# Assuming only rest mass as source of gravity and real observations

1. Jan 5, 2014

### Quantum Immortal

If we use only rest mass as the source of gravity, but use the rest of general relativity. What are the differences with observations. Excluding cosmology and dark energy.

I mean real observations, not just theory. I exclude from the question, cosmology, dark matter and dark energy. In my opinion 30% dark mater and 90% dark energy are a bit too suspicious.
Gravity is so weak, that rest mass alone should still be good enough for 99% of observations. What are the 1% that fail? Of observations, and not cosmology!!! Don't tell me about the gravitational attraction between photons... we can't measure that.

If you don't understand my exclusion criteria, just state all the differences you can think off, i'll just sort out what interest me.

Can we detect differences in the solar system?

Observed system of twin neutron stars close together? Just ignore the insides of the neutron stars, we can just assume theres more matter inside ( a difference i know of). Is there a difference in the way there orbit decays as they radiate gravity waves?

About stars, only neutron stars would be affected in an observable fashion?

We never observed a twin system of black holes right?

My guess, that in general only very energetic phenomena are problematic. Of witch, only a few are observable.

2. Jan 5, 2014

### Staff: Mentor

You can't. Using only rest mass as the source of gravity is inconsistent with the rest of GR.

Perhaps the question you meant to ask is, what observations other than cosmological ones tell us that rest mass is not the only source of gravity? If so, here are a couple:

(1) All of our observations indicate that there is a maximum mass limit for white dwarfs and neutron stars. But if rest mass is the only source of gravity, there is no maximum mass limit: as more mass is piled on and the object gets denser, its pressure just goes up to balance the increased gravity. The maximum mass limit comes from the fact that pressure is also a source of gravity, so as the object gets denser and the pressure goes up, the gravity pulling it inward also goes up, leading to a situation where even infinite pressure cannot prevent the object from collapsing once enough mass is piled on.

(2) Binary pulsar systems emit gravitational waves; this is well confirmed by observations. As the gravitational waves are emitted, the total mass of the system goes down; this is also confirmed by observations (the orbital parameters change). However, the rest masses of the individual pulsars do not change; the change in the total mass of the system is due to the change in the relationship between the two pulsars, i.e., to the change in binding energy. If binding energy did not contribute to the source of gravity, these observations could not be explained.

Last edited: Jan 5, 2014
3. Jan 5, 2014

### PAllen

There is also evidence, outlined in the following paper that kinetic energy contributes to gravitation.

http://arxiv.org/abs/gr-qc/9909014

(Note, the re-analyzed experiments described establish that KE contributes to passive gravitational mass (more precisely, that passive gravitational mass = inertial mass only if KE/c^2 is included in both. However, a difference between passive and active gravitational mass would be un-precedented.)

Last edited: Jan 5, 2014
4. Jan 6, 2014

### Quantum Immortal

Elaborate?
Its not a frequent approximation to just use the rest mass?
You can't just put zeros in the rest of the stress-energy tensor?

Yea, i was suspecting something like that....
But the pressure keeps increasing, isn't the increased pressure change the nature of the object?
white dwarfs will not just become neutron stars?
and neutron stars just become black holes?

total mass of the system? How you measure that?
You mean, the rate of decay of the orbits, are consistent with a reduction in the gravitational self energy, that it self contributes as a source to the gravitational field..... non linear stuff....
It doesn't behave just like two electric charges with constant charges...

The solar system is fine right?
Any others?
So, only very extreme situations need more then the rest mass....
right???

that is observable? Or is equivalent of measuring the gravitation pull between photons?

5. Jan 6, 2014

### pervect

Staff Emeritus
I think I already mentioned this in some other thread, but theoretical calculations of the induced velocities from a relativistic flyby shows that the induced velocities are not proportional to either the rest mass of the flyby object, nor to the relativistic mass of the flyby object. In the ultrarelativistic limit, the relativistic induced velocities are similar to those induced by a newtonian body flying by whose Newtonian mass is twice the relativistic mass of the flyby object.

See http://dx.doi.org/10.1119/1.14280

6. Jan 6, 2014

### Quantum Immortal

That's just theory right? Not experimentally measured....

7. Jan 6, 2014

### Staff: Mentor

"The rest of general relativity" requires that the source of gravity be the full stress-energy tensor, not just rest mass. That is, there is no freedom in GR to choose whether or not the source of gravity is just rest mass, or includes other stuff; the source of gravity is the stress-energy tensor, which includes the other stuff.

Sometimes the other stuff is negligible compared to the rest mass, but that doesn't mean you're only using rest mass as the source of gravity; it means the source just happens to be such that other stuff besides the rest mass is negligible in that particular case. If the latter is what you meant in the OP, then OK, but it didn't seem like it; it seemed like you were asking whether you could "use the rest of GR" but somehow modify the equations so only the rest mass could act as a source of gravity. You can't.

For some cases, yes. For others, no. But it didn't seem like you were talking about approximations. See above.

That amounts to assuming that the other stuff besides rest mass is negligible. It is not the same as modifying the field equation so only rest mass appears. See above.

Sort of. If you could somehow take a white dwarf and compress it and compress it, you could, in theory, cause it to change structure to a neutron star. But there would be a whole range of unstable states in between where you would not be able to control the process; it might collapse to a neutron star or it might end up collapsing straight to a black hole.

At any rate, the key point is that the pressure of white dwarfs and neutron stars has to be a source of gravity, not just their rest mass; otherwise there wouldn't be a maximum mass limit for these objects.

By the orbital parameters of the pulsars. Over time enough measurements of enough parameters have been collected to solve a system of simultaneous equations that gives, among other parameters, the total mass of the system.

This is one way of putting it, yes; but you have to be careful here, because if you think about gravitational self-energy as a "source" of gravity, you are using the term "source" in a different way than we were using it before. Gravitational self-energy does not contribute to the stress-energy tensor; it can't be localized, so it can't be captured in any tensor. The best you can do is to look at integral quantities over finite spacetime regions (the "total mass of the system" referred to above is one such quantity), and show that, for example, the total mass of a bound system is not just the sum of the rest masses of its constituents; there is a (negative) contribution from what is usually called "gravitational binding energy".

Not if you include binding energy. The Sun and planets all have masses (measured, for example, by looking at the orbital parameters of bodies orbiting them) that are less than the rest masses of their constituents. So gravitational binding energy makes a (negative) contribution to their gravity.

AFAIK pressure in all these objects is too small to make a significant contribution to their gravity. It is possible to have a star that is massive enough for pressure to be significant in determining its gravity, but the Sun is too small for that.

8. Jan 6, 2014

### Quantum Immortal

Ok see it as an approximation. If you take the approximation that the rest mass is the source of gravity, what observational differences you get?

You mean, that you can't make a black hole, just by piling up matter, if the only source of gravity is rest mass?
Or a neutron star? There density would just reach some maximum?

9. Jan 6, 2014

### Bill_K

No light deflection, and an incorrect precession of Mercury. What you're talking about is a scalar theory of gravity.

10. Jan 6, 2014

### Quantum Immortal

its not what i mean
Still use the left side of GR

11. Jan 6, 2014

### Staff: Mentor

The rest mass is not part of the stress energy tensor. There is no "rest of the stress-energy tensor".

I think you mean that sometimes the other stuff is negligible compared to the energy. The rest mass is not part of the stress energy tensor at all.

12. Jan 6, 2014

### Bill_K

My understanding is that the closest analog of the rest mass is the trace of the stress energy tensor. "Coupling to the rest mass" means coupling to the trace of the stress energy tensor, as in scalar gravitation theories.

13. Jan 6, 2014

### Bill_K

I don't think you know what you mean. "Putting zeroes in the rest of the stress energy tensor" is not a Lorentz invariant restriction. So what this amounts to is picking a particular rest frame and doing the slow motion approximation.

14. Jan 6, 2014

### PAllen

Did you even look at the paper? There is a whole section on experimental verification. Yes, it is verified experimentally.

15. Jan 6, 2014

### Staff: Mentor

Agreed, but then even the trace isn't "part" of the SET, it is more like a summary of the entire SET.

While you could certainly talk about scalar gravitation theories which perhaps use the trace of the SET, those are different theories so I would hesitate to call them "GR with just the trace".

16. Jan 6, 2014

### WannabeNewton

No gravitomagnetism, which is a shame really because gravitomagnetism is probably the coolest thing in general relativity

17. Jan 6, 2014

### Staff: Mentor

I guess this is partly a matter of terminology. "Rest mass" could mean "energy density in the rest frame, in mass units", which would mean the 0-0 component of the SET in the rest frame. Or it could mean the trace of the SET, as Bill_K says. Or it could mean something like the invariant length of the 4-momentum that you get when you integrate the SET (contracted with some timelike unit vector) over a spacelike slice, which is not even a local concept, and only really makes sense if the spacetime is asymptotically flat (it's more like the "total mass of the system" I referred to in a previous post). I'm not sure which of these would be the "canonical" meaning in GR, though the last comes closest to matching up with the standard definition in SR. But I suspect the OP meant something more like the first.

18. Jan 6, 2014

### Staff: Mentor

Yes; if pressure is not a source of gravity, pressure would always be able to balance gravity and keep the object stable without collapsing. It's the fact that pressure is a source of gravity that forces collapse above some maximum mass (because as the pressure increases to balance increased gravity, it makes gravity increase more, which requires more pressure, which increases gravity more, etc., to the point where above some maximum mass there is no equilibrium possible at all).

A neutron star is a stable equilibrium state, so it could still exist if pressure were not a source of gravity.

19. Jan 7, 2014

### Quantum Immortal

I just read the abstract, i couldn't believe you can measure that....

I'm pretty sure that statement is not correct. In GR its just frame dragging. Even in a relativistic scalar theory you'll get a "magnetism" like effect. Its exactly what is happening in electromagnetism. Magnetism, is just a relativistic effect of electrostatics....

hmmm
It seams to me, that the mass limits simply get increased.
You still get a collapse in the end

I think that you are just seeing the non relativistic models for these things. You forget that the materials will just hit there limits eventually. Electrons eventually combine with protons to form neutrons, then neutrons merge to form a quark plasma, then sub quark physics takes over. Eventually you get a BH.....

I have hard believing, that there is some type of matter that can withstand arbitrary amounts of pressure.

20. Jan 7, 2014

### WannabeNewton

No you won't. The Ampere equation which governs the generation of magnetostatic fields, given canonically by $\vec{\nabla}\times \vec{B} = \vec{j}$, is directly sourced by an electric current $\vec{j}$. If we have a Lorentz covariant gravitational field equation that is only sourced by rest mass then you obviously can't have a gravitomagnetic field because you need a mass current term in the Lorentz covariant gravitational field equation in order to source a gravitomagnetic field just like you need an electric current term in the Ampere equation to source a magnetic field. So at the least you need a vector theory of gravity in order to get gravitomagnetic fields. You have a fundamental misunderstanding of the relationship between relativity and electromagnetism because you're trying to use a single electrostatic Maxwell equation (Gauss's law) when you need to be using all four Maxwell equations in order to achieve Lorentz covariance.