Gravitational vs Inertial Mass

[Naty1]

(I realized I have a confusing post title but can't figure how to edit it..It should read "Gravitational curvature vs gravitational force"

Under 'mass' Wikipedia makes a statement:

Albert Einstein developed his general theory of relativity starting from the assumption that this correspondence between inertial and (passive) gravitational mass is not accidental: that no experiment will ever detect a difference between them (the weak version of the equivalence principle). However, in the resulting theory gravitation is not a force and thus not subject to Newton's third law, so "the equality of inertial and active gravitational mass [...] remains as puzzling as ever

http://en.wikipedia.org/wiki/Gravitational_mass#Gravitational_mass
Inertial and Gravitational Mass



What do you all think about this? Isn't that a bit of an exaggeration??

 

[A.T.]

However, in the resulting theory gravitation is not a force and thus not subject to Newton's third law, so "the equality of inertial and active gravitational mass [...] remains as puzzling as ever
http://en.wikipedia.org/wiki/Gravitational_mass#Gravitational_mass
Inertial and Gravitational Mass

Stating that "gravitation is not a force" without mentioning that free falling objects are not considered accelerated in GR anymore, is telling just half of the story. This omission also causes the puzzling:

Since in GR a free falling object is not accelerated, it's inertial mass is irrelevant for it's trajectory, and does not have to be equal to an "active gravitational mass" causing an attractive force which doesn't exist in GR.

 

[daytripper]

Was there a recent redefinition of gravity or something that I'm unaware of? What's all this about gravity not being a force? If it's not, then why am I being accelerated downward? If I'm not, then why do I feel a force on my back (I'm laying down)?

 

[Dale]

Was there a recent redefinition of gravity or something that I'm unaware of? What's all this about gravity not being a force? If it's not, then why am I being accelerated downward? If I'm not, then why do I feel a force on my back (I'm laying down)?

If you feel a force on your back (while laying down) then you are being accelerated upwards.

 

[D H]

Was there a recent redefinition of gravity or something that I'm unaware of? What's all this about gravity not being a force?

Gravity is a pseudo-force in general relativity. Nothing new here, just something you haven't been taught. Imagine you are floating around weightlessly in a spaceship with no windows. Is there any experiment you can conduct in the confines of this spaceship that will let you determine whether you are in in some region of (nearly) flat space between galaxies or in orbit around some massive object such as a planet or a star?

The answer, according to Einstein's equivalence principle, is no. Einstein's equivalence principle is intermediate between the weak and strong forms of the equivalence principle. The strong form has been tested and now stands as one of the (if not the) most accurately verified claims in all of physics. For example, see http://physicsworld.com/cws/article/news/20870 and http://physicsworld.com/cws/article/print/21148.

If it's not, then why am I being accelerated downward?

Because you aren't in an inertial frame. Gravity is a pseudo-force. All pseudo-forces (e.g., centrifugal force, coriolis effect, inertial force (frame acceleration)) result from attempting to explain physical laws that strictly apply in inertial frames only in a non-inertial frame. All pseudo-forces have one thing in common: The force acting on some object is proportional to the mass of the object. Clue #1 that gravitation is a pseudo-force: The gravitational force acting on some object is proportional to the mass of the object. Clue #2 is the equivalence principle.

If I'm not, then why do I feel a force on my back (I'm laying down)?

That is a real force; it's called the normal force.

 

[daytripper]

Ok, I think I'm starting to understand. I didn't realize I never understood WHY space-time curvature causes me to drift toward masses. In the trampoline analogy, gravity pulls the marbles toward the bowling ball. What can accelerate me other than a force? With centrifugal force, it's my inertia moving forward as, for instance, a car turns. What causes this? Why can't I understand gravity? haha

 

[Naty1]

DH posted:

Gravity is a pseudo-force in general relativity.

THAT must be what Wikipedia was trying to say...I still think it's an obtuse statement...

It's no wonder there are lengthy threads here where we are trying to understand each others context and choice of words...not to mention different interpretations of some mathematics...

"All pseudo-forces (e.g., centrifugal force, coriolis effect, inertial force (frame acceleration)) result from attempting to explain physical laws that strictly apply in inertial frames only in a non-inertial frame..."
Nicely laid out!..haven't seen that description before

Thanks DH.

 

[George Jones]

DH posted:


THAT must be what Wikipedia was trying to say...I still think it's an obtuse statement...

It's no wonder there are lengthy threads here where we are trying to understand each others context and choice of words...not to mention different interpretations of some mathematics...

"All pseudo-forces (e.g., centrifugal force, coriolis effect, inertial force (frame acceleration)) result from attempting to explain physical laws that strictly apply in inertial frames only in a non-inertial frame..."
Nicely laid out!..haven't seen that description before

Thanks DH.

You might also like to look at

https://www.physicsforums.com/showthread.php?p=1636657#post1636657.

 

[atyy]

The "puzzling as ever" is a phrase from Rindler, Relativity: Special, General, and Cosmological, OUP 2001, p22: http://books.google.com.sg/books?id=fUj_LW51GfQC&printsec=frontcover#PPA22,M1.

 

[A.T.]

The "puzzling as ever" is a phrase from Rindler, Relativity: Special, General, and Cosmological, OUP 2001, p22: http://books.google.com.sg/books?id=fUj_LW51GfQC&printsec=frontcover#PPA22,M1.

Okay, here the "active graviational mass" in fact means the energy stress tensor, causing space time curvature. That was not clear in the wiki text.

It also says that inertia is not interaction with the own gravitational field. Is there a good explanation why not, somewhere?