How does Gravitational Mass work?

[MigL]

That is simply the equivalence principle.
You remember the thought experiment of the elevator, in space, accelerating upward at 1g being indistinguishable from standing on the Earth ( to a local approximation ) ?

[geordief]

20 minutes ago, MigL said:

That is simply the equivalence principle.
You remember the thought experiment of the elevator, in space, accelerating upward at 1g being indistinguishable from standing on the Earth ( to a local approximation ) ?

Yes I understand that ,but what about Einstein's passage?

Are those "equations" rigororous or are they really just "illustrative"? ( this is a book for  the layperson)

[Markus Hanke]

18 hours ago, studiot said:

In these circumstances you cannot simply say that if you move a 'mass' at point A to another point B the total mass will remain the same or that the effect on the rest of the system of this mass will be the same at point B as it is at point A, because of the reconfiguration of the system.

Indeed! Well said.

[Strange]

6 hours ago, geordief said:

Yes I understand that ,but what about Einstein's passage?

Are those "equations" rigororous or are they really just "illustrative"? ( this is a book for  the layperson)

Those equations are correct; it is basically just Newton's laws of motion and gravitation. (We now know that the gravitation one is only an approximation, but a good one.)

7 hours ago, geordief said:

  If now, as we find from experience, the acceleration is to be independent of the nature and the condition of the body and always the same for a given gravitational field, then the ratio of the gravitational to the inertial mass must likewise be the same for all bodies. By a suitable choice of units we can thus make this ratio equal to unity. We then have the following law: The gravitational mass of a body is equal to its inertial mass."

This is a really insightful passage.

People often say that we don't know why inertial mass and gravitational mass are equal. Well, the answer is because we chose to give them units that make them equal!

[swansont]

It might help to think about it as this: consider that terms in Newtonian gravity to be gravitational "charge" much like we have electric charge — it's the relevant property to the force.

F_g = GAa/r^2 where A and a are the gravitational "charges" of the two objects — the quantity of whatever property that makes them attract each other

There is no a priori reason that this charge has to be mass, and we could have a situation as we do with a proton and a positron in a uniform electric field. Both feel the same force, but they accelerate at different rates because F = ma and they have a different mass.

But what we observe is that gravitational "charge" is the inertial mass. Further, we see that it doesn't depend on the composition of that mass. A mass of iron and a mass of hydrogen will behave the same, gravitationally. Basically mass is mass — brand name and generic are the same thing.

!

Moderator Note

(Several posts, including this one, have been moved from the "mass without object" discussion as it's really this gravitational mass discussion)

 

[geordief]

On 12/9/2019 at 3:48 AM, MigL said:

The field does not need to 'expand' as it is already there,

I have been chewing on this cud for some time now.

If the field was/is  already there does that mean that there, was a gravity field formed sometime after BB that has evolved to the configuration we now see and that evolution was accompanied by gravitational waves at every step of its progress?

Any gravity field we see is  a part of the universal gravity field and that universal gravity field is the "descendant" of the first gravity field that was formed after BB.....

And that first gravity field was caused when the Higgs field  caused mass  to exist?

That might  explain why you can't have mass without a gravity field or vice versa,I suppose.

Edited December 13, 2019 by geordief

[MigL]

You can't separate the field form the mass/energy causing it.
It does not evolve, and didn't originate with the Higgs interaction.

As mass/energy changes configuration/collects/breaks apart, all individual components carry their field with them, changing/adding/subtracting respectively.
Asymmetric changes ( as opposed to symmetric ) generate gravitational waves which carry away some of the mass/energy, such as the recently observed orbiting BH merger.

[geordief]

40 minutes ago, MigL said:

It does not evolve 

So we can't talk about an overall gravity field ,say for the Earth? And we can't talk about it evolving?

[md65536]

1 hour ago, geordief said:

So we can't talk about an overall gravity field ,say for the Earth? And we can't talk about it evolving?

Sure, why not? A mass doesn't emit gravitational energy just by being there, though, so it doesn't "evolve" in a stationary system.

The Earth's not perfectly symmetric, so by simply spinning, it emits a tiny amount of energy as gravitational waves (negligible?).

Changes in the gravitational field are more due to Earth's interaction with other masses. For example, according to the gravitational wave wiki, the total energy of the Earth orbiting the Sun loses about 200 watts emitted as gravitational waves. This is an extremely small fraction of the total energy. Regarding your original question, there isn't a decrease in mass in this case, because the energy comes from the kinetic energy and gravitational potential energy of the system, ie. decay in orbit.

Edited December 14, 2019 by md65536

[geordief]

9 minutes ago, md65536 said:

so it doesn't "evolve" in a stationary system

 

But the Earth is not stationary .It evolves as a system and it's contribution to the overall gravitational field **must evolve too,I'd have thought.

And I was using the Earth as an example so as to extrapolate to the Solar system,our  Galaxy,our group of Galaxies and so on to imagine an interconnected global (and dynamic-so not synchronous) gravitational field.

If  there was a point in time that could  be identified as that time when gravity first came into play (apparently not as a result of a Higg's interaction) could that point in time be considered as some kind of an origin of the field?

** ie to  the field of the Solar system 

[MigL]

Gravity as we know it ( GR ) would have appeared as soon as our universe moved from the quantum foam stage to one where geometry became apparent. Somewhere around the Planck scale/era ( if it ever was that compacted ).

[Markus Hanke]

Just to clarify something here: spacetime is the gravitational field. There is no gravitational field separate from spacetime - gravity is a geometric property of spacetime. So you have spacetime, which makes up the entirety of the universe, and its local and global geometry, which manifests as “gravity” in the way we experience it.

[geordief]

8 hours ago, md65536 said:

so it doesn't "evolve" in a stationary system.

Sorry I misunderstood you to be implying the Earth  could be stationary in my previous reply to your post.

It was the system you  were describing  as stationary. (still not sure What that means)

 

Still ,it was the Earth's place in this dynamic system that  made me think of describing Earth's contribution (which I accept cannot be considered in isolation) evolving in a similar  way to the way I wonder whether it is possible to talk of the whole system evolving from its earlier origin until "now" ( No one "now" but all the "nows" perhaps meeting  at this origin when spacetime came into existence)

Edited December 14, 2019 by geordief

[geordief]

6 hours ago, Markus Hanke said:

Just to clarify something here: spacetime is the gravitational field. There is no gravitational field separate from spacetime - gravity is a geometric property of spacetime. So you have spacetime, which makes up the entirety of the universe, and its local and global geometry, which manifests as “gravity” in the way we experience it.

So it is possible to talk of a global geometry....Could  that geometry  in principle  describe the process from the origin of spacetime until "now" in one sweep ? Aside from the practicalities ,would that be a thought experiment?

 

Or maybe by global you just meant non local? (the aggregation of local measurements?)

[MigL]

A global geometry, as you are considering, is not possible.
Maybe Marcus or Mordred can provide further insight, but as far as I know, a single, or global, 'foliation' ( or Cauchy surface ) of space-time is not possible.
Aggregations of local surfaces are.

[Markus Hanke]

4 hours ago, geordief said:

So it is possible to talk of a global geometry

“Global” in this context stands in contrast to “local”, and just means an extended region of spacetime (but not necessarily all of spacetime), which of course does have geometry - which is to say it is everywhere endowed with a metric. You do in fact need to “go global” to some degree in order to see GR effects, because every small enough local region will just look like the Minkowski spacetime of SR.

4 hours ago, geordief said:

Could  that geometry  in principle  describe the process from the origin of spacetime until "now" in one sweep ?

Yes, you can apply GR to the universe as a whole. The FLRW solution is an example for this.

4 hours ago, geordief said:

Aside from the practicalities ,would that be a thought experiment?

I am not sure we are really talking about the same thing now, but cosmological solutions are more than just thought experiments. Standard cosmology, i.e. the Lambda-CDM model, is an example of a global/cosmological solution. 

4 hours ago, geordief said:

Or maybe by global you just meant non local? (the aggregation of local measurements?)

Essentially yes, that is what is meant. This can be an extended region of spacetime, or even the universe as a whole.

[studiot]

30 minutes ago, Markus Hanke said:

which of course does have geometry - which is to say it is everywhere endowed with a metric.

A metric is not a rquirement for a geometry either.

For example whilst a metric is required for a congruence relation, it is not required for a similarity relation, though it has its uses if there is one.

Edited December 14, 2019 by studiot

[Markus Hanke]

48 minutes ago, studiot said:

A metric is not a rquirement for a geometry either.

This is true, but I think geordief asked his question in the context of GR, which is explicitly a metric theory of gravitation. My response was intended to remain in that same context.

[studiot]

4 hours ago, Markus Hanke said:

This is true, but I think geordief asked his question in the context of GR, which is explicitly a metric theory of gravitation. My response was intended to remain in that same context.

 

A metric is certainly required if you are going to use a coordinate system and the abolute differential calculus (tensor calculus) and establish connection conditions and parallel transport (as in GR).

What may be helpful to geordief could be Weyl's explanation of why doing this results in local geometry at the bottom of page 204 and the beginning of page 205.

 

the point is that P and P* are used in the development of the derivatives at P and (P+dP), making the calculus locally linear.

[md65536]

18 hours ago, geordief said:

Sorry I misunderstood you to be implying the Earth  could be stationary in my previous reply to your post.

It was the system you  were describing  as stationary. (still not sure What that means)

No, I never said anything was stationary (I said "a mass" in a stationary system doesn't emit gravitational waves). I went on to explain how Earth contributes to radiated changes in the gravitational field. My point is you can't look at the Earth all by itself and assume it must be making changes. It seems like you're ignoring parts of answers that go against what you say 'you'd have thought', and just repeating your original position. Do you understand that it's asymmetric acceleration that emits gravitational waves?

13 hours ago, MigL said:

Maybe Marcus or Mordred can provide further insight, but as far as I know, a single, or global, 'foliation' ( or Cauchy surface ) of space-time is not possible.

Why not? All it means is putting all of spacetime into an ordered set of hypersurfaces, right? The problem (if I understand it) is that you can do it, in an infinite number of ways, basically requiring an arbitrary choice of decomposition that's not universally meaningful. (Or to try to put it in simple terms, you can arbitrarily define single moments throughout the universe that each include only events that are space-like separated, but your choice won't meaningfully represent a single moment elsewhere.) If it wasn't possible, what would that mean? That a foliation can't include all of spacetime? Or that some space-like hypersurfaces must intersect (which seems to go against causality)?

Edited December 15, 2019 by md65536

[geordief]

7 hours ago, md65536 said:

No, I never said anything was stationary (I said "a mass" in a stationary system doesn't emit gravitational waves). I went on to explain how Earth contributes to radiated changes in the gravitational field. My point is you can't look at the Earth all by itself and assume it must be making changes. It seems like you're ignoring parts of answers that go against what you say 'you'd have thought', and just repeating your original position. Do you understand that it's asymmetric acceleration that emits gravitational waves?

I have come across the  description that acceleration causes gravitational waves  but not till now this distinction between asymmetric and symmetric acceleration? Is that an important distinction?

If the Earth (or any body or collection of bodies) undergoes changes  such as loss -ie redistribution of all the ice in the world , would that cause any  change to its the gravitational field? (say measured from the Moon)

 

I confess to being a slow (and obtuse) learner .If I am repeating my original positions (actually I would say most of my "points" are framed as , and in actuality are questions),  then thank you for telling me that  as I do not want to waste your or others' time.

 

If I do this ,I will try to "cut it out". Ophiolite ,who some will remember as a respected poster here and elsewhere once criticised me for "cherry picking" arguments  and that too can be a habit which is hard to disengage from. 

 

 

 

[MigL]

The way I understood Geordief 's question, md65536 ...

On ‎12‎/‎14‎/‎2019 at 7:11 AM, geordief said:

Could  that geometry  in principle  describe the process from the origin of spacetime until "now" in one sweep ?

He is not considering global space-time ( otherwise known as 'block universe' ) as that already includes past, present and future, and as such, is not subject to evolution.
What he is considering are the 'foliations' of space-time, and how the foliations 'evolved' from the origin till now.

As each foliation is an instant in time, the concept of a global foliation is non-sensical, as that implies a common global instant in time, otherwise known as a 'universal now'.
That was my objection to the ill-posed question.

Edited December 15, 2019 by MigL

[geordief]

Edit from 

2 hours ago, geordief said:

I have come across the  description that acceleration causes gravitational waves  but not till now this distinction between asymmetric and symmetric acceleration? Is that an important distinction?

It seems that MigL did talk about a distinction between asymmetric and symmetric changes

https://www.scienceforums.net/topic/120718-how-does-gravitational-mass-work/?do=findComment&comment=1125407

 

That is the same thing?

 

[MigL]

I don't know if you have access to Gravitation ( Misner, Thorne, Wheeler ) Geordief, as that has a 'fairly' readable explanation of gravitational wave phenomena.

[geordief]

30 minutes ago, MigL said:

The way I understood Geordief 's question, md65536 ...

He is not considering global space-time ( otherwise known as 'block universe' ) as that already includes past, present and future, and as such, is not subject to evolution.
What he is considering are the 'foliations' of space-time, and how the foliations 'evolved' from the origin till now.

As each foliation is an instant in time, the concept of a global foliation is non-sensical, as that implies a common global instant in time, otherwise known as a 'universal now'.
That was my objection to the ill-posed question.

More or less ,but I was also wondering whether there could be a (privileged) frame of reference based at the that origin  (the origin of spacetime itself) that would get around the "problem" of all the discordant "nows"

https://www.scienceforums.net/topic/120718-how-does-gravitational-mass-work/?do=findComment&comment=1125449

"..... wonder whether it is possible to talk of the whole system evolving from its earlier origin until "now" ( No one "now" but all the "nows" perhaps meeting  at this origin when spacetime came into existence)

1 minute ago, MigL said:

I don't know if you have access to Gravitation ( Misner, Thorne, Wheeler ) Geordief, as that has a 'fairly' readable explanation of gravitational wave phenomena.

No ,but thanks for the pointer.(I am  just starting  Einstein's Popular Exposition /GR section anyway  and that will probably take me a good few weeks,  if I am lucky to get through)