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This is a great moment. I’ve collected all the three puzzle pieces of classical mechanics, quantum mechanics and statistical mechanics. Now, I finally get started to learn physics.

 

A relatively rigorous statement of the 2^nd Law of Thermodynamics:

It is almost impossible for the sum of the entropies of the microcanonical ensembles of all the macroscopic subsystems of an isolated system which has not reached statistical equilibrium to decrease.

a priori judgement: proposition to be justified independent of all experience beyond what is needed to grasp the concepts involved

a posterior judgement: proposition to be justified dependent on some experience beyond what is needed to grasp the concepts involved

analytic judgement: proposition in which all concepts are related solely by their definitions

synthetic judgement: proposition in which some concepts are not related solely by their definitions

How is a synthetic proposition a priori possible?

Certain cognitions even abandon the field of all possible experiences, and seem to expand the domain of our judgments beyond all bounds of experience through concepts to which no corresponding object at all can be given in experience.
And precisely in these latter cognitions, which go beyond the world of the senses, where experience can give neither guidance nor correction, lie the investigations of our reason that we hold to be far more preeminent in their importance and sublime in their final aim than everything that the understanding can learn in the field of appearances, in which we would rather venture everything, even at the risk of erring, than give up such important investigations because of any sort of reservation or from contempt and indifference.

Is time objective?

Time is objective, or otherwise we would be able to manipulate time according to our will. Nevertheless. how we “feel” time depends on individuals.

 

Is time uniform?

When it comes to “uniformity”, a reference is required. Generally, we take time itself as the reference, but in this case, it is meaningless to say time elapses uniformly with respect to time. The uniformity of time varies from one reference to another. For example, when we take atomic clock as a reference, time is almost uniform; when we take our feelings as a reference, time is not uniform at all — time seems to elapse faster when we are excited and more slowly when we are bored.

 

Is time relative?

The theory of relativity suggests time is relative. Time is simply one of the parameters that specify an event. Different observers can have different scaling of time, so their time parameters can be different for the same event. Therefore, it is possible that two events happen simultaneously in one observer’s eyes, but not simultaneously in another observer’s eyes.

 

Is time elapsing?

Time does not necessarily elapse. Perhaps, spacetime is a manifold obeying certain mathematical structure, on which each point stands for an event. The groups of points that specify our brain activities may be in such complicated states that form consciousness, and further memories. The memories include information about the so-called “past” but not “future”. Even if we have the memories, it does not necessarily mean we have gone through the past and will step into future, but merely means the points specifying our brains have that information. The information misleads us to have a sense of memory, and then a sense of time. Because memories only include information about the so-called “past”, we feel time is always elapsing forward. Therefore, time elapsing may be a misconception of human beings, and a unique capability of human consciousness, which is essentially memory. We can never be sure whether time is truly elapsing, because every evidence comes from the dubious memory.

 

The difference between time and space?

If time and space have the same status, why doesn’t space elapse? Why is an object replicative in time but unique in space? Why are conservation laws about time but not space?

Time and space have the same status but they are not equivalent. They have opposite signs in the metric tensor, as well as opposite signs in the wave equation, being completely symmetric. The most significant difference between time and space, in our universe, is perhaps their different dimensions. Time is one-dimensional, while space is three-dimensional, which is the answer to the above questions. Because time is one-dimensional, an object remains itself with time; if time were multi-dimensional, it would dissipate and vanish like a wave. Because our brain remains intact with time, the memory can be formed, and thus we feel time elapsing. But because space is three-dimensional, no stable “spatial memory” can be formed, so we do not feel space elapsing. Conservation laws should be written in the form of a continuity equation. Because time is one-dimensional, the equations include a total derivative of time; if time were multi-dimensional, the equations would include a divergence of time, just like that of space.

 

The arrow of time?

The second law of thermodynamics has been regarded as the arrow of time. But every physics law seems to be time reversible, so why is it necessary for entropy to increase in a closed system? If time elapsing is a misconception of human beings, there would be no “direction” of time anymore. Memories are formed in such a way that they only include information about the so-called “past”, which has lower entropy than “future”, so we have sensed the arrow of time. Even if time were reversed, our memories would be restored as well, so we would not be able to notice a difference. What we would feel like would be exactly the same as how we feel when everything goes right. The memory determines that time must “elapse” in only one direction.

The universe is a formal system, consisting of a fundamental element and a generating rule, which produce a series of new elements. Time is embodied in the causal relationship among these elements.

 

Metaphysics is unverifiable, but it sheds light on Physics.

Premise 1: Being real is more perfect than being unreal.

Premise 2: God is the most perfect.

 

You can certainly imagine a thing than which nothing more perfect can be imagined, because if you understand the phrase “most perfect being”, you have already imagined such a thing. If this thing does not exist in reality, you can then imagine it existing in reality, which is more perfect. And it contradicts the assumption that the previous thing is the most perfect that you can imagine. Hence, in reality there exists a being than which nothing more perfect can be imagined, and it is God. Therefore, God exists.

 

Flaw: You can imagine a thing than which nothing more perfect can be imagined, and in your opinion, it exists in reality. Now that you have already imagined it existing in reality, you cannot imagine a more perfect thing. And imagining it exists in reality does not mean it truly exists in reality.

Socrates: Let us then, in the first place, be careful of allowing or of admitting into our souls the notion that there is no health or soundness in any arguments at all. Rather say that we have not yet attained to soundness in ourselves, and we must struggle manfully and do our best to gain health of mind …… Whereas he seeks to convince his hearers that what he says is true, I am rather seeking to convince myself; to convince my hearers is a secondary matter with me. For if what I say is true, then I do well to be persuaded of the truth, but if there be nothing after death, still, during the short time that remains, I shall not distress my friends with lamentations, and my ignorance will not last, but will die with me, and therefore no harm will be done …… And I would ask you to be thinking of the truth and not of Socrates: agree with me, if I seem to you to be speaking the truth; or if not, withstand me might and main, that I may not deceive you as well as myself in my enthusiasm, and like the bee, leave my sting in you before I die.

Philosophical arguments often include incomplete induction and analogy. It first establishes several known examples with certain logical relationship. All of these examples share the same structure. It then proposes a new argument, unknown whether it is true or not. If this argument has exactly the same structure as the previous examples, it is deduced that the same logic must hold for this argument.

In Phaedo, the Forms of absolute beauty, justice, and goodness are invisible and immortal whereas the so-called beauty, justice, and goodness in the material world are visible and changeable. The body is visible and changeable; the soul is invisible. Following an analogous structure, it is deduced that the soul is immortal.

The essence of this problem is whether we could find a pair of opposites, other than the possible pair of life and death, so that among the opposites there is a process to convert A to B, but there is no process to convert B to A. If we could not, it would be very quirky to assume that life and death is the only pair that satisfies this condition, so it would be more natural for us to believe life is generated from death, namely there is reincarnation.

However, beyond life and death, there is actually a pair which satisfies this condition: the state of low entropy in a closed system versus the state of high entropy in that closed system. The former automatically becomes the latter, but there is no way for the latter to go back.

There are many pairs of opposites and pairs of processes which turn one into its opposite, e.g.

The less is turned into the more through the process of increase; the more is turned into the less through the process of decrease.

The parts are turned into the entirety through the process of composition; the entirety is turned into the parts through the process of division.

The coldness is turned into the hotness through the process of heating; the hotness is turned into the coldness through the process of cooling.

The asleep is turned into the awake through the process of waking up; the awake is turned into the asleep through the process of falling asleep.

……

It seems that for every process which turns one into its opposite, there is always a reversed process which turns the latter back into the former. All things which have opposites seem to be generated out of their opposites. And, does it still work for life and death?

The life is turned to death through the process of dying; the death is turned to life through the process of … ?