Some Questions on Time Dilation.

[I_am_learning]

Ok, Finally I understand it like this,
So far experiments have shown that gravitational Force is always proportional to mass so that given a gravitational field, all objects accelerate at the same rate. But for other type of forces such a electric forces, the acceleration isn't always found to be constant except for special cases like of collection of protons.
So, Gravitational Force can't produce proper acceleration but other forces can.

And I seem to have further understood that,(Pelease don't think I am going hypothetical and fantacy-ical, I am just trying to understand. Should I make mistake, correct me) Should it be discovered that gravitational force is also due to gravitational charge and that objects can be gravitationally uncharged by some means, then difference between proper or coordinate acceleration Vanishes, And then we start saying to someone that ""It is a special case that you come to have same charge(gravitational):mass ratio so it seemed that gravitational force is inertial force"".

 

[I_am_learning]

Ok, Finally I understand it like this,
So far experiments have shown that gravitational Force is always proportional to mass so that given a gravitational field, all objects accelerate at the same rate. But for other type of forces such a electric forces, the acceleration isn't always found to be constant except for special cases like of collection of protons.
So, Gravitational Force can't produce proper acceleration but other forces can.

And I seem to have further understood that,(Pelease don't think I am going hypothetical and fantacy-ical, I am just trying to understand. Should I make mistake, correct me) Should it be discovered that gravitational force is also due to gravitational charge and that objects can be gravitationally uncharged by some means, then difference between proper or coordinate acceleration Vanishes, And then we start saying to someone that ""It is a special case that you come to have same charge(gravitational):mass ratio so it seemed that gravitational force is inertial force"".

 

[Dale]

Hi thecritic,

You have already received a bunch of very good responses, but allow me to add my thoughts too.

First, we need to understand what a coordinate system is. A coordinate system is simply a mathematical mapping between physical events and a set of four numbers. The numbers serve as a kind of "address" for referring to the events. There are some mathematical constraints on the kinds of mappings that can be considered, e.g. They should be continuous and differentiable etc.

Once you have a coordinate system then you can define a particle's coordinate acceleration simply as the second time derivative of its position. This says nothing about the forces on the particle, it is just a description of how the mapping of the particle's "address" is changing.

Now, we want to use our coordinate system to do physics. Roughly speaking we can define an "inertial coordinate system" to be a coordinate system in which the laws of physics take their "textbook" form. We can make any number of experiments (dropped coins, bent light, strain in a cantilever, etc.) to determine the deviation from the "textbook" form at any given point, and we call any such experiment an "accelerometer". An inertial coordinate system can then be equivalently defined as one where any accelerometer with zero coordinate acceleration reads 0. Then proper acceleration is equal to the coordinate acceleration in an inertial coordinate system.

Finally, for the equivalence principle to apply to the electric force it is not sufficient for electric charge to merely be proportional to inertial mass, but it must be equal to the inertial mass.

Sorry about the length of this post, but I am too tired to make it more concise. I hope it helps anyway.

 

[I_am_learning]

First of all thank you all for your help.
Now I seem to understand where the asymmetry lies in the Twin Paradox Where one of the twin goes on proper acceleration. But the paradox Isn't still over for me.
Look at this scenario. Suppose A and B are at present moving towards each other at relativistic speed. Further suppose A and B observe each other (after light travel time correction) to be of the same age at this instant. Now, since both see each others time pass slowly they should find each other younger when they meet. Where is the problem? Am I missing a very simple point?

 

[Dale]

... at present ... at this instant. ... Am I missing a very simple point?

Yes, the relativity of simultaneity. Different frames will disagree on what is the "present" and "this instant".

 

[I_am_learning]

Yes, the relativity of simultaneity. Different frames will disagree on what is the "present" and "this instant".

Ah! so shame of me to forget that there is not definite present for two frame of reference.
Thanks for all the help you have provide. But I am going to start a new-thread to discuss the difference between proper acceleration and co-ordinate acceleration.

 

[A.T.]

Ok, Finally I understand it like this,
So far experiments have shown that gravitational Force is always proportional to mass so that given a gravitational field, all objects accelerate at the same rate.

It is the other way around:
So far experiments have shown that in a gravitational field all objects accelerate at the same rate, so for massive objects we can treat gravity as a force always proportional to mass. But this force concept doesn't make sense for massless objects like photons, which are still affected by gravity in the same way. The effect on light another way to identify inertial forces.