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Everything posted by md65536

  1. The frequency increases (blue shifts) the faster that you move toward the light source. At c/2 gamma is about 1.15, the frequency would be 1.15 times what was emitted, if moving toward the source (or redshifted to 1/1.15 times the emitted frequency if moving away). Everyone will measure the speed of light as c in their inertial frame. The two detectors I mentioned I was referring to A and B. Acceleration complicates things. The equivalence principle implies that you can set up a scenario where an accelerating O measures the same things as an O in a uniform gravitational field. So....
  2. Sure! It's "length contraction". In case I wasn't clear, I was talking about two different cases, depending on what the 10 LY refers to. Either the 10 LY is the distance from Earth to destination as measured by Earth, and John measures that as length-contracted to a shorter distance. Or 10 LY is the distance that John measures, and Earth measures a longer distance that John measures as length-contracted to 10 LY.
  3. You said the trip was 10 light years, but didn't say what frame that's measured in. It sounds like you intended that to be in the Earth's reference frame, so Earth would measure the trip taking 11.11 years. In John's reference frame, the distance to the destination is length-contracted, so even though the destination approaches John at 0.9c, it arrives at John sooner than 11.11 years. Gamma is ~ 2.29, the contracted travel distance is 10 LY/gamma = 4.36 LY, taking 4.84 years at .9c, measured by John. This could be true (until the last sentence) if it was 10 LY as measured by John.
  4. That doesn't matter because you can use a short pulse of light, ie. simply use many many photons instead of one, and they'll all behave the same with respect to speed. Some of the photons can be detected at the first point, and others at the second. Yes and no. Assuming flat spacetime, yes: It is assumed that the speed of light is the same everywhere, and that agrees with experience. With GR, not really. Measuring the speed of light from a distance, at a different gravitational potential, isn't really meaningful. The local speed of light is invariantly c. Some might say "the coordinate
  5. https://www.fallacyfiles.org/redefine.html https://www.logicallyfallacious.com/logicalfallacies/Definist-Fallacy 1. Define "heaven" to be something that's "scientifically supported." (Or maybe something simply vague enough that it can't be scientifically refuted?, ie. "not even wrong"?) 2. Therefore, heaven is scientifically supported. QED. 1. Define something as whatever I want to argue. 2. Therefore, whatever I want to argue.
  6. Time t will vary along with v, but also with d (length of travel), which itself should vary, and depends on time and expansion. You're giving an example where the differences in v and t are small, and difference in d is negligible? (Due to being nearby and/or negligible rate of expansion? Or assuming a fixed distance of expanded space, instead of being sent from a common source that is receding over time?) However if we were talking about an object at the cosmological horizon, light from it would arrive after infinite time. For any speed less than c, there should be another nearer horizon
  7. There's this: https://www.forbes.com/sites/startswithabang/2018/07/28/ask-ethan-where-does-the-energy-for-dark-energy-come-from/ Including: Unfortunately I can't find anything about how expansion affects the energy of moving objects. I'd assumed it would be the same as with light.
  8. I don't think that's right. I think the rock would have to lose energy to the expansion, which means it would arrive at a lower speed relative to its destination than its speed relative to the source when launched. Suppose a photon and a neutrino were sent, with the same energy. Say they arrived roughly at the same time, and the photon was red-shifted to half its energy. Wouldn't the neutrino need to have roughly half the energy it was sent with? In this example, the neutrino's speed is so close to c that it can lose half its energy to a decrease in speed and still be moving at a spe
  9. My point is that "if time stopped" doesn't mean anything on its own, it needs more details, and those details can describe something that breaks the laws of physics including causality, or something that doesn't.
  10. It's a fictional example. Everything has their own clock, and they can't all be stopped "at the same time". In fiction where "time stops" in some contrived way, some observers' clocks stop while other observers keep observing, because if there's nothing to observe that some clocks have stopped, the stop is meaningless and doesn't look good on tv etc. When they use "time is stopped" for things like time travel, it's some made up way with most likely no basis in reality.
  11. I roughly calculated an order of magnitude somewhere between a Planck length and a quark. It depends on how big you say the universe is. There are many orders of magnitude between Planck length and quark though; it would be around some billionths the size of a quark, and some billions of Planck lengths.
  12. Sure, everything has their own clocks. I'm giving an example the breaks the laws of physics. For example, say you have two observers A and B, a light year apart, and A sends a message to B. Then you stop time for A and B, but let the message keep going. Then start time so that A and B measure the message taking say only an hour, as if it instantly jumped across space while they and their clocks were stopped. But then suppose there's another observer C moving at high speed relative to A and B. Normally, if A and B, in their rest frame, are a light year apart and there's an event at
  13. And of course relativity of simultaneity, which is directional. A pair of clocks placed on a line perpendicular to their direction of motion remain synchronized with each other. Please work through an example of this on paper or numbers. Put it into geometry or use equations. You can reiterate the same philosophical questions for 10+ years and still not be any closer to a philosophical understanding of the answers. For example, suppose you have a stick 1 light second long, and you send light from one end (event A) to the other (B) and back (C). In the rest frame of the stick, the tim
  14. The two frames are equivalent, the same reasons for length contraction apply equally to both of them. Motion is relative. If A is in motion relative to U, then U is in motion relative to A. Only moving things* are length contracted. If A measures "the world" as length contracted, then the world is moving relative to A. Any part of the world not moving relative to A, won't be length contracted according to A. * Or, trying to be more accurate: "the lengths of, and distances between, objects as measured in their rest frame, are contracted in frames in which they're moving".
  15. I can't see how you could possibly break causality. Time is relative, and time is what clocks measure. Time, or a clock, will stop on a black hole event horizon according to an observer outside the horizon. That doesn't break causality, which is perfectly fine with that type of "time stopping". But you probably mean if all of time stops at once? That doesn't make physical sense in the universe as we know it (ie. described by General Relativity) so you'll have to specify what you mean by it. However, if you came up with an arbitrary definition of simultaneity that made physical sense
  16. It sounds like you've moved on from the length-contraction aspects, but if a bubble is expanding at a rate of c in the bubble's frame, it should also expand at a rate of c in the ship frame. If it's a given size before you accelerate, I don't think it's possible to make it length-contract any smaller than that size by accelerating, if it's expanding at c. As a very rough look at this, suppose you have a particle moving away from you at c, and is "now" at location x, a billion light years away. Now say you accelerate so that the distance to x contracts to 1m. But due to relativity of simul
  17. It doesn't mean cloth, just like if someone talks about the makeup of spacetime, they don't mean it's made of cosmetics. In SR there's no single universal frame of reference that space is "in". The ship frame and the huge bubble frame are equal, there's no such thing as "one frame contains spacetime and the other doesn't". You might wrap your head around that by taking your example and having half your universe moving relative to the other half and vice-versa. Which is the universe? Or consider a universe made only of two identical ships moving relative to each other. Each, in its own fra
  18. The "closing in" is a change of the length contraction factor, which only happens during acceleration. But combining this idea with this: As an example, suppose the ship has its back against a brick wall, and then the entire ship accelerates away from the wall in some coordinated way (it can't keep accelerating "simultaneously" according to the pilot because the ship never shares a single inertial frame while accelerating), it doesn't matter for this example how. If the pilot accelerates fast enough, SR says that the wall can contract toward the pilot faster than the pilot moves away f
  19. Sure, but it's best not to refer to it as "the universe" because 1) you're intentionally avoiding real properties of the universe that require GR, and 2) you're unintentionally treating your simple model as if it should be like the real universe. So let's call it a "bubble", say a spheroid region one billion light years in diameter, with a boundary and some stuff in it at relative rest, in an inertial frame. Then it has an inertial ship passing through it from one edge through the middle to the other edge. The ship has a proper length of 10m. The ship is traveling fast enough that the bub
  20. I got this wrong. There is a paradox if the ship starts in the middle of the simplified universe and accelerates, ending up sticking out both ends. It's resolved by Born rigidity https://en.wikipedia.org/wiki/Born_rigidity : If the ship started "inside" the universe and accelerated quickly enough that its 10m rest length would stick out both ends, that ship could not maintain a 10m length during that acceleration, and it would not stick out both ends. If the ship starts outside the simplified universe and is already inertial and 10m before the back of the ship enters the 1 m contracte
  21. There's no paradox. You're talking about a finite spacetime that seems to be flat. Or basically an object with a proper length of over ten billion light years. You're calling that "the universe", which is fine as long as you avoid attaching meaning to that label, like that everything else you specify must be within that. Not everything in the (flat, toy) universe gets length contracted. Only the stuff that is moving relative to you does. The pilot isn't moving relative to the ship. If the ship is part of the universe, the universe won't be contracted to 1m, only the stuff moving relative
  22. These two statements aren't consistent with each other. If the bike rider accelerates, ie. changes inertial frame, there is a shift in relative simultaneity with respect to the distant source clock. If the rider accelerates towards it, the coordinate time of the distant clock can change from 12:34 to 13:44 in a small local time, as in your example. But if the bike rider then accelerates away and returns to its former reference frame, the coordinate time can change from 13:44 to 12:34, or even earlier if it accelerates away more. If the first change in relative simultaneity is "the source
  23. Are you okay with saying that the source clock runs backward if/while the very distant rider accelerates away from it? If that's not okay then what you wrote could be phrased differently to avoid it (eg. relative time instead of how the clock itself runs).
  24. Yes, you're correct that it's about distance. The effect still occurs at low speed where time dilation is negligible. Google "Andromeda paradox", the effect can happen at walking speeds if the distance is large enough. The reason direction matters is that if the distant location is far enough, the travel time of light is long enough that you can move a significant distance even at slow speeds. If a source is millions of light years away, you can walk on the order of light days between "now" and when light arrives. Time dilation still applies but with vanishing speed it approaches zero. At
  25. Actually, I think you can prove to yourself that a moving mirror must be able to change the angle of reflection. Try this: Have a box with a mirror on one interior surface, and two holes such that if you shone a beam of light through one, you could reflect it off the mirror and out the other hole. Consider that the stationary frame. Now in a moving frame (in a direction of the mirror's normal), the box is moving while the light makes its way from one hole, to the mirror, and out the other hole. If you draw this on paper using 3 positions for the box for when light enters, reflects, and exits,
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