B Question about “Inertia arises from interaction with the Universe’s mass”

[ESponge2000]

TL;DR Summary

When I am on a carousel spinning round and round we may feel dizzy and equate
1) the carousel is converting an energy source into mechanical energy and that is a force

2) excluding the effects of gravity from the equation, we are otherwise merely at rest and we ascertain that by not feeling dizzy if the carousel is turned off

Does this not imply that aside from gravity, A change in velocity within an inertial frame would be the same for all inertial frames ?

Or maybe a better way to put it is if we take the voyager 1 space probe in interstellar space where it is only subject to the little amounts of gravitational Force of our distant solar system and galactic space time curvature (very small ) and we discard it

We now have that no matter what velocity the probe is traveling relative to us, the probe is for the most part at rest . That must mean that if relative to us it is moving at a mere constant velocity, then regardless of however much the probe’s inertial frame is different from ours, both earth and the probe agree on what equates a “ change “ in inertial frame. This means what equates a change in an inertial frame , minus gravity, is not relative to an observer , is this correct ?

And stems from a balance of universe Mass dictating that all inertial frames absent space time curvature due to mass, will in a localiy hold to the same agreement on what constitutes a change in velocity vs a constant velocity ?

 

[ESponge2000]

Or simply said is it true you can’t have this

Alice and Bob are 10,000 miles apart and neither one are near any planets nor stars

This can’t happen right ?

Bob: from my perspective , Alice is changing inertial frames frames right now , I am not feeling the effects of an acting force

Alice , from my perspective it is Bob who is changing inertial frames I am not feeling any effects of An acting force

They both must agree on this part am I right ? On this they can’t both be right , unlike with constant velocity they will not need to agree on who is in motion , but they do have to agree and can detect who has an external force acting on them or otherwise an internal one such as the choice of action of organisms using energy from the food we consume

Well also assume both are traveling at velocities less than 1% of c relative to each other so their clocks are for the most part in sync as far as Alice and Bob take a minute to make their observations on each other

For another topic in physics , are only living organisms built with the ability to manipulate energy and force spontaneously and all other force stems from predictable chain reactions stemming from the motion states at the beginnings of the universe ?

 

[Pencilvester]

Alice and Bob are 10,000 miles apart and neither one are near any planets nor stars

This can’t happen right ?

Bob: from my perspective , Alice is changing inertial frames frames right now , I am not feeling the effects of an acting force

Alice , from my perspective it is Bob who is changing inertial frames I am not feeling any effects of An acting force

They both must agree on this part am I right ?

If you have two objects at rest relative to each other* in flat spacetime, both equipped with accelerometers, and both accelerometers always read zero, then, as measured in an inertial frame (and each object’s reference frame is inertial in this scenario), neither object’s velocity will change.

Does this not imply that aside from gravity, A change in velocity within an inertial frame would be the same for all inertial frames ?

No, if you drive away from your house, your inertial neighbor might determine that your velocity changed by 25 mph, but an inertial alien passing by at 0.999c wrt your neighbor will say your velocity changed by less than 25mph.

*EDIT: being at rest wrt each other is not a necessary condition for the rest of my statement— I initially put it in because that’s what I assumed was the case in the OP’s Alice/Bob scenario, but after re-reading, I realized OP did not specify this.

 

[ESponge2000]

I misspoke what I meant is that all observers in inertial frames that are constant (and generally not significantly influenced by the effects of gravity for purposes of this exercise), will agree on which objects are accelerating and which objects are not accelerating…. The magnitude of acceleration will be relative but the question of “is Bob accelerating? Yes or no” will not be a question of relativity , right ?

Also let’s assume that the forces at play are kept constant (constant forces and constant mass of objects means constant acceleration) for a duration of time that is longer on all observers clocks than the duration of a lightbeam traveling roundtrip between all the observers, such that there is mutual agreement that any discrepancies in measurement simultaneity don’t apply to this acceleration test…

And my find is they can both be accelerating and not agree on the amounts each one is , or one can be accelerating and not the other , but they can’t in any case disagree on if one object is accelerating or not accelerating , is this correct ?

Aside from all this, one thought experiment i need to examine is where 2 objects separated in space are accelerating in the same direction by the same amount force and are the same mass, both started out at rest with each other, And there’s like a little delay before the second object began the acceleration …. Now between the 2 objects it gets interesting when the acceleration is high enough that special relativity comes in.

 

[Pencilvester]

I misspoke what I meant is that all observers in inertial frames that are constant (and generally not significantly influenced by the effects of gravity for purposes of this exercise), will agree on which objects are accelerating and which objects are not accelerating…. The magnitude of acceleration will be relative but the question of “is Bob accelerating? Yes or no” will not be a question of relativity , right ?

There will always be agreement between inertial frames on which objects are accelerating and which are not.

 

[Dale]

TL;DR Summary: When I am on a carousel spinning round and round we may feel dizzy and equate
1) the carousel is converting an energy source into mechanical energy and that is a force

It is not true that forces are converting energy sources into mechanical energy. I believe that you have been told this already.

Does this not imply that aside from gravity, A change in velocity within an inertial frame would be the same for all inertial frames ?

Proper acceleration is not the same as a change in velocity. I know that you have been told this already because I told you it just earlier this week or late last week.

Change in velocity is not invariant, proper acceleration is. Even if you restrict yourself exclusively to inertial frames, change in velocity is not invariant, proper acceleration is.

We now have that no matter what velocity the probe is traveling relative to us, the probe is for the most part at rest .

This is a self-contradiction. If the probe has any velocity relative to us then it is not at rest in our frame. That is what it means to have a velocity relative to us.

That must mean that if relative to us it is moving at a mere constant velocity, then regardless of however much the probe’s inertial frame is different from ours, both earth and the probe agree on what equates a “ change “ in inertial frame.

We will agree on proper acceleration, which is invariant. We will not agree on changes in velocity which are not invariant.

And stems from a balance of universe Mass dictating that all inertial frames absent space time curvature due to mass, will in a localiy hold to the same agreement on what constitutes a change in velocity vs a constant velocity ?

All inertial frames will agree on what constitutes proper acceleration. They will not agree on changes in velocity.

 

[Pencilvester]

Even if you restrict yourself exclusively to inertial frames, change in velocity is not invariant, proper acceleration is.

Could you enlighten me on this? I was under the impression that with the unique class of cartesian coordinate systems associated with each inertial frame, whether or not an object’s velocity is changing is invariant (among those coordinate systems). But are you simply saying that non-inertial coordinates can be associated with a given inertial frame? If that’s the case, I think my understanding of exactly how the concept of reference frames is defined is flawed.

 

[Dale]

Two different inertial frames will not agree on a change in velocity. This can be derived from the velocity addition formula.

Two different inertial frames will agree if the change in velocity is 0, but that is the most that can be said.

 

[Pencilvester]

Two different inertial frames will not agree on a change in velocity. This can be derived from the velocity addition formula.

Two different inertial frames will agree if the change in velocity is 0, but that is the most that can be said.

Ooooh, okay, gotcha. I understood one of the OP’s questions to essentially be “Will two different inertial frames ever disagree on whether an object’s velocity is changing or not?” and I had assumed that’s the question you were answering. I did not read carefully enough!

 

[PeterDonis]

a balance of universe Mass dictating that all inertial frames absent space time curvature due to mass, will in a localiy hold to the same agreement on what constitutes a change in velocity vs a constant velocity ?

This, and the thread title, make it seem like you are thinking of speculative models (the first, IIRC, was due to Dennis Sciama in the 1950s) that attempt to account for inertia as a gravitational interaction with the rest of the mass in the universe. These models are speculative, and have nothing to do with the basic fact in relativity that proper acceleration is an invariant.

 

[Dale]

Ooooh, okay, gotcha. I understood one of the OP’s questions to essentially be “Will two different inertial frames ever disagree on whether an object’s velocity is changing or not?” and I had assumed that’s the question you were answering. I did not read carefully enough!

Part of this is carryover from their last thread where I very carefully explained that "proper acceleration" is not the same as "change in velocity" and I carefully showed that proper acceleration is invariant and change in velocity is not. And now they are back to "change in velocity" and asking about it being invariant again.

So your interpretation of what they said here is perfectly reasonable, but I see their wording differently. To me "A change in velocity within an inertial frame would be the same for all inertial frames ?" jumps out as problematic because it is a specific topic that they have already asked about and already had explained. So don't feel bad on your part! You are contributing well

 

[ESponge2000]

a proper acceleration means a non-gravitationally assisted change of velocity from a perspective of an object that is not being acted upon by a force , right or wrong ?

 

[Dale]

a proper acceleration means a non-gravitationally assisted change of velocity from a perspective of an object that is not being acted upon by a force , right or wrong ?

Proper acceleration means the thing that is measured by an accelerometer. That is the definition of proper acceleration, and definitions tell you what words mean.

The meaning of proper acceleration doesn’t have anything to do with perspectives nor with changes in velocity. Once you have the meaning of proper acceleration clear, then you can use the concept to do things.

You can identify objects that are not being acted on by a net force as ones that have zero proper acceleration. And then you can define their perspective. And then you can describe changes in velocity from that perspective. But the meaning of proper acceleration does not come from changes in velocity from the force free object’s perspective. It comes from the accelerometer measurement that you had to use in the beginning to establish the rest of those concepts

 

[Ibix]

a proper acceleration means a non-gravitationally assisted change of velocity from a perspective of an object that is not being acted upon by a force , right or wrong ?

The word "proper" here is used in the same sense as "property" (or "proprius" in Latin and similar words in modern Romance languages like Spanish), as something that belongs to the object, and not in its modern English sense of "right" or "correct".

Proper acceleration is something you can measure in a small closed box: you just release an uncharged particle from rest relative to you and see if it stays at rest relative to you. If it doesn't, you are undergoing proper acceleration. It's probably easier to support the particle with a spring and see if it extends - so a spring balance is actually an accelerometer. And that means that if you have a sensation of weight then you are undergoing proper acceleration. Newtonian physics makes an exception to this rule for gravity; relativistic physics does not. That is all proper acceleration is: release a particle you know to be inertial and see if it remains stationary. Or, alternatively, see if you need to apply a force to keep it stationary.

Note that none of this says anything about a "change in velocity" on your part. You can sit on a weighing scale all day without changing your position with respect to the scales or your surroundings. You will still be undergoing proper acceleration. Literally all proper acceleration is is a measure of your failure to follow an inertial path.

In flat spacetime, having non-zero proper acceleration will lead to you changing velocity with respect to more or less anything, and (both in SR and Newtonian physics) there's always a global inertial frame available. That means you can often get away with being lazy and not separating the concept of proper acceleration from coordinate acceleration relative to that global frame. But it is sloppy in an SR context, and it comes back to bite in a GR context.

Proper acceleration is just a measure of your degree of deviation from inertial motion, no more, no less.