Calculating gravity with high precision ?

[Fermifaq]

Calculating gravity with high precision ?

Few questions / concepts I am trying to get clarified...adding all the mass and all? types of energy ?

Q Does a hot brick have a slightly stronger gravitational field than a cold brick ?

Q Does a spinning brick have a slightly stronger gravitational field than a cold brick ?

Q Does a brick orbiting a stationary observer have a slightly stronger gravitational field than a stationary brick at the same distance ?

Q does a wound spring have a slightly stronger gravitational field than an unwound spring ?

 

[phinds]

What do you think and why?

 

[TumblingDice]

I'm ready to be the first person with egg on my face. I'm going to say, "yes" to all but #3 for the same reason. That is, if you consider the objects as a system, the one with higher energy will have greater mass. Since heat in any definition represents more energy, and rotation is absolute acceleration, and a wound spring has more energy in that state of configuration, I'm going with more energy > greater mass of system > greater gravitational influence.

In the slim chance that I'm thinking correctly, I can't be as confident about an object in free fall, as an orbiting brick. What if the two bricks were orbiting each other? Introducing an observer at rest relative with one brick skews the thought experiment, but if ignored, and if I haven't gone totally off the deep end yet, maybe relativity balances this one out...?

 

[WannabeNewton]

In general relativity there is no such thing as the "gravitational field" for arbitrary space-times. In the case of linearized gravity (which would be a perfectly reasonable regime given that your system consists of a brick and bricks are not self-gravitating), the gravitational field is derivative of a rank 2 tensor field. Tell me, how do you quantify the "strength" of a rank 2 tensor field? How are you going to compare the "strengths" of two different rank 2 tensor fields solving the linearized Einstein field equations for different stress-energy tensors?

At best all I can make of your question is that for non-relativistic sources that are not self-gravitating, the time-time component (energy density) of the stress-energy tensor dominates the time-space components (momentum density) and the space-space components (momentum flux) of the stress-energy tensor.

 

[yuiop]

What about passive gravitational mass? Does a hot brick weigh more than a cold brick? Does a spinning brick weigh more than a non spinning brick? Does a wound spring weigh more than an unwound spring? etc

 

[TumblingDice]

@WannabeNewton: I always appreciate when you add technical insight because even though it's over my head, I figure it helps guide others who do understand, who help others, and adds value to all. (yea for the home team!)

But I just gotta' say, the understanding level that the questions were posed from and perhaps wanting to learn if E=mc^2 translates into a greater gravitational influence... Maybe I'm wrong, but your reply went over my head, and if the OP's terminology of gravitational 'field' was less than accurate, I'm guessing your info might be too far ahead for him/her, too.

 

[Fermifaq]

ref But I just gotta' say, the understanding level that the questions were posed from and perhaps wanting to learn if E=mc^2 translates into a greater gravitational influenceTumblingDice, you get me and my question, thanks.as in " if i take a blowtorch to a brick and then place that brick on my scales will it weigh more because it is hot ?"
ie, because the total mass+energy of the brick has increased, thus so has its emission of gravitinos wotever

if so, then we can get onto the 'quacking and the feathers' R Feynman

 

[WannabeNewton]

But I just gotta' say, the understanding level that the questions were posed from and perhaps wanting to learn if E=mc^2 translates into a greater gravitational influence...

Well the problem is that it isn't that simple. In Newtonian gravity the only source of the gravitational field is the mass density; the rotation of a source doesn't contribute to the gravitational field. In GR, rotation of a source does contribute to the gravitational field but rotation is momentum density and lies in the time-space components of the stress-energy tensor. Energy density (which includes $E = mc^2$) is the time-time component of the stress-energy tensor. Do you see why you can't just compare these things in the way you're trying to? It just isn't that simple that's all I can say. What you can say with total and complete confidence is that in the Newtonian limit, energy density of a source unequivocally dominates momentum density of said source.

 

[Fermifaq]

I do get the vast bulk of mainstream science but i do admit i do struggle a bit with GR

What to count

When to count it

and how to count it

My question in the OP is primarily 'what to count' when wanting to calculate gravity to high precision

Apologies if my question wasn't as concisely worded as it 'needs' to be

 

[TumblingDice]

Well the problem is that it isn't that simple.

How about OP post #7? If we could use an accurate spring to measure the mass of a brick, would the spring extend the brick closer to the Earth, all things remaining equal, if the brick's temperature increased. Hoping to keep in the spirit of keeping the question simple - no folks jumping in with stuff like the density of the air is going to change, the spring tension will change as it reaches equilibrium temp with brick, or other creative energies.

 

[Fermifaq]

TumblingDice

your hired !

Its very easy to turn a yes/no + caveat into a GUT post...i get some of what
WannabeNewton is referring too, though probably not enough.

side note, my mission is to try and calculate the gravity in a galaxy, ref dark matter and 'actual' star/mass positions etc...relating to galactic rotation and gravitational forces (gravity,which i believe travels at the speed of light ?)

 

[WannabeNewton]

How about OP post #7?

Yes, now that is a meaningful question with a meaningful answer! See here: http://arxiv.org/abs/gr-qc/9909014

Comparing rotating extended objects to extended objects exposed to a temperature field on the other hand is a different ball game.

 

[TumblingDice]

Way cool, WannabeNewton! The *exact* premise, "does a hot brick weigh more..."

Well FermiFaq has a lot of good fodder to cull through. I cheated and read the ending first.

" We can thus tell our students with confidence that kinetic energy has weight [sic] not just as a theoretical expectation, but as an experimental fact."

So then, how about the "wound spring"? Is the stored energy manifested as kinetic energy at the atomic level that would add gravitational mass? It's a mechanical thingy, right? (Are you smiling?)

 

[WannabeNewton]

So then, how about the "wound spring"? Is the stored energy manifested as kinetic energy at the atomic level that would add gravitational mass? It's a mechanical thingy, right?

If the spring is compressed then it gains spring (elastic) potential energy and its mass increases hence it would weigh more.

(Are you smiling?)

Only because you asked

 

[WannabeNewton]

By the way, here's a relevant exercise from one of my GR texts for anyone interested (I have yet to solve the exercise completely myself). It's taken from "Gravitation: Foundations and Frontiers"-Padmanabhan.

 

[TumblingDice]

side note, my mission is to try and calculate the gravity in a galaxy, ref dark matter and 'actual' star/mass positions etc...relating to galactic rotation and gravitational forces (gravity,which i believe travels at the speed of light ?)

Repeating your quote so my exchange with WannabeNewton doesn't drown out or hijaak your goals.

Could calculating "gravity in a galaxy" be done with measurements of orbiting speed and estimated mass of the most distant visible objects from the center of a galaxy's rotation? Something like the reverse process of objects orbiting too fast in galaxies that required 'more gravity' ...

Just a thought...

 

[Fermifaq]

I am reading and thinking...on topic ,do carry on !

Before solving 'Dark matter ?' ...(which i have some issues with) i wanted to clarify how mass and gravity is calculated.

I have yet to see 'full fat' gravity maths and GR maths applied to galactic rotation in a truly convincing manner. (Convincing to me) The topic is complex and mass media goes light on dark matter (scuse the pun). While i don't foresee a+nother FTL neutrino debacle ref dark matter i am yet to be thoroughly convinced of its necessity as there appear to be numerous complexities which can and do effect galactic rotation curves.

Dark matter is a convenient explanation for sure but as we are still in the pre detection phase and likely to remain so for some time to come I am poking the beast with a stick...Id be very happy if we found a bucket of the stuff then i could move on to something else.

If i can tick off a few more boxes, gravity strength/galactic gravity calculation wise then i might let the scientific mainstream off the hook ref dark matter ( let them get on with it)...a kind of checksum approach that i use

Dark Matter ; the Undetectable Mass (FULL VIDEO)


Introduction to Newton's Law of Gravitation


General Relativity: 2a - Equivalence Principle


General Relativity: 2b - Equivalence Principle






There is a huge discrepancy between the easily observed mass and some rotation curves...that totally demand explanation and investigation...hence my renewed interest in gravity anything.

Dark Matter and Galaxy Rotation < well worth watching

 

[yuiop]

We seem to have skipped past "Does a spinning brick weigh more than a non spinning brick? ".

Any ideas?

 

[Nugatory]

We seem to have skipped past "Does a spinning brick weigh more than a non spinning brick? ".

If I take two identically constructed boxes containg a turntable and a brick on the turntable, set one of the turntables rotating so that the brick is spinning, and carefully weigh the two boxes... Yes, the one with spinning brick will weigh more.

 

[yuiop]

We seem to agree that a hot brick weighs more than a cold brick and has more 'passive' gravitational mass.

Now consider 2 very large bricks separated by some weighing scales, in an otherwise empty universe. They are gravitationally attracted to each other and a force can be read on the scales. Will this reading be larger if the bricks are heated? Will the mutual gravitational attraction be measurably greater? In this situation the two bricks are gravitationally bound, so presumably binding energy will have to be taken into account.

 

[Nugatory]

Now consider 2 very large bricks separated by some weighing scales, in an otherwise empty universe. They are gravitationally attracted to each other and a force can be read on the scales. Will this reading be larger if the bricks are heated?

Yes. And because this force is the mutual gravitational attraction, also

Will the mutual gravitational attraction be measurably greater?

yes

In this situation the two bricks are gravitationally bound, so presumably binding energy will have to be taken into account.

No. The gravitational binding energy is in the spring of the spring scales, which has been compressed. It will show up in the mass of the entire system, not in the individual masses (and this is why when you asked about the rotating brick, I carefully put it in a sealed box).