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Pardon me for asking in layman's terms, but I find it the quickest. When an astrounaut's watch has orbited earth in high speed for a sufficient amount of time, it is delayed by a detectable amount of time compared to an identical watch left back on Earth. Ok. Relativity.

But since the spacecraft, or earth are not tethered to a tangible point in space, we could perceive this scenario as Earth orbiting the spacecraft, and thus observe that the Earth-based watch is running slower.

In other words, how do we decide, that it is the rocket moving fast around Earth, and not otherwise? And so, how does the astronaut's watch, and all satellites in orbit, for that matter, "know" it is their time, that should be slower?

marko-36
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    This is a very known "problem" and is almost as old as relativity itself. It is known as the Twin Pardox. https://en.wikipedia.org/wiki/Twin_paradox – J. Manuel Jun 28 '19 at 11:56
  • Thank you, but the article gets real heavy after scrolling down and it also states, that it is a thought experiment. But is there a clear explanation to this phenomenon, let's say, there probably is a simple way to explain how and why time-dilation in GPS satellites is accounted for. – marko-36 Jun 28 '19 at 12:05
  • Well, the bottom line is: Which one has being accelerated in some point after the experiment starts. The astronaut was in earth, and then accelerated by burning rocket fuel and then decelerated when entering earth’s atmosphere. During this time earth reference system was still exactly at the same state. – J. Manuel Jun 28 '19 at 12:11
  • The thought experiment is your question itself (the "paradox") and not the answer to it. The answer is mathematically proven within relativity theory itself – J. Manuel Jun 28 '19 at 12:20
  • @J.Manuel This isn't an example of the twin paradox. This is just time dilation in looking at one inertial frame's time from the perspective of another inertial frame – BioPhysicist Jun 28 '19 at 12:58
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    How does the acorn still on the oak tree know that it is the one that is supposed to fall, not the one on the ground? – Jon Custer Jun 28 '19 at 13:30
  • Two cars travel from Stockbridge to Boston, one along the Massachusetts Turnpike and the other with a detour through Texas. How does the second car's odometer "know" that it should advance farther than the first car's and not the other way around? – WillO Jun 28 '19 at 13:39
  • I won't dupehammer this, but what time dilation is and the reasons why it happens are discussed in detail in What is time dilation really?. – John Rennie Jun 28 '19 at 16:18
  • @AaronStevens. This is exactly the paradox. The OP is not asking about time dilation. He is asking why do we affirm that the astronaut’s clock will be “delayed by a detectable amount of time compared to an identical watch left back on Earth” and not the other way around, since not earth nor the astronaut is “tethered to a tangible point in space”. In other words, who is orbiting the other: The astronaut or earth. – J. Manuel Jun 28 '19 at 17:34
  • @J.Manuel I agree you can call it a paradox. It just isn't the twin paradox (or at least what makes the twin paradox the famous example that it is). The twin paradox doesn't just focus on the fact that from one twin's reference frame the other's clock is slower. The twin paradox specifically focuses on the event of the traveling twin changing reference frames and coming back to Earth. In other words, even though the confusion of the twin paradox results from this "symmetric time dilation", the twin paradox goes further and applies it to that specific scenario of the twin that turns around. – BioPhysicist Jun 28 '19 at 17:47
  • @AaronStevens. This is the point. Nobody seems to see that what the OP is asking is “specifically focuses on the event of the traveling twin changing reference frames and coming back to Earth”. Reread the question and you will see that he is asking why do we can affirmatively claim that the next astronaut going to the ISS will have his clock “delayed by a detectable amount of time compared to an identical watch left back” with us. He is exactly making the twin paradox. (Lets forget gravitational effects to the clock (GR), and just focus on the speed part (SR) ;-) – J. Manuel Jun 28 '19 at 18:01
  • @AaronStevens : I definitely have some sympathy for your viewpoint. But an alternative view is this: We have "ordinary" paradoxes where two observers disagree about the time interval between different events --- e.g. the event where I leave earth and the event where I arrive at Alpha Centauri. Then we have another class of paradoxes where two observers disagree about the time required for a round-trip journey (or at least something that they both agree at the end was a round-trip-journey) from and to a single point in space. (CONTINUED) – WillO Jun 28 '19 at 18:06
  • (CONTINUED). It's not unreasonable to call the latter "twin" paradoxes ---and by that definition, twin paradoxes include the usual "one twin makes a round trip to Alpha Centauri" case and the present "one twin makes a complete orbit around the earth" case. – WillO Jun 28 '19 at 18:07
  • @WillO Yes I agree. If you decide to call it a twin paradox then it is a twin paradox. – BioPhysicist Jun 28 '19 at 19:37
  • @AaronStevens : :) – WillO Jun 28 '19 at 19:52
  • @AaronStevens : but seriously....my point was that this definition is not arbitrary. The essence of why the usual twin paradox seems paradoxical is the round-trip aspect----so it does make some sense to lump together various versions that partake of the same essence. – WillO Jun 28 '19 at 20:12
  • @WillO The OP question seems to be inspired by these news saying that astronaut come back younger than they would be if stayed on earth, specially the part that says: “…but actually their velocity time dilation has a bigger effect…, …so astronauts end up aging slower than people on Earth”. So, he is puzzling why the astronaut gets younger if he can claim to be at rest. Therefore, the rounds trip: earth->ISS->earth, his implicit in his question, especially in the second paragraph. – J. Manuel Jul 04 '19 at 14:03

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If you want to talk about special relativity you have to learn about it.

Inertial frames are important to special relativity:

An inertial frame of reference in classical physics and special relativity possesses the property that in this frame of reference a body with zero net force acting upon it does not accelerate; that is, such a body is at rest or moving at a constant speed in a straight line

...

All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity

So the simple answer is that it is only inertial frames where time and space can be transformed to each other with no measurable effect.

Rotating frames, as the rocket going around the earth , are not inertial frames. This means that one can decide which frame is rotating and which is not. The earth frame is not rotating, the rocket is, thus the relativistic effects can display themselves making corrections to the rocket timing. This is taken into account in the GPS measurements:

Because an observer on the ground sees the satellites in motion relative to them, Special Relativity predicts that we should see their clocks ticking more slowly (see the Special Relativity lecture). Special Relativity predicts that the on-board atomic clocks on the satellites should fall behind clocks on the ground by about 7 microseconds per day because of the slower ticking rate due to the time dilation effect of their relative motion

goes on to discuss general relativity effects . Keep in mind that GPS works .

anna v
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  • The key point in OP's question is not about reference frames and relativity. He seems to be guided by the same kind of thoughts that led to the "twin paradox". Who will have is time dilated if both can claim that the other was in motion. See paragraph 2 of the question. – J. Manuel Jun 28 '19 at 17:51
  • @J.Manuel the same solution is for the twin paradox, they are not on inertial frame, the one that moves accelerates and decelerates when going and coming.. I am answering directly on the rotation the question has. – anna v Jun 28 '19 at 19:02
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It is misconception that this has to do with the twin paradox. The twin paradox is a paradox because both of them could say the other is moving relative. Now this is because speed is symmetrically relative. Though, in your case, acceleration is absolute.

The clock on the spaceship and the clock on ground has time dilation because of:

  1. SR, the relative motion of the spaceship relative to a fixed point on the ground (the clock that is at rest on the ground). It is very important to understand that the relative motion of the spaceship is relative to the clock on the ground, and though the ground is moving too (Earth rotating), the spacecraft is moving relative to that fixed point on the ground where the ground clock is. The spacecraft is is orbital, which is, a circular motion, thus, acceleration. Acceleration is absolute and in this case the spaceship is accelerating relative to the fixed point on the ground (where the ground clock is).

  2. GR, the spaceship is in a area where the stress-energy is very little compared to the ground on Earth (where stress-energy is much stronger)

The SR effect would make the clock on the spaceship tick slower. The GR effect would make the clock on the spaceship (orbiting Earth) tick faster.

The two effect's net is that the GR effect is dominant, and the clock on the spaceship (orbiting Earth) ticks faster.

or clocks on GPS and Galileo satellites running slightly faster.

https://en.wikipedia.org/wiki/Time_dilation

Árpád Szendrei
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  • This answer is missing the key point in OP’s question. Who is orbiting what? The OP don’t seem to doubt about the existence of inertial frames of reference; he wants to know why does the astronaut’s watch will be “delayed by a detectable amount of time compared to an identical watch left back on Earth” and not the other way around. This is clear on paragraph 2 of the question. Who is at "rest". – J. Manuel Jun 28 '19 at 17:41
  • @J.Manuel like you see the other answer's comment, it is about the fact that the spaceship as it orbits, is not in an inertial frame. The orbiting spaceship is accelerating. That is why there is no paradox. – Árpád Szendrei Jul 04 '19 at 11:28
  • I undestand. The point in my comment and the core in OP’s question is: “Who is accelerating? The spaceship or the earth?”. Accelerating or not, who is moving. Ask any astronaut right now in the ISS and they will tell you that they don’t feel any acceleration. As far as their concern, earth is orbiting them. Therefore, if everybody can claim to be at rest, why do we affirm that after the astronauts come back to earth, their clock will be the one with an earlier time then the rest of us? This is exactly the core at the so called “twin paradox” with a slightly different setup. – J. Manuel Jul 04 '19 at 13:27
  • @J.Manuel this is the point where you go wrong "Ask any astronaut right now in the ISS and they will tell you that they don’t feel any acceleration. As far as their concern, earth is orbiting them." The reason they do not feel the acceleration, is that the rate of acceleration is very little, and it is a nonlinear acceleration (orbital motion) and that they are inside the spaceship, floating anyway. The twin paradox is only true for linear motions, and constant velocities. – Árpád Szendrei Jul 04 '19 at 13:48
  • Orbiting is just "falling forever". A falling person never feels himself falling. This is the equivalence principle. – J. Manuel Jul 04 '19 at 14:32
  • @J.Manuel correct, but that equivalence principle says, that a free falling person cannot tell, whether he is in a gravitational field or accelerating. Free falling is accelerating. – Árpád Szendrei Jul 04 '19 at 17:42