### Memory In Metastable Vacuum

We have seen in several blog posts that an hologram of the body can easily be formed in the viciniy of the body and that this holographic body can take the consciousness, making it equivalent to a 'soul'! However, in order for the natural hologram of the body to actually form a body independent of the usual body, the seemingly empty space must be able to retain the memory of the hologram. One way in which a seemingly empty space can retain memory is through what they call it 'vacuum metastability'.  We will closely exermine what this fancy term rifers to.

Stability

A stable state of an entity is  a state that the entity returns to whenever external forces tries to dislodge it off that state. If you try to topple a stable object by pushing it, the object can tilt but will return to upright possition immediately you cease pushing it. An unstable object will keep on moving in the direction of the push even after you cease pushing. So in an unstable state, a slight, dislodging force is amplified leading the entity at that state into an entirely different state. But a stable state leads to a return to the original state. So we can say that in general, a stable state develops a force in the opposite direction of the force that tries to remove it off the stable state. A spring is a good example. If you pull a spring, it shrinks back to its original size. If you try to compress it, it expands back again to its original size. Such is the nature of every stable entity. Work has to be done in dislodging the system off the state, in whichever direction you try to dislodge it into. So the stable state is the state with the lowest energy, at least amongst the neighbourhood states. Since a 'vacuum state' , in Quantum Field Theory is normally seen as 'the state with lowest energy,' it is normally presumed to be a stable state. But there is another concept: metastability.

If you were careful, you will realize that a spring realy does not have only a single stable state. Yes, if you pull a spring, it returns back to its stable state. However, if you keep pulling it, then at some point it will attain a new stable state. The spring will not return to its original state any more but will behave like a longer spring, returning to a new lenght when you try to change it. We say that the spring is metastable, not just 'stable'. This metastability is general in all materials but is more manifest in metals. If you try to bend any metal, you find that it springs back to original shape, provided that the force is small enough. But if you force it more, it permanently bend and begin to be once again stable but in a new position. This is how all 'memory' works. Pushing an entity into a new stable state is making it to 'remember the push' in some way. So you can, for instance, inscribe some writings/drawings in a solid but not easily do so in a fluid. The latter almost immediately returns to the original state with no writtings rather than attaining a new stable state with writtings on it.

The concept: 'vacuum metastability' , as used in QFT (Quantum Field Theory ) is a misnomer because what is metastable is realy 'something in vacuum', not the 'vacuum' itself, unless maybe we are talking of quantum gravity where the 'field' in question is the 'space-time' itself. You can understand it this way: Usually we think of 'space time' as 'stable' with the 'flat spacetime' being the stable state. When a gavitating object comes to the region, it 'bends' the 'spacetime', but the 'spacetime' returns to its original state immediately once the gravitating object gets off the region. But in QFT, the 'field' in question is often the 'higgs field'. One can model the higgs field's vacuum state as a stable state or as a metastable state.

In QFT, we model particles (the waves) as an ensemble of quantum harmonic oscillators (QHO). A QHO is a quantized classical oscillator. The classic oscillator is just a spring. A spring oscillates around its stable state. Thinking of oscillation in terms of energy, we say  that it keeps changing energy from kinetic then to potential then back to potential and so forth. The kinetic energy is at its maximum where the potential energy is at its minimum, and you can see that this happens at the spring's stable state. So you see that the stable state is a state with the least, local, potential energy.

https://www.researchgate.net/publication/329750275/figure/fig1/AS:705200490831876@1545144307878/Illustration-of-vacuum-decay-for-a-potential-with-a-metastable-vacuum-at-the-origin.png

You will encounter the above diagram if you search more on 'vacuum metastability'. You can understand it this way: Think of the horizontal axis as to represent the length of a spring. Then the vertical axis represents the potential energy of the spring. When you pull a spring, you increase its potential energy. The potential energy similarly increases when you compress it. So the 'valley' depicts the spring's natural resting place, which is the stable atate. Moving to the left is like 'compresing the spring'. So it is like 'climbing up hill' towards the left, of which you will roll backwards all to way to the stable position, i.e. the valley. Climbing up the hill increases the gravitational potential energy.

So you can get a clue on how the mathematics of quantum field theory is modelled in the analogy of a spring, or elastic materials in general. They are like saying that the quantum waves are waves in some 'elastic medium' that pervades everywhere. But then note that they tended only to model the spring as though it has only a single stable state. So their 'energy' equations for the quantum fields often have only a single 'valley' (gotten from quadratic equation). In most cases where we are concerned with waves in an elastic medium, we can ignore the other stable states of the medium, provided that the forces that creats the waves donnot sufficiently stretch the medium. So you will find the 'energy' equations of a spring failing to show the obvioud fact that the spring is metastable, not stable. They inherited this oversimplifications of classic oscillator when they were making the analogy in modelling the Quantum Harmonic Oscillator. When we realize that all the classic, waving mediums are actually meta-stable, we will begine to realize that perhaps the most accurate modelling of quantum fields are as the meta-stable ones. Hence we realize that the quantum fiels can as much 'store memory' as any other classic medium!

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