Inertial Objects: Acceleration & Direction

In summary: This is a really good question, and it gets at the heart of why Einstein's theory of gravity (general relativity) is so different from Newton's theory of gravity.In Newton's theory, there is an absolute space and an absolute time, and if you are at rest relative to that absolute space and time, you feel no acceleration. If you are accelerating, you are definitely not at rest relative to this absolute space and time. That's pretty simple, right?But in Einstein's theory, there is no such thing as an absolute space and an absolute time. Instead, space and time are relative, and so is acceleration. So an object's acceleration can only be measured relative to some other
  • #1
jaketodd
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Are two objects, accelerating at the same rate, and in the same direction, considered inertial to one another? If so, I will post my resulting question. If not, it's safe to disregard this thread.

Thanks,

Jake
 
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  • #2
jaketodd said:
Are two objects, accelerating at the same rate, and in the same direction, considered inertial to one another?

There is no such thing as "inertial to one another". An object which is accelerating (more precisely, which has nonzero proper acceleration, i.e., an accelerometer attached to it reads nonzero) is not inertial, regardless of its state of motion relative to other objects.
 
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  • #3
PeterDonis said:
There is no such thing as "inertial to one another". An object which is accelerating (more precisely, which has nonzero proper acceleration, i.e., an accelerometer attached to it reads nonzero) is not inertial, regardless of its state of motion relative to other objects.

Well if two objects are not moving, relative to one another, aren't they in inertial reference frames? And then, to the reference frame of a third object, the first two would be accelerating. How does that play out?

Thanks,

Jake
 
  • #4
jaketodd said:
Well if two objects are not moving, relative to one another, aren't they in inertial reference frames? And then, to the reference frame of a third object, the first two would be accelerating. How does that play out?
Google Bells spaceship paradox.
 
  • #5
jbriggs444 said:
Google Bells spaceship paradox.

I don't see how length contraction is involved here. But thanks.

Please see my previous post:

jaketodd said:
Well if two objects are not moving, relative to one another, aren't they in inertial reference frames? And then, to the reference frame of a third object, the first two would be accelerating. How does that play out?

I'm just looking for a simple answer to that simple scenario.

Thanks,

Jake
 
  • #6
jaketodd said:
I don't see how length contraction is involved here.
If two objects are not moving relative to one another but are both accelerating then Bell's paradox and length contraction are very relevant. As is the notion of Born rigidity.

The situation may seem simple but may be surprising. Do you imagine, for instance, that both objects have the same proper acceleration?
 
  • #7
jbriggs444 said:
If two objects are not moving relative to one another but are both accelerating then Bell's paradox and length contraction are very relevant. As is the notion of Born rigidity.

Okay. I half way give up on this. All I wanted to find out is if two objects, accelerating relative to a third, but not to one another, then they'd be inertial. Then I wanted to ask this: To the first two objects, they would just see each other, not moving, nothing special going on. But to the third (let's say the first two are sandy planets), it would see sand flying off the first two planets - but to the two planets, they would not see any of their sand flying off. So how can both scenarios coexist in the same universe?
 
  • #8
jaketodd said:
if two objects are not moving, relative to one another, aren't they in inertial reference frames?

First, what you mean to ask, I take it, is are they at rest in inertial reference frames. An object is always "in" every frame. It just isn't at rest in every frame.

An object that is accelerating (in the sense of proper acceleration) cannot be at rest in an inertial frame, because it isn't moving inertially. Go read my post #2 again, carefully.

jaketodd said:
if two objects, accelerating relative to a third, but not to one another, then they'd be inertial

Go read my post #2 again, carefully. Note that it specifies a particular meaning for the term "accelerating", a meaning which has nothing to do with whether the object is accelerating relative to any other object. Note also that the definition of "inertial" depends on that definition of "accelerating", and also has nothing to do with the object's state of motion relative to any other object.

In the statement of yours just quoted above, you have not given sufficient information to tell whether the first two objects are inertial or not, because you have said nothing about whether accelerometers attached to them read zero or nonzero. (Or, equivalently, whether the first two objects feel acceleration.) So there are two possibilities:

(1) The first two objects are both feeling acceleration, and the third is not. Then the third object is inertial, and the first two are not.

(2) The first two objects are not feeling acceleration, and the third is. Then the first two objects are inertial, and the third is not.

jaketodd said:
To the first two objects, they would just see each other, not moving, nothing special going on.

This would be the case for #2 above. But it would not be the case for #1.

jaketodd said:
how can both scenarios coexist in the same universe?

They can't. Either #1 above, or #2 above, can be the case, but both cannot be the case in the same universe.
 
  • #9
What determines which objects (any objects) feel acceleration? And how can anything feel acceleration when it's always possible to have another object, or set of objects, be inertial? So like sand flying off two planets that are feeling acceleration, compared to them not, and the first object feeling acceleration. It seems that both of those scenarios would exist, depending on which #1 and #2, as you labeled them, you look at. It seems to be a point of view, instead of a concrete reality. Maybe this is why it's called Relativity? But, that would mean different observers, would not only see things moving, accelerating etc. differently, but entire portions of reality would be different - like sand flying off accelerating planets (for some people), and planets holding perfectly still, with no sand flying off (to other observers).
 
  • #10
jaketodd said:
What determines which objects (any objects) feel acceleration?

You measure this with an accelerometer. It's the same as the feeling of weight; when you feel weight standing on the surface of the Earth, you are feeling acceleration. A bathroom scale is a kind of accelerometer.

jaketodd said:
how can anything feel acceleration when it's always possible to have another object, or set of objects, be inertial?

Um, because some things feel acceleration and others don't? I don't understand what your issue is here; surely you are not claiming that all objects must be in exactly the same state of motion?

In any case, it is straightforward to verify with accelerometers that some objects feel acceleration and others don't.

The rest of your post appears to just compound this error. I think you are confused and need to take a step back.
 
  • #11
jaketodd said:
It seems to be a point of view, instead of a concrete reality.

Whether or not a given object feels acceleration at a given instant is an invariant; it does not depend on "point of view". As I said, you can measure it directly with an accelerometer. The two alternatives #1 and #2 that I described are distinguishable by such direct measurements, so the fact that they are different, and that only one can be true, is an invariant and does not depend on "point of view".
 
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  • #12
jaketodd said:
Okay. I half way give up on this. All I wanted to find out is if two objects, accelerating relative to a third, but not to one another, then they'd be inertial. Then I wanted to ask this: To the first two objects, they would just see each other, not moving, nothing special going on. But to the third (let's say the first two are sandy planets), it would see sand flying off the first two planets - but to the two planets, they would not see any of their sand flying off. So how can both scenarios coexist in the same universe?

Let's make our three objects clocks. If the first two objects are accelerating while maintaining a constant distance between themselves as measured by themselves. and are separated along a distance parallel to the acceleration, then the clocks will run at different rates as measured by these two clocks. If instead, it was the third object accelerating, then they would run at the same rate.
So if the question is: Can the two clocks tell, in any objective manner, whether it is them or the third object that is accelerating? The the answer is Yes.
 
  • #13
PeterDonis said:
Whether or not a given object feels acceleration at a given instant is an invariant; it does not depend on "point of view". As I said, you can measure it directly with an accelerometer. The two alternatives #1 and #2 that I described are distinguishable by such direct measurements, so the fact that they are different, and that only one can be true, is an invariant and does not depend on "point of view".

Thank you for bearing with me, by the way...

So wouldn't an accelerometer read differently if viewed by a) an observer watching the accelerometer accelerate, and b) an observer, accelerating the same as the accelerometer? Or would the accelerometer read the same in both scenarios?

Thanks,

Jake
 
  • #14
jaketodd said:
wouldn't an accelerometer read differently if viewed by

No. I don't even have to read the rest of your post to give that answer. A given accelerometer's reading at a given instant is an invariant, as I've already said. So it must read the same no matter who is viewing it.

As an example, remember that I said a bathroom scale is a kind of accelerometer. When you stand on your bathroom scale, it reads nonzero. But you are at rest relative to the scale. And if I am flying by in a spaceship and look at the reading on your scale, I see the same reading that you see standing on it.
 
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  • #15
PeterDonis said:
No. I don't even have to read the rest of your post to give that answer. A given accelerometer's reading at a given instant is an invariant, as I've already said. So it must read the same no matter who is viewing it.

As an example, remember that I said a bathroom scale is a kind of accelerometer. When you stand on your bathroom scale, it reads nonzero. But you are at rest relative to the scale. And if I am flying by in a spaceship and look at the reading on your scale, I see the same reading that you see standing on it.

Okay, thanks; I think that resolves it.
 
  • #16
jaketodd said:
Okay, thanks; I think that resolves it.

In other words, there would be sand flying off the planets no matter what reference frame you're in (to reference an earlier post by me in this thread).
 
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  • #17
jaketodd said:
All I wanted to find out is if two objects, accelerating relative to a third, but not to one another, then they'd be inertial.
No, they are not inertial. An inertial object is one where an attached accelerometer reads zero. It has nothing to do with the relative motion with any other object.
 
  • #18
jaketodd said:
In other words, there would be sand flying off the planets no matter what reference frame you're in (to reference an earlier post by me in this thread).
You aren't in a reference frame, you are in all reference frames. A reference frame is just a choice of coordinates to use. There may be one particular one you choose to use. So yes, sand is either flying off the planets or it isn't. What frame of reference you choose to use can't change that.
 
  • #19
Ibix said:
You aren't in a reference frame, you are in all reference frames. A reference frame is just a choice of coordinates to use. There may be one particular one you choose to use. So yes, sand is either flying off the planets or it isn't. What frame of reference you choose to use can't change that.

Yes, got it.
 
  • #20
jaketodd said:
In other words, there would be sand flying off the planets no matter what reference frame you're in

Assuming the planets were feeling acceleration, yes.
 
  • #21
Dale said:
No, they are not inertial.

Actually, as I said in post #8, we don't know that for sure from the scenario as given, since the OP appeared to be using "acceleration" to mean coordinate acceleration (or acceleration relative to some other object), not proper acceleration. If "acceleration" in the scenario as stated means coordinate acceleration, it is possible that the third object is the one with nonzero proper acceleration, and the first two are inertial (option #2 in post #8).
 
  • #22
Okay, I have a new complaint :wink:

I understand now that accelerometers are invariant. But what are accelerometers really measuring? If two things can move inertial to each other, but accelerating to a third, and all points of view/reference frames show acceleration on the accelerometers, then doesn't that imply an "ether" of some sort? I know that word is blasphemy, but doesn't this all imply that there is some master thing that accelerometers measure against - given that regardless of reference frame, accelerometers read identically?
 
  • #23
PeterDonis said:
Actually, as I said in post #8, we don't know that for sure from the scenario as given, since the OP appeared to be using "acceleration" to mean coordinate acceleration (or acceleration relative to some other object), not proper acceleration. If "acceleration" in the scenario as stated means coordinate acceleration, it is possible that the third object is the one with nonzero proper acceleration, and the first two are inertial (option #2 in post #8).
e.g. an apple falling off a tree relative to a couple of fellows sitting on the ground beneath or a couple of fellows falling from the branch above onto the ground below.
 
  • #24
jaketodd said:
But what are accelerometers really measuring?
Proper acceleration.

jaketodd said:
If two things can move inertial to each other,
Two things don’t move inertial to each other. Each one is independently inertial or non inertial regardless of motion relative to each other.

jaketodd said:
then doesn't that imply an "ether" of some sort?
Nope. The aether provided for an absolute velocity. We are talking about an invariant acceleration.
 
  • #25
jaketodd said:
I understand now that accelerometers are invariant. But what are accelerometers really measuring?
Typically they measure the force required to deflect a known mass so that its trajectory follows a given path. As Peter Donis pointed out previously, a bathroom scale does this -- measuring the force required to keep you on a path centered above the bathroom scale.
 
  • #26
jaketodd said:
If two things can move inertial to each other
As Dale points out, this doesn't make sense.
jaketodd said:
all points of view/reference frames show acceleration on the accelerometers, then doesn't that imply an "ether" of some sort?
No. It means there must be a frame-independent way of describing the path an object with no proper acceleration follows, and what acceleration it must feel to follow some other path. There is. It turns out that unaccelerated objects follow paths called geodesics which, in flat spacetime, turn out to be straight lines.
 
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  • #27
jaketodd said:
what are accelerometers really measuring?

Others have already responded, but I'm going to throw another term into the mix: path curvature. An accelerometer measures the degree to which an object's path through spacetime is curved.
 
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  • #28
jaketodd said:
doesn't this all imply that there is some master thing that accelerometers measure against

Yes. The "master thing" is the geometry of spacetime; that's what defines which paths through spacetime are straight and which are curved--or, to put it another way, how curved a particular path through spacetime is.

This is not the same as an "ether" because, as @Dale has already pointed out, it only gives an absolute meaning to acceleration (more precisely, proper acceleration), not velocity. Also it does not pick out any particular reference frame as being special; a given path through spacetime has the same curvature (accelerometer reading) in all reference frames.
 
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  • #29
jaketodd said:
... then doesn't that imply an "ether" of some sort?...
"Some sort" can mean anything. Originally "ether" meant an absolute reference for velocity, not for acceleration.
 
  • #30
Ya, I give up.
 
  • #31
jaketodd said:
Ya, I give up.

If you want a quick summary of all the responses you've been getting, here it is:

(1) There is no such thing as "things moving inertial to each other". Things can be at rest relative to each other, but that tells you nothing about whether they are moving inertially or not.

(2) Moving inertially means an accelerometer attached to the object reads zero. This is an invariant, independent of any choice of coordinates or reference frame, and all observers will agree on the readings of a particular accelerometer.

(3) There is an absolute thing according to relativity, and it is the geometry of spacetime. The geometry of spacetime is also an invariant; it's the same for all observers and in all coordinates or reference frames.
 
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  • #32
That's good, thank you very much for doing that. :smile:
 
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  • #33
jaketodd said:
thank you very much for doing that.

You're welcome!
 
  • #34
jaketodd said:
Are two objects, accelerating at the same rate, and in the same direction, considered inertial to one another? If so, I will post my resulting question. If not, it's safe to disregard this thread.

Thanks,

Jake

I would say no, in both interpretations of the question that come to mind for objects acclerating "at the same rate and in the same direction" that I can think of.

"At the same rate" sounds simple, but it depends on whether you mean that their acceleration in some inertial frame of reference is the same, or whether you mean their proper acceleration is the same.

The first interpretation of "at the same rate" leads to Bell's spaceship paradox. This may be worth reading about, but seems like it's veering away from the topic the OP is interested in.
 
  • #35
pervect said:
I would say no

The "no" answer is obvious for the question as stated, for the reason I and others have already stated several times: there is no such thing as "inertial to each other".

I suspect that you are inadvertently reading "inertial to each other" to mean "at rest relative to each other". (I also suspect the OP of having the same confusion, which is why I've commented on this before in this thread.)
 
<h2>1. What is an inertial object?</h2><p>An inertial object is an object that maintains its state of motion (either at rest or moving at a constant velocity) unless acted upon by an external force.</p><h2>2. What is acceleration in relation to inertial objects?</h2><p>Acceleration is the rate of change of an object's velocity over time. In the context of inertial objects, acceleration can occur when an external force is applied, causing the object to change its state of motion.</p><h2>3. How does the direction of an inertial object affect its motion?</h2><p>The direction of an inertial object affects its motion in that it determines the path the object will take. An object will continue to move in a straight line unless acted upon by an external force, which can change its direction.</p><h2>4. What factors can affect the acceleration of an inertial object?</h2><p>The acceleration of an inertial object can be affected by the magnitude and direction of the external force applied, as well as the mass of the object. Objects with larger masses require more force to accelerate compared to objects with smaller masses.</p><h2>5. How is inertia related to inertial objects?</h2><p>Inertia is the tendency of an object to resist changes in its state of motion. Inertial objects have a high level of inertia, meaning they will resist changes in their motion unless acted upon by an external force.</p>

1. What is an inertial object?

An inertial object is an object that maintains its state of motion (either at rest or moving at a constant velocity) unless acted upon by an external force.

2. What is acceleration in relation to inertial objects?

Acceleration is the rate of change of an object's velocity over time. In the context of inertial objects, acceleration can occur when an external force is applied, causing the object to change its state of motion.

3. How does the direction of an inertial object affect its motion?

The direction of an inertial object affects its motion in that it determines the path the object will take. An object will continue to move in a straight line unless acted upon by an external force, which can change its direction.

4. What factors can affect the acceleration of an inertial object?

The acceleration of an inertial object can be affected by the magnitude and direction of the external force applied, as well as the mass of the object. Objects with larger masses require more force to accelerate compared to objects with smaller masses.

5. How is inertia related to inertial objects?

Inertia is the tendency of an object to resist changes in its state of motion. Inertial objects have a high level of inertia, meaning they will resist changes in their motion unless acted upon by an external force.

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