I enjoyed the question and appreciated Mike's explaination as well. I couldn't help to also think of Newton's first law of motion: "every body presists in a state of rest or uniform motion as long as it is not acted upon by an exterior force." The same equation applies F=ma. Gerry mentioned if only the mass of the Earth increased, I would think, m increases and that in proportion to the uniform motion changes due to the exterior force (which in this case didn't change but is the force of gravity from the Sun)
Nonetheless, as mass increases, a bell graph could be plotted until the uniform motion or obit changes. It would have to begin to spiral. m is proportational to F... as m increase, F increases.
f=ma.
True in maths, but mass/energy doesn't spontaneously increase or decrease ( based on observations in this universe ) without what would be labelled as a third ( or fourth, fifth .... ) body being introduced/leaving the system - and by definition from/to an 'infinite' distance away coming closer/farther. When that type of scenario is analysed it all works out as discussed before. But if you allow mass appearing 'out of nowhere' then for sure you'll start sucking adjacent stuff in. It's not silly to speculate about this, by the way. All we can know is that we haven't seen it. Yet. After all, if one is unlucky enough to live nearby one of these hypothecated 'white holes' ( say, the exit of a wormhole/tunnel ) then it would be self evident behaviour.
As for Newton's First, it's really a restatement of earlier thinking, eg. Galileo, and more than anything is really a definition. It is generically named the Law of Inertia. Mach had a lot to say about this topic, as did Newton in his 'spinning pail' ( water bucket ) experiment. Further along one path from here leads to 'what do you mean by mass' and Higg's etc....
Quote:
[aside]For that matter some of the 'ancients' as well, but with the longer passage of historical time it is harder to understand/be-sure what might have been their assumptions/meanings. They generally were more keen on circles and/or "Earth seeking" paths as being the base paths from which deviations ought be judged.[/aside]
There is a possible deep circumlocution here, which is not often stated. Some approaches :
- you can start by saying/assuming that you know what is meant by a straight line. Then any deviation from that is acknowledged as being due to a force. So we define forces in this way. Include the special case of no movement, with regard to some reference frame, as being a ( degenerate, because the line endpoints are equal ) straight line too.
- you can say the ( uninterrupted/free ) passage of light defines straight lines. Now any deviation(s) from the path of light would be a clue that some force is present.
- move up to Einstein, and light paths are the shortest distances between two points under any possible circumstances. Whether one deems that as "a straight line" is now your own pleasure ie. frame dependent. Observers in general will not necessarily agree on this, and of course time is now a malleable/wobbly thing too. So a true/proper/fair-dinkum general relativity 'metric' must have the property of yielding path integrals ( ie. how far apart are two spacetime events ), when minimalised ( null geodesics ), as being that which light travels upon - with nought else lesser. So nothing can beat light from any A to any B. The gravitational force now "disappears" under GR, as spacetime itself has changed and movement on curved paths is the way spacetime is structured. It just so happens that mass or energy determines that structure. Other ( non-gravitational ) forces are still present, and we detect them by movement off GR determined paths and not alteration of those paths per se. ( The inability to encompass other forces with a 'geometric' explanation akin to GR is what all the fuss is about with, for instance, string theory. See Lisa Randall's Warped Passages and others ). This would all be a fancy exercise in natural language, if not for the fact that the mathematical apparatus of GR ( when solvable!! ) is absolutely stunning in it's agreement with measurements.
Quote:
[aside]There is a tremendous analogy here with the Principle of Least Action ( originally an idea of Fermat ). See Feynman's sum over histories approach in quantum mechanics, electrodynamics especially, to determine the 'expectation' ( most likely value ) of the wave/particle propagation. You get all of optics flowing from that point onwards, as it translates to a principle of least ( propagation ) time.[/aside]
The possible circularity ( in a philosophic sense ) is that after plonking everything in a geometry basket, as per GR, then I still come back to the first questions involving 'rest', 'motion' etc. That's because one has yet to explain what space and time really are. So what, when you get down to it, is a "point" ? Go for it ..... :-)
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal
RE: I enjoyed the question
)
True in maths, but mass/energy doesn't spontaneously increase or decrease ( based on observations in this universe ) without what would be labelled as a third ( or fourth, fifth .... ) body being introduced/leaving the system - and by definition from/to an 'infinite' distance away coming closer/farther. When that type of scenario is analysed it all works out as discussed before. But if you allow mass appearing 'out of nowhere' then for sure you'll start sucking adjacent stuff in. It's not silly to speculate about this, by the way. All we can know is that we haven't seen it. Yet. After all, if one is unlucky enough to live nearby one of these hypothecated 'white holes' ( say, the exit of a wormhole/tunnel ) then it would be self evident behaviour.
As for Newton's First, it's really a restatement of earlier thinking, eg. Galileo, and more than anything is really a definition. It is generically named the Law of Inertia. Mach had a lot to say about this topic, as did Newton in his 'spinning pail' ( water bucket ) experiment. Further along one path from here leads to 'what do you mean by mass' and Higg's etc....
There is a possible deep circumlocution here, which is not often stated. Some approaches :
- you can start by saying/assuming that you know what is meant by a straight line. Then any deviation from that is acknowledged as being due to a force. So we define forces in this way. Include the special case of no movement, with regard to some reference frame, as being a ( degenerate, because the line endpoints are equal ) straight line too.
- you can say the ( uninterrupted/free ) passage of light defines straight lines. Now any deviation(s) from the path of light would be a clue that some force is present.
- move up to Einstein, and light paths are the shortest distances between two points under any possible circumstances. Whether one deems that as "a straight line" is now your own pleasure ie. frame dependent. Observers in general will not necessarily agree on this, and of course time is now a malleable/wobbly thing too. So a true/proper/fair-dinkum general relativity 'metric' must have the property of yielding path integrals ( ie. how far apart are two spacetime events ), when minimalised ( null geodesics ), as being that which light travels upon - with nought else lesser. So nothing can beat light from any A to any B. The gravitational force now "disappears" under GR, as spacetime itself has changed and movement on curved paths is the way spacetime is structured. It just so happens that mass or energy determines that structure. Other ( non-gravitational ) forces are still present, and we detect them by movement off GR determined paths and not alteration of those paths per se. ( The inability to encompass other forces with a 'geometric' explanation akin to GR is what all the fuss is about with, for instance, string theory. See Lisa Randall's Warped Passages and others ). This would all be a fancy exercise in natural language, if not for the fact that the mathematical apparatus of GR ( when solvable!! ) is absolutely stunning in it's agreement with measurements.
The possible circularity ( in a philosophic sense ) is that after plonking everything in a geometry basket, as per GR, then I still come back to the first questions involving 'rest', 'motion' etc. That's because one has yet to explain what space and time really are. So what, when you get down to it, is a "point" ? Go for it ..... :-)
Cheers, Mike.
I have made this letter longer than usual because I lack the time to make it shorter ...
... and my other CPU is a Ryzen 5950X :-) Blaise Pascal