B GR interpretation of a scenario

[PeterDonis]

You would introduce a fictitious force accelerating B, C, and F towards A.

Note that this is true regardless of whether you think there is "absolute space" or not. The key point is that you are using coordinates in which A is at rest.

 

[name123]

Why would the answer you gave to #2 and #3 not also work for #1? What role does "absolute space" play in the reasoning in #2 and #3? Particularly since being at rest vs. moving at a constant speed makes no difference whatever to your explanation?

Because in #1 how F, B and C moved to A should in the theory be equally as explainable as how A moved to F. And I do not know how to explain how F and B and C would significantly move to A in Newtonian physics. Nugartory considered that you could add fictitious forces to do it, and while that would work, it would no longer be Newtonian physics (as Newtonian physics doesn't include those added forces). Absolute space in Newtonian physics removes the need to explain how F, B and C moved to A because Newtonian physics would deny that they did (significantly). The main change would be a change in A's velocity vector relative to absolute space due to the gravitation, the change being in the direction of F.

How were you thinking you could get rid of absolute space and explain a change in F's velocity vector in the direction of A, and the same velocity vector change to the velocity vectors of B and C? What in Newonian physics would be responsible for such changes?

 

[PeterDonis]

Because in #1 how F, B and C moved to A should in the theory be equally as explainable as how A moved to F.

Motion is relative, so these are the same thing. That's just as true in Newtonian physics as in relativity. "Absolute space" in Newtonian physics does not mean motion is not relative. It just means Galilean invariance instead of Lorentz invariance.

Absolute space in Newtonian physics removes the need to explain how F, B and C moved to A because Newtonian physics would deny that they did (significantly).

This is not correct. See above.

The main change would be a change in A's velocity vector relative to absolute space due to the gravitation

This is true, but it doesn't mean what you think it means. See above.

I think you need to get clear about exactly what "absolute space" means in Newtonian physics; once you get clear about that the apparent problems you think you see should go away.

 

[name123]

Motion is relative, so these are the same thing. That's just as true in Newtonian physics as in relativity. "Absolute space" in Newtonian physics does not mean motion is not relative. It just means Galilean invariance instead of Lorentz invariance.

In Newtonian physics all motion is relative to absolute space, and when I am discussing motion with regards to Newtonian physics, I am discussing it relative to absolute space. From https://en.wikipedia.org/wiki/Galilean_invariance:

Among the axioms from Newton's theory are:

1. There exists an absolute space, in which Newton's laws are true. An inertial frame is a reference frame in relative uniform motion to absolute space.
2. All inertial frames share a universal time.

It seems to me that Newtonian physics predicts and explains that in such a scenario the magnitude of change in A's velocity vector (relative to absolute space) in the direction of F > than the magnitude of change in F's velocity vector (relative to absolute space) in the direction of A.

I do not see how it predicts or explains that in the scenario, relative to absolute space, A's velocity vector would undergo no change, and that it could explain F, B and C undergoing a change in their velocity vectors relative to absolute space instead. Why would A's position remain constant relative to absolute space, but not F, B, and Cs'?

 

[PeterDonis]

It means that motion is relative to absolute space

That's not what Newtonian physics says. Wikipedia is not a good source (and the galilean invariance page in particular seems to me to invite a number of serious misunderstandings). You need to actually look at a textbook on classical mechanics.

The "B" level answer to the general question you are asking is that there are only two really significant differences between Newtonian mechanics and relativity:

(1) Newtonian mechanics obeys Galilean invariance, and relativity obeys Lorentz invariance. Everything else about motion flows from that, and if you understand the implications of that, you can forget all about "absolute space" and the other things that are confusing you.

(2) In Newtonian mechanics, gravity is a force; in relativity, it isn't. That makes relativity simpler because it doesn't have to try to deal with the question of why objects don't feel gravity as a force, i.e., why objects moving solely under gravity are in free fall, weightless. In Newtonian mechanics this has to be dealt with by a special ad hoc assumption that gravity works different in this respect from all other forces. In relativity, the question doesn't even arise.

In particular, as far as choosing coordinates, inertial vs. non-inertial frames, etc., there is really no difference between Newtonian mechanics and relativity, other than the invariance difference above. In both cases, you can choose coordinates in which any object you like is at rest, but those coordinates might not be inertial; and if they are not inertial, additional coordinate artifacts will appear that do not have a straightforward interpretation as being caused by a "source" (these are called "fictitious forces" in Newtonian mechanics, but similar effects appear in non-inertial frames in GR).

 

[name123]

That's not what Newtonian physics says. Wikipedia is not a good source (and the galilean invariance page in particular seems to me to invite a number of serious misunderstandings). You need to actually look at a textbook on classical mechanics.

The "B" level answer to the general question you are asking is that there are only two really significant differences between Newtonian mechanics and relativity:

(1) Newtonian mechanics obeys Galilean invariance, and relativity obeys Lorentz invariance. Everything else about motion flows from that, and if you understand the implications of that, you can forget all about "absolute space" and the other things that are confusing you.

(2) In Newtonian mechanics, gravity is a force; in relativity, it isn't. That makes relativity simpler because it doesn't have to try to deal with the question of why objects don't feel gravity as a force, i.e., why objects moving solely under gravity are in free fall, weightless. In Newtonian mechanics this has to be dealt with by a special ad hoc assumption that gravity works different in this respect from all other forces. In relativity, the question doesn't even arise.

In particular, as far as choosing coordinates, inertial vs. non-inertial frames, etc., there is really no difference between Newtonian mechanics and relativity, other than the invariance difference above. In both cases, you can choose coordinates in which any object you like is at rest, but those coordinates might not be inertial; and if they are not inertial, additional coordinate artifacts will appear that do not have a straightforward interpretation as being caused by a "source" (these are called "fictitious forces" in Newtonian mechanics, but similar effects appear in non-inertial frames in GR).

Although you think wiki isn't a good source, if you look at the page https://en.wikipedia.org/wiki/Absolute_time_and_space you will see a quote from Isaac Newton from (I assume) Philosophiæ Naturalis Principia Mathematica.

Absolute space, in its own nature, without regard to anything external, remains always similar and immovable. Relative space is some movable dimension or measure of the absolute spaces; which our senses determine by its position to bodies: and which is vulgarly taken for immovable space ... Absolute motion is the translation of a body from one absolute place into another: and relative motion, the translation from one relative place into another ...

— Isaac Newton​

Lower down you will notice in the section titled Differing Views how Newtonian physics has been modified, that:

Even within the context of Newtonian mechanics, the modern view is that absolute space is unnecessary. Instead, the notion of inertial frame of reference has taken precedence, that is, a preferred set of frames of reference that move uniformly with respect to one another.​

My point that you snipped was that relative to absolute space, certain results could be explained, but not others. A further point is that I am not clear how by removing absolute space those results unexplainable by Newtonian physics (which has absolute space) are by the removal of absolute space are suddenly explainable by modified Newtonian physics.

 

[PeterDonis]

relative to absolute space, certain results could be explained, but not others

Only if you insist on using your incorrect concept of what "absolute space" means and what role it plays in Newtonian mechanics. Stop reading Wikipedia and look at a textbook.

Thread closed.