Losing mass, gravity, curved space, and more

[gonzo]

I have sort of a vague question. Am I right in saying that only mass and not energy cause space to curve and have gravitational effects (and other affects that only depend on mass)? Or does the "relativistic mass" of a photon cause similar but reduced effects?

That's sort of just a lead in question ... I was thinking about how all the stars in the universe are coverting mass to energy all the time, which means the total mass of the universe it constantly shrinking and the energy of the universe is increasing (yes, I know that the mass-energy stays the same). My question is if this has any major effects on the physics of the universe? Is it it just too negligable to matter, or does the relativistic mass or other energy effects function the same as the missing mass in all relevant cases, or what?

 

[da_willem]

It is energy (E), or relativistic mass (E/c) that curves spacetime, so a photon (only energy) as well as rest mass causes gravity. This answers your second qeustion as well...

 

[Garth]

Yes, but remember energy is only one component of the stress-energy-momentum tensor that determines the curvature of space-time we call gravity. Pressure and angular momentum also affect the curvature.

Garth

 

[gonzo]

I understand what you are saying Garth, but not what you mean ;)

In other words, can you please explain a little better your point in pointing out that aspect? Thanks.

 

[Garth]

In other words, can you please explain a little better your point in pointing out that aspect? Thanks.

I was answering your original question.
Einstein's GR field equation
R_ab-(1/2)g_abR = 8piGT_ab
relates curvature, which is included in the tensors on the left hand side of the equation to the distribution of mass, energy, momentum and stress, which is included in the tensor on the right hand side.

Mass, energy, momentum and stress, such as pressure, all contribute to the curvature of space-time and the phenomena we call gravity. It is not just mass on its own, or energy, not even just the total energy that includes the (rest) mass of the particles in the system that cause gravity as your original question enquired.

Two practical outcomes of this are:

1. The fact that a Friedmann universe with pressure in it decelerates more quickly than the same universe with no pressure.

One might have thought that pressure, say from a hot gas as in a universe coming out of the Big Bang, would cause the universe to expand more quickly, but in fact it slows it down. To get an accelerating universe you need negative pressure i.e. tension, such as has been introduced as Dark Energy.

2. The fact that a spinning body drags space-time with it so that inertial compasses (gyros) precess in the same direction as the parent body's rotation. The Gravity Probe B satellite is at this moment measuring this frame-dragging or gravito-magnetic precession caused by the Earth.

I hope this helps,
Garth

 

[gonzo]

Thanks, that was interesting.

 

[da_willem]

Yes, but remember energy is only one component of the stress-energy-momentum tensor that determines the curvature of space-time we call gravity. Pressure and angular momentum also affect the curvature.

Garth

True. But pressure is a form of internal energy, so if you say energy is the cause of gravity you're not very far from the truth and you will not have to explain about the energy-momentum-stress tensor. Especially because the contribution of pressure is only significant in very large stars, and stresses and angular momentum also constitute only minor effects. But in principle ofcourse you're right, it's the tensor that is the source of curvature in GR

 

[Garth]

But pressure is a form of internal energy

this is a very "hand-waving" way of trying to tie everything down to a Newton + SR explanation. (i.e. Newtonian gravity but with the insight that energy also has a mass equivalent) Much better to be transparent from the start and explain that there are other surces of curvature in GR as well. Then you can also discuss the curvature of an empty universe, the cosmological constant, dark energy etc.

Garth

 

[da_willem]

this is a very "hand-waving" way of trying to tie everything down to a Newton + SR explanation. (i.e. Newtonian gravity but with the insight that energy also has a mass equivalent)

These were the guidelines from which Einstein preceded finding a theory of gravity in accordance with his SR. mass->energy->momentum four vector->energy momentum-stress tensor.

From a didactic point of view you're probably right, Being vague (or in my case inaccurate) about theories will only confuse newcomers. It will probably also give people the feeling the present theories are not capable of 'explaining' a wide range of phenomena, and support all these off-topic posts about their own theories.. So next time I will try to be accurate and complete.