What follows are my own train of thoughts spurred on from
reading Einstein's Relativity: The
Special and the General Theory. I use these ideas as jumping off points
into the highly speculative which is not covered in the book.
In his book, Einstein explains how the special theory of
relativity comes about after taking seriously two positions about the nature of
reality and following both of them through to their logical conclusions. These
are the constancy of the speed of light in
vacuo and that of relativity: the idea that there is no preferred reference
body of uniform motion in the universe, such that the physical laws are
independent of such motion.
That the speed of light should be constant is of course a
surprising and rather counter-intuitive outcome. It highlights how our own
reasoning and intuition can lead us astray and therefore the need to
continually check our reasoning against our experience. Naturally one may
expect that light should propagate as any other physical or classical
mechanical object: the speed one observes of it will depend upon one's speed
relative to it. Travel towards the light and you should see the light
approaching more quickly, travel away from it and you should measure it
travelling more slowly. Not so, says experience. No matter how we choose the
motion of our uniform motion frame of reference, we cannot help but arrive at
the same value for the speed of light as any other observer. The value for the
speed of light is not simply the speed of some classical object, it is a
fundamental property of the universe: a law of nature.
That a speed value should be a law is made more sensible
when it is considered outside of the context of light. Suppose that there is a
maximum speed limit in the universe, a speed of causality. We may reason that a
causality speed is necessary even for causality itself, since a cause that
creates an effect instantaneously cannot be clearly distinguished as cause or
as effect itself. Causality can be understood as an organization of events in
time, for time to occur, there must be some duration of events and between
events. If there is no finite speed limit, then all events could occur at once,
time itself ceases to exist.
Because the upper speed limit is absolute, it is observed to
be the same in all frames of reference. It is not possible to observe a faster speed.
Light then simply assumes the value of the speed of
causality, being a limiting case where it may reach the fundamental speed
limit. The question of why the speed of light is the value that it is (approx.
300,000 km/s), is really a question of why the relative magnitudes of the
forces of nature are what they are. Or to put it another way, why the values of
the fundamental constants (tunable parameters) have assumed their relative
values. This we are unable to answer as yet, nor do we possess a map on how to
go about answering it. The question of why light travels at the speed of
causality and not some lower speed gets to the nature of electrodynamic theory:
let us suppose simply that it is a requirement of the theory that energy be
exchanged at the speed of causality and a fact of observation that this is
accomplished by the emission of photons (particles of light)2.
Now, since ultimately speed is fundamental and absolute,
then to satisfy observation distance and time must contract to maintain its constancy.
We typically think of speed as arising from a change in distance over time:
speed emerges from the simpler concepts of distance and time. But with a
fundamental speed of causality, we denote it as c, it is revealed that speed itself comes first, and distance and
time must follow. Because there is a finite speed limit, therefore the
experience of time occurs.
One might imagine that the space-time structure itself
emerges in response to the speed of causality. In order for a speed to manifest
itself, both distance and time are required. As photons are emitted, space-time
unfolds in response.
There is no dark energy
Rather the expansion of space is driven by the emission of photons. The rate of expansion will be in accordance with the emission of photons, that is the matter density in the universe. Therefore the rate of expansion should slow down over time.
Conceiving of speed before distance and time presents us
with great difficulty. The task is perhaps made a small measure easier by way
of analogy. Consider a clock with a set tick rate. The tick rate may be
anything relative to another clock, such as how the clocks of computers are
measured against each other in cycles per second. The clock is cyclical, within
the clock there is no distinction between the same position in successive
cycles. Beyond a single cycle, the notions of time and distance do not exist
within the clock. Further, the position and time within a cycle are
inextricably linked, to specify one is to fully specify the other. The clock
does not assume any arbitrary position at any arbitrary time, rather it assumes
an arbitrary tick rate (clock speed) at its inception, and from this its
position with respect to time is fully specified for all time. The challenge
then is to apply this analogy to the universe as a whole. Imagine there is
energy that is always cycling at a finite speed. It cycles in such a way that
neither distance nor time as we understand them are necessary. However, as this
cycling spills out into our experience, distance and time necessarily follow.
I note that the analogy may be taken one step further and
the notion of distance essentially done away with entirely. Rather than
envisioning a cycle we imagine a slowly blinking light that softly transitions
from full brightness to full darkness in repetition. It serves just as well as
a clock and transitions state within each cycle, but it does not traverse any
distance, not even a cyclical one. However, I am unable in my imagination to
extend the analogy to do away with time completely. It may be that a sort of
'cycle-time' remains as fundamental that gives rise to our more familiar
experience of time. This cycle-time would be perfectly symmetrical, in contrast
to time as we experience it. However, the necessity of 'cycle-time' is unclear
to me and I admit that it may simply be a consequence of trying to take the
analogy too seriously.
The Photon Wavefront
If the expansion of space-time is driven by photon emission then the edge of space-time is given by the photon wavefront, the furthest edge at which photons have managed to reach since the big bang. It does not seem to me that this should coincide with the edge of the observable universe. I am tempted to speculate that the edge of the observable universe should be about half of this distance, since the light will have had to reach the edge and then make it back to us, but I feel that this half-hearted reasoning is almost certainly wrong.
A Space-Time Continuum?
How is it that space-time is a continuum yet the speed of causality is finite? This is essentially Zeno's Paradox. If space-time is irreducibly continuous, then it seems that there can be no causality. Any event would take infinite time given it propagates at finite speed. It would appear as though we must have some fundamentally discrete space-time unit, space-time must be quantized. General relativity is formulated in terms of continuum geometry, but this seems to be at odds with causality. General relativity must therefore be reformulated in terms of a discreetum. Of course there have been many attempts to quantize gravity3, none as yet successful in displacing general relativity from its pedestal.
Why Isn't Light Slower Than Causality?
An interesting question. While we can perhaps convince ourselves that causality must have an upper speed limit, it does not seem necessary that light itself should propagate at this speed, rather than at some lower speed. This seems to speak to the nature of light: photons are fundamental and cannot be composed of any simpler elements with a manifestation in our experience. Photons are the transmitters of energy, they may be conceived of as causality agents.
Footnotes
1 This is not made explicit in Relativity, and I have yet to explore how the theory of electromagnetism was formulated in sufficient detail to credibly make this claim. This is what I have inferred based upon what I have read in Relativity and elsewhere, a point I need to follow up on.↩
2 More inference on my part.↩
3 Among these are string theory, loop quantum gravity, shape dynamics, etc. The Wikipedia article provides a decent introduction.↩
References
Einstein, Albert. (2006, Original publication 1920) Relativity: The Special and the General Theory. Toronto, Canada: Penguin Books.
Quantum Gravity
(August 8, 2017). Available at: https://en.wikipedia.org/wiki/Quantum_gravity
(Accessed: August 9, 2017)
