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Time on the Quantum and Classical Levels




A λ-hopping perspective once again gives a way to visualize and get an understanding of a tricky question in physics.






Why Does the question arise about the arrow of time:
According to Sean Carroll:The puzzle is to reconcile microscopic reversibility with macroscopic irreversibility.”  Craig Callender adds to this the notion of causation. His notion is that we can influence where we will die by current actions, but no current action we take will influence where we were born.

I will concentrate on Sean’s puzzle, and I think it also is the same puzzle as Craig’s (but I will not go into that here...it is just too philosophical. :)


Why do we need reconciliation between the microscopic and the macroscopic?
In general we understand the operation of a big machine (the universe) via the operation of its parts (quantum mechanical particles). If quantum mechanical parts show reversibility in time we would expect the classical objects built from them to show reversibility. If we cannot do this we are forced into magical thinking and invoke things like “emergence” and other mystical concepts.

As it stands now the microscopic quantum world can run backwards or forward in time and make good movies that do not violate physical laws. For example if we smash particles into other particles the movies look like reasonable happenings run forward in time and run backward in time. This is not true on the classical level. If we run the making of an omelet backward we have a movie of the unmaking of an omelet, something that is never seen.
  
The Puzzle of Time Resolved:

a. Reproducibility
In going from the microscopic (atoms and molecules below the Planck Mass) to the macroscopic (mass clusters above the Planck Mass) something fundamental happens to objects, they loose the ability to be replicated perfectly. Replicating perfectly corresponds to having the quantum mechanical property of interference. This is the same as having the ability to λ-hop. That’s the answer to the arrow of time, I know it is too simple.  In Section 31 we derive the limiting mass of the quantum world to be the Planck mass. This is something new in physics that has not been suspected and is the source of the arrow of time. We cannot find or make a single quantum mechanical particle that exceeds the Planck Mass. If we have an object that has a mass that is above the Planck mass it must consist of an assembly of moving quantum mechanical particles.

This is why all classical objects (anything above the Planck Mass) cannot have perfect copies. As we follow any classical object we find it different at every time instant because its internal structure (of quantum mechanical particles) has changed. This is not true of low mass particles like atoms or molecules which move (hop) without changing any internal structure (electrons, quarks etc.). Over time classical objects become more and more disordered because their constituent parts have to move with respect to each other. Said another way we consider a classical object as a constant entity in spite of the fact that it is constantly changing (has to age) because its internal quantum components must move with respect to each other. This is entropy. We can also visualize entropy via a Xerox machine making a copy of a picture, then using the copy to make another copy. Repeating this copying process we get fuzzier and fuzzier pictures . It is easy to see the time order of the copies. This is the arrow of time.

For example take an ice cube:

We take an ice cube and take pictures of it at intervals while it is melting. Each picture captures a slightly different ice cube. If we play the pictures of the ice cube backward and forward we will note that the sequence of unique objects is slightly different going in each direction. We also notice the increase of disorder in the forward direction because the ice cube melts (entropy).  It will be very frustrating to take the puddle and make a movie of it growing back into an ice cube.
 
If we take an atom (in the ice cube) and take pictures of it at intervals, each picture captures a perfect atom. If we play the pictures of the atom backward and forward we only see an atom that is not changing in time. The concept of disorder (entropy) makes no sense here, because there is only a single unchanging object. This seems trivial, but disorder stops at the quantum level or more precisely at the onset of λ-hopping.

b. The Nature of Clocks
On the quantum level where all particles λ-hop, clocks are an integral part of every object. Just as every particle has a wavelength every particle has a period. This comes from deBroglie’s equation and is not speculative science, it is the wave nature of matter. Every quantum particle has time as part of its construction. Particles have time with respect to themselves. They do not need to find an external clock to have time.

On the classical level all the objects are jumbles of particles and their clocks. Because of this when we observe a classical object by itself we do not get any sense of time (outside of something like temperature). To have time with classical objects we need to find or make clocks.

c. The Concept of Now
In
Section 30 particles were explained (postulated) as multiple appearances of something called a Planck Instance, that exists for a Planck Time. It made sense to do this because it fits with E = hf the basic building block of quantum mechanics. Note that in Section 30 and Section 35 a case is made that the Planck Instant is essentially a neutrino.

A Planck Instance (separated by a period of time) was needed to have a photon. A Planck instance with a spin sequence was needed to have a real particle with a mass, a wavelength, and a period (see
Section 30). At an instance of time called “now” we are at a loss to find a particle (or photon). A memory that is accessible by the observer is necessary. See reference in Section 37, “Making Time with Pretty Girls and Hot Stoves”.

This way of looking at “now” brings to mind how we perceive musical tones. If we pluck a string we can ask the question where does the tone start. At the release of the string “now”, there is no sound. At the first back and forth of the string there arises the first inkling of a tone. I believe this is as good as we can do to give a now to the tone. The “now” of a tone starts as a pluck (the tick of a clock) and ends a wavelength and period later (the duration of the clock) as a sound object.

The “now” of a photon starts as a Planck Instant and ends a wavelength and period later at another Planck Instant. These two Planck Instances form a wave which is the most primitive quantum mechanical object, essentially a photon. To get more sophisticated quantum mechanical objects (particles) we need to introduce spin to the Planck Instances
Section 29 (Visualizing Spin). 

d. Is Time Real?
I believe this question is equivalent to the question: Is change real?
I will leave this with the reader. However, I think I know how Zeno would answer this question.



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