## Questions: Metric Expansion of Space, Dark Energy, Probability

My head has been swimming. Perhaps I should have continued studying theoretical physics when I was younger, but there’s nothing that can change that now. I’ve always been fascinated by the sciences of the very large and the very small. Developing theories about the nature of space and time has been a past time of mine since I could grasp the concept of such things, and in this my cousin was my chief partner in scientific blasphemy. Forgive me now in lacking rigorousness and academic references, I simply wish to bounce ideas off the aether and see where I’ve gone terribly wrong and also what might be of merit.

Today, the LHC at CERN is carefully winding up and pitching beams of highly energetic particles (more accurately wavicles, perhaps better described as multi-dimensional folds) at one another, hoping that in the interactions, we can better understand the stuff that makes us what we are. The more elusive Why will probably forever lie beyond the pale of comprehension, and yet we strive to corner it with data, formulate hypotheses, develop and test theories, add to the Katamari Damacy ball of equations used to explain what we find, and then reduce them to elegant truisms to test in further experiments. What has amazed me since youth, is that no matter how much we know, and continue to learn, there seems to be a growing number of questions and increasingly perplexing problems concerning our current understanding of things and the gaps in our ability to explain what we think we know.

The expansion of space has puzzled me. We have a clear picture from observational data that the universe is not only expanding, but that the rate of expansion is accelerating. When I was young enough to grasp this concept of expanding space, my first reaction was to ask, where the center was and what is at the edge. We know now that there is essentially no center, that the best idea we have is that all of the universe came into being all at once, in a flash, commonly (and perhaps mistakenly) referred to as the singularity in a “Big Bang”. There is no edge and therefore no center, but perhaps this is completely wrong, misleading and confusing. To stick with what we understand clearer, we take the speed of light to be constant (and from what we have observed, so far this appears to be the case). Therefore, the more distant an object, the longer light emitted from it has taken to reach us. The result is that the further into deep space we peer through our telescopes, the further into the past. What we have found is that all the light from these distant objects appears to have a shift in their spectrum. Light emitted by plasma of elements contain a signature spectrum or frequency gaps and bands (which correspond to the energy jumps made by electrons as they absorb and emit energy in the form of photons). What scientists Slipher, Hubble and others have observed is that the light from distant objects contain spectra of familiar elements, but the gaps and peaks in intensities are all shifted towards the red end of the spectrum, the result of the Doppler effect leading to the conclusion that most everything in space appears moving away from us (though some objects like the Andromeda galaxy are blue-shifted, and thus moving towards us). Another startling observation is that the further an object, the more intense the red-shift. One explanation was that not only are they receding faster from us, but that the expansion of space between us and the distant object can account for that shift.

Contemporary cosmological models accept the Universe as not only expanding, but expanding at an accelerating rate. That is, space itself is expanding, everywhere all at once, the effect of which is that objects are being pushed increasingly further apart. What’s more is that the rate at which objects are being distanced is accelerating. Why? One possible explanation is this idea of “negative pressure”. That is, if gravity represents a positive pressure, to bring all matter together, then this Dark Energy can be thought of as the source of this negative pressure, which fuels this increasing expansion of space. Is it anti-gravity? Not quite (to explain this exceeds my own grasp of the concept), but regardless, we can still ask, “From where does this pressure come?” If there is no meaningful “outside” to the universe from which to create a negative pressure, how can it be created internally?

To be clear, Dark Matter and Dark Energy have little to do with one another in this line of thought. In my understanding of things, Dark Energy is simply a way to account for the energy budget of the Universe, to explain what we can (or can’t) observe. Dark Matter is the place holder to account for all those gravitational forces we observe in the structures of our universe which cannot be accounted for by the observed quantities of luminous (radiative) matter.

With my very limited understanding of the math operating behind these deeper theories of how the way things are and the ways in which we presently explain what we can observe today, I’d like to put forward some very modest ideas and see if someone can help point me to a deeper understanding of the current state of theory and my own ignorant blunders.

I’d like to posit that space, empty space, contains probabilities. Probabilities of what? being different, nothing more. These probabilities taken together total 1. The probability then exists with 100% certainty that it will change. How and why? We do not understand enough to conjecture, let alone speak of what that change may entail, but change comes at 100% certainty. Here time cannot have any meaning. It either has happened that the probability has manifest, or it is yet to manifest (the granularity of time perhaps?).

If space is taken first to be a region with a probability of 0 that anything different could happen, then that region of space effectively does not exist. Who cares what it is, if it cannot be anything otherwise? There is no way of knowing even whether it is since it is completely inert. In a way, we have found a way to define absolutely “nothing”. If a single quanta of space exists, it must be because the probability for its existence, or for its being something other than what it was, must have been other than 0. If we imagine this singular region as being different and assign probabilities to each way that it could be different, we get a range of possible states coexisting simultaneously within one single quanta of space. That is, until the probability manifests as an actuality, in this case, they come into existence.

If the probabilities produce the existence of some state, and if there were some underlying symmetry or structure of the probabilities governing the possible existence of states in which the existence of one necessitates the existence of a counterpart, then there is a distinct possibility that the single quanta of space can exist in actual multiplicities, that is, divide. I realize how sloppy this all is, but from this, I understand time to be an artifact of the concurrence of these probabilities taking place in relation to one another. That is equally sloppily stated, but I think it gets the point across: that there exists no meaningful time-frame without relationship to something else, and that space itself is nothing more than the state of a set of probabilities and time is a by-product of probabilities manifesting themselves. The granularity of space is then seen as the minimum distance for one state to manifest a different state which is a probability of the relationship to something other than itself as dictated by the underlying structure of those probabilities. Can we probe these shapes? In what ways does the Standard Model and Quantum Field Theory allow for this way of thinking? We currently have a minimum distance, the Planck distance, and know the energy required to probe at that distance. What happens to time, and energy at these scales? Can they be thought of in terms of the evolution of probabilities, and probabilities the process by which space expands?

To zoom out a bit and assume that there is some mechanism causing space itself to expand, and that it is internal, or inherent to space itself, does that account for the relativistic effects on light due to gravity and the expansion of space? Could it be possible that the speed of light could be explained by the same mechanism behind the expansion of space? Does space expand equally everywhere and all at once?

If the mechanism for the expansion of space can be described mathematically as the existence of probabilities that something will exists where there wasn’t something before, can this be reconciled with the idea of the conservation of energy? Does it require energy for space to expand by these means? What would the model for this look like? Do we have a problem of an exponential demand on energy or can this be resolved by the existence of other features of space-time? We already know that it is probable for a particle/anti-particle pair to spring into existence, that this is latent within any region of space. I suppose it’s this idea of probabilities at very small scales and the idea of quantum foam, which have led me down this line of thinking. That and the idea of asymptotic freedom by way of Frank Wilczek.

Is there anything that sounds right? Where did I go wrong? Perhaps probabilities are problematic because the language exists within the framework of mathematics, but it is through mathematics that we have put into language this picture of the world. Is probability a deep enough technology or concept to probe the foundation of all there is? It certainly can speak to what isn’t, and could never be.

Bibliography:

“The Lightness of Being” by Frank Wilczek

“The Quantum World: Quantum Physics for Everyone” by Kenneth W. Ford

“New Theories of Everything” by John D. Barrow

“On Space and Time” by Various Contributors, Edited by Shahn Majid