An orbiting laboratory is considered in GRT as a free falling laboratory and free falling systems are locally inertial.
The orbiting stability according to the least action principle seems to deny such a possibility. A force acts against any attempt to fetch objects away from the center of mass of the orbiting laboratory, regardless of small distances considered.
But it seems Einstein was right.
Aleksei,
Can you estimate the distance from the center of mass where g is of order of g at the ground?
"It has the same intensity as a gravitational force at ground level, if the orbit is at the level of the earth's ground (v=10km/s)."
Please concentrate...calculations already done.
I kindly invite you to do it yourself now.
Aleksey,
"you really think that there is such force even for very small distance? I thought you admit that there is no such force for small distancies, but it increases very fast then you go from the center of mass."
According to your opinion, such force what should it be due to??
What force would increase very fast if you detatch from the center of mass??
It is not a strong force which increases with distance (to a very small distance).
"The force will be of order of d/REarth, there d is the distance from the center of mass."
Please recalculate....displacement is for sure in radial direction, the force is much stronger than the negligible quantity you propose.
"Do you think that all videos from the space, showing real free falling are fake or what?"
In satellites in free space the force is negligible since the gravitational potential is negligible, since the distance from earth surface is thousand kilometers usually.
You cannot perform experiments close enough to Earth's surface at 10 km/s (36.000 km/h) in atmosphere, everthing would burn away. Only in GPS statellites with 3 km/s (11-12.000 km/h) but 3 thousand km over the Earth surface, it would be possible to appreciate such stability force, there no man have ever been present.
"of course, everythere d
Aleksei,
You are right about the 400 km and the fact that in such case the force should be comparable to the one on Earth, then.
Tidal force has nothing to do with any orbit stability.
The stabilty is given through the LEAST ACTION PRINCIPLE minimising the angular momentum. The force derives from the variation of the angular momentum of the mass in orbit. Tidal forces are there to disturb such stability.
Infact there is micro gravity and there the free fall is tested.
Aleksei,
I know there isn't any strong force here, I was kidding, since I didn't imagine a force which increased with distance...
Regarding tidal forces if you intend "spaghettification" it is what happens, you are right. Every object tends to follow its own orbit, and different orbits are due to the very slight variations of the gravitational field with the distance, for which saturn rings are the most marvellous example.
I wonder why tidal locking is not explained in such way in Wikipedia.
Anyway you are right the Orbital station is virtually inertial, since it is at 400km and the gravitaional acceleration there should be almost the same as g, but it is negligible.
"Minimal angular momentum (norm of angular momentum,minimiation of a vector is impossible) corresponds to absnce of rotation (J=0)".
The least action principle is based on the minimisation of angular momenta. In this case there is a variation of the angular momenta in the attempt to dethatch the mass from its actual orbit, (the rotation axis is the center of Earth).
According to such principle in the case of constancy of the field there should be recall force. centripetal acceleration is already the gravitational interaction thanks to the equivalence principle.
What is left are small variations of the field and it is not very clear why the residuals should be a force increasing with distance.
Aleksei,
in a problem where it is present an induced variation of the angular momentum only that is the one to be minimised and corresponds fully to the action.
Stefano
I can give you guys the real world practical answer, because we in fact have had and do have such orbiting laboratories at NASA, and in the late 1980s through the early 1990s were very actively pursuing them for experiments and processes that required low or no gravity.
No design was ever proposed that even claimed to be "zero gravity." The best that could be obtained was "microgravity." There has been less (but some) interest since because of two factors: nanotechnology promised the ability to manufacture similar materials without expensive access to microgravity, and the 1996 Space Commercialization Act forbid NASA to fly commercial payloads on either the Shuttle or the aircraft that fly parabolas to simulate microgravity.
The principle sources of gravity in such a laboratory are (1) disturbances due to other activities, and (2) tidal forces which were discussed above. Disturbances can be addressed by making the laboratory very large and heavy (expensive to launch) and curtailing other activities. Tidal forces can be addressed by placing the laboratory farther from earth (also more expensive).
http://en.wikipedia.org/wiki/Micro-g_environment gives tidal forces in low earth orbit as 0.33 μg/m.
So even if disturbances were completely eliminated, such a laboratory would at best be inertial only for isolated point-sized observers in differentially small volumes.
Dear Robert,
Microgravity is already something quite good. It has a negligible value compared to the acceleration provoked by the same gravitational potential.
It would be very interesting to know how the passage from gravity to microgravity is performed:
A train on the surface of Earth, in vacuum could reach in principle 10km/s, which is approximately the orbiting speed at ground level. It would run almost weightless.
Inside the train I set a tower of some meters where I set twin oscillators one on top of the other.
When the train is still, the oscillator below will shoot its photons which will be seen redshifted (Pound and Rebka)
If I make train move, and reach the 10 km/s speed, at such speed the Redshift will be negligible if compared to the (1+gh/c^2) value. It has to be very close to zero since other values like (1+gh/c^2), would violate the energy conservation laws.
Here though there is no mechanism of compensation of the time dilation with the first order doppler effect of free falling (gh) to make the difference, since there is no first order doppler effect.
What would be the law in between the initial value (1+gh/c^2) and the negligible final value depending only on the tidal effects of the gravitational field??
According to the Schwartzshild solution the frequency shift of the oscillators is close to (1+3/2*gh/c2) for the orbiting system which does not seem to make sense....
Anyway the answer to the initial question is no, since the tidal effects increase by approaching to the massive object.
The Einstein's intuition was right to the extent that most of the gravitational attraction is cancelled 99%.
This falsifies the Strong equivalence principle. SEP is a very good approximation of reality, the closer we get to a small scale.
"Stefano, you were answered before: it is inertial only locally (it is quite obvious already in Newtonian mechanics). Einstein was understanding it from very begining, and that is the reason why general relativity takes the form it takes."
Yes, from 1907.
That it is quite obvious in Newtonian Mechanics I would not say that at all, since Newton would never choose a free falling reference frame as Inertial.
The revolution was the cancelling out most of the gravitational effects with inertial which brougth together with the Stress Tensor of energy-momenta to extend special relativity.
"And if you do your calculations in right way, there can be no "redshift" proprtional to h, only h^2 and higher (corresponding to "microgravity"). Don't forget to take into account the acceleration of the train/other body due to trajcetory curvature that should be of order of g."
Schwartzshild solution does not seem to be enough....or it is???
A short contribution to the explanation in the order of the Theory of Reference Frames that distinguishes the First Type of the Gravitational Field from the Second Type: an orbital reference frame (second type) in suitable physical conditions can be an inertial reference frame with respect to a reference frame supposed at rest while a reference frame in free fall (first type) never can be an inertial reference frame with respect to a reference frame supposed at rest.
It happens basically for three reasons: 1. absolute reference frames don't exist; 2. the Generalized Principle of Inertia is valid; 3. the correct application of the Principle of Relativity.
according to GRT a free falling reference frame is a good approximation of a galilean inertial system.... I know Fock says that it is not inertial since it is not isolated...
A reference frame in free falling isn't inertial for two reasons: firstly because it doesn't respect the Generalized Principle of Inertia and secondly because it doesn't respect the Principle of Relativity. What Fock says on isolated systems in case regards another question and precisely the difference between Galilean reference frames and Einsteinian reference frames that is largely examined in TR.
"A reference frame in free falling isn't inertial for two reasons: firstly because it doesn't respect the Generalized Principle of Inertia and secondly because it doesn't respect the Principle of Relativity. What Fock says on isolated systems in case regards another question and precisely the difference between Galilean reference frames and Einsteinian reference frames that is largely examined in TR."
The Einsteinian inertial reference frame is the free falling one as far as I know.
As a matter of fact Einstein didn't like the term "inertial", in fact he maked use of that not many times perhaps because he saw in that term something that was connected with the concept of absolute. He preferred to use the concept of "coordinate system supposed at rest" and the concept of "moving coordinate system". And I agree that an absolute inertial reference frame doesn't exist but it is possible and useful to define a relative inertial reference frame.
At heart of this definition there is a resting reference frame, I repeat "supposed at rest", but just this state of rest has relative and non-absolute character. For example I can suppose that my still laboratory on the earth is a resting reference frame, but in the meaning relative, because all in the Universe is moving and nothing is in a state of absolute rest. After this definition inertial reference frames with respect to my laboratory are all reference frames that have uniform speed with respect my laboratory. Consequently a reference frame in free falling with respect to the earth cannot be considered an inertial reference frame with respect to both the resting laboratory and any other reference frame at rest on the earth, because it is accelerated.
If our laboratory is instead in free falling we could assume it is the resting reference frame and then in that event inertial reference frames are all those reference frames that move with the same acceleration of the laboratory. In that case therefore the earth and all still reference frames on the earth aren't inertial with respect to the laboratory.
The Einsteinian reference frame then is open, non- isolated and interacting with the Universe while the Galilean reference frame on the contrary is closed and isolated. Consequently the GRF is protected more than the ERF with respect to perturbations and interferences in concordance with the R. Shuler comment about very large and heavy laboratories.
I not was enough clear on the concept of "reference frame supposed at rest" and I apologize for.
Let us consider then two reference frames S[O,x,y,,z,t] and S'[O',x',y',z',t'] that are in relative motion with uniform relative speed v. I define these two reference frames as inertial because they have different speeds but equal accelerations with respect to any other reference frame of the universe. Origins and coordinates of these two reference frames generally are different and they can coincide only in particular physical situations and anyway not all for always. It is manifest that relative geometric points defined by respective coordinates into the two reference frames in relative motion are different and it happens without any destruction of the space topology. In the described physical situation I can consider one of the two reference frames is "supposed at rest" with respect to other without it involves some distruction of the space topology but only for reasons of expedience.
The question instead concerns transformation equations that relate coordinates (x,y,z,t) of the first reference frame S and coordinates (x',y',z',t') of the second reference frame S' in relative motion. The question has different answers:
1. In classic physics Galileo's transformations are valid.
2. In modern physics (Special Relativity) Lorentz's transformations are valid and in General Relativity they are valid only in local way. In GR the space-time element is non-linear, it involves in the presence of the gravitational field the linear motion isn' t possible or it is possible only approximately in local way for very small paths.
3. In post-modern physics numerous and different formulations of Lorentz' s transformations are valid.
4. In contemporary physics transformations of the Theory of Reference Frames are valid whether for inertial or non-inertial reference frames.
Scientists think differentially about these different answers.
REGARDING THE CENTRE OF MASSES, I HAVE A QUESTION. IF YOU CONSIDER A SYSTEM OF MASS DISTRIBUTED IN A SPACE. DOES IT IN THE END COLLAPSE INTO THE ONE POINT MASS AT THE CURRENT CENTRE OF MASS?
Yes if they are initially at rest or posessing negligible diverging speeds.
Dear Akira, you are right. Until now in physics dynamics of orbiting laboratories has been studied little, but I am sure that in future it will be investigate more because space missions will increase. In physics mathematical models are necessary in order to describe scrupulously the behavior of physical systems and often those models are distant from the physical reality like for example the point mass. The choice of point mass is a question of expediency when it is not important to consider the internal structure of the system. Let us consider also the point has zero volume. In the event of laboratories it is manifest the the internal structure is important and consequently that mathematical model isn't right. In that case I think fundamental principles of physics can help to understand and explain the behavior of moving laboratories in the space.
I think dynamics of the collapse of a physical system is different whether from the collapse into one point mass or from the collapse into the centre of the mass.
It will gather to the center of mass of the system, A body will form having a mass approximately the sum of the masses..
Akira,
it is possible in one instant as a boundary condition. Then everything moves.
Yes Akira,
but the motion of charges does not emerge from a warped space-time... it is quite different since the principle of equivalence between gravitation and inertia demonstrated in the etvos experiment does not hold for electric charges but only for their masses.
Your discussion is giving excellent outcomes. Electric charge and mass are two different physical realities and attempts of unifying them are fruitless. A contribute to the discussion: electron and proton have the same electric charge (except for the sign) but they have very different masses. It proves there isn't a direct relation between mass and charge.
Yes in fact I don't see how to integrate them either. But that does not mean that space-time is not suitable to explain gravitation phenomena.
The space-time is necessary and suitable to explain all physical phenomena and not only gravitational phenomena. Problems are born when one wants to give to space and to time a physical behavior and meaning that they don't have and when one wants to unify what it isn't possible to unify. It doesn't exclude that some unifications can be done. For example electric and magnetic phenomena have been unified into one only theory, preserving suitable differences and without generating confusions.
Dear Akira,
I would want to do before an useful explanation about terms in order to a better understanding. From my viewpoint modern physics is represented by four fundamental theories: Special Relativity, General Relativity, Quantum Mechanics, Standard Model. Consequently it regards almost all the past century (20th century) and the current physics cannot be considered modern. The current physics, always from my viewpoint, is represented by three directions of research: 1. post-modern physics that is in continuity with modern physics, 2. neo-classic physics that would return substantially to classic physics with some change, 3. contemporary physics that from my viewpoint is represented by the Theory of Reference Frames, Deterministic Quantum Physics, Non-Standard Model.
I agree with you fully that definitions of space and time are very important in physics. From absolute space and absolute time in classic physics there was a change to one only absolute space-time in modern and post-modern physics that has worsened things. In fact in modern physics Einstein searched for giving operative and non-metaphysical definitions of space and time but then he reached the definition of one only metaphysical space-time.
My critical research starts just from these considerations in order to reach new definitions of space and time, that are more concordant with the physical reality and successively a new fundamental physics that strives to eliminate many incosistencies and contradictions that are present in modern and post-modern physics.
Dear Akira, in order to have an useful exchange of views I send you the link of a paper of mine.
Best regards.
Daniele Sasso
Article Physico-Mathematical Fundamentals of the Theory of Reference Frames