B Are objects accelerating at the same rate in the same direction considered inertial to each other?

jaketodd

Gold Member
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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PeterDonis

Mentor
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.

jaketodd

Gold Member
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

jbriggs444

Homework Helper
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?

jaketodd

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

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

jbriggs444

Homework Helper
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?

jaketodd

Gold Member
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?

PeterDonis

Mentor
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.

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.

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.

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.

jaketodd

Gold Member
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).

PeterDonis

Mentor
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.

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.

PeterDonis

Mentor
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".

Janus

Staff Emeritus
Gold Member
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.

jaketodd

Gold Member
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

PeterDonis

Mentor
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.

jaketodd

Gold Member
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.

jaketodd

Gold Member
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).

Dale

Mentor
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.

Ibix

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.

jaketodd

Gold Member
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.

PeterDonis

Mentor
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.

PeterDonis

Mentor
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).

jaketodd

Gold Member
Okay, I have a new complaint

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?

jbriggs444

Homework Helper
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.

Dale

Mentor
But what are accelerometers really measuring?
Proper acceleration.

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.

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.

jbriggs444

Homework Helper
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.

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