In conventional representations of both Special and General Relativity, space and time occur within/as an abstract four-dimensional geometry. This geometrical representation is accurate in its modelling of relativistic relationships, however, the geometry is truly abstract in that its structure is unable to be directly drawn on paper or readily visualized.

The abstract nature of the geometry arises from the rule used to calculate the distance between two points from the difference/shift in the space-time co-ordinates that define the points.

In our ‘normal’ (Euclidean) geometry a distance is given by Pythagoras’ theorem. That is, the square root of the sum of the squares of the changes in the co-ordinates. For example, given two points in a plane at co-ordinates  and  their separation  is obtained by the formula  .(1)

In space-time geometry however, the "distance" between events is given by sum of the squares of the space offsets minus the square of the time difference. The subtraction of the time and space ‘distance’ terms causes the separation to take on values that do not accord with our ordinary understanding of geometry. For example, when the separation in space equals the separation in time the value of s is zero. Also, when the separation in time exceeds the separation in space, the value of  is negative and that means the separation is an imaginary number. Only when we choose a reference frame such that the separation in time is zero, do the events have the same separation as we would measure in a Euclidean model.

This is the geometry of special relativity and it is this abstract space-time geometry, and not our ‘classical’ geometry that becomes ‘curved’ by gravity in General Relativity.

In summary, observations of light and time provide compelling evidence that the descriptions provided by Relativity are accurate and that our ‘classical’ model of space and time arises from an illusion. The illusion fits our experience of the world because we cannot readily achieve speeds that make relativistic effects of readily apparent.

Even if a flaw in Einstein's theories were discovered, the observed behaviours of light and time so fundamentally contravene our classical ideas that there would appear to be no way to revert to the classical model. A new interpretation would have to include the phenomena that are included in Einstein's model.

As an example, look at what occurs when a spaceship makes a series of high speed runs from the Earth to Proxima Centauri (To us, about 4.27 light years away). On each run the ship backs up, accelerates to his travelling speed then coasts at a constant speed along the segment between Earth and Proxima Centauri.

Let the runs begin at 1/2 the speed of light and increase in progression 3/4, 7/8, 15/16, 31/32, 63/64, 127/128... up to a 20th run which is at 1048575/1048576 of the speed of light.

Now, relativity shows that for the traveller, distances along the direction of travel ‘shrink’ according to the formula :-

(2)  Where  is the distance as those in the ship see it and  is the distance from earth's viewpoint.

To those still on Earth, the ship takes 8.54 years to complete the journey at half the speed of light, as expected. But when they look at ship they notice that it's time is going ‘slower’ than theirs and the ship and occupants appear to ‘age’ only 7.396 years during the journey.

The following graph shows the journey times for the twenty runs from the ship viewpoint. Notice that as speeds approach the speed of light, the journey times reduce dramatically, even though the actual increments in speed appear slight. On the 20th run, at 1048575/1048576 of the speed of light, the distance shrinks to 0.0059 light years and the ship and occupants experience a journey time of 2.15 days. Whereas to those on Earth the ship look looks almost ‘frozen’ and the journey still takes 4.27 years, plus a couple of days.

Interesting transformations occur when the ship accelerates and decelerates. As the ship accelerates the distance to Proxima Centauri ‘closes up’ and time on Proxima Centauri rushes forward.  From the traveller's perspective, at the end of acceleration to near light speed, the distance has closed-up almost to nothing and time on Proxima Centauri has moved forward by almost 4.27 years.

Also, to those on the ship, time on both Earth and Proxima Centauri slow almost to a halt.  When the ship decelerates at the other end, the distance to Earth ‘blows out’ back to 4.27 light years.  The deceleration is, in effect, an acceleration toward Earth and Earth's time now seems to rush forward.  Earth now ‘ages’ by about 4.27 years.  On the return journey, the same effects occur. As the traveller accelerates, time and space ‘collapse’ with time on Earth rushing forward.

To those on Earth, the Ship's return trip will occupy more than 8.54 years while those on the Ship will a few days.

This feature of Relativity, wherein an observer's relationship to another location can be dramatically altered by acceleration is often not apparent in a geometrical representation. Nevertheless it is a "standard" feature of relativity.

Under sufficient acceleration, a remote location can become almost immediately present, no matter how far away it seems to be at the moment. This suggests that space is not a separate ‘backdrop’.  Instead, ‘space’, like the speed of light, is ‘personal’ and results from the way in which an observer's ‘past’ and ‘present’ relates to the ‘past’ and ‘present’ of other matter.

If we extending the traveller's experience to that of light then it appears that photons experience no space or time. Relativistic space-time geometry appears to concur, events that can be connected by a light ray occur with ‘zero’ space-time separation regardless of their physical separation in space. In effect, it would seem that light occupies a time-space no-man’s land in which photons individually experience no space and no time during their transfer from the source to the destination.

If relativity holds, then a photon appears to go from one present to another without experiencing space or time. It just ‘is’, without time or space, very like a ‘time capsule’ of energy frozen in stasis that only ‘comes alive’ when it interacts.
 

It is possible that our experience has us seeing time from an inverted viewpoint. With relativity as a road map, one can straight-forwardly construct an ‘inverted’ model of space-time. One in which photons are fixed in a kind of "wake" in time and the existence of matter occurs at the speed of light so that photons always appear to approach and depart at the speed of light.

To visualize the situation, begin by taking a particles ‘existence’ to happen at the speed of light. That is, the speed of light is the ‘rate’ at which a particle's present moves through time. Picture it as though successive moments of the particles past existence move out through the "space/past" of time around it like layers of an expanding onion.

For example, our conventional view light has it moving a speed of about one foot (actually closer to 0.982ft) in a nanosecond, a billionth of a second. In this ‘inverted’ view the past existence of the particle as of one nanosecond ago would form a spherical shell in time of approximately one foot in radius around the particles present.

Now picture energy and photon emission. Under stable conditions, the energy within the particle (or set of particles) is somehow ‘locked’ in its existence. However, when a photon is emitted, this existence changes its structure (decays), it recoils (changes ‘direction’ in time) and a fragment of its energy (the photon) is jettisoned into its past.

The photon is embedded in the surface of the expanding ‘shell’ that is the "wake" the particles past until it intersects another particle's present (or photon). In effect, the photon is like an artefact embedded in the particle's past.  When the wake crosses the existence of another particle it becomes part of that particle's present. Effectively the destination experiences an event from the previous particle's past.

In this inverted model the distinction between ‘space’ and ‘time’ becomes blurred. It's as though ‘space’ now occurs as a combined result of the way in which time moves into the ‘past’ together with the way one ‘present’ relates to another. In effect, when you ‘see’ something then you experience, in your present, some part of the past of the object you observe. Similarly, when you are observed the observer directly experiences part of your past.

4.1 Integrating Relativistic Relationships
From this inverted viewpoint, one can construct how one ‘present’ relates to another from the relationships within relativity.

Begin with two stationary particles separated a foot apart, call them particles A and B. Each moves ‘through’ time at the speed of light and intersects a fraction of the other's past existence, as the other particle was, a nanosecond ago. A is one nanosecond in B's future and vice/versa.

Now, look at what occurs from A's perspective if B were moving according to the rules of Special Relativity. For A, B's existence can now be represented as having two components, one ‘forward’ in time (matter-like) and the other ‘across’ time (light-like). Assign these ‘forward time’ and ‘across time’ "existences" to vectors that are can be added to form an overall ‘existence’ vector  .

In order to be consistent with relativity, a simple rule applies to the existence vector in that it's magnitude is constant, that is, the "speed" of light.  Consequently, relative to A the rate of B's "forward" existence drops as B's velocity increases, with  falling to zero as B approaches the speed of light.

The rate at which a particles ‘forward’ existence can be obtained using Pythagoras’ theorem. i.e..
 

(1)  Where  is the speed of light, represents the velocity ‘across’ space and  represents the ‘forward velocity’ of existence.

(2)

The time dilation factor from Special Relativity.

If we apply the relationships that are contained in relativity then from an observer's perspective;

4.2 Existence, Causality and Antiparticles
The section above refers to existence as having a vector-like character having matter-like and light-like components. This way of looking at relativity now opens up a way to differentiate between time and existence.

The difference arises because the matter-like vector of existence can be drawn equivalently in two directions, say 'up' and 'down'. Either way, the model will still apply provided the rules of relativity are consistently adhered to.

However, drawing the existence vector in the opposite direction is not equivalent to moving back in time as we conventionally imagine. The particle still passes through time at the speed of light, and photons still arrive and depart at the speed of light. The past moves 'outward' in time in a fashion similar to the way that the wake of a boat moves outward regardless of the boat's direction.

Particles with opposite existences could exist together and there would be no outward way to distinguish them from the way they moved with respect to one another or exchanged photons. The reason is that, in this context, what we refer to as the "arrow of time" is actually determined by the outward and inward flux of fields and photons that occurs in the same manner regardless of the 'direction' of existence.

In my view, it is this relationship between the existence of matter and light/time that underlies causality. Causality will work regardless of the sense of the existence of an object.

I think it is worthwhile to highlight this difference because physics contains some well known situations where particle models involve time reversal and I wonder whether this is actually a form of existence reversal instead.

When the British physicist Paul Dirac developed relativistic models of fundamental particles, he obtained negative energy particle solutions that are now understood to correspond to anti-particles. In mathematical representations, the solutions for anti-particles are equivalent to time-reversed solutions for standard particles. Given that conventional models do not distinguish time from existence then it is quite possible that the so-called reversed time is in fact a reversed existence within a generally "outward" time.

Because and up/down existence is distinct from the "arrow of time" particle/antiparticle creation and annihilation can be represented in a vector form.

For example, one form of antiparticle creation/annihilation involves the exchange of existence from a photon pair to an electron/positron pair. Creation involves a pair of photons interacting to produce a particle/antiparticle (electron/positron) pair, and destruction reverses the process where a particle/antiparticle pair collides and produces a pair of photons. In either case, energy is conserved with each photon having an energy equivalent to a particle mass given by the equation E=MC².

When you add in the existence vectors for the particles then it also becomes apparent that the overall "existence" is conserved with energy. The two "across time" vectors of the photons cancel and the "up/down" existences of the particle/antiparticle also cancel.

It now becomes possible to visualize how a particle can have a corresponding ‘time reversed’ or ‘negative energy’ antiparticle and for causality to hold. Additionally, one can also see how an antiparticle could be equivalently viewed as a ‘negative energy’ particle existing ‘up’ in time or a ‘positive energy’ particle existing ‘down’ in time.

4.3 Representing Kinetic Energy and Momentum
The principle of a conservation of light-like and matter-like existence can be developed into a vector representation of existence and energy.

In the new representation, an object moving with respect ot the observer, has two components of energy, a rest energy, , and a ‘photon-like’ energy,  .  Both component energies add as vectors to form a total Relativistic energy . That is:-
 

(3)

Where the ‘photon-like’ energy  is the energy that a photon would carry if it had the same momentum as the particle.

Note that is not the kinetic energy,  . The kinetic energy is the difference in magnitude between the rest energy and the relativistic energy. That is:-
 

(4)

Whereas the ‘photon-like’ component energy is given by:-

 
(5) or:-  (6)

Fig 4.1 Energy of a moving particle drawn as vectors, where e" is the photon-like energy.

Interestingly, this representation removes the requirement to include momentum as a separate "property".

Some situations and examples include:-

• The crossing over from ‘matter-like’ existence to ‘photon-like’ existence that occurs when a particle meets antiparticle and two photons are generated. The overall existence vector sums are zero overall and the total energy is conserved.
• Anything with a matter-like existence cannot be made to reach the speed of light by adding kinetic energy. The tip of the ‘rest energy/existence’ vector always remains the same distance ‘above’ the horizontal axis so the vector can never make a ‘zero’ angle with the axis.
• Elastic collisions of particles. Energy now has a ‘direction’ of existence that can be used to analyse particle dynamics. You can now calculate the outcomes of elastic collisions without the need for the separate distinctions of mass and momentum.

The vector representation of energy and existence can be applied to make it clear that the scattering characteristics observed in the experiments are a purely relativistic effect that results from the conservation of existence and energy and involve no requirement to model a photon (or electron) as a propagating wave. (For further critical analysis of the relevance of wave/particle duality see Quantum Theory and Wave/Particle Duality ).
 

Fig 4.2 A photon of energy e° scatters off an electron at an angle  and departs with energy e'. The electron, as a result of the collision, departs with photon-like energy e".

First look at the overall conservation of the relativistic energy. The relativistic energy  of the departing electron must be mc² plus the difference between the energies of the incoming and resulting photons (e° - e').
Secondly, the components of  are mc² and and e" (as per fig 4.1). Hence, by Pythagoras,
 

Now by applying vector conservation to the electron scattering (note vector quantities are shown in bold)

By substituting (9) back into (7) and  solving for e' in terms of e° gives,
 

4.5 Summary
So far, we have examined the fundamental basis and relationships in special relativity and have presented those relationships in a new context in which the existence of individual particles is considered as "occurring" at light speed.

The rationale behind the model is twofold. First, that relativity shows that there is a clear dichotomy between the existence of photons and that of matter (particles). Secondly, it is also clear from relativity that every particle must exist in its own local, immediate, context of space and time.

By adopting this approach to relativity it becomes possible to see how existence is distinct from time and causality. In particular, that existence can have two senses without disturbing the "arrow of time". Furthermore, it is pointed out that this feature of the model allows for the representation of phenomena such as anti-particles without the need to invoke time reversal or negative energy.

Extending the model of dual matter-like and light-like existence by modelling the existence of energy as a vector quantity then allowed us to shown how mechanical interactions of particles can be modelled directly, without the need to invoke momentum as a separate property.

Finally, the model was applied to show how the Compton effect could purely result from the relativistic relationships of existence and energy and does not depend on quantum mechanical relationships or any other form of "wave mechanics".
 

In that sense, much of QED is very accurate, atomic energy levels, scattering, crystal diffraction all sorts of stuff. My work involves solid state lasers, semiconductors, laser ring gyroscopes (that track rotation to very fine limits). Other aspects of my work involve interferometry with GPS signals. It is clear to me that the mathematical relationships that were used to predict the operation of those devices are mind numbingly accurate.

The predictions of QED are an extension of the properties of a set of equations that have been found to fit the phenomena. You cannot derive Schrödinger's equation from a fundamental theory, Schrödinger literally just went in and worked with certain forms of equation until he found one that fitted, and fitted spectacularly. Why it fits and how the world is put together so that it works that way is still a wonderful, interesting, mystery.

To my mind there are two questions,

1) Are the QED predictions right? (i.e. Is that what we see?)

6.1 EPR
I think that the difficulty with some mathematical relationships in QED is that they yield statements of probability. This means that to make use of the results people often need to make logic statements that relate to probabilities.

Recent work by Dr Rachel Garden (Thames NZ); on the nature of logic within quantum mechanics provides a clear, straight-forward analysis of the issues that arise around the interpretation of quantum probabilities and in particular, with respect to the logical foundation of experimental tests of the EPR issue.

Rachel's work is available in a paper; "Logic States and Quantum Probabilities"; International Journal of Theoretical
Physics, Vol 35, No. 5, 1996.

Section 3.2 of the paper addresses a critical issue in regard to the proof of non-locality through the application of Bell inequalities. Earlier in her paper, Rachel Garden shows that certain the logic relationships within quantum electrodynamics are not bivalent. In contrast, Bell inequalities can only be derived using bivalent logic and consequently, are not valid when applied to quantum experiments that involve non-bivalent determinations.

The outcome is that provided the determinations are not bivalent, then it is completely unnecessary to draw the conclusion that non-local effects are required to explain the results.

The issue with non-bivlaent logic is reasonably simple to understand. In non-bivalent logic negation does not mean the opposite, instead it is a form of denial. Denial is familiar in everyday language. For example, the statement "It is not raining" does not mean that it is sunny.

Similarly, in a quantum polarization experiment, a photon exiting a polarization analyser via channel "A" doesn't mean it has polarization A it just means that it was not exactly lined up to go via "B", a type of denial.

When you correct the logic, then the whole problem evaporates, or as Rachel Says "According to the logical analysis of quantum theory, the failure of Bell's inequality is not only not paradoxical, it is expected. Whenever maximal valuations are not bivalent, these inequalities fail."