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#1321 |
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You have to look at the consequences on a single clock because there is no saying what happens with regard to synchronisation and so forth between different clocks in your postulate because you haven't and can't express it mathematically. (For example, what are the equivalents to the Lorentz transforms in your Universe. No-one knows and no-one will ever know.) What we can do is to ask what happens on a single clock with a round trip and what we find is a paradox. So your postulate is not self-consistent.
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Gulielmus Princeps Haroldum Principem in catino canino impulit |
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#1322 |
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Gulielmus Princeps Haroldum Principem in catino canino impulit |
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#1323 |
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I’d rather be a rising ape than a falling angel. - Sir Terry Pratchett |
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#1324 |
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#1325 |
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If the times were the same, then no time dilation would have occurred, which means the postulate was not applied.
If Bob sends two photons to Alice, 2 seconds apart, and Alice receives them 4 seconds apart, what difference would it make whether Bob did that on his own, or was prompted by Alice sending two photons previously? |
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#1326 |
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Gulielmus Princeps Haroldum Principem in catino canino impulit |
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#1327 |
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Because you cannot directly compare Alice's and Bob's clock (as you have not written down and cannot write down the relevant transformations), but you can compare round trips on a single clock and that leads to an irreconcilable paradox, as ypu have bow worked out yourself. Hence your postulate is logically impossible.
ETA: and because in the round trip scenario Alice is able to measure the round trip duration for each photon leading to the paradox. |
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#1328 |
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#1329 |
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#1330 |
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#1331 |
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#1332 |
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#1333 |
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Gulielmus Princeps Haroldum Principem in catino canino impulit |
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#1334 |
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You'd measure it how we just explained.
You take some information about an event that lasts a second long, broadcast half way across the observable universe which means the information is received with the affects of time dilation, broadcast it back, which time dilates it again, and future Alice will receive the doubly dilated measurement from past Alice. If you remove the postulate and there is no time dilation, things work as you expect. If you add the postulate and there is time dilation, things work as has been described. It may not work how you expect, but that's a contradiction between your expectations and the postulate, not the postulate and itself. |
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#1335 |
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Different scenario.
A supernovae goes off in Alice's galaxy. She says it lasted 14 days. Bob observes this and says it lasted 28 days. So Bob sends a signal to Alice that lasts 28 days from start to finish. How long is the signal that Alice receives? 56 days right? How could it be anything else? |
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#1336 |
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You'd use the measured time between the photons arrival to determine that the photon arrival is different now compared to what it was in the past? I don't think so. You need a separate clock.
You can only measure the duration of events by some reliable clock. It is meaningless to say that your clock was ticking faster or slower in the past, as you don't have any means of judging that. Your whole scenario depends on the claim that two events one second apart according to your clock, are, after a round trip, four seconds apart. That leads to the paradox that we have all described till we are puce in the face. If you say now that the gap between the two photons is the same now as when they were emitted, four seconds, according to some reliable clock, then there is no difference in the gap and no time dilation. Your claim is that there is a real and measurable difference in the gap between the photons' emission and detection, and if there is then that leads inexorably to the paradox. |
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#1337 |
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I think that's an important part of what's missing here.
For time dilation to do something, there needs to be an event with a duration. In our "send 2 photons scenario", the event started when the first photon was emitted, and ended when the second photon was emitted
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Photon 1 takes off at tA=0, photon 2 takes off at tA=1, Photon 1 arrives at tB=0 Photon 2 arrives at tB=2 Intuitively, photon 2 stayed in the air longer. This postulate says the duration between 1 and 2 is 1 second, which is dilated to 2 seconds, which means photon 1 didn't take off at t=0, the photon took off at t=-1. This postulate, counterintuitively, says both photons stayed in the air longer. |
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#1338 |
Penultimate Amazing
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If space is expanding but clocks aren't going faster or slower, the pulse length will increase. So that doesn't actually distinguish the two scenarios.
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#1339 |
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#1340 |
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#1341 |
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Not for a single photon.
If Alice sends a photon and gets a response T years later, then pinging back would get a second response another T years later. It's when Alice sends two photons, or a steady pulse, or a supernovae happens, something that has a duration, a start time < end time, does that duration get dilated. Emitting a single photon as an event has a duration of 0 (start time = end time) so 0(1+z)=0. There's nothing to accumulate. |
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#1342 |
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I’d rather be a rising ape than a falling angel. - Sir Terry Pratchett |
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#1343 |
Penultimate Amazing
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Precisely
Yes for a single photon.
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You keep revealing you don't know anything, and you're wrong about everything. |
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#1344 |
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#1345 |
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It takes off at 0 and -1? It takes off before it takes off? The fact that you have to write such arrant nonsense to attempt, unsuccessfully to rescue your garbage idea, is because your garbage creates unresolvable paradoxes.
And you're only doing half the thought experiment again. You need to do a round trip and you need to measure all the events on the same clock, which is the only means you have of measuring durations. There is no absolute external time against which your clock runs faster or slower. And when you do that, you come up with a nonsense scenario in which each photon in a sequence takes a longer time on the round trip than the previous one, and the time taken depends on what number in a sequence a photon is. Which is patent nonsense, as is your idea. |
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#1346 |
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#1347 |
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The end of the event is signaled by photon 2. Photon 2 is emitted one second after photon 1. Therefore, at the end of the event, the emission of photon 1 is one second in the past. When the postulate is applied and time is dilated, photon 1 was actually emitted two seconds in the past. Say here's a normal universe, photon 1 (top) leaves before photon 2 (bottom) by one ~, and arrives by one ~ sooner. Code:
~~~~~~~~~~~~ ~~~~~~~~~~~~ t-------------------> Code:
~~~~~~~~~~~~~ ~~~~~~~~~~~~~ t-------------------> |
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#1348 |
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#1349 |
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Caption from and old New Yorker cartoon - Why am I shouting? Because I'm wrong!" |
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#1350 |
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Huh? Not at all.
We're going to define an event with a duration of one second that begins by emitting photon and ends with emitting a photon. Since the event is one second long, at the end of the event, the beginning of it will be one second in the past. That's tautological. |
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#1351 |
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Giving benefit of the doubt, we should consider the possibility that we are witnessing an accidental and good-faith attempt to demonstrate that someone can indeed be that stupid.
Inasmuch as Helland physics says space is not expanding, it should not be terribly difficult for a neutral arbitrator Carol to figure out how to position herself exactly halfway between Alice and Bob. At some arbitrary time of her own choosing, Carol sends messages to both Alice and Bob telling them to start sending photons to each other. When Alice and Bob receive those messages, Alice sends a photon to Bob and Bob sends a photon to Alice. According to Helland physics, quoted above, "Clocks always get faster in the direction the photon is traveling." The scenario described above is perfectly symmetric. A photon is traveling toward Alice, so clocks get faster in the direction of Alice. A photon is traveling toward Bob, so clocks get faster in the direction of Bob. Whenever Alice receives a photon from Bob, Alice immediately sends another photon to Bob. Whenever Bob receives a photon from Alice, Bob immediately sends another photon to Alice. It's as though they're holding mirrors that reflect each other's photons. By symmetry, the speeding up of Alice's clock is exactly the same as the speeding up of Bob's clock. So the local clocks of both Alice and Bob are speeding up by exactly the same rate so long as they are sending photons to each other. But (as we may infer from precise astronomical observations of similar physical processes) Alice and Bob don't see any change in the unperturbed ground-state hyperfine transition frequency of the caesium 133 atom, which both Alice and Bob continue to measure as 9192631770 Hertz. That means physical processes in the vicinity of Alice and Bob are speeding up at exactly the same rate at which their local clocks are speeding up. Which means neither Alice and Bob can rely on any local experiments to detect the alleged fact that both their clocks are speeding up. But both Alice and Bob notice that the photons they receive from each other are redshifted from the frequencies each of them claim those photons had at the time of transmission. From which they infer that their local clocks are running faster than the distant clocks that were used to measure those frequencies at their point of transmission. Now we could have run this experiment by positioning Alice and Bob at any two arbitrary points of space, from which it follows that either
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Last edited by W.D.Clinger; 27th March 2023 at 04:24 PM. Reason: added previously omitted word "atom" |
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#1352 |
Penultimate Amazing
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"As long as it is admitted that the law may be diverted from its true purpose -- that it may violate property instead of protecting it -- then everyone will want to participate in making the law, either to protect himself against plunder or to use it for plunder. Political questions will always be prejudicial, dominant, and all-absorbing. There will be fighting at the door of the Legislative Palace, and the struggle within will be no less furious." - Bastiat, The Law |
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#1353 |
Illuminator
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That's the nicest thing you've ever said to me.
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If you have a series of observers: A B C D E F As a photon goes from A to F, each clock it passes will be faster than the last. And same goes for F to A. But A and F aren't changing speed relative to each other. This is why light travel time distance is not just (demit)(1+z). You have to add up the slices of (1+z) for all z's up till your target z. IOW, the sum of the time elapsed around A (ie,z=0), and around B, and around C, etc. |
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#1354 | ||
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OECD healthcare spending Public/Compulsory Expenditure on healthcare https://data.oecd.org/chart/60Tt Every year since 1990 the US Public healthcare spending has been greater than the UK as a proportion of GDP. More US Tax goes to healthcare than the UK |
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#1355 |
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#1356 |
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One thing that recent pages of this thread has highlighted for me is that some people don't understand the difference between counter-intuitive and paradoxical. It's usually people who think that, for example, SR makes contradictory claims, but it can go the other way - those who, like Mike, claim that something which results in truly paradoxical and contradictory outcomes is merely "counter-intuitive".
ETA: I'll just add that the latter can never be expressed in a mathematically coherent and self-consistent way. |
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#1357 |
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#1358 |
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#1359 |
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It continued:
--- Therefore, at the end of the event, the emission of photon 1 is one second in the past. When the postulate is applied and time is dilated, photon 1 was actually emitted two seconds in the past. --- The "paradox" arises when you dilate the time of when photon 2 was in the air by itself. If you dilate all the times, including when photon 1 was in the air by itself, the flight times for both photons are equal and the paradox is resolved. |
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#1360 |
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Here's what I have:
Code:
dt = 0 dts = [] for (let z = 0; z<=20; z+=0.1) { d = z/(1+z) * 13200 dts.push({z: z, dt: dt}) dt += 1 - 0.0000756 * d } It looks like the slope of this line is equal to the area under the curve for z/(1+z)*c/H0. |
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