Dought regarding equivalence principle

[einstein_vishnu]

i have some doughts regarding the principle of equivalence.we have seen that the inertial mass and gravitational mass are same.now consider the nucleus where in nucleons are binded due to which there wiil be mass reduction,this is inertial mass.then how come there is decrease in gravitational mass?,if this decrease is only in inertial then the raio of two masses would be different depending on the binding forces.is there any real explanation for this.i feel we can to some extent show that equivalece priniciple is not valid

 

[pmb_phy]

we have seen that the inertial mass and gravitational mass are same.

They have the same numerical value. They are not defined the same way and therefore they do not have the same physical meaning.

now consider the nucleus where in nucleons are binded due to which there wiil be mass reduction,this is inertial mass.then how come there is decrease in gravitational mass?

Since m_g = m_i, where m_i = inertial mass and m_g = gravitational mass, there will always be a reduction in inertial mass whenever there is a reduction in gravitational mass.

,if this decrease is only in inertial ..

Where did you get this impression?

For a description of the physics of why this works in the case you give, go to www.geocities.com/physics_world, click on "On the concept of mass in relativity", turn to page 52 and read the section called "Why does E = mc²?" (Note: There are a lot of gramatical errors and typos. Please let me know if you find any. I would be very grateful.)

Pete

 

[einstein_vishnu]

of course i am talking about the numerical values,they are defined in different contest i agree, but the reduction in the mass is purely due to inertial,because there is no question of gravitational mass in nuiclear interaction.thanku for the reply

 

[DW]

They have the same numerical value. They are not defined the same way and therefore they do not have the same physical meaning.

In relativity, yes they are.
Consider geodesic motion
$$F^{\lambda } = m\frac{DU^{\lambda }}{d\tau } = 0$$
$$m\frac{dU^{\lambda }}{d\tau } + m\Gamma ^{\lambda }_{\mu }_{\nu }U^{\mu }U^{\nu } = 0$$
$$- m\Gamma ^{\lambda }_{\mu }_{\nu }U^{\mu }U^{\nu } = m\frac{dU^{\lambda }}{d\tau }$$
$$mg^{\lambda} = m\alpha^{\lambda}$$
The m on the left is then called gravitational mass. The m on the right is then called inertial mass. They are identically the same thing and are the only kind of mass that really is, which is invariant.

 

[pmb_phy]

of course i am talking about the numerical values,they are defined in different contest i agree, but the reduction in the mass is purely due to inertial,because there is no question of gravitational mass in nuiclear interaction.thanku for the reply

The reduction in mass is not just inertial because E = mc² does not just apply to inertial mass, it also applies to gravitational mass. Einstein showed this exact thing in 1911 in his paper On the Influence of Gravitation on the Propagation of Light. That paper is online at

http://www.itba.edu.ar/cargrado/fismat/fismod/transf/htm/einstein_5.htm

See Section 2 On the Gravitation of Energy where Einstein poses the question

One result yielded by the theory of relativity is that the inertia of a body increases with the energy it contains; if the increase in energy amounts to E, the increase in inertia mass is equal to E/c², when c denotes the velocity of light. Now is there an increase in of gravitating mass correponding to this increase in inertia mass? If not, thena body would fall in the same gravitational field witgh varying acceleration according to the energy it contained. That highly satisfactory result of the theory of relativity by which the law of conservation of mass is merged with the law of conservtion of energy could not be maintained, because it would compel us to abandon the law of the conservation of mass in its old form for inertia mass, and maintain it for gravitational mass.

<Einstein presents his argument and concludes>

The increase in gravitational mass is thus E/c², and therefore equal to the increase in inertia mass as given by the theory of relativity.

I highly recommend reading this article. It is a very important article if you want to learn the equivalence principle.

Hope that helps.

Pete

 

[DW]

The reduction in mass is not just inertial because E = mc² does not just apply to inertial mass, it also applies to gravitational mass. Einstein showed this exact thing in 1911 in his paper On the Influence of Gravitation on the Propagation of Light. That paper is online at

http://www.itba.edu.ar/cargrado/fismat/fismod/transf/htm/einstein_5.htm

See Section 2 On the Gravitation of Energy where Einstein poses the question

I highly recommend reading this article. It is a very important article if you want to learn the equivalence principle.

Hope that helps.

Pete

What Einstein said is irrelevant to your argument. The energy "it contains" or center of momentum frame energy or rest energy is the mass which is invariant. As with any frame center of momentum frame energy is conserved. That is mass conservation. This says nothing of Planck's outdated concept of mass that you keep spamming.