# Which one is moving?

## Main Question or Discussion Point

if we have two particles, one is stationary, the other powers off in a circular loop around the other close to c. If there is no external measurement of time of position how do we know which one is moving or should experience time compression? what happens?

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phinds
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if we have two particles, one is stationary, the other powers off in a circular loop around the other close to c. If there is no external measurement of time of position how do we know which one is moving or should experience time compression? what happens?
(1) saying "one is stationary" is a meaningless statement. You have to say stationary restive to WHAT.
(2) Anything in rotating motion is accelerating and acceleration is not relative the way linear motion is so you know for sure that the "rotating one" is moving.
(3) What's also true is that they may both be moving relative to something else.
(4) NOTHING "experiences time compression" (and I assume you mean "time dilation" which is the proper terminology). Time dilation is something measured from a reference frame that is moving relative to the thing that is said to have time dilation, NOT in the frame of reference of that thing.
(5) If you want to understand time dilation, length contraction, differential again, etc, start with two things in linear motion. Acceleration complicates things.

1> I agree, in the absence of a frame of reference they are equivalent.

2> see 1, through what

3> the spontaneous existence or annihilation of something else should not effect the observation of the initial two objects relative to each other.

4> I beg to differ, that is the question I am asking, if it can be dilated for one observer it is implicitly compressed for the other, without getting back into the external reference debate.

5> Spin and angular momentum seems way more puzzling than linear mechanics to me.

Ben

phinds
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4> I beg to differ, that is the question I am asking, if it can be dilated for one observer it is implicitly compressed for the other, without getting back into the external reference debate.
Differ all you want, you are wrong. NOTHING "experiences time compression (/dilation)". You can OBSERVE time as dilated in another body but you cannot "experience" it yourself. Perhaps you are confusing time dilation with differential aging.

If you see an object as time dilated, it sees you as time dilated.

while I may use the "wrong" words, I do know that a satellite and even people on top of a mountain compared to those in the valley will all struggle to agree on who;s atomic clock is correct. How do you rationalize inflation post bang in any other terms than I am already advocating?

phinds
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while I may use the "wrong" words, I do know that a satellite and even people on top of a mountain compared to those in the valley will all struggle to agree on who;s atomic clock is correct. How do you rationalize inflation post bang in any other terms than I am already advocating?
(1)I don't know what "inflation post bang" means (unless you mean the expansion of the universe or the inflationary period but I can't see how either one of those has any bearing on the topic at hand).
(2) You have changed the nature of your question from time dilation due to motion to gravitational time dilation. Please make up your mind which one you would like to discuss.

1> is implicitly clear. And its relevance is that space can expand faster the c while the matter within it may not be able to.

2> I have been very clear, in the absence of a frame of reference.....

PeterDonis
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if it can be dilated for one observer it is implicitly compressed for the other
No, it isn't. You are leaving out relativity of simultaneity. And you are incorrectly conflating the case of two observers both moving in straight lines at different speeds, with the case of one observer moving in a circle.

For the case of two observers moving in straight lines, but with different speeds, there is no common notion of simultaneity. So each one sees the other's clock running slow, but each one also sees relevant events like when light signals arrive or depart happening at different times. These differences all fit together into one coherent 4-dimensional spacetime picture. If you are not familiar with how that is done I suggest working through a good textbook on special relativity, such as Taylor & Wheeler's Spacetime Physics.

For the case of one observer moving in a circle around the other, the circular motion is periodic, which establishes a common notion of simultaneity. According to this common notion of simultaneity, the clock of the observer moving in a circle is running slow compared to the clock of the observer who is in the center, and both observers will agree on this.

None of these facts depend on having any external reference.

phinds
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1> is implicitly clear. And its relevance is that space can expand faster the c while the matter within it may not be able to.
(1) It is not clear. I've offered two possible explanations and you have not said which one you are talking about, not that it matters really since neither one has any relevance to the subject at hand
(2)It's not that "matter within it may not ... ", it's that "matter within it definitely cannot"
(3) Space does not "expand". Space is just geometry. Google "metric expansion". Space-time expands.

2> I have been very clear, in the absence of a frame of reference.....
I don't think so, and you still have not cleared up what you are talking about. First you were talking about time dilation due to motion and then you started referencing gravitational time dilation. Please decide which one you wish to discuss.

ok. what i am struggling with is, how does each party know which one is moving relative to the other. my thought experiment is not so much an orbit, but one where A and B intersect as A leaves B in a circle and re intersects and B on the loop back. From A's perspective did not B move and visa versa.

PeterDonis
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how does each party know which one is moving relative to the other
There is no such thing as "which one is moving" in any absolute sense. Motion is relative. Unless the two observers stay together for all time, then each one is moving relative to the other.

phinds
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ok. what i am struggling with is, how does each party know which one is moving relative to the other.
They are both moving relative to the other.

EDIT: I should just bow out. Peter's answers are better and faster

ok, so if they are equivalent because they are both having the same movement relative to each other, then who's clock slows down? that I really dont get?

if there is no external "clock" and you move away and back relativistically to me then your clock should be slow, but we are mirrors of each other? what am I missing?

russ_watters
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if we have two particles, one is stationary, the other powers off in a circular loop around the other close to c. If there is no external measurement of time of position how do we know which one is moving or should experience time compression? what happens?
[separate post]
ok. what i am struggling with is, how does each party know which one is moving relative to the other.
Your scenario is not symmetrical and you have actually defined which one is stationary and which one is moving in your first sentence. Maybe you only know it instinctively, but here's the reason for it: the "moving" particle is the "moving" particle because it was accelerated away from the rest it started with. The "stationary" particle remains "stationary" because it didn't experience an acceleration. This is how we know which has the slower clock (the "moving" one).
(1) saying "one is stationary" is a meaningless statement. You have to say stationary restive to WHAT.
You don't really need to say relative to what in this context, since reference frames aren't objects. In this scenario the starting point is that the two particles are stationary with respect to each other. This fully defines the reference frame they are stationary with respect to (themselves/each other).

This objection is mostly relevant when there is an assumed but unspecified reference frame, which we see in questions of the type: "how fast is Earth REALLY moving?".
There is no such thing as "which one is moving" in any absolute sense. Motion is relative. Unless the two observers stay together for all time, then each one is moving relative to the other.
The OP didn't ask or suggest absolute motion. That isn't the question. The question is why does one clock (the one "orbiting" the other) demonstrably tick at a slower rate than the other. And the reason it that it is accelerating.

Guys, it really doesn't seem like you are answering the question being asked, but rather picking up on ambiguity in the wording (which isn't all that ambiguous) and focusing on the ambiguity instead of the question.

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PeterDonis
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Moderator's note: Thread moved to the relativity forum.

PeterDonis
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if they are equivalent because they are both having the same movement relative to each other, then who's clock slows down?
There is no such thing as a clock "slowing down" in an absolute sense. Time is relative; there is no absolute time. Each one sees the other's clock slowing down.

PeterDonis
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if there is no external "clock" and you move away and back relativistically to me then your clock should be slow, but we are mirrors of each other?
If one of us accelerates and the other doesn't, then we are not "mirrors of each other"; there is an observable physical difference between us (one of us feels acceleration and the other doesn't). In this case, the one who doesn't feel the acceleration will have aged more (had more elapsed time) when the two come back together.

alright, but acceleration is a function of time and distance. If A loops out and back to B, lets say linearly to keep things simple, unless there is an external frame of position, then I can not accelerate through it, in my simple brain, for all the bits of relativity to make sense about acceleration and time, you have to have an external clock to reference it to. If everything is floating, and there is no "stuff", even if that might be progression through / or acceleration as the case might be - space time related to graverty dimples - if everything is amorphous then I dont see how it hangs together. However, if my movement is relative to some external register then it makes perfect sense, but everyone tells me there is no positional or temporal coordinates that we can measure things by as there is no frame of reference. Surely we can track our movement through time and gravity to provide that external cosmic dateum. clearly very confused!!!!!

Nugatory
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ok, so if they are equivalent because they are both having the same movement relative to each other, then who's clock slows down? that I really dont get?
If A and B are moving relative to one another, then both will correctly find the other's clock to be slower. Because of relativity of simultaneity, there is no contradiction and they're both right. This is time dilation.

If A and B start together, separate, and then rejoin (for example one is moving in a circular path so they meet up once on every rotation, or one of them flies around the world while the other stays put, or one takes a spaceship on a long trip away from earth and back again) they will experience different elapsed times between separation and rejoining. Both will agree about which one experienced more elapsed time - although because of the time dilation I describe in the previous paragraph, both will also agree that the other one's clock was running slow during the entire journey. This is the famous "twin paradox". The explanation is that they took different paths through spacetime to get from the separation to the reunion.

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PeterDonis
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acceleration is a function of time and distance
Which are relative. So it's better to think of acceleration the way relativity tells you to think of it: as proper acceleration, i.e., the acceleration you actually feel, and measure with an accelerometer. The proper acceleration of an observer at a particular point on his worldline is an invariant, independent of your choice of coordinates, reference frame, or anything else. Notice that when I described the difference between two observers in post #18, I did it in terms of one feeling acceleration, not in terms of any function of time or distance.

In other words, you are trying to think of "time" and "distance" as fundamental; but one of the key things you need to understand relativity is that you have to stop doing that, because they're not.

Nugatory
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alright, but acceleration is a function of time and distance....
You are confusing two things: coordinate acceleration which is a function of time and distance, and proper acceleration which is not. Proper acceleration can be directly measured without any external reference (an accelerometer will do that) and an object's proper acceleration is the same in all frames.

Because the two observers undergo different proper accelerations their situations are not symmetric, so there is no reason to expect that they must both have the same experience. This is in contrast with the time dilation that I described in the first paragraph of the post above; there they both experience zero proper acceleration so the situation must be symmetric.

I really have to repeat the advice above: get hold of Taylor and Wheeler. The time you spend studying it will not be wasted.

alright, my brain just exploded. For the sake of discussion, while clearly not universal, if we came up with a way of agreeing the passage of time against the CMR, that we would have an external clock? On one hand we seem to say their is no clock, they all float, but you cant go faster than light. While C maybe true, in the absence of A or B, it clearly is not true. If I asked a computer to carry out a complex calculation that we knew would take 1 second and we sent these two computers off in a linear line. or one stationary and the other moving in a circle, or both of them accelerating in a semi circle - argh, I still dont see how we know which one moves / accelerates relative to the other unless we measure that acceleration from outside the system.

Nugatory
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argh, I still dont see how we know which one moves / accelerates relative to the other unless we measure that acceleration from outside the system.
That's what an accelerometer does: Take a box; put a small weight in it; fasten that weight to each of the six sides of the box with six stretched springs; very carefully measure the length of each spring. If the box is accelerated (we're talking proper acceleration here) those lengths will change as the springs stretch, so we have a device that measures acceleration without external reference.

PeterDonis
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while clearly not universal, if we came up with a way of agreeing the passage of time against the CMR, that we would have an external clock?
Not in the sense you mean. We could all agree to use "CMB time" to set our clocks, but this time is still relative; it's the time measured by clocks that are at rest relative to the CMB, i.e., carried by observers who see the CMB as isotropic (looking the same in all directions). Time measured by these observers is still relative, and you still have to deal with all the same issues if you start talking about other observers moving relative to them.

On one hand we seem to say their is no clock, they all float, but you cant go faster than light. While C maybe true, in the absence of A or B, it clearly is not true.
Yes, it is. "You can't go faster than light" just means "the speed of any light ray, relative to you, is always $c$". It means you can't catch up to a light beam. Those statements do not require any absolute notion of space or time, or any absolute notion of who is moving or who is at rest, or any absolute notion of speed. They only require relative notions of all these things.