Is momentum conserved as a body falls through a gravitational field?

[PeterDonis]

there is not any observable physical difference.

Then you should reconsider your apparent belief that there is any difference. In other words, you aren't describing two different ways the world could be. You are just describing the same physical configuration using two different strings of words.

The difference is, I believe, that if the field (i.e. gravitational field/spacetime geometry in case at hand) can be conceived as a system's constituent then we may assign it physical properties (such as energy, momentum etc..) otherwise may not.

Why would you think that? How can we magically give anything physical properties by drawing a "system" boundary around it and saying it's "part of the system" instead of not.

In other words, since you agree that "part of the system" vs. "not part of the system" makes no physical difference, that is telling you that "part of the system" is a human convention, not physics. It's no different from assigning a coordinate chart. You can't change physics by changing coordinate charts. Similarly, you can't change physics by changing how you draw the boundaries of "the system".

 

[PeterDonis]

Or you can (more realistically) say it's subject to a force external to the system we are considering. For example we could hold the Earth in place with a sufficiently powerful rocket.

The "more realistically" juxtaposed with the Earth example is very entertaining.

 

[cianfa72]

How can we magically give anything physical properties by drawing a "system" boundary around it and saying it's "part of the system" instead of not.

Of course that's true. I was reasoning along the lines of Feynman in lecture 10-5.

He claims that in order to check out the law of conservation of momentum for electric charges, it makes sense to assign a momentum to the electromagnetic field. Hence the system he actually considers is "charges + field" assigning a physical property (momentum) to the field itself.

 

[PeterDonis]

He claims that in order to check out the law of conservation of momentum for electric charges, it makes sense to assign a momentum to the electromagnetic field.

Yes. But what he describes does not work for gravity.

 

[cianfa72]

Yes. But what he describes does not work for gravity.

Why not ? Could you be more specific ?

 

[PeterDonis]

Why not ? Could you be more specific ?

Because the energy and momentum "stored in a gravitational field" cannot be localized the way energy and momentum stored in an EM field can be. In more technical language, there is no stress-energy tensor for the "gravitational field" in GR, the way there is for the EM field.