[Sam Brown (OP)]

Sara asked us this question:

"Astronauts in a space ship orbiting the earth feel weightlessness because the ship is in free fall towards the earth. In deep space they still feel the same weightlessness. My question is: Is the ship in free fall in deep space too?"

What do you think?

[PmbPhy]

Sara asked us this question:

"Astronauts in a space ship orbiting the earth feel weightlessness because the ship is in free fall towards the earth. In deep space they still feel the same weightlessness. My question is: Is the ship in free fall in deep space too?"

What do you think?

Yes. In fact, anything which has only the gravitational force acting on it is in free-fall independent of where it is.

[Janus]

As PmbPhy pointed out, as long as nothing prevents them from freely responding to gravity, they are in free fall. And there isn't anyplace you can go that is completely free of gravity.

Get far enough away from the Earth, and you are in free fall around the Sun.
Get far enough away from the Sun, and you are in free fall around the center of the galaxy.
Get far enough away from the galaxy and you are in free fall around the barycenter of the local group of galaxies.
...

[geordief]

How does the object that is freefalling  "know " that the  environment is telling it to move in a particular direction?

It is not being bathed in gravitons,  is it ?-as these are only caused by changes in mass and energy.

Or does the simplest relative  motion bring about such a change and cause gravitatonal waves  to emerge?

[Bill S]

How does the object that is freefalling  "know " that the  environment is telling it to move in a particular direction?

Possibly, it doesn’t “know”, any more than the occupants of the craft (if that’s what it was) would know they were free falling, just by being there.

Incidentally, Richard Wolfson, “Simply Einstein”, uses the term “free-float” rather than free fall; the meaning is the same, but as he is writing for lay people, he considers it aids visualisation in the case of objects that are not obviously “falling”.

[PmbPhy]

How does the object that is freefalling  "know " that the  environment is telling it to move in a particular direction?

Because there is a gravitational field at that location telling it what to do.

[Bored chemist]

"Are ships in free fall in deep space?"
Not if the engines are running.

[geordief]

Because there is a gravitational field at that location telling it what to do.

I keep hearing that a field is not a thing but a model.

The object cannot "know" what any model is saying ,can it?

Must there be a model incorporating this knowledge aspect so that there is a handle on how the object is informed how to move.

I am aware of the "mass tells spacetime how to curve and spacetime tells matter (?) how to move but again spacetime is a model  and not a "thing" ,not so?

[Petrochemicals]

Nope a body in space is under the gravitational pull of the various objects in its vecinity, it is travelling in one way then the other, where as an object in orbit that is falling consistently to the barycentre of it and another object is in free fall. Free fall is only when the objects are in a declining orbit around each other that without extra force being input into the system the objects will collide.

Free motion as in Newtons 1st would be a better name

[geordief]

Free motion as in Newtons 1st would be a better name

Not to add anything but I was going to make exactly the same suggestion(had no concious idea Newton had had  a use for the term)

Well I was unsure whether "free motion" would cut the mustard either.

I went on to wonder,  though  whether motion is the natural state of a system...."being stationary" only existing really as an abstract concept.

[chris]

Everything has a curved trajectory

...except light that's not being gravitationally lensed, presumably?

[geordief]

Everything has a curved trajectory

...except light that's not being gravitationally lensed, presumably?

Surely even light since it moves in gravitational fields no matter how weak?

Isn't euclidean straightness an idealization (a mathematical limit)?

[yor_on]

I don't think it was for Einstein geordief. The way I got it he didn't consider trajectories 'curved'. As I read him he thought of them as the shortest path, and how can the shortest path be curved? I know, you can argue the opposite, but that's what I got from reading him.
=

" Already in the first papers in which Einstein starts making use of the metric tensor to give an account of gravitation, he is at pains to establish the status of the geodesic equation as describing the motion of particles as “straight and uniform” (geradlinig und gleichförmig) even when subject to gravity.  ...   Einstein thought of (static) gravitational fields not as invariant force fields diverting particles from inertial motion. Already, in 1912, he thought of equation (1) as describing inertial motion on one hand, and as describing motion in the presence of (static) gravitational fields on the other. "

It's funny but even when not knowing this I wondered how SpaceTime would 'look' if 'folded out' into what we normally would call 'straight lines'. Which also lead me to wonder how many simultaneous 'geodesics' there could be at one point in the SpaceTime we see astronomically. The answer I got was innumerable.
=

Ah, rereading you I think we're two of a same mind. You're perfectly right

" Mathematical truth is completely independent of experience. It doesn't depend on social conventions, and it is not possible that someday new evidence will overthrow what we know to be mathematical truth. It's rooted in logic, which is something that Kant understood extremely well.

The argument that non-euclidean geometry somehow refutes Kant's position on this demonstrates a misunderstanding of what he was saying. When Kant spoke in terms of Euclidean geometry, he wasn't asserting that it was the only possible geometry. Rather, he was asserting that our representations and how we experience reality is limited to three-dimensional space: " https://philosophy.stackexchange.com/questions/32834/was-kant-incorrect-to-assert-all-maths-as-a-priori

[geordief]

I don't think it was for Einstein geordief. The way I got it he didn't consider trajectories 'curved'. As I read him he thought of them as the shortest path, and how can the shortest path be curved? I know, you can argue the opposite, but that's what I got from reading him.
=

" Already in the first papers in which Einstein starts making use of the metric tensor to give an account of gravitation, he is at pains to establish the status of the geodesic equation as describing the motion of particles as “straight and uniform” (geradlinig und gleichförmig) even when subject to gravity.  ...   Einstein thought of (static) gravitational fields not as invariant force fields diverting particles from inertial motion. Already, in 1912, he thought of equation (1) as describing inertial motion on one hand, and as describing motion in the presence of (static) gravitational fields on the other. "

It's funny but even when not knowing this I wondered how SpaceTime would 'look' if 'folded out' into what we normally would call 'straight lines'. Which also lead me to wonder how many simultaneous 'geodesics' there could be at one point in the SpaceTime we see astronomically. The answer I got was innumerable.

Yes but those lines were not Euclidean ,were they?

A "straight line" in GR is the shortest path....

I find it interesting (insofar as I was able to understand it ) that some ( all?) of the proofs  demonstrating  the tensors determining spacetime curvature do seem to rely on plain Euclidean geometry.

The curvedness seems to be constructed from plain straight lines.

Euclidean geometry  seems to be like a mathematical lingua franca .

[PmbPhy]

I keep hearing that a field is not a thing but a model.

You are hearing something wrong. A field can detach itself and propagate through space far from its original source just as an electromagnetic wave does and that's all field. Its real because it carries energy and momentum and can influence whatever it comes in contact with. Besides. You're using the term model incorrectly. I recommend looking up the definition in Wikipedia.

[Halc]

Everything has a curved trajectory

...except light that's not being gravitationally lensed, presumably?

Surely even light since it moves in gravitational fields no matter how weak?

Yea, I agree with geordief here.  Sure, one can view light as taking a straight shortest path sort of like airline routes plotting a great circle that appears longer on a flat map, but then gravitational lensing isn't really bending of light.  Two interpretations of the same thing..

Light seems to have inertia even if it doesn't have proper mass.  It can push things, and conservation of momentum laws says that it must thus change direction when it bends around gravity wells since the gravitational object is getting the equal and opposite reaction.  This can indeed be depicted as light traveling in straight lines on bent (non-Euclidean) space.  Sub-light objects cannot take such a locally straight trajectory.

Another POV is that light obviously doesn't take the shortest path.  Enough gravity lensing (a series of hyperbolic turns around at least a pair of black holes say) will bend light back the way it came, and it might take years to make a trip that it could have done in seconds.

[yor_on]

What do you mean by " A "straight line" in GR is the shortest path.... "  ?
Try the quotes I gave and see if they agree with it.
=

Maybe I did misread what you meant saying that " Isn't euclidean straightness an idealization ". The way I understood that sentence was in pointing out that it was a limited truth, much like Newtonian physics versus relativity? You need to define your thoughts again.

[yor_on]

This one might give some insight in how Einstein saw it.
https://www.pitt.edu/~pittcntr/Being_here/last_donut/donut_2012-13/09-14-12_lehmkuhl.html

[jeffreyH]

Gravity deviates objects from inertial motion. It is the opposite of Newton's first law.

[geordief]

What do you mean by " A "straight line" in GR is the shortest path.... "  ?
Try the quotes I gave and see if they agree with it.
=

Maybe I did misread what you meant saying that " Isn't euclidean straightness an idealization ". The way I understood that sentence was in pointing out that it was a limited truth, much like Newtonian physics versus relativity? You need to define your thoughts again.

I haven't got around to reading  your  quotes (or PmbPhy's Wikipedia "model" page ) yet ,but I will soon)

Still ,just to clarify your question (with caveats on my strictly amateur  level of understanding) I was trying to claim  that the "straight lines" we use in mathematics  are idealizations in that whenever we try to draw one  in any physical situation they will be slightly off.

For the purpose of analysis  we ignore that  and so they are a mental construct really.

Not sure I can stand by my "they are a limit " comment  meaning they are what we get when a crooked line is straightened without limit.(it seems as if I am  trying to reinvent the concept of geodesics unnecessarily -too much time on my hands      )