Frame of Reference: Does Stuff in the Frame Matter?

[soup_]

Okay, weird question. Sorry if this is really stupid but it's been bugging at me for days now.

First, let me lay out my current assumptions/understanding of what's going on.

The current theory seems to be (to an amateur like myself) that there is no fixed space-time. That to talk about an absolute point in space or in time is meaningless. (1)

We can only talk about what we can observe from are own frame of reference. For example, I've heard that in some sense the edge of the observable Universe is something like 40 billion light years away (as the Universe has been expanding since the light left those distant points) but since the light (and therefore time) from the edge has taken 13.7 (or whatever) billion years to reach us, this is the distance we say it is from us as there is no sense of the word distance that would be appropriate to describe it as 40 billion. (2)

Therefore, there should be no difference to the Universe between our galaxy sitting still and every other galaxy moving away from us and, say, Andromeda sitting still and every other galaxy (including ours) moving away from it. Since there is no absolute frame of reference, we can't tell which it is (3) and it really doesn't matter. (4)

Ok, now into the troubling stuff.

Does this mean that if I stand in my yard and throw a ball down the street that there is no way to say for sure whether the ball is moving away from me or (especially if I have a pet cockroach sitting on the ball) if the ball is sitting still and the entire universe, or at least some big part of it surrounding the ball, is moving? (5)

If (5) is incorrect, that there is a difference, then I feel like one of my understandings above has to also be incorrect. Eg. There must be an absolute frame of reference, etc.
If (5) is correct, that there is no difference, then I am confused :)

Let's say I perform the atomic clock experiment where I have two synced up atomic clocks. I sit in my yard with one of them and I fire the other one into space. It goes around the Earth a few dozen times at a good speed and then (because I'm an awesome amateur rocket scientist in this hypothetical) it's on-board computer brings it safely back to me. I would observe that the clock I fired up has _lost_ time. That is, it will be behind the clock that's been holding my beer while I waited for the one in space to come back to me, correct? (6)

Ok, cool. Now what if instead of getting it to orbit the earth, I get it to orbit the sun? What if I launched it in mid summer, made it follow Earth's orbit at the same velocity as Earth but in the opposite direction, and had it land back in my yard in mid winter? What would the clocks read? (7)

What if I launched it in mid summer, again following Earth's orbit in the opposite direction, but this time tried to give it velocity such that it would land in my yard exactly one year later (ie. zero velocity in some sense, but obviously it is moving away from me at the rate at which the Earth traces it's orbit around the sun)? What would the clocks read? (8)

Ok, now suppose my distant cousin James, who lives on Jupiter nowadays, has been having the same issue with relativity. He knows what I've been up to and he's got an experiment of his own. He gets in his spaceship with a couple of atomic clocks and heads on over to Earth. But instead of landing on Earth and repeating my experiment he decides to give it a twist. He hangs out in the Earth's orbit around the sun, perhaps resting his beer on the clock I've just launched in (8) and sends one of his clocks to sit in my yard while he waits for the Earth to go around the Sun. After a year has passed, his clock shoots back up and he collects it with his Canadarm. I guess if he's feeling nice, he can also take his beer off my clock and let it back out into space so it can return to me and I can record my observations.
So, what would the clocks read? (9)
Let's call my clocks EY (Earth,yard) and ES (Earth,space) and my cousin's clocks JS (Jupiter,space) and JY (Jupiter,yard - being the one that sits in my yard).
Obviously, I don't care that JY and EY have never been synced and I'm only interested in EY relative to ES and JY relative to JS.

I feel like the experiments should match up. That it shouldn't matter that I'm sitting in my yard while all this is happening and he's sitting in his space ship. On the other hand if we both observe the same thing, let's say the clocks in space both lose time relative to the clocks on Earth, then James will have experienced the clock that was away from him having sped up while I would have experienced the clock that was away from me as having slowed down. Why? What's the difference? It feels like we've both performed the same experiment so shouldn't we observe the same results? (10)

If you disagree that we have performed the same experiment, then let me throw one more hypothetical. James and I meet up in space. Me in my space ship, him in his. Together we go past the edge of the Milky Way, out into no man's land. It's a long trip but we've discovered the secret to immortality, so we're fine. Once we get out a good distance from any galaxies, we sync up all four clocks. We exchange one set of clocks (or not, whatever) and we both engage our thrusters full throttle away from each other for a year. After a year is up (let's say we count in our heads, 1-one thousand, 2-one thousand and we are perfect counters) we reverse direction and meet back up in the middle. What do the clocks read? (11)

I guess that brings me to the "how much stuff is in the frame" part of my question. If clock ES slows down relative to clock EY in (6), (7), or (8), then why? Why not the other way around? The only reason I can fathom is that I have the Earth with me and this changes things somehow, but that doesn't make any sense... does it? (12)

Thanks for your patience,
soup

 

[Drakkith]

You still need one starting reference point to measure all this from. If your two spaceships are between galaxies when you meet, then they have some velocity unless you've slowed down. Because you have a velocity in relation to the rest of the universe, then you can't simply assume that your two clocks will read the same after you both fire your rockets away from eatch other. If he continues to accelerate and you slow down instead, then your clock starts to move faster in relation to your starting point, while his continues to slow down in relation to both yours and the starting point. Until you reach your initial velocity at the start, then your buddies clock with be ticking at different speeds in relation to yours and the initial points clock.

If, for example, your buddy decided to decelerate while you continued to drift at a constant velocity, then his clock would speed up in relation to yours until he was at his starting velocity in the initial frame of reference, at which time both his and a clock left in that frame would be ticking at the same rate, while yours would still be slower.

 

[soup_]

You still need one starting reference point to measure all this from. If your two spaceships are between galaxies when you meet, then they have some velocity unless you've slowed down. Because you have a velocity in relation to the rest of the universe, then you can't simply assume that your two clocks will read the same after you both fire your rockets away from eatch other. If he continues to accelerate and you slow down instead, then your clock starts to move faster in relation to your starting point, while his continues to slow down in relation to both yours and the starting point. Until you reach your initial velocity at the start, then your buddies clock with be ticking at different speeds in relation to yours and the initial points clock.

If, for example, your buddy decided to decelerate while you continued to drift at a constant velocity, then his clock would speed up in relation to yours until he was at his starting velocity in the initial frame of reference, at which time both his and a clock left in that frame would be ticking at the same rate, while yours would still be slower.

Hey, Drakkith. Thanks for your reply. I'm not sure I understand why it matters what the rest of the universe is doing. That is, how is it possible to have a "starting reference point". If we meet out in the middle of nowhere, our velocity and position relative to, say, Earth, seems irrelevant to me. You say "If your two spaceships are between galaxies when you meet, then they have some velocity unless you've slowed down." But relative to what? Looking at each other, we are standing still. Looking at the galaxies around us, some are moving towards us, some away, etc. Now let's sync up three clocks. We'll put one between us (we'll call it N for nowhere) and each hold onto one (ES and JS).

Scenario 13) We both activate our thrusters 1 million m/s directly away from each other for one hour then reverse the direction at 1 million m/s and meet back up at clock N.

Scenario 14) I don't activate anything. James activates his thruster away from me at 2 million m/s and clock N has a thruster and thrusts away from me (and towards James) at 1 million m/s. After an hour (counting on their own time), clock N and James reverse directions and we all meet back up again some time later.

In both scenarios, what will the clocks read when we meet back up?

 

[Drakkith]

You MUST have an initial frame to measure from.

Using scenario 13: If you are already moving forward, and both of you activate your thrusters and accelerate perpindicular to your forward movement (You'll be heading sideways relative to your forward movement), then when you meet back up, both of your clocks will read exactly the same, while clock N will read as having ticked faster.

Instead, if James turns around and activates his thrusters in the opposite direction that he is traveling, and you continue to accelerate in the direction you are already going, then when both of you meet back up, your clock will be slower than his, because you added velocity to yourself, while he decelerated.

In scenario 14: James clock will read as having gone slower than Clock N, while Clock N will read as having gone slower than your own clock, but faster than James's clock.

This is all based on my own knowledge of relativity, so i could be wrong here. I'd be grateful if someone reading this could tell me if I am right or wrong.

 

[pervect]

Lets do some simpler, but related, thought experiments. Suppose you have a clock on the ground. It's feeling gravity. But you toss another clock up in the air, a few hundred feet, so that it goes up, and lands back down. And it's a super-shock resistant clock, so it doesn't break, or jar when you toss it up, or when it hits the ground. You'll find that the clock you tossed up in the air reads a longer elapsed time than your 'stationary" clock at the Earth's surface.

The difference will be very small, but the effect that works in your favor will be the height of your thrown clock. Higher clocks tick faster. The fact that your clock is moving works against you, but it gains more time from being at at a higher altitude than it looses from its motion. It's possible to even write the equations of motion for the clock from this principle - the principle that it maximizes proper time.

This is what you expect from the general idea that "falling objects travel along geodesics", and that "geodesics extremize proper time". The clock you tossed up in the air is following a geodesic - the clock left on the ground, wasn't. Unfortunately, things aren't quite this simple. There's that word "extermize" in there, after all, not "maximize".

You can imagine three clocks, now. One is in low Earth orbit (at sea level!). One is lying on the ground. One is one you toss up, at just the right angle so that it falls back down at your starting point (it won't be quite straight up, it'll be some parabola so that it matches the Earth's spin.

You'll find that the clock you tossed almost straight up still has the longest elapsed time. The clock that was "stationary" on the surface will be in the middle. The one in the low Earth orbit will have the lowest elapsed time.

This demonstrates the next pitfall. All geodesics are not created equal - though they may "extremize" proper time, if you have multiple intersecting geodesics, they are not guaranteed to have the same proper time, and a geodesic path can actually have a shorter proper time than a non-geodesic path.

Life is simplest if you restrict yourself to a "small enough" region of space-time, so that multiple geodesics don't exist.

But, you may be intersted in the general case - how do I maximize the proper time of my clock, so that it has the universally longest time of any clock connecting the same two points. Well, you know that such a path of extreme time has to be a geodesic. The longest time is an example of an extreme, though as we see the reverse isn't true. So, we have to pick the right direction to launch our clock - one of them will give us the longest elapsed time. A little bit of thought and calculation tells you what the proper direction is - to regions of lower gravitational potential. If you've got enough time, you want to get it away from not only the Earth, but the Sun (but still have it land back in the same spot). With even longer periods of time, you might want to have the clock leave the galaxy. Though at this point the experiment starts to loose any real human interest, as you'll be long dead before it could return, and the Earth might not be there when you get back anyway.

 

[Drakkith]

I thought the moving clocks would tick slower, not faster.

 

[soup_]

Drakkith, I have a strong intuition that scenarios 13 and 14 are the same. If you ignore the thrusters and picture only the clocks, let's say from a birds eye view, and keep your camera centred on clock N, the two scenarios are identical. If you are not happy the fact that, say, the Milky Way, is moving differently relative to the group then imagine that before I start my experiment I give all the clocks an initial velocity that will ensure clock N's motion relative to the Milky way will be exactly the same in both scenarios.

See, my initial thought was that the results would be different some how, as you have also suggested, but after examination it seems ridiculous to me that where the thrusters are would change anything, since the motion of the clocks would be exactly the same relative to each other.

Am I drawing you into my confusion?

Life is simplest if you restrict yourself to a "small enough" region of space-time, so that multiple geodesics don't exist.

I see. I was not aware that gravity might be playing such a role in my initial set of questions. So, can you tell me, pervect, if in Scenario 13 and 14 one would be able to neglect this effect. Also, can you answer my question about what the clocks would read in these scenarios?

 

[soup_]

Ok. I think I've got it figured out.

You can't ignore the thrusters as I suggested. For some reason, the universe knows the accelerations at the start of and half way through the experiment. So even though the velocities are all the same when looking from above, the fact that in scenario 14, clock N is actually accelerating and my ship is virtually accelerating makes the difference. i.e., My ship only looks like it's accelerating from the point of view of someone who is sitting on clock N.

So what does that mean. If space really does have no absolute nature, then is the difference between actually accelerating and virtually accelerating due to the extra matter that gets left behind by the thrusters, that is, the force on the particles? (15)

Thanks for the help everyone.

 

[Mentz114]

soup,

then is the difference between actually accelerating and virtually accelerating due to the extra matter that gets left behind by the thrusters, that is, the force on the particles? (15)

Something like that.

The difference between "actually accelerating and virtually accelerating" is that you can feel 'actual' (proper) acceleration, but not the other. If you aren't standing on a rock, or in an accelerating something, you are in free fall and ... well, fall freely ! With proper acceleration, like rocket motors or solar sails, Newton's law of equal and opposite reaction gives the push. In free-fall there's no push and it feels like floating.