Implications of the statement Acceleration is not relative

[Nugatory]

There's always this visualization from Epstein:

"The reason you can't go faster than the speed of light is that you can't go slower. There is only one speed. Everything, including you, is always moving at the speed of light."

http://www.relativity.li/en/epstein2/read/c0_en/c1_en/

Or "A watch is to time as an automobile odometer is to distance; if the time on your watch is changing, you're moving; and the direction is forwards in time". This isn't exactly rigorously scientific, and some people dislike the analogy... But it is one way of interpreting the constant and non-zero magnitude of the four-velocity.

 

[Dale]

You have said that you can cause motion by choosing a specific coordinate system. I am asking questions about what happens when that specific coordinate system is chosen. You can't avoid answering the questions by attempting to use some other coordinate system(s).
...
You have chosen a "specific" one coordinate system that you have chosen

OK. If I am the one choosing the specific coordinate system then the one I would choose is the rocket's radar coordinates, as described in the Dolby and Gull paper I linked to earlier.

1. Prior to the firing of the rocket engine, you select the specific coordinate system. Do you make the rocket move?

2. While the engine is firing, you select the specific coordinate system. Do you make the rocket move?

No, the rocket is always at x=0, by definition, and therefore it never moves since dx/dt=0 always.

Also, the radar coordinate system covers the entire spacetime, so I only select it once, I don't make any new selection before during or after firing the engine.

 

[GregAshmore]

OK. If I am the one choosing the specific coordinate system then the one I would choose is the rocket's radar coordinates, as described in the Dolby and Gull paper I linked to earlier.

No, the rocket is always at x=0, by definition, and therefore it never moves since dx/dt=0 always.

Also, the radar coordinate system covers the entire spacetime, so I only select it once, I don't make any new selection before during or after firing the engine.

Thank you for the further information. This gives a much different impression than you have given so far. Up to now, you have made it sound as though the act of selecting the coordinate system at the appropriate time is what causes the motion of the Earth.

[Edited to remove reference to an earlier discussion on this forum.]

In my opinion, it is wrong to say that a choice made by an analyst is the cause of anything in the system being analyzed. The physical system will behave according to the laws of nature, regardless of how, or whether, the analyst chooses to go about his business. The analyst is a spectator of the scene, not an actor in it. (Unless he happens to also be the one firing the rocket.)

You may disagree as to the use of the term "cause"; that is of course your right. But you might think about stating the case for causation in a way that emphasizes the properties of nature rather than your prerogative to choose how you analyze nature.

 

[GregAshmore]

Thank you all for the details on how proper acceleration is calculated. From this moment on, I am by [my] rule not permitted to speak further on the subject until I have learned to do the calculation for myself.

This will do it for me on this thread. I learned a lot. Hopefully I will show a bit more competence as I move forward with study and especially working of problems.

I owe George a rework of my analysis of the twin paradox. I'll post it when it's done--could be a week or two.

 

[Dale]

Thank you for the further information. This gives a much different impression than you have given so far. Up to now, you have made it sound as though the act of selecting the coordinate system at the appropriate time is what causes the motion of the Earth.

It is the selection of the coordinate system which causes the motion of the earth. I don't know what you think that I have said differently now than I have at any time previously.

Perhaps you were simply not aware that coordinate systems on spacetime cover both space and time in a single coordinate system? I don't know how you could be unaware of that fact in a discussion about spacetime, especially given the references I and others have provided. Particularly the Dolby and Gull reference which I have repeatedly recommended and which clearly spells out how to develop such a coordinate system.

The physical system will behave according to the laws of nature, regardless of how, or whether, the analyst chooses to go about his business. The analyst is a spectator of the scene, not an actor in it. (Unless he happens to also be the one firing the rocket.)

Agreed.

But you might think about stating the case for causation in a way that emphasizes the properties of nature rather than your prerogative to choose how you analyze nature.

The point is that some things which you think belong to nature actually do not belong to nature but to the analysis itself. The choices the analyst makes don't cause any changes in nature, but they do cause changes in the analysis.

Whether or not a given object is moving is not a property of nature, it is a property of the analysis. Therefore, the analysts choices are in fact the cause.

 

[Dale]

I am by [my] rule not permitted to speak further on the subject until I have learned to do the calculation for myself.

A very wise rule. If you have trouble with the computations, don't hesitate to ask. I would not consider that "speaking further on the subject".

Also, if you use Mathematica, I can share code as needed, although writing your own is itself quite instructive.