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Time-lattice model is proposed. Using the correspondence of the model and the Ising model for simple cubic lattice system, we study the time phase transition, the electroweak phase transition, and the BEC transition for time. The time field is the Higgs field. Four types of the fields are found before the electroweak phase transition, after which there is only one type of Higgs field coming from the infinite correlation of the lattice time states, going with electromagnetic field and gravitowagnetic field. The symmetry breaking and the hierarchical structures, the relation between the change in energy and the Higgs formation, the reason why there are a few antiparticles and no negative mass are explored. For the Higgs field, its energy density and time condensation are discussed. A possible mechanism of the formation of black hole is assumed.

Symmetries play an important role in physical laws. The field variables can change at different spacetime points, while their referring group elements are the functions of the spacetime coordinates. Such transformation is called gauge transformation, which determines in a considerable degree the interaction form. We get an idea from Yang-Mills theory that more elaborate symmetries are able to produce connection fields accounting for nature’s forces [

In 1967-1968, a theory on weak and electromagnetic forces was set up by Weinberg and Salam [

In general theory of relativity Einstein supposed that there was a standard clock at each spacetime point, this means that time can exist at everywhere and has an orientation at each point. An object in stationary state, in terms of classical physics, may have zero space coordinates, and has a straight trajectory known as the world line due to time is always flowing. The object has a proper energy, which reminds us that there is a certain relation between time and mass for the dual relationship of time and energy. We define the time orientation of today as its positive direction, the opposition, negative. The world we can touch is in the time ordered state with positive direction. There is not any boundary of the universe, one part of which is our world, which is so big that we may approximately consider it as infinite. It seems reasonable to suppose that in the evolution process of universe, with the decreasing of temperature our world underwent a phase transition of time, a kind of second order phase transition. Suppose that a relative stable world emerged after rapid expansion of universe, the temperature fallen down so slowly that we can build a uniform space in this circumstances. Because of that given two points in a metric space, we can always find disjoin open sets containing them [

A time-lattice model is such a similar system, where state A represents positive time state (p-time state), and the state B does negative time state (n-time state). In Section 2, based on our successful approach to the simple cubic Ising model [

The Theory introduced and applied in reference [

Remember the correspondence relationship of the Ising model and the time-lattice model: The lattice spin-up state ® the p-time state of the lattice; the lattice spin-down state ® the n-time state of the lattice. The sub-block spin-up state ® the p-time state for the sub-block, the sub-block spin-down state ® the n-time state for it. The block spin-up state ® the p-time state for the block, the block spin-down ® the n-time for it. By using these correspondences we can directly understand the time phase transition while reading reference [

It is the infinite iteration of the self-similar transformations at the

is finite. There exists a turning temperature

blocks. The lower the temperature is, the longer the correlation length of the lattices is, and the bigger the sizes of the sub-block and the block are. We have proved there are two sub-systems in the system: The sub-block sub-system and the block sub-system [

Let

In this case the system energy is higher. When the system energy becomes lower than that of the disordered state, the situation turns over (the time shows global order), and

This case is available for the range

Because of the duality relation of the time-energy for the system, the p-time state may relate to the positive energy state, the n-time state to the negative energy state. Dirac equation indicates that the negative energy state leads to antiparticles, which is equivalent to the n-time state as interpreted by Feynman. The infinite correlation length for the lattices doesn’t get rid of a chance in which the antiparticles happen in a short time within a small area. The global p-time state for the system is a subsequence of the correlation of the time states for all of individual lattices, but a simple addition of ones. Whenever there is locally a possibility of the n-time state in an area, where may appear antiparticles. This means that for the individual original lattices, the local symmetry SU(2) of the time state exists still. For the whole system, its time ordered state can select either positive or negative. If the state were negative, the relevant Higgs would give the particles negative mass. The occurrence of the antiparticles is of locality, and whether the mass takes positive or negative is dependent on the global time ordered state. That the antiparticle mass is as the same as the particle mass guarantees that Hamiltonian obeys CPT (charge conjugation, parity, and time reversal) symmetry, which can be proved by the following. Let

The CPT unified operator is

The antiparticle mass in the state

Comparison of (4) and (5) illustrates that the Hamiltonian is invariant under the CPT operation:

According to [

where n is the side of the sub-block, and its spin

where

More complicated characteristics are that the hierarchies of these symmetries appear. Apparently, these symmetries show local gauge properties since the size of the sub-block and the block are finite. When the correlation length of the original lattices is of infinity the sub-blocks and the blocks disappear, the local symmetry

The Higgs field is just the time field, which quanta are the Higgs particles. The temperature

Using Debye theory [

where

Notice that there is neither sub-block nor block, only original lattices. In a low temperature region, when

where

where

The relative intensity changes into

The lower the temperature, the weaker the time liquidity, since more Higgs particles will pull up together in the condensation state. A subsequence of the effect is the time rhythm slow down, all of physical processes will slow their steps.

If the temperature

where

space volume, even though it is small, will be full of the releasing energy of the Higgs, and the mass density, by the formula

If we consider the model as big but finite, the consequence of the time condensation may be shown as

The condensations make the Higgs particles pull up together to release partly their freedom degrees, and the massless particles such as the photons and the gravitons get a chance to become massive and slow down their speeds. Meanwhile, the particles may change their propagation paths.

It is the most important to investigate all possible structures for the spacetime, which will provide us symmetries for the understanding of our world. From Equations (6) and (8), we know that the inner space of a block has about

Yougang Feng, (2016) Time Phase Transition and Higgs Formation. Journal of Modern Physics,07,536-542. doi: 10.4236/jmp.2016.76056