B Inertial Objects: Acceleration & Direction

[jaketodd]

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

 

[PeterDonis]

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]

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]

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.

 

[jaketodd]

Google Bells spaceship paradox.

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

Please see my previous post:

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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]

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.

 

[Ibix]

If two things can move inertial to each other

As Dale points out, this doesn't make sense.

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.

 

[PeterDonis]

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.

 

[PeterDonis]

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.

 

[A.T.]

... 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.

 

[jaketodd]

Ya, I give up.

 

[PeterDonis]

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.

 

[jaketodd]

That's good, thank you very much for doing that.

 

[PeterDonis]

thank you very much for doing that.

You're welcome!

 

[pervect]

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.

 

[PeterDonis]

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.)

 

[PAllen]

"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.

Aren't these the same thing? Not in magnitude, but if the acceleration of two particles is the same per some inertial coordinate system, their proper acceleration must be the same. In the Rindler case, neither proper acceleration is the same, nor coordinate acceleration in a given inertial frame.

 

[David Lewis]

… if the acceleration of two particles is the same per some inertial coordinate system, their proper acceleration must be the same.

Even if their proper accelerations are identical, the distance between the objects is frame-dependent. One observer may say the motions started at the same time, and another will say one object started moving before the other.

 

[PAllen]

Even if their proper accelerations are identical, the distance between the objects is frame-dependent. One observer may say the motions started at the same time, and another will say one object started moving before the other.

That is irrelevant to may point. My point is simply that identical acceleration in any given inertial frame implies identical proper acceleration (per simultaneity of that frame). thus the two cases are equivalent. I said nothing about distances.

If you want to allow for the case of varying proper acceleration that is associated with identical coordinate acceleration in some frame but not in another, then you cannot talk about identical proper acceleration without specifying a frame any more than you can for coordinate acceleration, because which proper accelerations you compare is frame dependent. That is, unless proper accelerations are constant, the "seemingly invariant" statement that proper accelerations are identical has no meainginIg without specifying a frame. And, if proper accelerations are identical per that inertial frame, then so are coordinate accelerations.

 

[jaketodd]

You're welcome!

Please consider the following: The two planets are moving with a non-zero impulse, and the observer starts moving, after the planets start moving, with the same, non-zero impulse. If you take the derivative of the two planets' accelerations, for a point in time, then the resulting impulse would match the impulse of the observer, and all "impulse-ometers" (if such a thing exists), would agree. However, the velocities of the planets, and the observer, would not agree! So all "impulse-ometers", for that point in time, would be reference frame invariant, even though the velocities differ. This point of view implies, that the amount of sand, flying off the planets, is reference frame variant, even though the "impulse-ometers" are reference frame invariant. The higher the velocity of the two planets, the more sand will fly off them. The only way I can see out of this, is by using the derivative of impulse (meters per second, per second, per second, per second), leading the way to "impulse-change-ometers!" Those would always agree, and be reference frame invariant. However, I think they would require spacetime bending back, and through itself.

Everyone's thoughts on this are welcome.

Thanks!

Jake

 

[jbriggs444]

Please consider the following: The two planets are moving with a non-zero impulse

What does that even mean?

 

[Dale]

@jaketodd can you clarify what distinguishes an impulseometer from an accelerometer?

This point of view implies, that the amount of sand, flying off the planets, is reference frame variant

Then the point of view is wrong.

 

[PeterDonis]

all "impulse-ometers" (if such a thing exists)

To know whether such a thing exists, we would have to know what you mean by "impulse".

 

[jaketodd]

To know whether such a thing exists, we would have to know what you mean by "impulse".

Impulse. I learned about it in high school honors physics class. It's the derivative of acceleration. It's how fast acceleration is changing.

Thanks, my friend. Jake

 

[jbriggs444]

Impulse. I learned about it in high school honors physics class. It's the derivative of acceleration. It's how fast acceleration is changing.

The first derivative of acceleration is more commonly known as "jerk". https://en.wikipedia.org/wiki/Jerk_(physics). It has dimensions of distance per time³
My first year physics class taught that "impulse" is a momentary transfer of momentum. It has dimensions of mass times velocity.

 

[Nugatory]

Impulse. I learned about it in high school honors physics class. It's the derivative of acceleration. It's how fast acceleration is changing.

That's not right. The derivative of acceleration is called "jerk".

Impulse is the integral of force with respect to time, so that (for example) applying 10,000 Newtons for two milliseconds is the same impulse as 20,000 Newtons for one millisecond. It's useful when analyzing collisions and sudden impacts, problems in which the exact acceleration profile is less interesting than the total momentum transfer. And because it is the integral of force over time, in principle it can be calculated from accelerometer readings.

 

[jaketodd]

The first derivative of acceleration is more commonly known as "jerk". https://en.wikipedia.org/wiki/Jerk_(physics). It has dimensions of distance per time³
My first year physics class taught that "impulse" is a momentary transfer of momentum. It has dimensions of mass times velocity.

Okay, then let's call it Jerk. So in my previous post, it would be "jerk-ometers" and "jerk-change-ometers."

Sorry about the confusion,

Jake

 

[jbriggs444]

Reading "impulse" as "time rate of change of acceleration"...

Please consider the following: The two planets are moving with a non-zero impulse, and the observer starts moving, after the planets start moving, with the same, non-zero impulse.

So we have two planets, both at rest and both with zero acceleration. In the initial rest frame, they are side by side and start accelerating simultaneously at a rate that increases uniformly from zero.

We have an observer standing to one side also at rest near the initial position of the planets. The observer begins accelerating later but also at a rate that increases uniformly from zero.

One assumes that we are dealing with proper accelerations here. Each entity experiences a uniform rate of increase in felt-acceleration over experienced-time.

Is this an accurate description of the setup so far?

If you take the derivative of the two planets' accelerations, for a point in time, then the resulting impulse would match the impulse of the observer, and all "impulse-ometers" (if such a thing exists), would agree.

As constructed, the rate of change of acceleration for all entities is constant. So yes, their "impulse-ometers" all read identically.

However, the velocities of the planets, and the observer, would not agree! So all "impulse-ometers", for that point in time, would be reference frame invariant, even though the velocities differ.

Certainly true.

This point of view implies, that the amount of sand, flying off the planets, is reference frame variant

The amount of sand that flies off is independent of velocity -- unless you imagine it blowing off in some sort of ether wind.

If you pick out a starting event and a stopping event, the amount of sand that flies off a planet between the two is a physical fact and is invariant.

The rate at which sand flies off can vary between frames because the time interval judged to have elapsed can vary between frames.

 

[jaketodd]

The amount of sand that flies off is independent of velocity -- unless you imagine it blowing off in some sort of ether wind.

It's called inertia.

 

[PeterDonis]

the derivative of acceleration

Ok, then you need to distinguish two kinds of "derivative of acceleration with respect to time":

(1) Derivative of proper acceleration with respect to the observer's proper time. We could call this "proper jerk", and it is an invariant, since proper acceleration and proper time are both invariants. Any actual observable, like how much sand is flying off of a planet, must depend only on invariants, so it would depend on this if it depended on jerk at all. (Also, a "jerk-ometer" would measure this, just like an accelerometer measures proper acceleration.)

(2) Derivative of coordinate acceleration with respect to coordinate time. We could call this "coordinate jerk", and it depends on your choice of coordinates, so it's not an invariant and no actual observable can depend on it.

Do you see the general rule here? If so, hopefully that will forestall further questions along these same lines.

 

[jaketodd]

Ok, then you need to distinguish two kinds of "derivative of acceleration with respect to time":

(1) Derivative of proper acceleration with respect to the observer's proper time. We could call this "proper jerk", and it is an invariant, since proper acceleration and proper time are both invariants. Any actual observable, like how much sand is flying off of a planet, must depend only on invariants, so it would depend on this if it depended on jerk at all. (Also, a "jerk-ometer" would measure this, just like an accelerometer measures proper acceleration.)

(2) Derivative of coordinate acceleration with respect to coordinate time. We could call this "coordinate jerk", and it depends on your choice of coordinates, so it's not an invariant and no actual observable can depend on it.

Do you see the general rule here? If so, hopefully that will forestall further questions along these same lines.

No, I don't understand what you mean. The "jerk-ometers" would all agree, yet the velocities would differ, creating two different realities, dependent on reference frame. The "jerk-ometers" are invariant because they rely on the geometry of spacetime, which is universal, as you have said.