When will the person at point B see train2 and why?

[A.T.]

In special relativity the fundamental object of consideration is Minkowski spacetime; special relativity explores the ramifications of Minkowski spacetime geometry. In these explorations the concept of 'frame of reference' is a tool, not an object of the theory.

Well, that distinction is moot. Minkowski spacetime and frames of reference are both mathematical tools.

 

[matheinste]

When I say <<I'm accelerating with a G-count of 1 with respect to the local inertial frame>>, then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

When I say <<I'm accelerating with a G-count of 1 with respect to space>> then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.


Cleonis

I hate to spoil a discussion by bringing logic into it but these statements imply that spacetime is the local inertial frame. As there are an infinity of "local inertial frames" then we have an infinity of background spacetime structures. So their is no preferred or absolute spacetime to which we can refer acceleration, but we already knew that.

Matheinste.

 

[JesseM]

Well, in this case the distinction is moot.

No matter what word one happens to use, in both cases the concept must be defined operationally, and the operational definition is identical for both cases.

When I say <<I'm accelerating with a G-count of 1 with respect to the local inertial frame>>, then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

Yes. Another way to define what you mean experimentally would be to say that if you are moving past an inertial coordinate grid made out of physical rulers and clocks, which can be used to define your position as a function of time x(t) in this frame based on a series of local measurements on the grid, then at the moment the first derivative of x(t) is zero (meaning you are temporarily at rest relative to the grid), the second derivative of x(t) is 1G.

When I say <<I'm accelerating with a G-count of 1 with respect to space>> then I mean that an accelerometer that is co-moving with me registers 1 G of acceleration.

If you want to define it that way, fine. But unlike with movement relative to an inertial frame, "acceleration relative to space" is not accepted terminology with an accepted meaning in physics, so it wasn't clear what you meant before you gave this definition. And it's also not clear if you associate some extra conceptual baggage with the phrase beyond the experimental definition you've given; any implications of "acceleration with respect to space" that go beyond the standard implications of "nonzero proper acceleration" might be ones that not all physicists would accept.

 

[Cleonis]

[...] And it's also not clear if you associate some extra conceptual baggage with the phrase beyond the experimental definition you've given; [...]

Well, the particular phrasing you refer to was written for dwspacetime, who started the thread. The phrasing was intended to be tangible.

In your reply you gave a phrasing that was designed to eliminate all ambiguity. Unfortunately, that level of precision makes it sound like http://en.wikipedia.org/wiki/Legal_writing#Legalese".

In an essay for an audience of specialists I would push for utmost precision, but not in a posting that primarily needs to be accessible.

When I read someone else's postings I don't attribute extra conceptual baggage to the other person, at least that is what I try. If I err in interpretation I strive to err on the side of caution.

Cleonis

 

[dwspacetime]

i do see both sides using legalese. :)

i did some search online. there is a university website about how to define the inertial frame which i don't remember what it is. there are some nonsense in it. but regardless, an inertial frame or a non-inertial frame or any kind of reference frame is an arbitraty coordinate system for us to measure the movement in spacetime. the movement happens in spacetime but not a reference frame. i use a ruler to measure my table to be 3.281ft long means my table takes 3.281ft long spacetime in the english (reference) frame and 1 meter long in the metrics reference system. my table takes space but not ruler. without necessity of measurement there is not need for reference frame. without reference frame things don't move? they move with or without referece frame in spacetime!

when a ball moves from pointA to point B in spacetime under any reference frame. there must be another reference frame in which we measure the spacetime moves from point B to point A relative the ball.

maybe there is not such a thing as a ball gets a force from nowhere and start to accelerate 'cause action and reaction is always a pair. how does a rocket get reaction to propell?

anyway i think i personaly want to go ahead to finish the book. it is really interesting to me.

 

[dwspacetime]

the original purpose of reference from is due to emptyness of the space itself i think. correct me if i am wrong. in the nothingness space without any matter to reference to you can not tell something is moving or not which brought the necessity of reference frame. by its very nature i think the movement should be always reference to a matter.

but a ball's accelerating is relative to the nothingness space which is really confuses me. maybe i think too much.

 

[atyy]

i do see both sides using legalese. :)

i did some search online. there is a university website about how to define the inertial frame which i don't remember what it is. there are some nonsense in it. but regardless, an inertial frame or a non-inertial frame or any kind of reference frame is an arbitraty coordinate system for us to measure the movement in spacetime. the movement happens in spacetime but not a reference frame. i use a ruler to measure my table to be 3.281ft long means my table takes 3.281ft long spacetime in the english (reference) frame and 1 meter long in the metrics reference system. my table takes space but not ruler. without necessity of measurement there is not need for reference frame. without reference frame things don't move? they move with or without referece frame in spacetime!

when a ball moves from pointA to point B in spacetime under any reference frame. there must be another reference frame in which we measure the spacetime moves from point B to point A relative the ball.

maybe there is not such a thing as a ball gets a force from nowhere and start to accelerate 'cause action and reaction is always a pair. how does a rocket get reaction to propell?

anyway i think i personaly want to go ahead to finish the book. it is really interesting to me.

Well, what do you mean by "move"? In physics, words are defined by saying what experiments we do and what results we get. The moment we do experiments to measure "movement", there is no more empty space. Suppose there is experimenter A, he does an experiment, and sets up a reference frame A in which the ball "moves". And suppose there is an experimenter B, she does an experiment using reference frame B, and the ball does not "move". Who is right? Well, they can both be right, because by using different reference frames, they used different definitions of "move". We can show that they are both right if we have an equation that consistently relates definitions in different reference frames.