B Solving the twin paradox with special relativity

[Grampa Dee]

Not at all. Relative velocity can be directly measured (for example, by timing round-trip light signals). Inertial frames are abstractions (and global inertial frames don't even exist if gravitating masses are present) and the physics is independent of any choice of frame, so focusing on them just obfuscates the physics.It means twin #2 felt a force. "Force of acceleration" is either redundant (since a felt force is identical to proper acceleration, what is measured by an accelerometer) or frame-dependent (since coordinate acceleration depends on your choice of frame and is therefore irrelevant to the physics).Not in your scenario, no. You say twin #1 never fires his rockets; that means he never feels a force at all.

If twin #2 fires his rockets, he feels a force. But if he does not fire his rockets, but just let's the gravity of the black hole determine his motion, he feels no force either.Neither twin will "experience" any acceleration--they both feel no force. They can measure that their relative velocity is changing by exchanging round-trip light signals, yes; that was the method I had in mind. But that measured change in relative velocity, when they both feel no force, does not mean they are "experiencing acceleration" even though they feel no force. It means the spacetime they are in is curved, i.e., there is a gravitating mass present.Physics has nothing to do with frames. It has to do with actual observables. Feeling a force (for example, when twin #2 fires his rockets) is a direct observable. So is spacetime curvature (as measured by round-trip light signals between the twins when they are at different distances from the black hole and neither one is firing rockets). The latter measurement is sometimes referred to as "relative acceleration" in the GR literature (and I'll refer to it that way below), but it has nothing to do with any choice of frame.Yes, as noted above.From just the relative acceleration between them, measured as described above, I don't think so. They would need a third "twin" separated from them tangentially (i.e., in a direction perpendicular to the direction of the black hole), so that each pair of twins could measure the relative acceleration between them. Those multiple relative acceleration measurements could determine the direction to the hole.

Thank you Peter; you've answered pretty much what I was asking... I'm sorry for my poor choice of words...it's not easy to express myself very clearly when it concerns scientific experiments.

I just wanted to add...

Grampa Dee said:
I understand that both twins will indeed experience an acceleration.

I wanted to say that both twins can measure (light signals) each others relative increase of velocities.

 

[PeterDonis]

both twins can measure (light signals) each others relative increase of velocities.

Yes. However, that is not the same as either twin feeling any force, which is what "experience acceleration" would normally mean.

 

[Grampa Dee]

Yes. However, that is not the same as either twin feeling any force, which is what "experience acceleration" would normally mean.

I understand; however, acceleration, for me, is first and foremost a change in velocity, which is usually measured with measuring rods (or light signals) as opposed to forces, and so I visualized more the experience of acceleration with measuring velocities...again, it's not easy for me to express myself scientifically due to the exactitude in speech that is needed.

 

[Sagittarius A-Star]

I understand; however, acceleration, for me, is first and foremost a change in velocity, which is usually measured with measuring rods (or light signals) as opposed to forces

You should distinguish between "coordinate acceleration" (what you describe) and "proper acceleration" (can be measured with an accelerometer).

 

[PeterDonis]

it's not easy for me to express myself scientifically due to the exactitude in speech that is needed.

When in doubt, it's best to not use words that can be ambiguous, but just to directly describe what you're measuring and how you're measuring it. Saying you're timing round-trip light signals, or saying you're using an accelerometer, makes it clear what you're measuring without having to worry about the ambiguity of terms like "experience" or "acceleration".

 

[Grampa Dee]

When in doubt, it's best to not use words that can be ambiguous, but just to directly describe what you're measuring and how you're measuring it. Saying you're timing round-trip light signals, or saying you're using an accelerometer, makes it clear what you're measuring without having to worry about the ambiguity of terms like "experience" or "acceleration".

ok; thank you for your time and patience, Peter.

 

[FactChecker]

I understand; however, acceleration, for me, is first and foremost a change in velocity, which is usually measured with measuring rods (or light signals) as opposed to forces, and so I visualized more the experience of acceleration with measuring velocities...again, it's not easy for me to express myself scientifically due to the exactitude in speech that is needed.

In non-inertial coordinate systems, it is very important to distinguish between the derivative of velocity (second derivative of position) versus the physical acceleration that can be used in F=mA. That is especially true with a rotating coordinate system, where the derivative of velocity can be huge even though there is no external force at all.
Additionally, in the context of SR, you need to start thinking about spacetime coordinates rather than simple spatial position coordinates. With simple spatial position coordinates, it is mathematically easy to think of the positions, velocities, and accelerations as all being relative. In spacetime that is no longer true. In spacetime, an accelerating path is easily distinguished from a nonaccelerating path without referring to any other reference frame. So accelerations are not relative in spacetime coordinate systems.

 

[Grampa Dee]

In non-inertial coordinate systems, it is very important to distinguish between the derivative of velocity (second derivative of position) versus the physical acceleration that can be used in F=mA. That is especially true with a rotating coordinate system, where the derivative of velocity can be huge even though there is no external force at all.
Additionally, in the context of SR, you need to start thinking about spacetime coordinates rather than simple spatial position coordinates. With simple spatial position coordinates, it is mathematically easy to think of the positions, velocities, and accelerations as all being relative. In spacetime that is no longer true. In spacetime, an accelerating path is easily distinguished from a nonaccelerating path without referring to any other reference frame. So accelerations are not relative in spacetime coordinate systems.

thank you FactChecker