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Take away the mass.Will the geometry exist?

In effect, if you add enough curvature into a specific region, matter should appear.

Quote from: Ęthelwulf on 04/04/2012 13:12:50In effect, if you add enough curvature into a specific region, matter should appear.This is going towards the Photon-only theory...

Quote from: yor_on on 03/04/2012 06:46:19Take away the mass.Will the geometry exist?Yes, it will. The reason why is because the equations of relativity dictate that:What this equation says is that if you remove all the mass in the universe, the curvature could still be non-zero. This is because of the presence, but highly ellusive today gravitational waves. So geometry can exist without matter.It is for this reason, I believe that matter emerged from curvature. In effect, if you add enough curvature into a specific region, matter should appear.

Quote from: Ęthelwulf on 04/04/2012 13:12:50Quote from: yor_on on 03/04/2012 06:46:19Take away the mass.Will the geometry exist?Yes, it will. The reason why is because the equations of relativity dictate that:What this equation says is that if you remove all the mass in the universe, the curvature could still be non-zero. This is because of the presence, but highly ellusive today gravitational waves. So geometry can exist without matter.It is for this reason, I believe that matter emerged from curvature. In effect, if you add enough curvature into a specific region, matter should appear.Remember this is space-time, so if you really have no matter and energy for all space and all time, it turns out that the only thing that determines the shape of the universe is the cosmological constant.

Quote from: Ęthelwulf on 04/04/2012 13:12:50Quote from: yor_on on 03/04/2012 06:46:19Take away the mass.Will the geometry exist?Yes, it will. The reason why is because the equations of relativity dictate that:What this equation says is that if you remove all the mass in the universe, the curvature could still be non-zero. This is because of the presence, but highly ellusive today gravitational waves. So geometry can exist without matter.It is for this reason, I believe that matter emerged from curvature. In effect, if you add enough curvature into a specific region, matter should appear.Remember this is space-time, so if you really have no matter and energy for all space and all time, it turns out that the only thing that determines the shape of the universe is the cosmological constant. If you set that to zero, you get a flat universe everywhere. It still has geometry ("flat" is a geometry), but it has no curvature. Essentially, the entire universe has the geometry of special relativity. This is obviously a bit silly to take seriously, since what would a matterless/energyless universe mean?Now, if you still take no traditional matter/energy, but add in a cosmological constant, then space can be curved, though you still have limited potential geometries. If you're simply looking at a region of space that contains no matter/energy, then it can also be curved, since matter/energy elsewhere in the universe can be causing space-time to curve or it could be emitting gravitational waves.I don't think anyone knows for sure whether having "enough curvature" could cause matter to appear spontaneously from the vacuum. It's intriguing, but probably needs quantum gravity, and we don't have a satisfactory theory for that yet.

Ok, here's what I recall from my GR coursework with a bit of help from Googling the curvature tensor:If the stress-energy tensor is zero and the cosmological constant is zero, then the Ricci curvature tensor is necessarily zero. The curvature tensor describes the deviation from flat space-time, and when it's zero, your space-time geometry is flat.

Quote from: JP on 04/04/2012 18:13:11Ok, here's what I recall from my GR coursework with a bit of help from Googling the curvature tensor:If the stress-energy tensor is zero and the cosmological constant is zero, then the Ricci curvature tensor is necessarily zero. The curvature tensor describes the deviation from flat space-time, and when it's zero, your space-time geometry is flat.Hmmm....... well as far as I know, gravitational waves are not trivial, nor are they really the presence of matter, so you may have a curved space without the presence of matter.Maybe as a little project, you can investigate this with another scientist and see who is valid.

Quote from: JP on 04/04/2012 18:13:11Ok, here's what I recall from my GR coursework with a bit of help from Googling the curvature tensor:If the stress-energy tensor is zero and the cosmological constant is zero, then the Ricci curvature tensor is necessarily zero. The curvature tensor describes the deviation from flat space-time, and when it's zero, your space-time geometry is flat.Hmmm....... well as far as I know, gravitational waves are not trivial, nor are they really the presence of matter, so you may have a curved space without the presence of gravity.Maybe as a little project, you can investigate this with another scientist and see who is valid.

Quote from: Ęthelwulf on 04/04/2012 18:18:16Quote from: JP on 04/04/2012 18:13:11Ok, here's what I recall from my GR coursework with a bit of help from Googling the curvature tensor:If the stress-energy tensor is zero and the cosmological constant is zero, then the Ricci curvature tensor is necessarily zero. The curvature tensor describes the deviation from flat space-time, and when it's zero, your space-time geometry is flat.Hmmm....... well as far as I know, gravitational waves are not trivial, nor are they really the presence of matter, so you may have a curved space without the presence of gravity.Maybe as a little project, you can investigate this with another scientist and see who is valid. Well if they exist without mass/energy, then as far as I can tell, Einstein's field equations are wrong. Of course, I believe you can have something generate the gravitational waves, and they can propagate into an empty region of space-time, but if you have a truly energyless/matterless universe, I don't see how this could happen... But then, such a universe might not be physically meaningful anyway.Actually, this is very reminiscent of EM waves. We know that EM waves certainly can propagate in a vacuum, devoid of any matter. But we also know that EM waves require sources to be generated, so in a truly matterless universe, you shouldn't have EM waves.

There seems to be an endless potential for the discussion of nothing. As an absolute amateur, it does seem to me that the nothings that scientists discuss tend to be very somethingy nothings. Could it be that absolute nothing is just too dull to catch anyones interest?

Quote from: Bill S on 04/04/2012 21:29:52There seems to be an endless potential for the discussion of nothing. As an absolute amateur, it does seem to me that the nothings that scientists discuss tend to be very somethingy nothings. Could it be that absolute nothing is just too dull to catch anyones interest?Maybe it goes deeper than that. For instance, four years ago to my knowledge, many people used to say space was nothing. It turned out that space really isn't nothing, but is filled with energy in a virtual form. Perhaps then, the reason that nothingness can exist is because we cannot infer on it - what we have no knowledge about is where the imagination fills.