How Does the Principle of Equivalence Lead to Gravity Curving Space?

[Mueiz]

Let us examine the second observer riding on the edge of the disc. The Newtonian equation for centripetal force is F = m*v^2/r. Now the velocity of a particle on a rotating disc is a function of its radial displacement, so let us say v = f*r where f is an arbitrary constant, then by substitution, the centripetal force is F = m*f*r so we see that centripetal force increases with radius. The second observer on the edge of the disc will be experiencing greater acceleration than the third observer nearer the centre of the disc. Now the relativistic centripetal force will be even greater F = m*f*r/sqrt(1-(f*r/c)^2) in the non rotating reference frame and greater still in the rotating frame F = m*f*r/(1-(fr/c)^2). So we can conclude (If I have estimated the relativistic versions correctly) that the observer on the arbitrarily large disc will be experiencing exponentially large "centrifugal proper force" at relativistic speeds and not the vanishingly small force you seem to be assuming when you claim the second observer is effectively inertial. An observer experiencing large proper force is NOT an inertial observer.

It seem to me that you did not understand the logic by which I conclude that the second observer is inertial
it is that only the circumference of a very large disc is almost a straight line to any degree of approximate ...so it is in uniform motion relative to the first observer who is inertial ...if we are in uniform motion relative to an inertial observer then we must be inertial too ...tell me what is wrong with this ..before going to calculation
i want you also to reply the question i gave in my previous input

 

[yuiop]

according to the opinion of absolute acceleration in empty space even gravitational field can not be detected .and the inertial frame you all have been speaking of can not be distinguished from that of fee-falling in gravitational field

Are you sure about that? If you are free falling in a gravitational field, and there is another observer falling with you but below you, then they will be moving away from you. In order to stay at a constant distance from you the other observer would have to accelerate constantly towards you. Even when they maintain constant distance from you there clock will be ticking at a different rate to yours. In a true inertial reference frame in flat space, observers at rest in the reference frame are stationary with respect to each other, all experience zero proper acceleration and all their clocks are running at the same rate. Clearly there is no arrangement of the vertically separated fallers in the gravitational field that can duplicate being in a true inertial reference frame in flat space. The falling observers only approximate an inertial reference frame, if they are very close together, so that the errors are small. All these difference come about as a result of tidal effects and that is what distinguishes a real gravitational field from the pseudo-gravitational field that results of artificial acceleration in gravitationally flat space.

 

[yuiop]

It seem to me that you did not understand the logic by which I conclude that the second observer is inertial
it is that only the circumference of a very large disc is almost a straight line to any degree of approximate ...so it is in uniform motion relative to the first observer who is inertial ...if we are in uniform motion relative to an inertial observer then we must be inertial too ...tell me what is wrong with this ..before going to calculation

You conclude that the observer on the edge of a very large disc is inertial because locally they appear to traveling in approximately a straight line, but that is not the definition of inertial motion. Inertial motion is motion with zero proper acceleration and the observer on the edge of the large disc would be experiencing very large proper acceleration at high velocities and is therefore not inertial by definition.

 

[Mueiz]

In the above two quotes you are descending into nonsense based on some sort of home grown understanding of Mach's principle. You seem to be claiming that it is impossible to rotate a disc or accelerate a rocket far from any gravitational sources. Are you aware that Einstein ultimately rejected Mach's principle? Are you aware that the Kerr solution is a vacuum solution that defines the metric for a spinning massive body in the ABSENCE of any other reference bodies and is specifically defined as a spinning massive body in an otherwise

Let us save our effort and concentrate in Thought as abstract
I think it is not a subject of physics '' who said and How someone understands''
suppose this is my own opinion and convince me with facts and logic , i really mentioned some sources in order that someone may want to read more about the issue

 

[Mueiz]

You conclude that the observer on the edge of a very large disc is inertial because locally they appear to traveling in approximately a straight line, but that is not the definition of inertial motion. Inertial motion is motion with zero proper acceleration and the observer on the edge of the large disc would be experiencing very large proper acceleration at high velocities and is therefore not inertial by definition.

Then if someone want to apply Pythagoras Theorem in the ground of his house ,he must remember that the Earth is not flat

 

[Dale]

Your accelerometer measures the deviation from the inertial frames which are special frames in gravitational field but in zero gravitational field all frames are inertial and your accelerometer
is useless

This is incorrect. As I said above an accelerometer measures proper acceleration, which is the magnitude of the covariant derivative and is a frame invariant quantity. An accelerometer's operation does not rely in any way on reference frames and is completely insensitive to gravitatonal fields.

 

[Mueiz]

This is incorrect. As I said above an accelerometer measures proper acceleration, which is the magnitude of the covariant derivative and is a frame invariant quantity. An accelerometer's operation does not rely in any way on reference frames and is completely insensitive to gravitatonal fields.

why quoting the my opinion leaving leaving reasons and discussion?

 

[Dale]

why quoting the my opinion leaving leaving reasons and discussion?

Because I am on a mobile device, so I can only hit the most imoprtant point. In this case, your misunderstanding of accelerometers.

Why did you ignore my entire post?

 

[Mentz114]

This is incorrect. As I said above an accelerometer measures proper acceleration, which is the magnitude of the covariant derivative and is a frame invariant quantity. An accelerometer's operation does not rely in any way on reference frames and is completely insensitive to gravitatonal fields.

Muez is taking an extreme fundamentalist Machian line - that there is no inertia in the absence of gravity. He admitted this in an earlier post, but won't restate it because he likes a good ( if pointless ) argument.

why quoting the my opinion leaving leaving reasons and discussion?

State your belief that there is no interia in the absence of gravity.

 

[yuiop]

Let us save our effort and concentrate in Thought as abstract
I think it is not a subject of physics '' who said and How someone understands''
suppose this is my own opinion and convince me with facts and logic , i really mentioned some sources in order that someone may want to read more about the issue

I gave you some facts. Here...

You conclude that the observer on the edge of a very large disc is inertial because locally they appear to traveling in approximately a straight line, but that is not the definition of inertial motion. Inertial motion is motion with zero proper acceleration and the observer on the edge of the large disc would be experiencing very large proper acceleration at high velocities and is therefore not inertial by definition.

.. and here ...

Are you sure about that? If you are free falling in a gravitational field, and there is another observer falling with you but below you, then they will be moving away from you. In order to stay at a constant distance from you the other observer would have to accelerate constantly towards you. Even when they maintain constant distance from you there clock will be ticking at a different rate to yours. In a true inertial reference frame in flat space, observers at rest in the reference frame are stationary with respect to each other, all experience zero proper acceleration and all their clocks are running at the same rate. Clearly there is no arrangement of the vertically separated fallers in the gravitational field that can duplicate being in a true inertial reference frame in flat space. The falling observers only approximate an inertial reference frame, if they are very close together, so that the errors are small. All these difference come about as a result of tidal effects and that is what distinguishes a real gravitational field from the pseudo-gravitational field that results of artificial acceleration in gravitationally flat space.

.. but you have chosen to ignore them and have not responded to these counter arguments.

I mention what people understand by Mach's principle, but since he did not clearly define it and since you seem to be championing the principle, then the only way to proceed with a sensible discussion would be for you to define what you think Mach's principle is or whatever principle it is that you are championing that you think demonstrates that the predictions of General Relativity are wrong.

I will give you a simple though experiment for discussion purposes. Imagine we have a very large gravitational body that is rotating at 1 rpm as measured by a Sagnac device. At a very great distance we have a very small but luminous particle that is not rotating as far as a Sagnac device is concerned. Now if we pay attention to the Sagnac devices, we say the distant star is stationary and the large star is slowly rotating. Now if we pay attention to the popular description of Mach's principle we are forced to conclude that all motion is relative to the majority of mass in the universe which in this case is the slowly rotating large gravitational body. By this definition the large body is not rotating and the distant small body is orbiting the large body at some great superluminal velocity of say 100c. Does that make sense? Is that what you are claiming. Now if we had another small satellite orbiting the large massive body in geo-synchronous orbit so that it was always above the same point on the massive body, then the Machian interpretation would be that the satellite is magically suspended above the massive body without requiring orbital motion or centripetal force. The Machian interpretation of gravity would then be that near bodies are attracted by gravity and distant bodies are repelled by gravity and somewhere in between gravity is neutralised. Now if we had another satellite at the same radius as the apparently stationary satellite, but orbiting in the opposite direction then the Machian interpretation is that gravity works on objects that moving but not on stationary objects at the same distance. At different distances, the Machian interpretation is that the force of gravity depends upon whether an object orbits clockwise or anticlockwise. Is that how you understand how the universe works?

In summary the Machian interpretation predicts:
1) Objects really can orbit at velocities much greater than the speed of light.
2) Gravity does not act on objects at a certain critical distance and stationary objects can hover.
3) Gravity attracts or repels depending on distance.
4) The force of gravity depends on the orbital direction and not just on orbital velocity.
5) The speed of light is not locally isotropic in all directions to an inertial observer.

Is that how you see things?

 

[Dale]

IMO, Mach's principle is way too sloppy to be of any actual use in physics, and discussions of it tend to degenerate into rather distasteful discussions of other fantasy universes.

 

[Mueiz]

Are you sure about that? If you are free falling in a gravitational field, and there is another observer falling with you but below you, then they will be moving away from you. In order to stay at a constant distance from you the other observer would have to accelerate constantly towards you. Even when they maintain constant distance from you there clock will be ticking at a different rate to yours. In a true inertial reference frame in flat space, observers at rest in the reference frame are stationary with respect to each other, all experience zero proper acceleration and all their clocks are running at the same rate. Clearly there is no arrangement of the vertically separated fallers in the gravitational field that can duplicate being in a true inertial reference frame in flat space. The falling observers only approximate an inertial reference frame, if they are very close together, so that the errors are small. All these difference come about as a result of tidal effects and that is what distinguishes a real gravitational field from the pseudo-gravitational field that results of artificial acceleration in gravitationally flat space.

Sorry I miss this important input without intention...I agree with this ...it is a successful method to distinguish free-falling frame of gravity from your supposed special inertial frame in zero-gravity region ...I was wrong in the argument that there is no way to do so...
but this was just one of my arguments and of course as you Know wrong argument does not mean wrong opinion i will use other arguments in my coming inputs
I also hope that Mach will forgive me in using wrong argument to confirm his great idea of rejecting absolute space-time

 

[Mueiz]

I gave you some facts. Here...
.. and here ...
.. but you have chosen to ignore them and have not responded to these counter arguments.

I mention what people understand by Mach's principle, but since he did not clearly define it and since you seem to be championing the principle, then the only way to proceed with a sensible discussion would be for you to define what you think Mach's principle is or whatever principle it is that you are championing that you think demonstrates that the predictions of General Relativity are wrong.

I did not claim at all my opinion (which is that all frames in zero-gravity region are inertial )
imply that the predictions of general relativity are wrong on the contrary I said that it will not affect these prediction for the reason that the (incorrect) fact that acceleration could change the geometry of space-time was not used in formulating GR (although it is always stated in textbooks dealing with GR even those of Einstein in introducing GR) what is used is that acceleration affect the geometry in the presence of gravitational and can for example cancel the geometrical effects of gravitation ( equivalence Principle) .
the first place this (incorrect) fact is used is the rotating disc experiment which i claim to be in correct
I can summarize my opinion like this:
There are two Assumptions regarding the effect of acceleration on the geometry .one of them deals with gravitation this one is true and it is used in formulating GR so Will cause no problem .the second one deals with zero-gravity region this is incorrect and is not used in GR
so can not affect it ..but unfortunately - although not needed - is used by Einstein in rotating disc experiment to confirm the idea that acceleration changes geometry whither there is gravity or not .
where did Einstein get the right to generalize his knowledge about gravitational region to
include non-gravitational region from .
if acceleration can cancel gravitation that does not mean it must be similar to it in all aspects let alone that acceleration does not cancel all the feature of gravitational field
because anyone who know the mathematics of GR know that acceleration change the metric to be flat but can not case full Riemann tensor to vanish whose existence is an absolute property and has nothing to do with any observer's worldline .

 

[Dale]

Mueiz, please respond to the points raised in post #66. You misunderstand what an accelerometer measures in GR and you are coming to incorrect conclusions based on that error.

Also, this statement is false:

I did not claim at all my opinion (which is that all frames in zero-gravity region are inertial )
imply that the predictions of general relativity are wrong

Your claims about accelerometers are in direct opposition to the predictions of general relativity.

 

[Mueiz]

Mueiz, please respond to the points raised in post #66. You misunderstand what an accelerometer measures in GR and you are coming to incorrect conclusions based on that error.

Also, this statement is false:Your claims about accelerometers are in direct opposition to the predictions of general relativity.

No my understanding of accelerometrs is similar to yours i just use a quality terms(deviation from inertial frames ) because i am not going to do calculation I want the accelorometr just to tell me whither there is acceleration or not ,so need not quantity terms of your (magnitude of the covarian derivative) is it not true that an accelerated observer is that who is not inertial
the point of disagreement is the work of the accelerometer in zero-gravity
I want you to disscus the paradox i gave in aprevious input
I kno that you and others have may other points I did not discus but I need time because I have been discussing with more than three persons and using a dictionary very often to write and understand

 

[Altabeh]

An equivalent formulation of the Principle of Equivalence is that at any local (that is, sufficiently small) region in spacetime it is possible to formulate the equations governing physical laws such that the effect of gravitation can be neglected. This has nothing to do with "accelerometers" and the leaky argument of using "proper acceleration", which I strongly believe, is very sloppy and non-general because it has its specific coordinates (Fermi frame) to be valid! You have to look from a Fermi frame comoving with the freely-falling particle to measure a globally vanishing proper acceleration! If one claims something else, there might be a possible misunderstanding!

"Locality" is always referred to as the very requirement to define principle of equivalence for a general observer!

AB

 

[Dale]

No my understanding of accelerometrs is similar to yours i just use a quality terms(deviation from inertial frames ) because i am not going to do calculation I want the accelorometr just to tell me whither there is acceleration or not ,so need not quantity terms of your (magnitude of the covarian derivative) is it not true that an accelerated observer is that who is not inertial
the point of disagreement is the work of the accelerometer in zero-gravity

Whether or not you are going to do a calculation is not relevant, nor is the choice of reference frame, nor presence or absence of gravity. (1) An accelerometer measures proper acceleration by definition and (2) in GR the proper acceleration is the frame invariant magnitude of the covariant derivative. If you cannot accept those two statements then there is no reason for further discussion.

http://en.wikipedia.org/wiki/Accelerometer
http://www.scribd.com/doc/38324661/Accelerometer
http://en.wikipedia.org/wiki/Proper_acceleration
http://www.lightandmatter.com/html_books/genrel/ch05/ch05.html

I want you to disscus the paradox i gave in aprevious input

Which post? I don't think there is much point to further discussion while you don't understand how an accelerometer works in GR.

 

[Mueiz]

IMO, Mach's principle is way too sloppy to be of any actual use in physics, and discussions of it tend to degenerate into rather distasteful discussions of other fantasy universes.

But it is important to show whither Rotating Disc Experiment correct or incorrect because it is used in two of the most important books in physics (The meaning of Relativity and The Evolution of Physics both by Einstein ) and many beginners and advanced student of physics
are made to gain the idea of the effect of acceleration on geometry thrrough this experiment

 

[Mueiz]

Whether or not you are going to do a calculation is not relevant, nor is the choice of reference frame, nor presence or absence of gravity. (1) An accelerometer measures proper acceleration by definition and (2) in GR the proper acceleration is the frame invariant magnitude of the covariant derivative. If you cannot accept those two statements then there is no reason for further discussion.

I accept those two statement in a gravitational field
I also accept them in zero gravitation field if i agree that there could be acceleration there
but you do not want to discuss me about the existence of accelerated motion in zero-gravity region which is the point of dis agreement... you want to force me to agree with you that there is accelerated motion in zero-gravity region and then discuss with you the results which anyone must accept

Which post? I don't think there is much point to further discussion while you don't understand how an accelerometer works in GR.

post #47... I think the Paradox could be an easy way to show me and other users of this forum
the points in which appear my ignorance and lack of understanding which would be of great
benefit to me and maybe you...Heisenberq once said ''how wonderful that we have met with a paradox . Now we have some hope of making progress''

 

[Mueiz]

You conclude that the observer on the edge of a very large disc is inertial because locally they appear to traveling in approximately a straight line, but that is not the definition of inertial motion. Inertial motion is motion with zero proper acceleration and the observer on the edge of the large disc would be experiencing very large proper acceleration at high velocities and is therefore not inertial by definition.

But Einstein use this approximation in his calculation (without even improving it by supposing that the disc is very large)
Is it O.K. for Einstein to use the approximation that the motion of the edge of the disc is locally uniform ..and not O.K. for Mueiz to use the approximation that the edge of a large rotating disc in a uniform motion ?.
If you do not want to use this approximation but want to use the acceleration ,that is not wrong but do you know that Einstein use this experiment to prove that acceleration can affect geometry?
will you become angry again if I say for the second time that it is not fair to assume what you are going to prove ?
am i wrong if I say that this Experiment can not lead us to the fact that acceleration can affect the geometry ?
Einstein said in his The Meaning of Relativity of 1921 page 34 '' but if k' rotates we get different result. suppose that at a definite time t ,of K we determine the ends of all the rods .With respect to K all the rods upon the periphery experience Lorentz contraction ,but the rods upon the diameter do not experience this contraction ( along their length ) . It therefore follows that U/D > pi . It therefore follows that the laws of configuration of a rigid bodies with respect to K' do not agree with the laws of configuration of rigid bodies that are in accordance with Euclidean geometry."
the line under the word Lorentz transformation is mine

 

[Mueiz]

State your belief that there is no interia in the absence of gravity.

not only is there no inertia in the absence of gravity there is nothing..zero-gravity is out of the range of applicability of such concepts

 

[Mueiz]

I will give you a simple though experiment for discussion purposes. Imagine we have a very large gravitational body that is rotating at 1 rpm...

In summary the Machian interpretation predicts:
1) Objects really can orbit at velocities much greater than the speed of light.
2) Gravity does not act on objects at a certain critical distance and stationary objects can hover.
3) Gravity attracts or repels depending on distance.
4) The force of gravity depends on the orbital direction and not just on orbital velocity.
5) The speed of light is not locally isotropic in all directions to an inertial observer.

Is that how you see things?

here to attain this predicts you use Mach Principle with other Assumptions regarding zero gravity region such as that object can be accelerated in the absence of gravity which can not be proved by GR which based on Equivalence Principle related to gravitational field and cannot also be prove experimentally till now(to the best of my knowledge none did any experiment in zero-gravity region) . in fact the properties of zero gravity can be predicted using pure intellectual principles such as Postulates of Symmetry and Simplicity.

 

[Dale]

I also accept them in zero gravitation field if i agree that there could be acceleration there

This has got to be one of the most absurd positions that I have ever seen anyone take. So, a rocket in deep space suddenly turns on its engines. The fuel burns and according to you what happens? Do the exhaust gasses just build up because they cannot accelerate away, or do they accelerate away but the rocket's accelerometer reads 0 despite the thrust force generated by the rocket engine?

 

[Altabeh]

not only is there no inertia in the absence of gravity there is nothing..zero-gravity is out of the range of applicability of such concepts

What do you mean? Zero-gravity doesn't have to do anything with a theory like SR! There is still gravity in SR to hold your frame tight but there is supposed to be no effect of gravity on your clocks and thus your calculations! In fact it is "neglected", not "supposed to disappear"!

AB

 

[Mueiz]

This has got to be one of the most absurd positions that I have ever seen anyone take. So, a rocket in deep space suddenly turns on its engines. The fuel burns and according to you what happens? Do the exhaust gasses just build up because they cannot accelerate away, or do they accelerate away but the rocket's accelerometer reads 0 despite the thrust force generated by the rocket engine?

The fuel will not burns for burning is microscopically a type of motion
Can you tell me why did you describe this position as absurd
It does not contradict GR because GR is based on Equivalence Principle which is related to gravity
It does not contradict any experiment because none perform any experiment in zero gravity
It is based on symmetry and simplicity
Is it absurd only because you did not find it in a textbook before now?

 

[Altabeh]

It does not contradict GR because GR is based on Equivalence Principle which is related to gravity

Not gravity but "curvature"! We no longer have gravity in GR!

I think the only problem you have here is that you've completely misunderstood one big idea! If gravitational constant G was zero, then the universal effect of gravitational fields would disappear and you were surely right! There is nothing like a pure flat spacetime in any region in reality and due to this fact the always use "asymptotically" flat when the theory is trying to get special relativistic! You cannot think of zero-gravity at all!

AB

 

[Mueiz]

Not gravity but "curvature"! We no longer have gravity in GR!

we can use the phrases gravity .. gravitational field and so on, only to mean non-zero curvature and i think that is not a problem

I think the only problem you have here is that you've completely misunderstood one big idea! If gravitational constant G was zero, then the universal effect of gravitational fields would disappear and you were surely right!

this is a quite different situation

There is nothing like a pure flat spacetime in any region in reality and due to this fact the always use "asymptotically" flat when the theory is trying to get special relativistic! You cannot think of zero-gravity at all!AB

This is somewhat new attitude toward the question... i will try to discuss you if you give your reasons and arguments or deny those of mine mentioned in different stages of this discussion for other people may complain if i repeat them here

 

[Altabeh]

we can use the phrases gravity .. gravitational field and so on, only to mean non-zero curvature and i think that is not a problem

Please don't play with words. Gravity has its own place and is definitely used within the realm of classical mechanics ONLY! "Gravitational field" is different from gravity as gravity is a force but gravitational field is like a geometrical status that a piece of manifold or the entire of it has in the presence of matter and energy! This is not always the case. As in the Rindler spacetime, we have a gravitational field that is in charge of accelerating away two momentarily at rest points in the grid of spacetime uniformly but yet the Riemann tensor vanishes! So the precense of gravitational field doesn't always enforce nonvanishing of curvature, contradicting your statement above!

This is somewhat new attitude toward the question... i will try to discuss you if you give your reasons and arguments or deny those of mine mentioned in different stages of this discussion for other people may complain if i repeated them here

I've not read any of your ideas yet, but you can list them in a post briefly so I can decide whether they deserve to be given a shot or not by me!

AB

 

[Dale]

The fuel will not burns for burning is microscopically a type of motion
Can you tell me why did you describe this position as absurd

It is absurd because it is directly contradicted by decades of experience burning rocket fuel in zero gravity. "Symmetry and simplicity" as you put it are irrelevant in the face of contradictory experimental evidence.

 

[Mueiz]

It is absurd because it is directly contradicted by decades of experience burning rocket fuel in zero gravity. "Symmetry and simplicity" as you put it are irrelevant in the face of contradictory experimental evidence.

can you tell me please one experiment
nobody could claim this . all the outer-space regions attained by people and their instruments are not of zero-gravitational field even if you were out of our solar system you are in gravitational field