Maybe it is easy but I am fairly confused. If a bubble of gass is 1m deep in the sea when left go will move up due to gravity pulling down havier water molecules. All is explained by the law of difference in pressure but in the case of Earth's gravity closer to the Earth's center gravity starts disapearing and at the very center it is equal zero. Having this proprety should a less denser matter just stand still at the center of Earth with iron atoms around it like it were in space far from Earth's gravity so feel the same effect as astronauts do affected by antigravity or instead will move from the center? EDIT: If we place 10 tones of water in outer external gravity free space and when it formes a sphere and before it freezes we introduce a bubble of gass 10 cm deep inside it, I assume due to sphere's gravity the bubble will go towards the surface. But what if we place the same bubble in the center of the water sphere? It will get squizzed but I pressume that the inner parts of the sphere are not involved in creating pressure to the bubble, just only the outher part where there is gravity present. So if the bubble in the center doesn't feel gravity should it try extremely slowly to leave the center of that water sphere?
Large parts of the interior of the earth are solid when you look at them for a short time. If you bent a rock harder and harder over a period of say 100 years, it would break. This is why we get earthquakes. Mountains and other structures on opposite sides of a geologic fault move slowly past each other. They are jagged. Pieces press into each other. Forces build until something breaks. This clears the obstruction and everything moves suddenly.
But over geologic times, rock bends and flows smoothly.
Image from https://paintdigi.com/2018/02/10/beauty-of-the-mountains-folded-mountains-2/, credited to commons.wiki.org
Over time, denser rocks have sunk to the Earth's core. Lighter rocks have floated up. The core is made primarily of nickel and iron, because these are common dense materials. But gold is more common in the core than at the surface.
The surface is rich in lighter materials, such as silicon. Granite forms deep underground, and rises to the surface to form mountains.
This applies to gas bubbles too. Most Helium on Earth is underground. It is slowly formed as radioactive materials such as uranium decay. Natural gas is found underground. It is formed as organic materials are buried and slowly decay and turn to oil. Sometimes these remain where they are formed. Sometimes they escape to the surface. And sometimes they are trapped underground on the way to the surface.
Image from https://en.wikipedia.org/wiki/Natural_gas
Update - Gold was a poor example of a denser element being more abundant in the core. It is true, but there is more to it than density.
The most abundant elements in the crust are light and/or abundant. According to this, the top 5 are in order oxygen, silicon, aluminum, calcium, iron.
The most abundant elements in the core are dense and/or abundant. They are guesstimated here as iron, silicon, nickel, sulphur, and chromium. There are no direct measurements of course.
Iron and silicon are everywhere. But the crust is 4% iron and the core is 85%. The crust is 28% silicon and the core is 6%. By and large, the denser elements did sink.
There are some special cases, and gold is one of them. As shown here, gold is especially rare at the surface.
Most elements in the yellow band are rare at the crust because they mix well with iron. They followed most of the iron to the core. Gold is 0.001 PPM in the crust and 0.5 PPM in the core. There isn't much of it anywhere.
Update 2 - A bubble at the very center of the Earth will experience no force driving it toward the surface. The bubble will be attracted to all nearby matter. Since there is an equal amount of matter on all sides, all the gravitational forces cancel.
If the bubble is a little bit off center, there will be more attraction toward the center than away from it. So gravity will pull the bubble toward the center. But it will also pull the rocks around the bubble toward the center. Like a bubble in water, the rocks would be more strongly attracted than the water - they weigh more. The rocks would fall and the bubble would rise.
But the attraction isn't very strong near the center because most of the Earth is pulling outward. The imbalance is small.
As you get farther from the center, the imbalance gets bigger. At the surface, the whole Earth is pulling in a downward direction. Gravitational acceleration reaches 1 g.
If a bubble was at the very center, more factors than gravity would determine whether it stays there. Rock underground does not stay still. It slowly flows. Some parts of the interior are liquid. The inner core is solid. But even solid rock can flow slowly. The deep underground flows are poorly understood. They exist - they are the cause of Earth's magnetic field.
So nobody knows where the bubble would go.
Gas bubbles would simply be squashed and dissolve into the rock. But the phenomenon can occur with "bubbles" of lighter rock and metals. While the Earth's core is solid, solids can deform over geological time (seen clearly in folded sedimentary rock stratifications) and, contrary to some answers, we have no reason to think the core is any different. A bubble of lighter rock or metal would work its way slowly upwards. Even if it were dead centre under no net gravitational force, geological movements would presently shift it in some random direction and kickstart its rise. Over time, the core has been purged of the lightest rocks and probably only regions of impure iron still get subducted a short distance, before bubbling back up again. I don't think we know enough about the core to put any quantitative detail on that.
Further out, the phenomenon is still active. Areas of the mantle close to the core get extremely hot and undergo thermal expansion. This can lower their density enough for them to rise up through the mantle as lava plumes and when they reach the surface they flow out sideways over vast areas, creating landscapes such as the Deccan flats. New plumes have been detected on their way up, though none are due to arrive for a long time yet.
Firstly, the earth's inner core is solid so your low density unobtanium bubble wont be going anywhere. If the core was a 'perfect' liquid (and the earth was exactly spherically symmetric), the bubble would be stable if it was places at the exact centre of the earth. But the bubble would be in an unstable equilibrium - if it was even a little bit off the centre then the (initially tiny) local variation in hydrostatic pressure across the bubble's diameter would cause it to drift further from the centre and start to rise like a bubble. But then if you add viscosity and shear stress and other fluidy properties to the liquid core, the hydrostatic forces might be insufficient to cause it to move at all and it might 'stick' in place like a small bubble in honey.