A Quantum Mechanical Interpretation of the Consequences of Special Relativity
Einstein's theory of Special Relativity
Einstein's theory of Special Relativity predicts that for objects travelling at a significant fraction of the speed of light time dilates. Experimental observations are in agreement with the predictions. For example ordinarily short lived particles such as Muons when at rest are observed by a stationary observer to exist for significantly longer periods when travelling at speeds approaching the speed of light.
Mathematically Speed = Distance/Time
As the speed of light is expected to be constant in any frame of reference (consequent to Maxwell’s equations) the mathematical conclusion for the increased lifespan of Muons traveling close to the speed of light would be that the values for distance and/or time have changed.
- In the Muon’s inertial frame of reference the distance travelled by the Muons has decreased.
- In the observer’s inertial frame of reference time has slowed down for the Muons allowing them to live longer.
The difficulty with understanding such mathematically derived conclusions is that they are counterintuitive (which is not to say that they are wrong). Copious experimental observations illustrate clearly and consistently that clocks slow down when in motion precisely as predicted by Special relativity. Thus for example we can confidently predict that an astronaut travelling at near light speed for a year will return to Earth biologically younger than his twin brother by around thirty years.
A typical explanation of Time Dilation is that time flows at a slower rate for the astronaut than for his twin brother on Earth. The analogy of time flowing conjures up images of water moving along in a river. But as time does not appear in any real sense to be a tangible identifiable substance like water can it truly be said to be flowing at different rates? The passage of time can only be measured indirectly in terms of a perceived interval between events. The most accurate measurement of time is currently in terms of the interval between 2 quantum mechanical conditions of a Cesium 133 atom. But what really is it that we are measuring when we state that we are measuring time?
Does Time exist?
Physics defines Time as “that which is measured by clocks”; that is all. There is no evidence to substantiate that time exists as part of the fabric of the universe. It is probable that human beings dreamt up the notion of time as a convenient way of 2 or more people being in the same location to share a task. For example an agreement for 2 people to meet for a hunt at sunrise on the bank of a river next to a large rock is in effect a synchronisation of the event of sunrise with 2 people and a unique geographical point on the planet. The human notion of time serves the purpose of accurately synchronising events for a species that owes much of its success to organised cooperative behaviour.
Although today we would associate sunrise with a specific time indicated on a wristwatch (or more accurately an atomic clock) there is no "known" absolute benchmark of time in any inertial frame of reference. i.e. there is no "known" universal standard time anywhere in the universe with or without the relativistic effects of speed and gravity. Significantly the sunrise over our spot on the river will never be precisely at the same local time from any one sunrise to any other sunrise as measured by an atomic clock situated by the rock. This is due in part to perpetual changes in the orbit of the Earth and in part to the uncertainty of the location and velocity of quantum particles. Quantum observations suggest that it may be impossible to predict or measure the precise local time of any event in the universe. Without any direct evidence of its existence as part of the fabric of the universe it is perhaps more useful to think of time as being an imaginary interval between 2 events.
Can there be a more intuitive way of explaining the observations predicted by special relativity?
The observation that high speed Muons last longer than Muons at rest could be interpreted in one of the following two ways:
- Muons decay at the same rate regardless of their speed. The speed of a Muon causes time to slow down in its inertial frame of reference so that for a stationary observer for whom time is running faster a high speed Muon appears to decay more slowly than a stationary Muon. “Proper time” is the time experienced by the Muon in its inertial frame of reference being less than the time measured by the stationary observer calculated as per the following expression.
- Muons decay at a rate that reduces according to their speed relative to a stationary observer. “Proper events” is the reduced number of decay events experienced by the Muons in their inertial frame of reference as compared with the higher number of decay events observed by the observer calculated as per the following expression.
The first interpretation founded on Special Relativity is based on the assumption that time is part of the fabric of the universe and that time literally flows at one rate for a stationary observer and at a reduced rate for the particles in motion relative to the stationary observer.
The second (alternative) interpretation assumes that time is merely a human notion and is not part of the fabric of the universe in any real sense. In this case time dilation is no longer a plausible explanation for the increased life span of high speed Muons. Since time dilation can no longer be an explanation the inference is that the high speed Muons last longer than relatively stationary Muons as a direct consequence of their relative speed.
Whilst Particles such as Muons are observed to decay into different particles it is not understood what exactly triggers the change but it is typically characterised as the spontaneous process of one elementary particle transforming into other elementary particles without any apparent external cause. There would seem to be 2 plausible interpretations:
- Quantum particles decay or transform spontaneously without any external influence.
- Quantum particles decay or transform due to the influence of quantum events in their vicinity.
In the first interpretation the notion that a fundamental indivisible particle may transform itself with no external influence is both counter-intuitive and inconceivably difficult to conclude from experimental observation, which is not to say that it is necessarily incorrect.
In the second interpretation, from the assumption that particle decay is influenced by other quantum events in the vicinity it follows that the rate of decay would be governed by the frequency of such quantum events.
From the same assumption that particle decay is influenced by other quantum events in the vicinity it follows that the frequency of quantum events would be governed by the values of influential properties of the quantum particles such as angular momentum.
Based on observations of particle decay slowing down in a highly predictable way according to the speed of the particles relative to a stationary observer we can further infer that the values of influential properties of quantum particles in a given inertial frame reduce with respect to the speed of the quantum particles. By considering the wave properties of a quantum particle the inference would be that the energy of the wave is reduced through dissipation over a longer distance.
An atomic clock detects an arbitrarily prescribed number of changes between 2 quantum mechanical states of Cesium 133 atoms and registers this as one second of time. A moving atomic clock detects fewer changes than a relatively stationary clock. According to Special Relativity this is due to time slowing down in the inertial frame of reference of the moving clock. However in this alternative interpretation where time is no longer considered to be a real variable the conclusion is that there are fewer quantum events occurring in the inertial frame of reference of the moving clock as a consequence of its relative inertia.
In any given inertial frame of reference the relative frequency of different types of quantum events would be expected to remain constant such that any specific measurement carried out within an inertial frame of reference would be identical to the same measurement carried out within any other inertial frame of reference. Thus for example the same values would be recorded for the average half life of a Muon at rest measured within any inertial frame of reference.
Special Relativity states that relative motion causes time to dilate. The observational evidence is that relative motion causes clocks to slow down and also causes a reduction in the frequency of all events within a moving inertial frame of reference. Thus whilst time is defined as “that which is measured by clocks” the consequences of Special Relativity do not hold clocks to be special. Although these observations can be characterised as Time dilation there is no evidence to substantiate the material existence of time and that which does not exist cannot dilate.
This alternative interpretation is founded on the same set of observations that substantiate Special Relativity but without invoking the assumed variable of time and instead substituting a relative frequency of quantum events.