Why acceleration exists in relativity but velocity to spacetime does not

[Cleonis]

How do you define "free motion"?

That was already covered in the assumptions declared at the start:
Assumption:
- The only long range force besides gravitation is electromagnetic interaction. If we eliminate electromagnetic interaction we obtain a pure gravitational reading.

Cleonis

 

[atyy]

That was already covered in the assumptions declared at the start:
Assumption:
- The only long range force besides gravitation is electromagnetic interaction. If we eliminate electromagnetic interaction we obtain a pure gravitational reading.

Cleonis

How do you know you've eliminated the electromagnetic interaction?

If we're discussing special relativity, then the "gravitational reading" means flat spacetime.

I don't think you can define any of these terms until you already know about inertial frames. When you do know about inertial frames, you also know about noninertial frames. So there is no difference between "actual measurement" and "inference on theoretical grounds".

 

[Cleonis]

Switching sides, are you? :-)
I learned SR from Taylor and Wheeler's _Spacetime Physics_, and the main principle I took away from that is that the theory of "relativity" is actually about *invariants*--things that *don't* change when you change reference frames. IIRC, Taylor even makes an explicit statement somewhere in the book that "relativity" is a bad name, and the theory really should be called the "theory of invariants". I think there's also a similar statement in the classic GR text, Misner, Thorne, and Wheeler's _Gravitation_.

Certainly, emphasizing the importance of thinking in invariants over thinking in terms of relativity is better.
Then again: the feature of invariants is not unique to SR, galilean relativity has its own invariants.

In my opinion any text that claims to be an introduction to SR ought to emphasize precisely the feature that differentiates SR from galilean relativity. SR-spacetime affects how objects relate to each other in space and in time. SR-spacetime is an active participant in the physics taking place.

Compared to SR-spacetime galilean spacetime is pretty passive. In galilean spacetime, when two twins separate and later rejoin then the stay-at-home twin and the traveling twin won't notice anything special. In SR-spacetime however, the twins find that the difference in their journeys has had a physical effect.

The transition from galilean relativity to SR was a transition from a comparitively passive spacetime to a spacetime that is an active participant in the physics taking place. In my opinion in any introduction to SR the story ought to revolve around that.

Cleonis

 

[PeterDonis]

The transition from galilean relativity to SR was a transition from a comparitively passive spacetime to a spacetime that is an active participant in the physics taking place. In my opinion in any introduction to SR the story ought to revolve around that.

I suspect that most relativists would say that GR is the theory that has spacetime being an active participant in the physics. Spacetime in SR is predetermined--as you know, since you've called it a "background structure". It's always flat Minkowski spacetime. Only in GR is spacetime affected by the dynamics.

In fact, if I wanted to quickly summarize the difference between galilean relativity and SR, I would simply say that galilean relativity uses galilean spacetime, whereas SR uses Minkowski spacetime. The physical effects you cite (e.g., the twins aging differently) I would not say are due to spacetime "participating" more in SR--they're just due to SR using a different spacetime. Galilean spacetime, if we lived in it, would have physical effects too: after all, objects are predicted to experience inertial forces (e.g., centrifugal force) in pre-SR physics.

 

[Cleonis]

if I wanted to quickly summarize the difference between galilean relativity and SR, I would simply say that galilean relativity uses galilean spacetime, whereas SR uses Minkowski spacetime. [...] Galilean spacetime, if we lived in it, would have physical effects too: after all, objects are predicted to experience inertial forces (e.g., centrifugal force) in pre-SR physics.

The theme of inertia is worth a thread of its own, I think. I will start a new thread, copying this quote.
The theme is: inertia in theories of motion.

I will call the new thread: 'History of theories of motion; the role of inertia'.

Cleonis