Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Sam Brown on 01/10/2018 14:37:18

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?

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 freefall independent of where it is.

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.
...

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?

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 “freefloat” 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”.

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.

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

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?

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

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.

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.
This negates the entire purpose of the term. I cannot think of a single named object then that meets this description of free fall. The sum of its kinetic and gravitational potential energy would need to be a positive number, and as I said, nothing seems to meet that description except the highenergy ejecta from stars and such.
I can be in free fall in my kitchen, albeit only for a moment since somebody inconveniently put a floor in my orbital path.
Free motion as in Newtons 1st would be a better name
Newton's first references objects with no forces at all acting upon them. I cannot think of anything that meets this description, not even the ejecta. Everything has a curved trajectory due to the impossibility of having no forces acting upon it. I suppose there are a very few precise points between galactic superclusters where such forces are at least balanced and relatively stable for a while, allowing an object to move in an actual straight line in any frame where it isn't stationary.

Everything has a curved trajectory
...except light that's not being gravitationally lensed, presumably?

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)?

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.
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" 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.
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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 noneuclidean 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 threedimensional space: " https://philosophy.stackexchange.com/questions/32834/waskantincorrecttoassertallmathsasapriori

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.
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" 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 .

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.

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 (nonEuclidean) space. Sublight 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.

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.
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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.

This one might give some insight in how Einstein saw it.
https://www.pitt.edu/~pittcntr/Being_here/last_donut/donut_201213/091412_lehmkuhl.html

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

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.
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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 ;) )

But space is curved and that is why the path is the shortest distance, that being the curved motion from the point of view of the observer. Due to the acceleration of gravity being greater one side as compared to the other. They are under there own relative motion. Only question is which body is going under acceleration ?

But space is curved and that is why the path is the shortest distance, that being the curved motion from the point of view of the observer. Due to the acceleration of gravity being greater one side as compared to the other. They are under there own relative motion. Only question is which body is going under acceleration ?
I think neither are since an accelerometer on either body will read zero.
I also think it is spacetime (rather than space) which is curved

But space is curved and that is why the path is the shortest distance, that being the curved motion from the point of view of the observer. Due to the acceleration of gravity being greater one side as compared to the other. They are under there own relative motion. Only question is which body is going under acceleration ?
I think neither are since an accelerometer on either body will read zero.
I also think it is spacetime (rather than space) which is curved
But if relativity is to be believed, how could space be curved and relative from the point of the observer simultaniously ? Surely the observer should see a straight line space due to acceleration being relative ? I think pedant is the word.

But if relativity is to be believed, how could space be curved and relative from the point of the observer simultaniously ? Surely the observer should see a straight line space due to acceleration being relative ? I think pedant is the word.
Pedant? Do you mean "dependent"?
Do you disagree that we should be discussing "spacetime" rather than "space"?
It is not my understanding that motion caused by gravity can be called "relative acceleration" but I am not really qualified to give an opinion and will defer to others better able to do so.
Actually it is my understanding that acceleration is not relative but absolute but again I could be wrong.

I do not see how space and "space time" are different.
Free fall acceleration of earth is dependant upon distance, is in no way constant
(https://upload.wikimedia.org/wikipedia/commons/thumb/5/50/EarthGravityPREM.svg/1177pxEarthGravityPREM.svg.png)
Thus will give a linear view to the observer, unless it is NOT relative ?
From https://en.m.wikipedia.org/wiki/Structure_of_the_Earth
Pedant https://www.thefreedictionary.com/pedant

Ok Geordie but you should check both the quotes and article I linked. Einstein did not geometrize SpaceTime. As far as I get it he tried to unify EM and gravity into a 'field', observer dependent .He was not happy with people thinking of SpaceTime as a geometry. So the discussion is slightly out of rails I guess, if we want to understand the way he thought about it :)
" Dennis proceeded to a detailed account of what Einstein did think he was doing in general relativity. In brief, it was all about unification. In Einstein's special theory of relativity, we learned that the apparently distinct electric and magnetic fields were really just observer dependent manifestations of the one entity, the electromagnetic field. What for one observer might look like a purely magnetic field may manifest for another as a mix of both electric and magnetic fields.
It is the same for motion in general relativity. What may appear as motion in a gravitational field for one observer may manifest for another as gravitationfree motion. This was the real import of Einstein's famous elevator thought experiment and his principle of equivalence. Gravity has not been geometrized. It has been relativized. Inertia and gravity are unified in general relativity. Einstein's research trajectory then leads naturally to the focus of his last decades, a unified field theory that would merge gravity with electromagnetism. " by John D. Norton
I suppose, or if you like, at least suspect that the 'fifth dimension' he looked for later was to find a way around observer dependencies, to unify those too into one 'field'.

Acceleration is differing from a uniform motion in that it isn't frame dependent .Earth can be seen as accelerating at one gravity and so when you stand on a scale, you actually prove that acceleration.
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Maybe a better way to express it is that it (a acceleration/deceleration) is locally provable, as well as locally unchanging no matter what frame of reference you use, whereas a uniform motion is dependent on what frame of reference you use to define it.