2.0 Space-time Geometry
3.0 Some Features of Relativity
4.0 A New Context for Relativistic Relationships
4.1 Integrating Relativistic Relationships
4.2 Existence, Causality and Antiparticles
4.3 Representing Kinetic Energy and Momentum
4.4 Compton Scattering Example
5.0 Action at a Distance
5.1 Fields as the Past Existence of Matter
5.3 Electromagnetic Interactions
6.0 A Note on Quantum Theory and EPR
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 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 :-
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..
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
. That is:-
Where the ‘photon-like’ energy is the energy that a photon would carry if it had the same momentum as the particle.
is not the kinetic energy,
. The kinetic energy is the difference in magnitude between the rest energy
and the relativistic energy. That is:-
Whereas the ‘photon-like’ component energy is given by:-
Interestingly, this representation removes the requirement to include momentum as a separate "property".
Some situations and examples include:-
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
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,
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".
This way of representing action at a distance has been dramatically successful in modelling action at a distance, particularly in regard to gravitational and electromagnetic interactions. In particular, the relationships evident in Maxwell's field equations were, I believe, the first equations to embody the Lorentz transformation which is the key to special relativity.
Nevertheless, I think that it is important to recognize that despite the success, the notion of a field is no more than a kind of framework on to which we can quite elegantly fit a set of relationships that relate to particle interactions at a distance. Other frameworks can be equally valid provided that they produce equivalent results and are consistent with observations.
The reason I say this is that modelling a distinct, extended entity such as a field into the type of model that I have presented is problematic. The main reason being that the model is based on a distinct local existence for all entities and does not naturally allow for the representation of an extended entity.
From the perspective of the framework for special relativity outlined above, it seems to me that the simplest way to model action at a distance that is consistent with the existence relationships of light and matter is to postulate that the existence of one particle is superimposed on the past existence of adjacent particles together with that of any photons.
My rationale is that the postulate offers a framework that is consistent with special relativity and also contains sufficient features for us to construct a simple set of relationships that reproduce the relationships that underlie classical and relativistic field theory.
Please bear in mind that from here on, this work is highly speculative, with the intention of exploring new ways to approach the modelling of relativity and the interplay of particles, light and time. Also note, that at this time, my intention is to lay out a new framework within which the "laws" and relationships in physics can reasonably exist leaving much to explore. Given this, I would welcome your attention, responses and contribution. [e-mail < firstname.lastname@example.org >].
5.1 Fields as the Past Existence of Matter
In section 4.0 above I suggested that one could view a particle's past as an expanding shell in space/time that overlaid the existence of adjacent particles. I also pointed out that an emitted photon would be embedded in this shell of past like and artefact embedded in a wake.
Consider extending this idea by saying that the wake that the particle's existence leaves in time has a structure that reflects the particle's structure, and furthermore, that the existence of another particle in that wake is superimposed on that wake.
Alternatively, one could consider the "wake" to be the actual "past existence" of the particle as it spreads out over time.
Either way, I can see that such an approach would provide for the direct modelling of action at a distance, namely;
For a particle of mass m at a distance r from the observer, Newton's classical gravity law is described by the formula
It looks to me, that this situation could be accurately represented if it were that the flux of one particle's energy (from E=mc² ) into the past were to be superimposed on another particle's existence such that the each particle's existence "veers" toward the source by an rate proportional to the energy flux at the particle's current location.
That is, the flux of the particle's energy (or the effect thereof) creates a "well" of existence that falls off by the inverse square law around the particle.
Additionally, to be consistent with general relativity, the existence of photons would occur on top of the superposition of the total energy flux from surrounding particles.
While I do not currently have the resources to explore this way of modelling gravity further, I can see that there are many interesting avenues that arise by adopting this context. Examples include:-
5.3 Electromagnetic Interactions
The situation with respect to electromagnetic interactions requires an understanding of the relationship between electric and magnetic fields from a relativistic perspective. That is this, that relativity provides a way to completely model electromagnetic forces by using the electric force alone without the involvement of a magnetic field.
I say that this is important because it is not obvious as to how a transverse effect (such as a magnetic force) could arise from a radial force.
If one represents the electrical field as a vector force field that propagates at light speed, then by applying relativity one can show that what we term a magnetic field is actually an effect that results from the non zero curl of the electrical vector field that arises from the relativistic transformation of the electrical force field as perceived by an observer in motion with respect to a charge.
An easy way to see this is to consider the interaction of two moving charges, depending on which viewpoint you pick, one, the other or both would be considered to have a magnetic field. No matter which one you pick, you still get the correct answer for the resulting forces.
In effect, one way to regard a "magnetic field" is as a convenient, and observer dependent, rule to calculate the effect of the non zero curl of an electric field that results from relative motion of charges.
So even though the effect of a particle's structure propagating into the past will produce an effect equivalent to a radial force field under static conditions, this force field will act exactly like a combined electric/magnetic representation when relativistic effects are considered for moving and accelerating sources.
Returning to the modelling of an electromagnetic force. Clearly the situation is different from that of gravity because the effect can be either attractive, repelling or neutral depending on the type of particles involved.
To start with, if one takes the simplest option, then one could see that the effect could plausibly be the result of a spin or twist with respect to the particle's existence. The rotational structure would propagate into the past (like gravity), providing an inverse square force.
Certain features that are evident in particle interactions would support this type of model. For example,
Furthermore, photon interactions are clearly an electromagnetic effect. While I cannot pretend to detail the nature of the relationship certain features of photon/particle interactions would also support a "spin" interpretation of charged particle existence.
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?)
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."