How now works

The work of a curious fellow

Somehow now sorts through the very large number of possible futures of the universe and selects the one that is to survive the passage of now to enjoy its instant of reality and become the past.  I am going to be bold enough here to explore a possible mechanism by which this might be accomplished.  By “possible futures of the universe” I mean the possible states of the universe at a future time.

The state of the universe at any instant is the total information required to reproduce the universe as it exists in that instant. That is way too much information for us to handle. 

Fortunately we do not have to treat the universe as a whole to consider its future states.  There is enough empty space in the universe that the interactions with distant objects may be neglected even though in principle they are connected by gravity and electrostatic forces.

It seems to me there are two kinds of state changes.  Think back to the GPS satellite that we used to demonstrate the effect on time of relativity principle.  As it drifted around it orbit its position and velocity was constantly changing so from instant to instant the state of the universe was altered.  This sort of state change I would call a passive change.  The satellite is just following Natures preferred path, the path of maximal aging in this instance.

If I move my pen from the right side of the computer to the left, I have changed the state of the universe, even if most of the universe doesn’t care or even know.  Clearly both the pen-right and pen-left states are possible future states.  I would like to call this sort of state change an active change.  The pen did not by itself drift from the right to the left. The move required the active participation of a change agent.

I think that the active and passive state changes, as defined above, between them cover all possible changes in state with the possible exception of divine intervention, which is outside the scope of this essay. The underlying assumption is that every event has a cause, originating either in Nature’s preference for minimum fuss or in a prior event

Let’s handle the passive state changes first.  The passive state changes include no change at all.  Think about the satellite in orbit or a stone dropped from the leaning tower of Pisa.  They are both following the path of maximal aging, changing state as they go in accordance with Nature’s preference.  Their future states are predetermined, barring the intervention of an active state change agent, like the ground when the stone hits it.  As now approaches a predetermined future time the state approaches the predetermined corresponding state and that state is made real (realized) by the passage of now.

Active state changes are more difficult to explain.  Here I will lift another result from Einsteinian Relativity.  No object, or even information, can travel faster than the speed of light.  To do so would violate the law of causality, which says no event may happen before its cause in any reference frame.  The speed of an object is represented on a spacetime diagram, with time and distance in consistent units, by the slope of the curve connecting the series of events “object found here”.  Such curves trace out the history of an object’s location in space and are called world lines.

Imagine that an object is proceeding along Nature’s preferred path and scheduled to arrive on the t-axis at future time tf. If it is to suffer an active state change at the point (0,tf), the agent of that change, another object being swept along with the advance of now, anything from a planet to a photon, must be close enough to the t-axis to get there at time tf. In other words it must be on the green line in Figure 6 below.

Figure 6

Spacetime Diagram – Past light-cone of future time

Now if we turn time back on and now for both objects creeps up the t-axis toward tf at the speed of light, the volume of spacetime from which events might impact the state of an object at (0,tf) is reduced.   The green segment shrinks to zero length as now reaches tf.   At that instant no further changes at any point in space are possible, since each point is subject to the same analysis, and the state of the universe at tf is realized.

More specifically, let’s imagine that we want to predict the state of the universe at midnight tonight.  Remember that we threw out two spatial dimensions in drawing the spacetime diagram so the green segment actually represents a spherical volume in space.

As now approaches the appointed hour, the volume of spacetime in which events may have an impact at any particular point in the universe, changing the state of objects there, is shrinking.  At one nanosecond (10-9 seconds) before midnight nothing that happens outside a sphere in space of 0.30 meter radius can alter the state in which we will find that object at midnight.  At one picosecond (10-12 seconds) to midnight that radius has shrunk to 3x10-4 meters.  At one femtosecond (10-15 seconds) the radius is 3x10-7 meters) and at one attosecond (10-18 seconds) the radius is at 3x10-10 meters, about the separation of atoms in a solid.

For distances about 3x10-10 meters or less, object behavior is dominated by quantum mechanical effects. Does that mean that relativity theory no longer holds at those distances?  There has been some discussion that spacetime itself may become grainy at some point.  Even if that is true, the scale of that effect is thought to be at the Planck Time (about 5x10-44 seconds) and Plank Length (about 2x10-35 meters).  At that scale the distanced between the particles that make up the nucleus of an atom are enormous so now has plenty of room to carry on isolating the points in spacetime from anything that might cause a state change there.

As you can see, as now approaches the hour of midnight, relativity pares away the number of events that can affect the state at any point in the universe until ultimately the clock runs out on all the alternative states that were possible, leaving the universe in its midnight state.  Once that state is realized by the shedding of alternatives it becomes part of the frozen past as now sweeps on past the midnight hour.

We should consider in more detail the separation of state changes into passive and active, for very small systems where quantum mechanics must be used in their description.  The principle of maximal aging applies to large systems including those where relativity comes into play but we cannot assume it applies in quantum mechanical systems.  To pursue this thread of the discussion I need to offer some more information on quantum mechanics (QM) itself.

QM was developed in the first third of the twentieth century and has been hugely successful explaining the behavior of small objects, leading to the inventions that pretty much dominate human activity in the developed countries of the world, flat screen TV, medical imaging tools, digital cameras, computers… The list goes on. 

For all its utility, QM still holds some mysteries.  One of these is, “What does QM reality really look like?”  Most of our success in the field has been accomplished by assuming that it doesn’t matter.  Like our inability to visualize spacetime in relativity, our inability to visualize QM effects does not prevent us from applying the rules to make useful predictions about the future.

Another of the mysteries has to do with the fact that there seem to be two different processes required to explain the way a system evolves with time.  Einstein’s relativity theory covers physical evolution of systems from molecules to galaxies with the same formulas.  In QM a system behaves one way when you are not looking at it and another way entirely when you make an observation of the system’s state.  To date, physicists have not been able show how these two rules for the evolution of a system are connected.

The complete description of a QM system, as long as you do not look at it or otherwise interfere with it, is contained in an equation discovered by Erwin Schrödinger called by him the psi-function.  It includes all possible future states of the system, each with its own probability of being the actual state realized by the passage of now. When an active state change is forced on a system, which can only happen concurrent with the passage of now, the psi-function takes the newly realized state as its initial condition and guides the subsequent evolution of the system along Nature’s preferred path pending the next active state change. The psi-function for QM systems takes the role of the principle of maximal aging for large systems, each determining the stream of passive state changes that take an undisturbed system into its future.  I suspect but do not know that as system size increases, the psi-function evolves into the principle of maximal aging.

Let's move the story along at this point with a detailed examination of an event. I look at my desk and see my coffee cup with aromatic vapor rising from it.  My desired future state of the universe includes a sip of coffee in my mouth so I reach down, pick up the cup and take a sip and set the cup back down.  The whole business might have taken 5 seconds.

If we consider the coffee sipping episode an event, we find that it is not a point in spacetime but is contained in a volume of spacetime about 0.3 meters in x by 0.3 meters in y by 0.3 meters in z by 1,500,000,000 meters (5 seconds times 300,000,000 meters per second) in t.  We might subdivide it, into “reach for cup, lift cup, take sip, replace cup, for example.  Further we might try to subdivide each of those actions into the individual state changes that make it up.  In a spacetime continuum we might expect the difference between adjacent states and their extent in time to approach zero, and their number to approach infinity for any event however short its lifetime. For this subdivision of events into state changes we could approximate the continuum of state changes by a stream of discrete state changes separated by sufficiently small intervals.

Active state changes involve objects exchanging momentum. Let’s focus on the cup lifting episode in the sip of coffee event. The cup handle and the finger are composed of atoms that have a nucleus surrounded by a cloud of electrons. The nucleus carries a positive electric charge and the electron cloud a negative electric charge. From a distance large compared to the size of the atom these electric charges look like they are in the same place the atom appears electrically neutral. As the finger approaches the cup handle, at some point the separation gets small enough that the atoms appear negatively charged to each other and an electrostatic force begins to repel the pair of atoms. We take this separation to be the point of contact.

This repulsion couples the force from the finger to the cup. With millions of atoms involved, this force is sufficient to overcome the weight of the cup and up she goes. The electrostatic force mechanism may be thought of as an exchange of photons between the cup atoms and finger atoms with each photon transferring a bit of momentum between the atoms. So, exchange of momentum even between large objects may be analyzed in terms of photon emission and absorption.

Figure 7

Emission-Absorption Spacetime Diagram

Figure 7 is a spacetime diagram showing two snapshots of now labeled now (1) and now (2). Suppose atom B is to undergo an active state change by absorption of a photon emitted from atom A. The time now (1) is the time of the photon emission. At that time atoms A and B are in their positions (1). A little bit later at now (2), we find the emitted photon lying on the past light cone of the absorption event, atom A lying completely outside that light cone and atom B experiencing a steady bearing to the photon and decreasing range, a sure recipe for a collision.

Once Atom A has emitted its photon it has no further role in the life of atom B at or prior to the absorption event. Atoms A and B have a space-like separation during the time from emission to absorption. The probability of the B atom absorbing a photon from A took a dramatic jump at the time of the photon emission and is steadily increasing as the advance of now trims away the possibility of interference from other interactions. Ultimately the absorption probability reaches unity (100%) and the absorption event is realized, giving atom B a little nudge and changing is momentum and therefore its state. From then on until another event takes place, atom B follows the path preferred by its new, post-absorption, psi-function.

In the interest of full disclosure I should point out that I have greatly simplified the actual interaction between atoms. Atom A does not fire a single photon at atom B and B does not wait quietly on the t-axis for the absorption before firing a photon back at atom A. There is quite a cloud of photons flying in both directions, as well as between A and B and all their neighbors. In fact photons involved in the exchange of momentum between atoms are called virtual photons since they only appear in calculations and may not enjoy any physical reality. They do, however, give us a way to think about electrical forces that allows correct predictions to be made, so Nature behaves as though the virtual photons do exist.

To observe a quantum mechanical system means to bounce some photon or other object from it into our eye or some other detector.  On the scale of QM systems, a photon or other projectile creates a significant disturbance in the system.  Observation in QM is analogous to what I called an active state change in talking about large systems.  In QM it is thought that an active state change collapses the psi-function with its multitude of possible states to one of those states. Which state is realized is a matter of chance but the most probable is favored.

One school of thought holds that until an observation is made, the state of the system is indeterminate.  Schrödinger himself had a problem with this view.  He devised an absurd example to make his point.

Schrödinger wrote:

One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device (which must be secured against direct interference by the cat): in a Geiger counter there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The psi-function of the entire system would express this by having in it the living and dead cat (pardon the expression) mixed or smeared out in equal parts.

It is typical of these cases that an indeterminacy originally restricted to the atomic domain becomes transformed into macroscopic indeterminacy, which can then be resolved by direct observation. That prevents us from so naively accepting as valid a "blurred model" for representing reality. In itself it would not embody anything unclear or contradictory. There is a difference between a shaky or out-of-focus photograph and a snapshot of clouds and fog banks.

I am with Schrödinger on this one.  It is true that when a QM system is observed, it will be found in a definite state but I am inclined to think that it was the passage of now, not the observation, that reduced the mixed quantum mechanical state described in its psi-function to a single reality.  The radioactive sample in the Schrödinger cat example will emit radiation, or not, in an hour independent of whether the chamber is opened, and whenever the trap is sprung on the poor cat it will be now, not some future time when the chamber may be opened.  The notion that it is the passage of now rather than the act of observation that brings about the quantum state reduction is different than the usual quantum mechanical interpretation of events.

Let’s apply the quantum state reduction by now idea to Schrödinger’s cat.  From the time we seal up the chamber, the “dead cat” state and “live cat” state at the end of an hour are equally likely.  That was the condition Schrödinger set up.  As now sweeps through that hour, at each instant the “dead cat” or “live cat” decision is made.  Also the “decayed” or “not decayed” state of the radioactive sample is decided.  If at some instant the latter decision comes up “decayed”, the “live cat” probability at the end of the hour goes way down and the “dead cat” probability goes way up.  When now reaches the time that the cat has expired, the “live cat” probability reaches 0 and the “dead cat” probability reaches 1.  From then on until the chamber is opened, the cat lays dead and now moves on to settle other issues.  The opening of the chamber has nothing to do with the situation.

How do we reconcile quantum state reduction by now with the usual point of view that it is an active state change that brings about the quantum state reduction?  Avoiding a lot of potentially troubling details, the only time that anything can interact with a system is now so the distinction in mechanisms for the quantum state reduction when an active state change is involved may be a distinction without a difference.  The advantage in assigning the reduction to now is in the usefulness of that interpretation in understanding how a single state of a system may be selected by now when the system is simply following Nature’s preferred path as indicated by Schrödinger’s psi-function.

In summary, now is when what is, must be.  It is the great destroyer of possibilities.  If you want to conditions at some future time to be different than they are now, you best set up the conditions for that change before now gets too close to the chosen future time.


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