Hi Jane

Hi Jane

I've Just made one of my now infrequent checks on my website and found a link which seems to come from your thread; Can an electron be in two places at one time?

I'll therefore have a go at how the principle of proper interval locality interprets this question.

Firstly we assume that quantum events occur within space-time as described by the theory of relativity. For flat space-time the quantum event arena is defined by the Minkowski metric.

In my view modern physics fails to recognise the beauty, the power and the full significance of the relativistic metric in determining quantum behaviour and its role in communicating quantum state information throughout the world.

In my opinion as far as quantum behaviour is concerned the most important feature of the metric is the zero proper interval that can exist between spatially separated events.

How things happen in the world, causality, is governed by the zero proper interval.


The assertion is that in Minkowski Space-time it is possible to define two kinds of contiguity.

The first, let us call it. overt contiguity is where objects touch because the space separating them has zero magnitude. This seems intuitively correct and forms the foundation of our conventional notions of causality; where events can only directly influence each other if they are contiguous in both space and time.

Classical physics , perhaps with the exception of Newton’s gravity, and in part the methodology of quantum mechanics are based on this notion of locality.

The second is covert contiguity where objects touch because the combined value of their spatial and temporal separation has zero magnitude. It is my belief that this form of contiguity governs causality and I have named it proper interval locality.

If we try to formulate the laws of physics using overt contiguity, then quantum behaviour fails to conform to our rules of causality. This becomes evident when we try to explain the apparent wave-particle duality of matter and also the apparent non-locality of results from such as Aspect's experiment.

Schrödinger’s wave equation is deterministic but does not provide a causally continuous method of predicting the outcome of experiments. We can only use it to predict the probability of experimental outcome by applying a particular procedure. Why this procedure works is the greatest mystery at the heart of quantum mechanics? In my opinion proper interval locality can resolve this mystery!
In order to understand what is going on at quantum level we must reformulate the laws of causality in terms of covert contiguity ie "Proper Interval Locality". This way we can remove the discontinuity at the heart of quantum mechanics and since our method is base on the theory of relativity any inconsistencies between quantum mechanics and relativity are eliminated.

OK let’s have a look at your question about the electron being in more than one place at one time. In proper interval locality theory there are no half measures; any object in Minkowski space-time at a "given location" is connected by zero interval paths to every other location in space-time.(although often the possibility of interaction with matter in some parts of the universe will be very remote indeed. You are not likely to awake up in the morning and find yourself on Alpha Centauri.)

Objects can be considered to have a ubiquitous presence and may influence events any where in the universe. This not because we regard quantum objects as waves or particles but because of the structure of space-time itself..

Let us place your electron which we shall initially regard as a particle somewhere in space-time having no substantial spatial extension. To fix the path of the electron in space-time we arbitrarily select an inertial frame of reference relative to which we plot the events happening to our electron.

Let as select an event E1 from the history of the electron. Now draw a light cone with its apex at E1 lets call it LC1. All events on LC1 are now separated from event E1 by paths with zero interval magnitude. In other word the electron at E1 is covertly contiguous with all points on the light cone C. The electron has a presence everywhere on the light cone and the state of the electron at E1 may influence what happens on the light cone. This form of contiguity we shall call “primary covert contiguity”.

Lets now select a second event E2 somewhere on the light cone. Now draw a second light cone, LC2, with its apex at E2. All events on LC2 are covertly contiguous with E2; and since E2 is contiguous with E1 all points on LC2 are contiguous with the electron. Again the state of the electron at E1 may influence events on LC2. Since this form of contiguity requires at least two paths to form a contiguous connection with E1 we shall call this form of contiguity “secondary covert contiguity”.

We can select events and light cones ad infinitum until our electron is present everywhere in space-time. (Even those regions described as elsewhere, where conventional relativistic wisdom says our electron can have no influence.)

What is true for our electron at E1 is true for its entire history. If our world is characterised by Minkowski space-time then every event in the entire history of the universe is connected to every other event.

This however gives us a problem, how does nature prevent everything happening at once and creating one almighty cosmic traffic jam?

The answer to this question lies in the foundation of quantum mechanics. We propose that the particulate electron we placed in space-time has associated with it some simple harmonic process the frequency of which when measured relative to our reference frame is proportional to its kinetic energy.

Although we initially considered our electron as a particle we showed that it was directly contiguous with all points on its light cone and indirectly contiguous with all other locations in the universe. The harmonic process we associated with the electron is also contiguous with all events in space -time and its presence can be perceived as a wave-function relative to our inertial frame of reference.

In free space ie in the absence of matter, the portion of our electron’s wave-function that is propagated by secondary covert contiguity, universally destructively interferes with itself. This leaves only the part of the wave-function that is propagated by primary covert contiguity. This process of destructive interference is responsible for light travelling in straight lines at 186000 per hour.

Secondary covert contiguity becomes important when the electron exists in the presence of matter. Some of the secondary paths now become blocked and the process of destructive interference becomes inhibited resulting in phenomenon such as the interference of light and the entanglement of spatially remote events.

Of coarse the most important point about the universal contiguity of the electron is that it renders the photon redundant. The ability of the electron to appear to be in two places at the "same time" allows electromagnetism to be geometrically mediated by the structure of space-time!