Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: yor_on on 07/04/2012 09:15:28
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Assume two ships accelerating uniformly beside each other, and in the same direction.
Each one will have its own local (same) 'gravity', equivalent to the acceleration.
Do those fields influence each other?
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NO
If you are talking about gravity due to acceleration.
Say, a couple of m/s2
Then two side-by-side ships would be independent, and not affect each other. There would be no difference between that and building one ship twice as large.
If a spaceship was tailgating another spaceship, it is possible that the exhaust from the first ship would slow down the second ship. However, the gravity felt inside the ship would solely be dependent on the actual acceleration of the vessel.
Two rotating artificial gravity modules would also be independent in space and not affect each other.
Did you have a different hypothesis? Why?
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Although there would be the normal gravitational attraction between the two vehicles due to their masses (very small) is it possible that psuedo gravity generated by their acceleration would also have an attractive effect ?.
If they were accelerating at 9.82 m/s/s the occupents would feel the same gravity as they would from a 6*10^24 Kg body 6400 Km away, I think this is a GR question.
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Energy is mass according to Einstein.
Is there energy expended in a acceleration?
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The force of attraction between two bodies at rest, at the same velocity, or undergoing the same acceleration would be the same, except that the consumption of fuel would mean a decreasing mass.
The artificial gravity created by constant acceleration is due to inertial differences. I can not imagine how it could possibly extend beyond its reference frame, the ship itself.
The acceleration is changing the weight of the occupants, but it is not changing the mass of the occupants.
Isn't relativity based on velocity, rather than acceleration.
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If they are accelerating uniformly relative to Earth, their mass in Earth's reference frame will increase as they approach the speed of light. So both their inertia and the force of attraction between them will increase proportionately in Earth's reference frame, and the gravitational acceleration toward one another will remain constant.
Sorry about that. The gravitational force pulling the ships toward one another is proportional to the square of their mass, while the inertia is directly proportional to the mass. So the acceleration of the ships toward one another should be directly proportional to their mass. If special relativity increases the gravitational mass, as the ships approach c in Earth's reference frame, then gravity between the ships should cause them to orbit one another more rapidly in Earth's reference frame. This seems paradoxical. As the ships approach the speed of light in Earth's reference frame, the ships clocks must run slow in Earth's reference frame. But the orbital period of the ships has to be proportional to the passage of time on the ships. As clocks on the ships run more slowly, the ships should orbit one another more slowly. If gravitational mass of the ships is constant, but their inertial mass is increasing, their orbital period will slow in proportion to the time dilation.
Of course, to simplify the problem, I'm pretending they don't use up any fuel. In reality, their rest mass will decrease by the amount of fuel consumed.
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Assume two ships accelerating uniformly beside each other, and in the same direction.
Each one will have its own local (same) 'gravity', equivalent to the acceleration.
Do those fields influence each other?
Perhaps fields is the wrong word when talking about warped space-time (gravity).
(1)As I understand it there are no fields to interact (assuming the spaceships not to have sufficient mass or speed to produce noticeable space-time warp).
A spaceship accelerates primarily within spacial dimensions. The effect is short range and only felt by something in contact with the ship.
A gravitating mass accelerates primarily within the time dimension (space-time). This is gravity and it is long range.
(1) this is only approximately correct as all mass warps space-time. However, a space ship is unlikely to warp space-time enough to be noticeable. (Unless having considerable mass or travelling close to the speed of light.)
So, the answer to the question is essentially no.
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I have always assumed that relativistic mass applies to both inertia and gravity. Apparently, I was wrong. See the edited version of my previous post.
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I think we can use 'fields' for it?
The other way is to define it as creating 'geometrical warp-holes' of a sort :) as we then approach it purely geometrically, but 'fields' feels more intuitive for this. As for inertia and 'Gravity' being two sides of the same coin, they should be, shouldn't they? But to push/deflect something moving from/at its 'side' must always be easier than to try to push/deflect its motion, meeting it up front, so to speak. And if you accelerate something its inertia (resistance to motion) must grow, until it becomes infinite near lights speed, well, as I see it.
And it seems that the toughest thing is to meet it from the front, much in a similar way to how a Lorentz contraction is defined to 'work' only in the direction of its motion, and not 'sideways'.
It's not the mass that grows, as I think of it, but the inertia surely must.
Or we can use relativistic mass/energy and define it as it is this that 'grows' here.
So we have a equivalence to 'gravity' inside each ship, but you all seem to assume that this gravitational potential has to be restricted to the local 'insides' of the respective ships only?
Except you Phracticality :)
If I get you correct?
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yor_on
What I said was
"a space ship is unlikely to warp space-time enough to be noticeable. (Unless having considerable mass or travelling close to the speed of light.)"
It's all relative.
A spaceship accelerating at 1g (through space) gains velocity.
The surface of the Earth accelerating at 1g (through time) does not gain velocity.
Gravity is a long range effect but it requires a very large mass or a small mass travelling at very high velocity (close to c) for it to become a noticeably effect.
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"As for inertia and 'Gravity' being two sides of the same coin, they should be, shouldn't they?"
Gravity and acceleration in a sense yes but essentially the same side of the same coin.
Inertia is in a sense a property of mass as is gravity. So I suppose you could consider them to be opposite sides of the same coin in as much as gravity is concerned with making objects accelerate. Inertia is concerned with objects not accelerating.
Interesting point I need to give it more thought when I have time but my initial impression is inertia and gravity are not the same thing but may well be different aspects of the same thing.
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I need to correct myself here, although I'm not sure I'm agreeing with myself now either:)
Inertia, is it a property intrinsic to matter?
If it is it can't really grow with an acceleration, can it?
Then there is only the momentum that can grow.
So what is it that 'slows' you down infinitely, as you come forever closer to lights speed in a vacuum?
Relative mass is one expression, momentum another, what more?
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To see my point imagine it as 'forces' having 'arrows' that point towards the way they want to go. A momentum will always point in the direction of the motion of the 'force', whereas inertia will act the opposite, as I see it.
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So what is it that 'slows' you down infinitely, as you come forever closer to lights speed in a vacuum?
Relative mass is one expression, momentum another, what more?
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What more? Time you run out of it.
Think of space time as two vectors, one for space the other for time. The more you use of one the less you have available of the other. As your speed approaches c so you run out of time as time approaches infinite dilation.
Another way of thinking of it.
Approaching c mass increases towards infinity. This requires energy to approach infinity to further increase acceleration. By the mass/energy equivalence principle mass further increases towards infinity. Infinite mass means infinite gravity and zero passage of time.
As you approach c you literally run out of time.
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yor_on
How about this.
Inertia.
A property of matter by which it continues in its existing state of rest or uniform motion in a straight line, unless that state is changed by an external force.
Any freely moving object whether it has or does not have mass follows a geodesic in space-time. It will continue in this geodesic unless acted upon by an external force.
So, it would appear that a geodesic in space-time and inertia are essentially the same thing. Inertia then like gravity is a property of warped space-time. Gravity is the geodesic, inertia is why objects follow the geodesic. The geodesic represents the path of least resistance.
What do you think?
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Sort of elegant Mike, although I need to think about it some more. A geodesic is indeed (a result of) 'gravity', and when objects following a geodesic is acted upon they find inertia. But then you have something accelerating, if acted upon that too will find a inertia, but it is not following a geodesic. The idea has a certain symmetry to me though, and SpaceTime seems very much to be about symmetries.
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I think we could simplify this Question and instead of spaceships ask do highly accelerated particles in the LHC bunch due to gravitational attraction or do coulamb forces overwhelm this effect.
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Sweet idea Syhprum :) as with very high energies there must be a complimentary 'locally' strong gravity. What energies and what rest mass would we be talking about there? From that one should be able to calculate the 'gravity' at the end points of their trajectories, colliding I mean. And also, maybe, (?) be able to see if they've diverged due to experiencing gravitational 'forces' in their paths, although considering their accelerations I suspect that effect might be negligible, as too small to be noticed by our instruments?
But accelerating something in a particle chamber there must be a strong local gravity. What will it do to a particle near light?
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Sort of elegant Mike, although I need to think about it some more. A geodesic is indeed (a result of) 'gravity', and when objects following a geodesic is acted upon they find inertia. But then you have something accelerating, if acted upon that too will find a inertia, but it is not following a geodesic. The idea has a certain symmetry to me though, and SpaceTime seems very much to be about symmetries.
Thank you.
If it's accelerating it's not following a geodesic and therefore inertia does not apply. ???
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I think we could simplify this Question and instead of spaceships ask do highly accelerated particles in the LHC bunch due to gravitational attraction or do coulamb forces overwhelm this effect.
I don't know but I suspect that coulomb forces would still overwhelm the effect to a large extent.
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Now that's tricky Mike :)
If we assume that inertia is a intrinsic property of matter you must be wrong. If we assume that inertia is 'the tendency of a body to maintain its state of rest or uniform motion unless acted upon by an external force' then you might formulate it that way?
So, what is it?
A intrinsic property, or a special circumstance?
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Now that's tricky Mike :)
If we assume that inertia is a intrinsic property of matter you must be wrong. If we assume that inertia is 'the tendency of a body to maintain its state of rest or uniform motion unless acted upon by an external force' then you might formulate it that way?
So, what is it?
A intrinsic property, or a special circumstance?
I never said it was. It is an intrinsic property of space-time that affects matter.
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It all depends of course. Normally I would call inertia a property belonging to matter, but then the question is if it is there existing in a acceleration too? If it is a 'intrinsic' property it should. And then the next question will be if it is thought of as some type of unvarying property, as the modern definition of a rest mass? If it is so then momentum and 'energy' can be used to describe what properties we expect to raise in a acceleration, but not the inertia.
But if I imagine something moving and I then stop it. Is it its inertia that comes to rule in a uniform motion? But not in a acceleration? :) I would call that pretty weird if it was so?
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It can't be unvarying as you can have different 'uniform motions' as defined relative Earth for example. The inertia of a object moving faster than its twin should differ? Da* I'm not sure I understand the definition of inertia at all? As a resistance to motion I can see it, but when it comes to uniform motion versus an acceleration?
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Okay, I'm changing track here it seems :)
Didn't mean to do that, let's get back to the original question instead. We can use 'relativistic mass' or 'momentum' to define anything moving. And as relativity defines all 'motion' as questionable :) unless as defined relative something 'inertial' as being in a 'uniform motion'? Inertia hurts me head. but so do 'motion' ::))
So, are we happy with defining a accelerating ships 'gravity' to its own 'intrinsic' properties, ignoring the mass, or do we think that two accelerating ships/particles will influence each other gravitationally to a higher degree the faster they move relative Eh, Earth :)
It also have an importance for the view in which we imagine all accelerations as continuous displacements of a uniform motion, as it seems to me?
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Okay, I'm changing track here it seems :)
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So, are we happy with defining a accelerating ships 'gravity' to its own 'intrinsic' properties, ignoring the mass, or do we think that two accelerating ships/particles will influence each other gravitationally to a higher degree the faster they move relative Eh, Earth :)
It also have an importance for the view in which we imagine all accelerations as continuous displacements of a uniform motion, as it seems to me?
It seems to me that if the ships are traveling close enough to c then they would exhibit sufficient mass to warp space-time 'noticeably' enough to influence each other. Although their mass would always warp space-time, the effect would not become noticeable until their speed approached c.
Think of the two ships travelling parallel to each other. Imagine a line (world line) through the center of each ship in line with it's direction of travel. At low speed the world lines lines intercept a long way into the future of the ships. Approaching c the world lines intercept close to the ships. The ships world lines intercept due to their mass warping space-time.
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yor_on
When you talk about the inertia of an accelerating body is that a meaningful idea? The accelerating body must have inertia but surely, it cannot be apparent under acceleration. Acceleration must mask the effect of inertia?
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But if I imagine something moving and I then stop it. Is it its inertia that comes to rule in a uniform motion? But not in a acceleration? :) I would call that pretty weird if it was so?
It has uniform motion and hence inertia until you cause it to accelerate (stop) and it has uniform motion (zero) after you stop it, so it still has inertia. But I don't see how you can define inertia for an accelerating body? However we use acceleration to measure the objects inertia.
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Assume two ships accelerating uniformly beside each other, and in the same direction.
Each one will have its own local (same) 'gravity', equivalent to the acceleration.
Why do you assume that "local" means "is the same as"?
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I'm proposing that we have two identical objects accelerating with the same amount, as from some defined 'inertial frame of reference', as ? Well, I use Earth here, but we can use whatever you want to define as 'inertial' Pete. And I'm also assuming that the gravitational potential outside those objects is as similar as it can be.
Then, from the aspect of that 'inertial frame of reference' (Earth) their accelerations should be equivalent as I assume, and we can also assume that they find themselves being 'still' relative each other (possibly, depending on how you think of a acceleration, as displacements of/from a uniform motion to another, or not?:)
Maybe there are some things missing in this description, but for a starter it will do :)
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Mike, we better ignore inertia for this.
I think we can use momentum instead? Inertia is a description similar to rest mass in that it is a invariant local property of a object, expected to be the same everywhere, according to a main stream definition. You might say that the 'inertia' only is definable from a 'uniform motion' in relativity. Although I thought of it differently :)
But using momentum does describe it as I think of it.
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To see my point consider if different uniform motions will give you a different 'inertia'? When it comes to a local acceleration it won't as I see it. But if you're trying to stop two objects in a uniform motion, that you define as having different speeds relative you. Will the 'force' you apply be the same for making them 'unmoving' relative you?
But I keep losing the track here :)
So momentum will do for this I think?
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Mike, we better ignore inertia for this.
I think we can use momentum instead? Inertia is a description similar to rest mass in that it is a invariant local property of a object, expected to be the same everywhere, according to a main stream definition. You might say that the 'inertia' only is definable from a 'uniform motion' in relativity. Although I thought of it differently :)
But using momentum does describe it as I think of it.
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To see my point consider if different uniform motions will give you a different 'inertia'? When it comes to a local acceleration it won't as I see it. But if you're trying to stop two objects in a uniform motion, that you define as having different speeds relative you. Will the 'force' you apply be the same for making them 'unmoving' relative you?
But I keep losing the track here :)
So momentum will do for this I think?
Inertial mass M is defined as M = p/v
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So you know what inertia is then Pete :)
I've actually seen different definitions for it, as it been bothering me for a while.
Here's one good.
" Mass has two meanings, both of which can be viewed as proportionality
factors. "Inertial mass" is the factor that determines how much force
it takes to produce a given acceleration in an object, according to
Newton's first law of motion:
F = ma
"Gravitational mass" is the factor that determines how much
gravitational force is developed between two objects at a given
distance, according to Newton's law of gravity:
F = -GMm/r^2
where G is the gravitational constant, r is the distance between the
objects, and M and m are the masses of the two objects.
Inertial mass and gravitational mass are the same. (This is still the
subject of experiments seeking to verify it more and more precisely,
because it is intimately connected with Einstein's general theory of
relativity.) Because of this, the two equations above combine into
a = GM/r^2
On the surface of the earth, M (the mass of the earth) and r (the
radius of the earth) are fixed, and so a (the acceleration due to
gravity) is a constant, which we call g."
From Doctor Rick, mathforum.org (http://mathforum.org/library/drmath/view/56250.html)
So according to this inertia is equivalent to (rest) mass, as I read it?
If I use that definition then what we have in different uniform motions as I try to stop a object moving relative me is not its inertia, as that will differ relative the perceived 'speed'. Against it we have the fact that no matter your uniform motion (in space) you should expend the same amount of energy in a acceleration, or 'displacement' if you like, to start to move relative whatever frame you earlier found yourself being still relative.
Well, as I think of it.
In relativity "All inertial frames are in a state of constant, rectilinear motion with respect to one another; they are not accelerating in the sense that an accelerometer at rest in one 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).
In general relativity, in any region small enough for the curvature of spacetime to be negligible one can find a set of inertial frames that approximately describe that region."
This contains several ideas that makes sense, but inertia boggles me mind :)
And then you have its mass, which governs its resistance to the action of a force, and its moment of inertia about a specified axis, which measures its resistance to the action of a torque about the same axis. (http://www.physicsforums.com/showthread.php?t=460546) with accompanying math from PF :) as well as the definition of 'Moment of Inertia' in engineering.
And your definition too. All of them seems sort of valid to me? But then again, none of them touches uniform motion and what I should call that 'resistance' to 'stopping' as I apply a 'force' to make that object stand still relative me. As I see all uniform motion to be the same, as can be proved by accelerating something from a 'inertial frame' where its 'relative motion', meaning that 'inertial frames' uniform motion through space, doesn't matter.
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Sorry, had to add some text above to make the citation more understandable. As well as a link to that very nice and concise first citation.
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So you know what inertia is then Pete :)
If someone uses the term inertial mass as a synonym for rest mass then I disagree with them, for many reasons.
There are three terms which contain the term mass in them. They are (roughly):
1) inertial mass: m = m_i - determines how much momentum a body has. This is how Newton defined momentum in fact
2) active gravitational mass: m = m_a - the source of gravity
3) passive gravitational mass: m = m_p - What gravity acts on. Same as inertial mass.
It should be noted inertial mass density does not have the same value as active gravitational mass density.
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Ahh, I knew I didn't want to discuss this one :)
Yeah, I used inertial mass as you use relativistic mass, in my first way of thinking of it.
But inertia, as in a resistance to motion, must be directly coupled to the rest mass it consists of. And if it is so, and it not is so that this 'inertia' can be considered to grow in a acceleration, then it will be a function of the objects rest mass.
And that we can test by imagining different uniform motions of equivalent objects (in a equivalent portion of 'space'), relative some inertial frame, and then try to move that object, in its own frame, by mounting a equivalent rocket to it to see what 'force' is needed for it to begin to accelerate.
If the force locally are the same in all uniform motions, as defined differently from our 'inertial observer', then the inertia must belong to the rest mass, as I think of it :)
But then again..
Inertia is weird.
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The point is that the inertial frame 'stopping them' will in deed need a different force, but locally, as defined by the force needed to locally accelerate this object, all uniform motions should be the same. And that defines the inertia as a local expression of rest mass to me, if I'm thinking right here :)
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Hmm I'm not sure at all of that definition rereading it? As you accelerate you will find that you need more energy to accelerate, the closer you comes to lights speed in a vacuum, and as all accelerations can be described as 'displacements' from uniform motions?
Thinking that way we might use this instead.
Inertia must then be directly connected to your 'relative motion', which becomes truly weird in that inertia to know it will need a 'gold standard' of what 'relative motion' is? But it will be a fit to how I thought of it first, as responding to your (relative) motion by expressing a higher 'resistance'
You might assume it a geometrical expression relative the SpaceTime around you possibly?
I find Inertia quite frustrating.
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Let us put it like this. You define two uniform frames of motion, two equivalent earths :)
One of them moving double the speed of the other according to you measuring.
On each one you have a 'frictionless' table.
On each table you have one kg of invariant restmass, equivalent to each other.
Will you need more force to move the kg on the planet that you have defined to move 'faster', relative the other?
Or won't it matter? :)
Then we have the planets themselves, if we now mount a really big rocket to each one.
Will the force needed for a first displacement differ between them, assuming the two scenarios equivalent in all other aspects, except the speed, as measured from some 'inertial frame of reference'?
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You know Pete, you are using classical mechanic's here, right?
"In the theory of relativity, the quantity invariant mass, which in concept is close to the classical idea of mass, does not vary between single observers in different reference frames.
In classical mechanics, there are three types of mass or properties called mass: Inertial mass; passive gravitational mass; and active gravitational mass. Although inertial mass, passive gravitational mass and active gravitational mass are conceptually distinct, no experiment has ever unambiguously demonstrated any difference between them."
The invariant mass is what I use thinking of inertia, assuming it to be the same in all frames of reference. Then I assume that this mass also will be what defines inertia as well as the local 'gravity' described by it. All of those concepts should then, to me, be the same as in 'coupled' to each other. Invariant restmass, Inertia, gravity, invariant descriptions. But I'm not sure I understand Inertia at all. From a 'SpaceTime perspective' a inertial motion describes a straight path as I think of it, all uniform motions being geodesics.
Those geodesics are the absolute same as I see it, all relative motion becoming arbitrarily definitions, relative a observer. But then we have 'energy' and that 'stress' that motion places on SpaceTime. We also has a constant called 'c' that defines a limit of 'relative motion' so looked at from that perspective SpaceTime must have a way to define 'relative motion', especially if one expect different 'speeds' relative oneself to represent different inertia. It also has to do with frames of reference in that you may define motion as arbitrary relative any other single object, but what about defining it from all of SpaceTime?
For example, momentum of some inertial (uniformly moving) object. Is that a (invariant, well sort of, assuming a constant uniform motion) property of that object or is it a property between 'frames of reference'?
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To see my point here you need to reread what I wrote. The easy answer is that it is a property belonging to the object itself, depending on its 'motion', but the other answer will be that it can only exist as a property between frames of reference. And as there is no way for you to measure the momentum without using a reference frame, as relative some arbitrarily defined 'speed'' I wonder about a lot of things :)