Proper time and co-ordinate time.what is the difference?

I am confused between those two.. I got confusion when i searched Wikipedia.


Can someone explain it to me in simple understandable language so that i can easily distinguish between them?

 

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is the proper time the one which help us to understand time dilation?

 

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I think the simplest way to explain it is that "proper time" is the time which is measured by a clock in the same frame as the observer. In other words, if you are holding a clock in your hand, you are measuring your own proper time. A hypothetical clock "piggy-backing" on a particle will measure that particle's proper time ( massless particles excluded ).

"Coordinate time", on the other hand, is time which a hypothetical idealized observer at rest and in the complete absence of all gravitational fields would measure. Such an observer is of course unphysical, since nothing is truly at rest, and nothing is truly outside the influence of gravity.

It should be obvious from the above that only "proper time" ( which can be measured ) has real physical significance, whereas coordinate time ( which can, in the general case, not be measured ) is purely a mathematical tool.

As a practical example consider a massive particle falling freely towards a black hole. In the frame of the particle itself the fall takes a finite time, i.e. the particle measures a well defined and finite proper time. For an observer at rest infinitely far away outside all gravitational influences ( coordinate time ), the particle never reaches the event horizon; it just slowly fades away, taking an infinite amount of coordinate time without ever reaching the event horizon.

 

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Time dilation is a relation between two clocks in relative motion, or between clocks in places with different gravitational potentials. Time dilation is not defined for just one clock, only as a relation between two clocks. As a relation between physical readings this does, indeed, concern proper time.

 

marcus hanke,what helps us to understand time dilation? Comparing observer's proper time and looking into the proper time of someone moving with reference to observer?

 

so marcus,isn't what i said correct?so co-ordinate time is just used as a mathematical tool.. So,no other use of it?

 

Yes, that is one example. Time dilation also arises when one of the clocks experiences a different gravitational potential from the other ( gravitational time dilation ).

Yes, pretty much correct. Coordinate time is sometimes useful to examine the relationship between observers, purely in mathematical terms. It has no real physical significance as such.

 

i think general relativity explains gravitational time dilation. As u said,time dilation is different in different points in gravitational field as gravitational potential is different in different points..
A question...
Does gravitational potential depend on radius of the masses??
And isn't gravitational field depend on mass?
So isn't there a possibily that two equal masses haveing same gravitational field but different in gravitational potential?

 

I presume you are asking this in the context of GR. The answer isn't as straightforward as one might think; firstly, mass is not the only source of gravitational fields, all forms of energy are. In the Einstein field equations the following factors then have an effect on the exact geometry of the field :

1. Energy density
2. Momentum density
3. Pressure
4. Momentum flux
5. Shear stress

Secondly, the gravitational field is quite unique in that it is self-interacting; this makes sense, because we stated before that all forms of energy are sources of the field, so that must include the field itself as well since there is energy associated with it.

So the short answer is - yes, in general there will be some dependence on the radius and of course always on the mass, since that has a bearing on all the above listed factors within the body. It should be noted though that under certain circumstances much of this can be neglected in favour of symmetry within the problem, which make it much easier to solve the equations. For example, in the case of a static, stationary and uncharged mass most of these factors can be neglected, and the gravitational field at a given point outside the body depends only on the total mass ( this is called the Schwarzschild metric ).

 

and i have some confusion on gravitational field and gravitational potential. Question is does the amount by which light bends depend on gravitational field or gravitational potential?

 

marcus,i know that all forms of energy does can create gravitational fields as mass is energy... So my statement should actually is energy is the reason..but i think i do not have to go that deep inorder to answer my question..

 

this thread is weird...two posters I never ever saw in my entire emm life here and a feeling like its one user talking to himself.

I would like to ask a question to Markus Hanke, why is the massles particle excluded from "proper time" calculation?

 

Strictly speaking it is neither of the two, since in GR the "gravitational field" is really a geometric property of space-time. Therefore the bending of light depends only the geometry of space-time; light follows the "contours" of a curved space-time, so to speak. In more technical terms, it traces out null geodesics.

I think speaking of the gravitational "field" in GR can be confusing, because there are no forces involved per se. Personally I prefer to just think of it purely as the geometry of space-time, rather than in terms of forces and potentials.

 

i am little bit confused by your post. You used the word density with energy as depending on gravitational field. Isn't energy density deternine potential of gravitational field?

 

marcus,can you explain potential and field interms of curvature of space-time?

 

Because massless particles are not valid frames of reference. They trace out null geodesics in space-time, and therefore propagate always at exactly the speed of light. Since space-time intervals only equal proper time for time-like geodesics, the notion of "proper time" for a massless particle does not make any physical sense. At best you could look at it as a limit case for a very light body approaching the speed of light arbitrarily closely, in which case the proper time such a body experiences would go asymptotically towards zero.

 

no friend.i am not talking to myself.all the post were meant to marcus..
I think speed of massless particle is speed of light..

 

marcus,a question.
Can we see massless particle moving slowly in some other reference frame. I mean if massless particle move at speed of light with reference to observer,will it move at speed of light with reference to the one who is moving relative to observer?

 

Without going starting to go into the maths, you can think of curvature as being equivalent to "gravitational potential". It is not 100% correct, but it does help to illustrate the concept. Forces then arise as differences in potential, i.e. differences in space-time geometry.

It works both ways. You see, the field equations of GR are non-linear, so physically that means that the field is self-interacting. The degree of that non-linearity is very small for weak fields ( which is why these can be approximated by Newtonian gravity ), but does play a substantial role for very massive bodies.

 

marcus,why do massless particle trace out of the curvature of space-time?