Although there is an illusion about reality, that illusion is not about time. The illusion that we have about reality is in how we discover continuous space and motion, not in the discrete time delays of objects and action. We first discover space as the lonely dark empty nothing that explains why we no longer see an object that has moved behind another object. We learn about space by about the age of two and then we take space and motion for granted as a basic belief that anchors consciousness. We do not really often dwell on the irony of accepting the nothingness of empty space as a something that makes up most of the universe. We simply realize that objects continue to exist even when we do not sense them and the motion of objects in that nothing of empty space simply hides one object behind other objects.
While there are many, many more books and articles written about the illusion of space than the illusion of time, somehow we just don't get it. The vast majority of spatial illusions result from a confusion that we have with the time delays that we sense for objects and their backgrounds, what we call spatial depth dimension in an otherwise two-dimensional image. We know that with each of our two eyes we only perceive a two dimensional reality of object time delays and therefore the third dimension emerges as depth only by perspective. Each of our two eyes sees a slightly different two dimensional space from just the one dimension of time delay between objects.
Our brain largely organizes the world with the dual concepts of continuous space and motion and uses space and motion to keep track of where objects are and to help predict where objects are going. We imagine ourselves in a rest frame that does is not moving and that a reality exists for both moving objects outside of our brain and objects at rest with us in space. We seem to have a no trouble imagining space as a lonely empty nothing and it is especially ironic that we infer space from the continuum of sensation of a background of objects and the nothing of space emerges from what we do not see or sense. The object that we imagine as empty space is everywhere the same and in some sense immobile and fixed and it is the lack of sensation of any object that we feel is the lonely empty nothing of space that then defines most of the universe that we imagine.
But continuous space and time do not describe all objects in the universe for mainstream science. There are objects called black holes and very small objects at the Planck dimension and neither of these two objects exist in continuous space and time. These objects do exist in the reality of time delay and discrete matter and the Mollweide projection maps the two-dimensional sphere of the sky into the ellipse shown below. Likewise, we can map the two dimensions of time onto a Mollweide ellipse and show how the universe projects back onto itself in time.
There are always two different observers for every motion or action; one observer, called the rest frame, is not moving and is usually left behind as a result of motion of a second observer that is moving with some action in the moving frame. In general relativity, GR, each of the rest and moving frames have their own clocks and those different clocks keep different time but still provide a single objective and proper time that completely defines that action. Proper time represents the norm of the displacement of a moving object, i.e. what we really experience, in the four dimensional spacetime of GR.
Relativity imagines a proper time that is a continuous spatial dimension and in effect does away with time by making it just a fourth dimension of 4D spacetime. The motion of an object in spacetime is equivalent to time, but then there are motions within that object that must also be equivalent to time, and further motions within those motions as well that also affect time. These recursions of embedded motions and times are an integral part of the recursion of relativity but quantum mechanics handles embedded time somewhat differently than GR.
Quantum action always begins with a discrete excitation from a ground state of one matter wave as a source or origin. That source bonds a pair of emanating matter waves of two objects into coherent relative futures. The excitation evolves a ground state into an excited state that is a pair of complementary and coherent matter waves, each with complementary and coherent clocks and directions. In classical ballistics, every action results in a reaction or recoil and a bullet firing results in a recoil of the gun in the opposite direction. Likewise in quantum action, every excitation has two coherent matter wave complements as well.
In GR, the rest and moving frame clocks represent a proper time, the time that we experience as the present moment, and the clock amplitudes and phases of the two frames do not affect the path of the object and essentially remain coherent for all time. In quantum action, the rest and moving frame clocks begin together and are coherent for only some characteristic time. As long as two clocks remain coherent, they may interfere with each other and therefore affect each other's path. The quantum rest and moving clocks come into existence after some excitation of one or two sources and quantum clocks merge with discrete jumps or quanta into the same proper time norm that GR reports.
We therefore experience the same proper time in both quantum and GR times, and we sense the same matter changes of an object and the same motions emerge along with space as a result of sensation. However, there is an inherent decoherence rate for the two quantum clocks of a rest and moving frame that not only limits what we can know about their paths, that decoherence rate is what determines both gravity and charge forces.
What we sense about an object involves exchanges of matter amplitude and phase with the object matter waves and those matter and phase exchanges result in a complex neural packet of aware matter that we call a moment of thought. From all of these complex relations among impulses, the relative simplicity of objects at a particular moment emerges as the three dimensions of space in our brain.
What we actually sense about an object is, however, quite a complex set of both coherent and incoherent matter waves that represents a relational reality that comprises both us and the object. While what we imagine about an object represents a very much simpler Cartesian reality of time and objects in a mostly empty space, the relational reality of an object is ever so much more complex. This fundamental dualism is a prominent feature of all models of reality and yet matter time necessarily uses time and matter as primal conjugates and not the space and momentum of mainstream science. Since we do not actually sense the nothing of space and motion, we can deduce and can and do imagine the nothing of space to be just about anything that space needs to be.
The fact that there are two distinct clocks for each GR action, a rest clock and a moving clock, is also true for quantum action. However, a quantum action begins in the past with either one or two sources of matter waves that may or may not be coherent. Quantum clocks can be entangled and interfere with each other, which just means that the excited state of a source matter wave pair can remain coherent for a very long time and so can result in correlated and seemingly nonlocal actions. This seeming violation of GR's local causal principle of determinism is simply a characteristic of a quantum time and does not actually violate any quantum causal principle.
After all, while quantum clocks show interference effects as long as they are coherent, GR clocks are in a sense always coherent and phase has no meaning. Since the two clocks of GR do not interfere with each other as coherent amplitude and phase, the rest and moving clocks of GR merge smoothly into the proper time norm of experience. There is no role for the phase of coherent clocks in GR and so there are no interference effects in GR either.
In contrast to the importance of clock time in GR, time as an independent dimension seems to go away in the four-space of GR since there is no phase and no decoherence rate. There is only one possible future in GR and so GR time has no phase and is simply a dimension of displacement that is equivalent to space. Yet quantum atomic time is not only a progress variable, quantum decoherence time is also an integral part of reality and as a result, there is no quantum time operator like there is a quantum mass operator. Even though time is a prominent feature of general relativity and the mass-energy equivalence principle, E = mc2, quantum's adoption of mass-energy equivalence still means there is no expectation value for quantum time. While momentum and space have long had a warm and cozy quantum relationship as conjugates and are nicely complementary, mass and time are not quantum complements of each other like momentum and space for mainstream science.
Since there is not an expectation value for time or duration, this is known as the quantum time problem and this is what leads many to suggest that quantum time is an illusion. These arguments rest on the proposition that there is quantum space and motion as our
However, matter time plays a role reversal and proffers that instead of space and motion being the reality and time a consequence of motion, quantum matter and time are the reality and space and motion emerge as a mere consequence of the action of matter and time. Space is then just a convenient progress variable and the illusion of space is what allows us to keep track of objects in time. It is matter and time that complement each other and not momentum and space. Key in matter time is the matter-energy equivalence principle (MEE) and Lorentz invariance and the rigor of certain bounding assumptions for matter. For matter and time to complement each other, the universe must be of a finite total mass that is finitely divisible and these two assumptions become the basis for a quantum time operator that complements the quantum matter operator.
Time becomes the duration of an action and an integration of changes in an object matter spectrum. Just as action is the integration of an object's changes in matter over time, action is also the integration of an object's changes in the time amplitudes of its matter spectrum. An object's changes in matter over time define the object in the present moment, which is within the time spectrum of the universe. Likewise, an object's changes in time amplitudes as a function of matter define an object's matter spectrum that is embedded within the matter spectrum of the boson universe.