Some Questions on Time Dilation.

[A.T.]

It means a lot to me. It means your definition of "proper acceleration" fails if I managed to make the same charge:mass ratio because at that scenario you would say that the body isn't proper accelerating.

To avoid this misunderstanding one would phrase the definition more exactly: Forces which are not in general proportional to mass cause proper acceleration. Electric forces are not in general proportional to mass.

IBUT AS PER YOUR DEFINITION OF PROPER ACCELERATION, IF IN THE FUTURE A METHOD TO SHIELD THE GRAVITY IS INVENTED THEN THE WHOLE THEORY OF RELATIVITY FAILS.

I guess so. We will worry then.

OR IS IT THAT IT IS PROVED THEORETICALLY THAT GRAVITY CAN'T BE SHIELDED JUST AS IT HAS BEEN PROVED THAT NOTHING CAN TRAVEL FASTER THAN LIGHT?

Nothing is proved in physics. Physical theories can only be disproved.

You can also use light to measure your proper acceleration localy. If a light beam bends in your frame of reference, the frame is properly accelerated. It is not really practical though, because you have to measure a tiny amount of bending along a short path.

 

[I_am_learning]

To avoid this misunderstanding one would phrase the definition more exactly: Forces which are not in general proportional to mass cause proper acceleration. Electric forces are not in general proportional to mass.

How can one exactly define something when he has included the ambiguous word """in general""" in his definition? I am sorry but I am not still satisfied with your definition, AT. And for your suggestion to use light, I would rather go for this coin drop experiment so that it enables me sought out the answer what exactly is the difference between gravitational force and Electric Force in this scenario.
(As I have always been doing, I discard the probable answers. Please Please Please don't ever think that I am going to propose my own theory or I am deliberately trying to prove the existing theories wrong. These are just to help me understand.)

Probable answer: Gravitational Force is proportional to mass but not the electric Force.
my criticism==> Electric Force is also proportional to charge. Probably Gravitational Force is also proportional to gravitational Charge which in turn is proportional to the mass. So there is not much difference except that gravitational charge are always proportional to the mass. (Anyway, Why can't I suppose that gravitational Charge exist?)

 

[A.T.]

Forces which are not in general proportional to mass cause proper acceleration.

How can one exactly define something when he has included the ambiguous word """in general""" in his definition?

"In general" means not only in a specific scenario. The key is rather that "forces" doesn't mean specific forces in a scenario, but types of forces like the electric force.

And for your suggestion to use light, I would rather go for this coin drop experiment

And what if you don't have a coin? Then you cannot measure your proper acceleration and relativity must be therefore wrong? Sorry, you cannot prove that something cannot be measured by restricting yourself to a certain measuring device.

Probable answer: Gravitational Force is proportional to mass but not the electric Force.

Better: Gravitational force accelerates everything equally. The electric force does not. Therefore you can treat gravitational force as an inertial force in general, and not just in a specific scenario.

 

[sylas]

How can one exactly define something when he has included the ambiguous word """in general""" in his definition? I am sorry but I am not still satisfied with your definition, AT.

Well, it's a perfectly normal and correct way of putting it, and not ambiguous at all. It means that one might come up with a contrived case in which charge and mass is proportional (for example, comparing collections of protons) but the relation does not hold in general.

The point is that the mass has two roles. It represents a kind of "gravitational charge", or the amount of gravitational force produced, and it ALSO represents a "resistance to motion", or inertia.

These two turn out to be equal, for all particles, to the most accurate measurements scientists have been able to make... and scientists DO attempt to falsify this equivalence. This equivalence DOES hold in general, both as far as we have been able to test, and also in the physical laws we currently use to describe the natural world.

Cheers -- sylas

 

[ZikZak]

Probable answer: Gravitational Force is proportional to mass but not the electric Force.
my criticism==> Electric Force is also proportional to charge. Probably Gravitational Force is also proportional to gravitational Charge which in turn is proportional to the mass. So there is not much difference except that gravitational charge are always proportional to the mass. (Anyway, Why can't I suppose that gravitational Charge exist?)

The difference is that electric charge is not the inertia of the particle. Gravitational charge is.

 

[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.