Why two mass attracts each other?

[ash64449]

How can proper time be measured through clocks?

I thought that proper time is invariant interval between the two events in space-time.

And i do know that if invariant space-time interval is time-like,it is called proper time.

And sometimes only we can measure it through clocks.

So we cannot say that proper time is measured by clocks because clocks can only measure sometimes ( To Marcus Hanke)

 

[hansda]

Hansda, time is a measurement of the rate of change. Change always happens and will continue to happen for the foreseeable future. The rate at which change occurs depends on many different factors. As it relates to time.., the measurement of change, it is dependent on the frame of reference from which it is made...

While change does occur independent of being observed or measured, time requires an observation or measurement.., which is a comparison of some observed change, against an accepted standard. Clocks represent that standard. However, a comparison of the rate that two clocks record change, depends on both their relative positions in a gravitational field and/or their relative velocity with respect to each other.

Time is an abstract concept. A comparison of two rates of change, one agreed to be a standard rate. Because it is a comparrison of two rates of change, and change varies relative to many external conditions, time is not inherently invariant. But what it measures—change—happens whether it is being measured or not.

As you say, "Time is an abstract concept." and "time is a measurement of the rate of change"; so don't you think this "rate of change" can be invariant even if it is not measurable by a clock.

 

[hansda]

This is not accurate. Proper time is time as measured by a clock in its own frame of reference. In that frame of reference the clock represents the at rest frame for the measurement of the change being measured. For that measurement the clock's rate is not time dilated, it is not changing. Proper time is invariant, because it is measured by a clock collocated with the events being measured.., which is not time dilated relative to those events.

"Time Dilation" happens to "proper time". So, how "proper time" can be "invariant"?

 

[ash64449]

"Time Dilation" happens to "proper time". So, how "proper time" can be "invariant"?

Time Dilation is not proper time.

It is the ratio of Coordinate time to proper time.

If proper time changes,there is no time dilation...

Can you just answer or stick to the OP?

 

[hansda]

The curvature of spacetime is a description of the geometry associated with gravitation,

This is an observable fact.

it is not an explanation of why that geometry is.

That exactly is my question, WHY 'geometry' or 'spacetime curvature' is so?

Within the context of our direct experience gravity is always attractive. Theoretically, there are conditions that would result in a repulsive graviation and there is some cosmological evidence that suggests that at very large distances gravity is either repulsive or its attrive force is no longer dominant. This leads to the need for "Dark Energy" as an explanation, for those cosmological observations.

Do you mean "gravity" is simultaneously 'attractive' as well as 'repulsive' and in 'smaller distance range' 'attractive component of gravity' is dominant whereas in the 'longer distance range' 'repulsive component of gravity' is dominant.

The key concept in that regard is "geodesic deviation" :

http://en.wikipedia.org/wiki/Geodesic_deviation_equation

You will find that for two isolated bodies in space-time, their geodesics converge, i.e. the geodesic deviation is always negative. What that means is that these bodies will approach each other over time. This can be shown mathematically using the geodesic deviation equation; it is simply a consequence of the geometry of space-time.

I think "geodesic deviation" is due 'tidal force(perturbing force)' which can cause "attraction" as well as "repulsion".

 

[hansda]

Time Dilation is not proper time.

I said "Time Dilation" happens to "proper time".

It is the ratio of Coordinate time to proper time.

So, among the "coordinate time" and "proper time" ; which is 'variant' and which is 'invariant'?

If proper time changes,there is no time dilation...

WHY?

Can you just answer or stick to the OP?

If you are considering 'Einstein's model of gravity' there is no distinction between 'time' and 'spacetime' in concept.

 

[ash64449]

I think "geodesic deviation" is due 'tidal force(perturbing force)' which can cause "attraction" as well as "repulsion".

You don't understand the physics of geometry of space-time curvature until you fully understand how can equivalence principle can always show force to be attractive.

The science of space-time curvature is equivalence principle. and gravity is derived from it.

In order to show how gravity can be repulsive through space-time curvature, you "must" show its equivalence with acceleration of that repulsive force.

And i am sure there is no way you can show that and that is the reason why "gravity" is always attractive.

Please Think for some time and then ask questions. It should be you who should do the hard work. not the posters.

 

[Markus Hanke]

So we cannot say that proper time is measured by clocks because clocks can only measure sometimes ( To Marcus Hanke)

I don't think I ever said that, and if I did then I was obviously wrong. Proper time is precisely what a clock measures between two given events. For example, if you walk from point A to point B on the surface of the earth, then the elapsed time your wrist watch shows is the proper time between those events along the worldline you trace out. Proper time is always what clocks measure in their own frame of reference. Mathematically, this is just the arc length of a worldline segment. All observers will agree on this proper time. The opposite of this is coordinate time, which can be physically measured only in certain idealized circumstances.

Is it possible you confused these two ?

 

[ash64449]

So, among the "coordinate time" and "proper time" ; which is 'variant' and which is 'invariant'?

Coordinate time is 'variant'..

WHY?

I will give you a reference. I cannot keep on explaining every thing to you. Get a copy of Taylor and Wheeler's Space-time Physics.


And i can understand that you don't understand Special Theory Of Relativity. Please read the above book if you want to make some progress.

There is a very good advice for those who wants to study relativity. It is to start with invariant intervals and proper time is one such invariant interval.

So if you don't know these concepts clearly says that you don't know relativity.

 

[Markus Hanke]

I think "geodesic deviation" is due 'tidal force(perturbing force)' which can cause "attraction" as well as "repulsion".

No, all physically meaningful solutions to the Einstein field equations yield a negative geodesic deviation, meaning that gravitational sources always move towards one another. Of course it is mathematically possible to get a positive deviation ( i.e. repulsion ), but then you need a negative energy density as the source term. This is tantamount to the existence of exotic matter, for which there is no experimental or observational evidence.

 

[ash64449]

I don't think I ever said that, and if I did then I was obviously wrong. Proper time is precisely what a clock measures between two given events. For example, if you walk from point A to point B on the surface of the earth, then the elapsed time your wrist watch shows is the proper time between those events along the worldline you trace out. Proper time is always what clocks measure in their own frame of reference. Mathematically, this is just the arc length of a worldline segment. All observers will agree on this proper time. The opposite of this is coordinate time, which can be physically measured only in certain idealized circumstances.

Is it possible you confused these two ?

Yes. Confused. In Taylor and Wheeler,it says that proper time is invariant space-time interval between the two events.

It didn't say anything about proper time as being measured by the clocks.

EDIT: What if the clocks are synchronized with coordinate time? How can it measure proper time?

In the book Taylor and Wheeler, They gave an example about difference in time intervals in laboratory frame and rocket frame.(rocket frame moving).

I saw that the value of invariant interval is exactly (2 meters)^2. that is Time between two events is 2 meters of light travel time.

This is exactly what is measured by the rocket frame. In other words,it measured proper time. Clocks in the rocket measured proper time.

But in laboratory frame,it is different.Time interval between the two events in different in laboratory frame which means not 2 meters.(in rocket frame two events are not spatially separated but events are in laboratory frame). SO clocks didn't measure proper time.

And that is why i said Proper Time is measured by clocks sometimes.

 

[Markus Hanke]

I will give you a reference. I cannot keep on explaining every thing to you. Get a copy of Taylor and Wheeler's Space-time Physics.


And i can understand that you don't understand Special Theory Of Relativity. Please read the above book if you want to make some progress.

There is a very good advice for those who wants to study relativity. It is to start with invariant intervals and proper time is one such invariant interval.

So if you don't know these concepts clearly says that you don't know relativity.

Just to clarify this a bit - "invariant" here means that all observers will agree as to the length of the worldline between the same two events. It does not mean that different observers in different regions of space-time will agree on their own proper times between different events.

 

[Markus Hanke]

Yes. Confused. In Taylor and Wheeler,it says that proper time is invariant space-time interval between the two events.

It didn't say anything about proper time as being measured by the clocks.

That is just two ways to express the same thing - the time measured by a clock passing through both events in space-time is the invariant interval between those events.

 

[hansda]

You don't understand the physics of geometry of space-time curvature until you fully understand how can equivalence principle can always show force to be attractive.

The science of space-time curvature is equivalence principle. and gravity is derived from it.

In order to show how gravity can be repulsive through space-time curvature, you "must" show its equivalence with acceleration of that repulsive force.

And i am sure there is no way you can show that and that is the reason why "gravity" is always attractive.

Please Think for some time and then ask questions. It should be you who should do the hard work. not the posters.

Can you specifically mention the statements of the "Equivalence Principle" you are following here. There are 'weak equivalence principle', 'strong equivalence principle' etc...

 

[ash64449]

It does not mean that different observers in different regions of space-time will agree on their own proper times between different events.

Sorry,But i couldn't successfully grasp your statement. Do you mean that Different observers in different regions of space-time will disagree on proper time between the same two events for example event A and event B?

 

[ash64449]

Can you specifically mention the statements of the "Equivalence Principle" you are following here. There are 'weak equivalence principle', 'strong equivalence principle' etc...

The Equivalence principle which states that acceleration is indistinguishable from gravitational field.

 

[ash64449]

That is just two ways to express the same thing - the time measured by a clock passing through both events in space-time is the invariant interval between those events.

Ok. Then you mean there are many invariant intervals between the two events and that different observers will measure different invariant intervals?

And thus different observers will have their own proper time?

 

[Markus Hanke]

Sorry,But i couldn't successfully grasp your statement. Do you mean that Different observers in different regions of space-time will disagree on proper time between the same two events for example event A and event B?

In Special Relativity, all inertial observers will determine the same interval between the same two events. Hence the the space-time interval is invariant under Lorentz transformations.
In General Relativity, however, this is not necessarily the case. Two observers passing through the same two events, but along different worldlines, may measure different proper times. This is because in GR space-time is no longer uniformly flat, so the arc length of your worldline depends on the geometry of the underlying space-time. For example, this is why, in the "twin paradox", the accelerated twin experiences a different proper time even though he passes through the same two events.

So, to make it easy : inertial frames > proper time is invariant. Non-inertial frames > proper time depends on path taken.

 

[hansda]

I think "geodesic deviation" is due 'tidal force(perturbing force)' which can cause "attraction" as well as "repulsion".

No, all physically meaningful solutions to the Einstein field equations yield a negative geodesic deviation, meaning that gravitational sources always move towards one another. Of course it is mathematically possible to get a positive deviation ( i.e. repulsion ), but then you need a negative energy density as the source term. This is tantamount to the existence of exotic matter, for which there is no experimental or observational evidence.

What i have said above is from your wiki reference. Here is the quote from wiki

In general relativity, geodesic deviation describes the tendency of objects to approach or recede from one another while moving under the influence of a spatially varying gravitational field. Put another way, if two objects are set in motion along two initially parallel trajectories, the presence of a tidal gravitational force will cause the trajectories to bend towards or away from each other, producing a relative acceleration between the objects.[1]

 

[ash64449]

Just to clarify this a bit - "invariant" here means that all observers will agree as to the length of the worldline between the same two events. It does not mean that different observers in different regions of space-time will agree on their own proper times between different events.

But i think different observers in the same state of motion.(in SR,All objects in uniform motion) will agree with the same proper time.

I will take an example.

Think that the straight longest proper time(in space-time) between the two events is about 10 meters.(i don't know the units precisely)
Then all the observers in same straight line motion in space-time will agree that proper time is 10 meters.

But what if the observers take a different route in space-time? Value of proper time changes.And this one is too invariant. (i understood your post).

But value in the change of proper time for that particle is because he accelerated. And all observers in this same acceleration of that of particle will agree on this changed proper time but wouldn't agree on the earlier proper time.