# Space Probe vs the Sun - Relativistic Frames of Reference

Ok - that is where I was getting confused.
1) In my simplistic lack of understanding I thought there was a direct correlation between mass and gravity. I did not realise that an increase in relativistic mass does not cause an increase in the gravitational potential of a body.
I appreciate the time you've all taken to sort out the source of my confusion.
I may be back with other questions, but for the time being - thank you !

Just to make things clear, gravitational mass does not increase with speed.

why does the first line of the following abstract say "According to the general theory of relativity, kinetic energy contributes to gravitational mass." ?

(http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf)

2) Even if GR were simply Newtonian gravity with relativistic mass it is only the product of the masses that determines the gravitational force between two objects in Newtonian gravity. So if the sun's mass were to increase by a factor of gamma or if the probe's mass increased by a factor of gamma the force would be the same either way according to the naive approach.
Although its irrelevant as this approach is naïve and wrong, I disagree with your analysis here. Sun's mass increase by a factor of gamma would be MUCH larger than the probe's mass increase by a factor of gamma. Therefore the product of the masses would be different in each scenario . . . and the gravitational force would be different

Dale
Mentor
Although its irrelevant as this approach is naïve and wrong, I disagree with your analysis here. Sun's mass increase by a factor of gamma would be MUCH larger than the probe's mass increase by a factor of gamma. Therefore the product of the masses would be different in each scenario . . . and the gravitational force would be different
No, this is very basic algebra. Just write down the Newtonian equation for the gravitational force and multiply the mass of the Sun by gamma. Then write down the Newtonian equation for the gravitational force and multiply the mass of the probe by gamma. Then compare the two results.

D H
Staff Emeritus
why does the first line of the following abstract say "According to the general theory of relativity, kinetic energy contributes to gravitational mass." ?

(http://arxiv.org/PS_cache/gr-qc/pdf/9909/9909014v1.pdf)
That article is talking about the kinetic energy of an object in the object's rest frame -- in other words, the object's temperature. The intrinsic mass of a collection of particles is not the sum of the rest masses of the particles that comprise the collection. It is instead the sum of the relativistic masses of the particles with respect to the collection's center of mass frame.

No, this is very basic algebra. Just write down the Newtonian equation for the gravitational force and multiply the mass of the Sun by gamma. Then write down the Newtonian equation for the gravitational force and multiply the mass of the probe by gamma. Then compare the two results.
I must need remedial algebra classes I'm afraid ! even simpler:

if gamma = 1.5

(suns mass x 1.5)+(probe's mass) > (sun's mass)+(probe's mass x 1.5)

As you said the assumptions are all wrong but this is what I was referring to.

That article is talking about the kinetic energy of an object in the object's rest frame -- in other words, the object's temperature. The intrinsic mass of a collection of particles is not the sum of the rest masses of the particles that comprise the collection. It is instead the sum of the relativistic masses of the particles with respect to the collection's center of mass frame.

Ok - thanks again. I'm ready to wave the white flag at this point I think - but here's another stab at it:

Kinetic energy in the form heat increases the gravitational mass - yes?
Kinetic energy in the form of rotation increases the gravitational mass - yes ?
But kinetic energy in the form relative velocity does not increase the gravitational mass ?

Dale
Mentor
So what? What does this have to do with the gravitational force?
As you eloquently argued above it has nothing to do with gravitational force. Just showing where my miscalculation came from.

Dale
Mentor
Ah, I understand your post now.

Loudzoo:

Post # 25:

"Originally Posted by Loudzoo
It doesn't matter (and its impossible to determine) whether one body is moving away from the other or not. They are mutually moving away from each other. The sun's mass (and therefore its gravitational influence) must increase, whatever the frame of reference, determined by its velocity relative to the probe. Likewise the probe must also experience an increase in mass as determined by its relative velocity to the sun.

Is that correct ?

There are essentially two problems with your statements above:
1) as D H mentioned, the source of gravity in GR is not mass but the entire stress energy tensor. As you boost a system you not only increase its energy, but also its momentum, so other terms in the tensor become significant besides just the energy density component.

2) Even if GR were simply Newtonian gravity with relativistic mass it is only the product of the masses that determines the gravitational force between two objects in Newtonian gravity. So if the sun's mass were to increase by a factor of gamma or if the probe's mass increased by a factor of gamma the force would be the same either way according to the naive approach..."
First, just to mention, aspects of this stuff are VERY subtle...and the guys answering your questions here helped me with similar questions several years ago....still do....

I learned along the way that their answers are often more sophisticated than they appear and so deserve very careful reading, a lot of thought, but still may not become clear until other perspectives from other discussions are studied...so keep at it!!!!. A related issue if you studied this stuff many years ago as I did is that language (terminology) and explanation preferences change over time....[/QUOTE]

Dalespam's point #2 deserves careful attention....the difference between Newtonian and GR is MORE than just changes in mass....

I still scratch my head sometimes reading this stuff.........For example when Dalespam says above
the source of gravity in GR is not mass
I think he means..."not JUST mass"......

You posted:
Kinetic energy in the form heat increases the gravitational mass - yes?
Kinetic energy in the form of rotation increases the gravitational mass - yes ?
But kinetic energy in the form relative velocity does not increase the gravitational mass ?
I'd like to hear from an expert on those questions.

Regarding terminology, I think that in terms these guys prefer, they'd tend to say gravitational attraction changes rather than MASS...

My take is that all three affect gravitational attraction in GR. In othr words, any energy has gravitational effects...even when there is no rest mass...like light....

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Thanks Naty1 - that is encouraging ! I guess explaining concepts in simplified english will never be a substitute for the mathematics.

It now makes sense to me that all forms of energy will affect gravitational attraction in GR. What I'd be really keen to understand is how it affects the gravitational attraction in GR. In light of your suggestion, perhaps if I rephrase my previous question - DH, Dalespam or another expert might be able to elaborate ?

Are the following statements true ?
1) Increasing the kinetic energy in the form of heat of a body increases its gravitational attraction to another body
2) Increasing the kinetic energy in the form of rotational energy of a body increases its gravitational attraction to another body
3) Increasing the kinetic energy in the form of relative velocity of a body increases its gravitational attraction to another body

P.S. Happy to take advice on whether we should start a new thread on this . . .

Dale
Mentor
when Dalespam says above ... I think he means..."not JUST mass".
Yes, thanks for the clarification.

Dale
Mentor
Are the following statements true ?
1) Increasing the kinetic energy in the form of heat of a body increases its gravitational attraction to another body
Yes. This changes the time-time component of the stress energy tensor without changing any other component.

2) Increasing the kinetic energy in the form of rotational energy of a body increases its gravitational attraction to another body
Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

This is where the distinction between Newtonian physics and GR emerges. In Newtonian physics there would be no difference because the scalar mass density is unchanged, but in GR there is a difference because other components of the tensor have changed. In Newtonian physics this would still be a spherically symmetric problem, but in GR it is now an axisymmetric problem.

3) Increasing the kinetic energy in the form of relative velocity of a body increases its gravitational attraction to another body.
Similar as with 2).

Dalespam:
Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

Loudzoo:
"It now makes sense to me that all forms of energy will affect gravitational attraction in GR.."

Exactly.....Even PRESSURE affects gravitational attraction....

If you compress a jack in the box spring, the stored potential energy , not previously present, results in an increase in gravitational attraction accoording to the Einstein field equation. But, a very very tiny imperceptible effect.

Dalespam:

Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.
So both space and time is seen to change in the Einstein Field Equations...

Ok, so as a learning tool, can we explain to me and Loudzoo how this relates to frame dragging.... frame dragging and geodetics:

from wikipedia:

"Rotational frame-dragging (the Lense–Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects

" Linear frame dragging is the similarly inevitable result of the general principle of relativity, applied to linear momentum. Although it arguably has equal theoretical legitimacy to the "rotational" effect, ......]

Static mass increase is a third effect noted by Einstein in the same paper. The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein to derive from the same equation of general relativity. ...
http://en.wikipedia.org/wiki/Frame_dragging

and:

The term geodetic effect has two slightly different meanings as the moving body may be spinning or non-spinning.
SO: Non-spinning bodies move in geodesics, which is what is usually discussed in these forums, whereas spinning bodies move in slightly different orbits.

So it seems a rotating body move through spacetime just a bit differently than a non rotating body...In general this seems to make some sense since the energy is likely different.

Does a rotating body move through SPACE slightly differently??..Based on Dalespam's post above the answer seems YES since "spacial compnents" vary, right???

Is frame dragging the same as, or only a portion of, how we describe the change in
spacetime due to rotational energy???? Seems like the whole thing, right???

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Yes. This changes the time-time component of the stress energy tensor without changing any other component.

Here it already gets more complicated. Since the body is rotating there is a change in the momentum flux terms. So in addition to the increase in the time-time component there is now a change in the spatial components as well.

This is where the distinction between Newtonian physics and GR emerges. In Newtonian physics there would be no difference because the scalar mass density is unchanged, but in GR there is a difference because other components of the tensor have changed. In Newtonian physics this would still be a spherically symmetric problem, but in GR it is now an axisymmetric problem.

Similar as with 2).
Thanks DaleSpam and Naty1. I take from the above that different manifestations of increased kinetic energy will affect the magnitude of the increase in gravitational attraction to different degrees.
But would it be possible to summarise that in GR, an increase in the kinetic energy of a body increases its gravitational attraction to another body ?

Dale
Mentor
Not in general, no. For example, if two equal-mass objects inertially moving parallel to each other at the same speed pass a stationary massless observer at t=0 then they will collide at some t=T according to the massless observer. This time T will be greater the faster the masses are moving, meaning that the gravitational attraction has decreased.

Remember, the sign of the metric is opposite for the timelike and spacelike terms, so you generally expect the timelike and spacelike components to have somewhat opposite effects. Of course, even that is a big oversimplification and I am sure there are counterexamples.

Not in general, no. For example, if two equal-mass objects inertially moving parallel to each other at the same speed pass a stationary massless observer at t=0 then they will collide at some t=T according to the massless observer. This time T will be greater the faster the masses are moving, meaning that the gravitational attraction has decreased.

Remember, the sign of the metric is opposite for the timelike and spacelike terms, so you generally expect the timelike and spacelike components to have somewhat opposite effects. Of course, even that is a big oversimplification and I am sure there are counterexamples.
That example is helpful -thank you.

Presumably, if the massless observer was positioned on one of the objects she would not witness any relativistic effects given the zero relative velocity between the two objects (at least until they started gravitating towards each other) ?

To go back to the core of my original thread question: Assume two objects are moving away from each other with a significant relative velocity. Does an observer located on either object register an increase in gravitational attraction between the two bodies ?