Understanding the Effects of Relative Curvature and Mass on Space and Observers

[friend]

Mass curves space. And speed near the the speed of light increases mass. So for someone traveling near c and is passing a partice at rest, the traveling observe feels like he's at rest and the other particle is moving. So if the other particle is moving wrt his rest frame, does he see an increased curvature of space surrounding the particle approaching him? Whereas, a particle traveling along side the approaching particle will experience a different curvature?

Does the curvature of mass depend on the speed of observers since the mass of that object does depend on the speed of the observer? Thank you.

 

[Bill_K]

friend, We get this question (or some variation of it) at least a few times a week. Just so you know you're not alone in wondering. As the professor said, "I use the same questions on the exam every year, but to make it more interesting I change the answers." So I'll try to come up with a different answer!

In the first place, the "mass" you're talking about, that increases with the object's speed, is the "relativistic mass", which no one uses any more. When we say mass nowadays we mean rest mass, which does not change. But what does change is the particle's energy, and that's better to talk about anyway, since the source of the gravitational field is in fact energy, not mass. So - energy.

Does the curvature depend on the speed of observers?

Yes, surely it does! Most quantities in physics are like this - they change when we go from one rest frame to another. Charge becomes current, energy becomes momentum, and so on. The individual quantities we talk about are components of an object, a vector or tensor, that transforms in a known way when going from one frame to another. The frequency of a light ray increases if we move toward it. Similarly, the energy of a particle increases, and its gravitational field does too.

The gravitational field is represented by the curvature of spacetime, which is described by a tensor called the Riemann tensor. In vacuum the Riemann curvature tensor has ten independent components, and sure enough they change when we change to a different rest frame.

That does not, however, mean that the properties of the particle change. It does not, for example, become a black hole! But its gravitational field does look different to us, just from the fact that it's moving.

 

[friend]

The gravitational field is represented by the curvature of spacetime, which is described by a tensor called the Riemann tensor. In vacuum the Riemann curvature tensor has ten independent components, and sure enough they change when we change to a different rest frame.

Does that mean there is a preferred reference frame where the curvature of most things in the universe is minimized?

 

[Bill_K]

The rest frame of the particle.

Again, it is best not to think of "the" curvature as if it were a single quantity. Even in the rest frame, the curvature tensor has five independent components.