# A closed universe

1. May 2, 2014

### duordi134

If I am understand correctly a moving mass has more energy than a stationary mass. Mass and energy are two forms of the same thing so more mass is more energy and more energy is more mass.

Suppose we decided to take our (almost) light speed rocket ship and reach the edge of this apparently open universe using ourselves as the preferred frame of reference.

As we reach ever increasing speeds the universe would (from our frame of reference) be moving faster in the other direction.

This means the universal mass/energy in our preferred frame of reference would increase.

But if the universal mass increases ten fold we have a closed universe.

Meanwhile the edges of the universe are receding from us so we must at least maintain a little more velocity then they have to catch them.

So our universe is closed if we try to leave it but open if we stay where we are.

Have I made any errors here?

Duordi

2. May 2, 2014

### Matterwave

You assume that the critical density will not change when you are in a moving frame of reference (with respect to the CMBR) in a FLRW universe. Although the energy density of the universe will indeed be higher in a moving frame of reference, the "critical density" in this new frame (if there is still a suitable definition for such) will no longer be what it was either. You will have to transform the coordinates of the stress-energy tensor to be the correct for your new choice of coordinates.

I have not tried to analyze the FLRW metric and the Friedmann equations in a moving frame (why would you? lol), so I can't tell you off-hand how the solutions changes to show you exactly where your argument would go wrong. However, from physical arguments alone, the scalar curvature is NOT a function of coordinate choices (or frames of reference), and neither can the result of the universe's evolution. Therefore, whether the universe is closed or not cannot depend on your frame of reference. It is a property of the manifold (space-time) itself.

3. May 2, 2014

### Staff: Mentor

In the frame in which it is moving, yes. Energy is frame-dependent.

In some ways this works, yes. In others it doesn't. The way you are about to attempt to reason here is one of the ways it doesn't.

The "universe" itself doesn't move. The correct thing to say is that other objects in the universe would be moving faster in the other direction.

No, you wouldn't. You can't change the overall geometry of the universe by changing your state of motion. This usage of the concept of "mass" doesn't work.

If the universe is open, it has no edge because it's spatially infinite. If the universe is closed then it has no edge because it's a 3-sphere, just as the surface of the Earth is closed (has a finite area) but has no edge because it's a 2-sphere. So either way there is no edge to the universe.

Yes, you've tried to use the concept of "mass" in a way that isn't valid.

4. May 3, 2014

### duordi134

Thanks,

I will read up on mass as I seem to have some misconceptions about it.
Would you recommend a source?

I may ask some questions about mass in another post as my confused mind comes up with them.

Duordi

5. May 3, 2014

### Staff: Mentor

The term "mass" doesn't refer to just one thing in relativity; there are a number of distinct concepts that have that term connected with them. The main ones:

(1) Rest mass, or more properly invariant mass. This doesn't depend on an object's state of motion. However, its usefulness by itself is limited because you can only define it for isolated objects; the universe as a whole doesn't have a well-defined invariant mass, for instance.

(2) "Relativistic mass", which is more or less what you were using "mass" to refer to in this thread. This does depend on your state of motion, but it's the wrong concept of "mass" to use for just about anything else.

(3) The stress-energy tensor. This is what serves as the source of gravity in General Relativity. It is a frame-independent geometric object; individual components of the SET change from frame to frame, but all of its properties that are important physically, including the ones that determine how strong gravity is, are invariant. The SET includes mass (more properly, mass density), but it also includes momentum and stresses. The invariant properties of the SET of the universe as a whole are what determines whether it is open or closed, and since changing your state of motion doesn't change those invariant properties, you can't change whether the universe is open or closed by changing your state of motion.

If you're interested in how mass affects gravity, I would focus on learning more about the stress-energy tensor.