 says "D) I know that P3 doesn't know the digits, and C) I don't know the digits either." --- I believe this order is important because P3 can know the answer while the statement is being given. P3 says "E) I didn't know the digits but F) now I do." It does not seem to need to say more but it could say now P1 knows or now everyone knows. Solution: A) a and d must be different or it would know. B) The range must contain some number with ambiguous factorization. For example, 9*1=3*3. If the range contains 1 and 9, or just 3, then it is still good. Do this for all possibilities and you find the range must contain 0, 2, 3, or 4. If it contains 1 we already know it must also contain either 0 or 2. So, eliminate all possibilities where d>=5. C) Eliminate all remaining possibilities that have a unique product. I think that a key element here is the concept of common knowledge. At each step, everyone can eliminate any possibilities that are based on what was said, but not necessarily the possibilities that the others could eliminate. Anyway, that might not be important yet... D) P2 can eliminate all possibilities that add up to a unique sum. E,F) Here is the key to the puzzle and where most of the possibilities are eliminated. P3 can also eliminate all possibilities that add up to a unique sum. However, since it now knows what the answer is, it must be that it was possible for P3 to assume that P2 knew the digits. The answer must be a combination whose sum is not unique sum, but where all other combinations that add up to the same sum have a unique product. Edit: No wait, that's not what I implemented! I looked for combinations that P2 knew had a unique sum *among* only possibilities that have no unique product, but which P3 did not know had a unique sum. Very confusing! I'm not sure I got that right or implemented it right, but I end up with only one possibility left and that is

Intuition would be to minimize non-diagonal segments, so AjkC (However it's easy to add bad diagonal paths that would break the strategy.)

If the solution were 9xy1, the product would be the same as xy33, so Jack could claim that James doesn't know the digits. (Then, 9621 adding up to 18, and 9431 adding up to 17, both with products 108, might be possible reasons why John can eliminate 4333.)

What about 6332? Its product is also 108. It's the only such one that adds up to 14. If John supposes the answer is 4333, then James would have considered 6332 as a possible solution, and wouldn't have been certain that John wouldn't know the answer??? Is that enough to rule out John thinking it's 4333? Or would we have to also show that every other possibility that James might suppose that John might suppose, doesn't have 2 or more combinations that add up to 14? But wait... 8411 adds up to 14... So John considering 4333 as an answer might have considered that James knew both 6332 and 8411 add up to 14, so could say that John didn't know the answer, meaning that 4333 is still a possible answer to John?

Yes. If the range is known to be [3, 4], then Jack cannot know that James doesn't know the answer, as he states. If the range is [3, 4] then Jack knows that James must know the answer. The only way that Jack can assert that James doesn't know the answer is if the range includes factors that can multiply to the same product in different ways, eg. 9*1 or 3*3 (requires a range of at least [1, 9]) or 8*2 or 4*4 (range at least [2, 8]). First ruling out 0, the smallest range for which this works is [1, 4]. *We* know this much after Jack's statement, so everyone else (John, James) are able to know this after his statement too, so John can rule it out. No wait... my line of reasoning is wrong and might not go anywhere useful...

Yes that makes sense. That's what happens at speeds low enough to neglect relativistic effects. https://en.wikipedia.org/wiki/Einstein_synchronisation Clock synchronization can be "achieved by "slowly" transporting a third clock from clock 1 to clock 2, in the limit of vanishing transport velocity." Then you'd say these clocks measure the same time. Worse than conflated and confused, time dilation was completely ignored, and relativity was presented over simplistically. They cared about getting Einstein's hair right; the science wasn't important. I think it's terrible, because a lot of people base their understanding of things on fiction, then go on to be a politician who decides NASA's budget or what to do about climate change etc., all the while perpetuating "the science wasn't important." (Rant cont.) Fictional science is probably fine, but writers throw in real concepts or jargon to be more interesting or sound legitimate or whatever. How many people could earnestly debate multi-world theories, without ever taking a physics course? Where do they get their information?

What do you mean by time reference? In the situation described, with no one stopping, each observer would measure the other's clock ticking slower, in addition to seeing it tick much slower due to delay of light.

No, Insignificance gets relativity wrong. However the quote above was cut off right before it gets bad. https://www.springfieldspringfield.co.uk/movie_script.php?movie=insignificance I bolded the main wrong part, and strikethrough'd ... yuck. The character is only talking about delay of light and has neglected time dilation entirely, but explains it as if it's time dilation. In the striked part, the character is describing differential ageing or total time, and describing it as a differential rate of time (which is constant at a fixed relative velocity).

Time is like distance. (They're both measures of lengths between events) You can walk from the door to the corner of the house and then back, and say, "I'm decreasing the distance that I walked," but you're not really. You're decreasing the displacement between you and the door. The total distance you've walked can only increase. Time as measured by clocks is like that, it's the total elapsed. The problem isn't that there's some hidden physical difference by what must be the "true physical meaning of time" and "true meaning of space", it is merely a difference between the measurements we're choosing to consider, and of choosing the wrong analogies to compare them. A temporal analogy to displacement might be the minimum communication time between two locations, which would be the length of a light-like path between them. This can be increased or decreased, but it's not a measure we call 'time'.

Looking at blogs.scienceforums.net/pengkuan/2019/05/ I hope I'm not violating the mod edit. This does not agree with SR. If Betty is inertial and the Earth changes inertial frames, Betty will age more. I haven't read the whole thing but I think you're making a mistake in section 2. You have the Earth and star S in an inertial frame, and they both change velocity by the composition of v and v, half way through the experiment. It looks like you're treating these two events as simultaneous in all frames, which you can't do. That will give you errors. It looks like you have the Earth travel a length-contracted distance away, and then travel a length-contracted distance back, but measure that in Betty's frame. If you'd done it completely, it should work out to the same as if the Earth traveled away, stopped, and then came back, and the full separation between Earth and Betty when stopped would be the rest distance, ie. the distance between Earth and S in their frame. I suspect that you're essentially having Earth teleport twice between its length-contracted distance and rest distance, in a time that Betty counts as zero. If it was accounted, she'd age more then. This is a guess, I haven't been thorough.

Yes, I misread your post as talking about a circular orbit centered on the observer's viewpoint, which is possible for larger orbits. It should be possible to completely negate the relativistic Doppler effect with such an orbit, leaving only negligible(?) gravitational Doppler shift including due to the observer's acceleration as the Earth rotates. In the case you're speaking of, where the orbit is not centered on the viewpoint, the spaceship approaches then recedes as it passes nearest the observer, and the Doppler shift from that would be much much greater than the shift due to the Earth's rotation. This is true even at normal "slow" satellite speeds. https://en.wikipedia.org/wiki/Doppler_effect#Satellite_communication --- Partial info and does not handle satellite at relativistic speeds.

This is incorrect. Unlike length contraction, time dilation doesn't depend on the direction, only the relative speed. There's no Doppler effect in this case, so you can "see" the true time dilation effect. You don't say if it's a spaceship year or Earth year, but the effects are the same regardless. Radio waves are light. You can describe it based on how it looks. The video below has some effects from the spaceship's perspective, including orbit at the end. Let's say we're talking one Earth year and one spaceship day. The spaceship would orbit about seven times a second in lowest orbits. It would appear slowed to 1/365 our time, so the one day of spaceship time would be seen over our year. Since the spaceship sends out a day's worth of signal and light, the light that it emits (not reflects) would appear very dark... 1/365th as bright. It would also be red-shifted by that factor. The spaceship would see blue-shifting and a year's worth of Earth's light/signals (and the sun's too) in a day, so it would be intensely lit, which is why it wouldn't necessarily appear darkly reflective. By the way, the relativistic Doppler ratio is \( \sqrt{\frac{1 + \beta}{1 - \beta}} \), where beta is the speed as a fraction of c. If you negate the speed, you get the inverse Doppler ratio. If you take the average of the Doppler ratio and its inverse, you get the Lorentz factor. So, if you have a spaceship traveling at constant speed through flat spacetime on a path that you can divide up into equal-length segments in one direction and the opposite, and have it arriving at its starting point in some inertial frame (eg. some point on an Earth orbit), you can see that the average rate of time seen passing in inertial frame is equal to the Lorentz factor. (Actually that's true for any constant-speed closed loop through flat space-time, but I can't think of how to see that intuitively.)

Based on the clues, they all did (except the original doesn't say Nick finished). You've never heard of the Millennium Falcon? It's the ship that made the Kessel run in less than twelve parsecs!

I've said about all I have to offer on the topic, and do not seem to have done anyone a stitch of good. So I'm bailing. Apologies for acting out of frustration.

I still think that this is consistent with Einstein's definition of simultaneity and with the convention used to define it. I don't see how it shows an improvement over Einstein. Einstein's definition of simultaneity is the standard definition still used today. Einstein used a convention in his definition, he did not claim the definition derived from experimental observation or from assumption. No one in history has provided a better definition, without a convention, that has replaced Einstein's as the accepted standard. No one has proven Einstein wrong or improved upon his definition. Unfortunately I'm deficient in maths to be able to express any of these statements in equations. If anyone has an equation that shows any of the statements are wrong, then I concede utter defeat.

Relativity of simultaneity and conventionality of simultaneity aren't the same thing. Your link's referring to the former. In SR you have eg. the embankment frame, with 2 Einstein-synchronized clocks. Those clocks aren't synchronized in the train frame (they might be according to some alternative convention, I'm not sure, but your link doesn't show that). In the train frame, some other pair of clocks will be synchronized. However, in SR they will be synchronized using the same convention (it is still Einstein-synchronization). The measure of simultaneity is relative, and different in the different frames. The definition of simultaneity used is the same in the different frames. Other definitions of simultaneity may work, but they're not needed or used in SR. We don't say that the embankment's clocks are "synchronized according to an alternative simultaneity convention" in the train frame, meaning that they read the same time according to some other set of rules, we say they are "not synchronized", meaning they are not reading the same time.

This seems rather ambiguous because they mention the issue but don't seem to address it. They mention the "problem of simultaneity", quote Einstein suggesting it is merely a convention, mention the "problem of clock synchronization" but no resolution, and cite a reference that says the one way speed of light can't be tested, except that it is phrased ambiguously as though suggesting it no longer applies: Regardless, it is generally agreed that the one-way speed of light is measurable given synchronized clocks, with respect to the particular sync convention. It's so hard to try to argue a mainstream position on a poorly understood issue around here without being called a dick, rude, and being accused of bashing. I'm not aware of the contradiction you're bringing up. I think it's based on a fundamental lack of understanding of SR. Sorry to say that, like I said I think your understanding of the philosophical, conventionality of simultaneity side of things is the best that I've seen, but your examples of alternative simultaneities, and claims that the Lorentz transformation require them, contradict SR. At best I think you'll have to show an alternative simultaneity is in agreement with experimentally verified predictions of SR. I don't think anyone has a hope of finding a contradiction in SR by using SR incorrectly, and with a decent understanding of SR it becomes hard to see any weakness where there is a possibility of contradiction. My position is that Einstein's convention has never been proven non-conventional. Personally I think it truly is conventional, and that physically meaningful simultaneity is merely a local measurement, something more like in general relativity, but I won't argue that because I'm not aware of anything to back it up.

It seems no one on the non-conventionality side is getting it so I'll try to explain. Einstein's definition of simultaneity and the clock synchronization method it enables, allow us to define whether two distant events are simultaneous in a given inertial frame. Yet, there is no way to say for sure that the two events really "are" simultaneous independent of the definitions. The answer to that is in the realm of metaphysics. There is no way to measure it without using some assumption that is equivalent to assuming the simultaneity definition. Even if multiple conventions give the same answer, that doesn't tell you that it truly "is". This doesn't matter in science, because Einstein's definition works perfectly fine, and the measurements are useful whether or not the events truly "are" simultaneous in some philosophical sense, while the answer to something that can't be measured isn't useful. If you argue that one of the related quantities (simultaneity, synchronization, speed, delay of light, etc) truly "is" the only possible physical reality, you can effectively derive that Einstein's simultaneity convention "is" in fact the only real one, even though such a fact can't be measured without effectively assuming it. That makes it a crackpot argument. I don't think anyone here arguing on the non-conventionality side is a crackpot, in the sense of knowingly promoting a position that contradicts science. I think the crackpot ideas on this side come from a lack of understanding.

Would some references suffice? I've cited a couple in support of my position.

As Andromacus mentioned, equivalent synchronization is achieved with the two methods. See https://en.wikipedia.org/wiki/Einstein_synchronisation: Yes. No citations. No statement on whether or not you accept that Einstein's definition of simultaneity is conventional (are you avoiding it because you don't know what that means?). Only "um"s and sarcasm and unrelenting deep-seated misunderstanding. https://en.wikipedia.org/wiki/One-way_speed_of_light: Do you refute this? Do you understand "all experimentally verifiable predictions of this theory do not depend on that convention"? As I understand it, that means that the experimentally verifiable predictions do not prove that Einstein's simultaneity definition is non-conventional, because if it was then the predictions of SR would depend on it.

As you say, "Slow clock transport gives the same result". This assumption holds only if the other does. Enough of this farce. Can you back up your crackpot claims with any citations at all? I'll start: https://en.wikipedia.org/wiki/One-way_speed_of_light 'The "one-way" speed of light from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector.' You refuse to say whether you accept that standard simultaneity is a convention, but you argue as if it is an empirical fact, seemingly not understanding the difference.

It still assumes that the transported clock's time is the same as the stationary clock's.

Is this about the one-way speed of light? Since when do members have to offer up substantive proof of accepted mainstream science? There is no known or accepted theoretical way to measure the one-way speed of light independent of some coordination of times at two locations. Unfortunately there is too much argument in this thread between people who don't understand conventionality of simultaneity, and one who doesn't understand special relativity. I don't see any common ground understanding.