# Dought regarding equivalence principle

1. Jul 24, 2004

### 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

2. Jul 24, 2004

### pmb_phy

They have the same numerical value. They are not defined the same way and therefore they do not have the same physical meaning.
Since mg = mi, where mi = inertial mass and mg = gravitational mass, there will always be a reduction in inertial mass whenever there is a reduction in gravitational mass.
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

3. Jul 25, 2004

### 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

4. Jul 25, 2004

### DW

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.

5. Jul 25, 2004

### pmb_phy

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

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

Last edited: Jul 25, 2004
6. Jul 25, 2004

### DW

What Einstein said is irrelevent to your arguement. 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.