To rest or !rest

FYI

I’m including a lot of prerequisite preamble, but to cut to the chase, I try to imagine why I the CMB might cool down from the surface of last scattering and how the vacuum might function through virtual black holes. I also try to imagine a model that attempts to understand how and/or where that heat goes. And I wonder stuff like like, “What is mass? What is inertia? What does it mean to be at rest or not at rest (!rest)? What is space-time curvature?” Full disclosure, I am not an degree holding physicist or mathematician, just a science & physics enthusiast that likes to think out loud.

I’m also publishing this now, out of laziness. I will re-read it later as I have time and fix any mistakes. If you have a Medium account, feel free to leave notes with errors.

Intuitions

The traditional picture of stable rest-mass that children intuitively pick up is something along the lines of a solid billiard ball of “stuff.” We also get this somewhat from Newton and classical physics. It’s a predisposition and a bias towards our delusion. However, when you factor in our knowledge of atoms then we know that solid stable “matter” is mostly empty. And we now know that it's only by way of quantum electrodynamics (QED) that things seem solid due to the electron shells of charged electrons. So right off the bat we know our intuition is just plain wrong. But it doesn’t stop there.

That's not the end of the road by a long shot. One now has to say how the electron is both considered to be not only to exhibit particle-wave duality, but how it can be both a point particle and can have mass, unlike the massless photon. If it’s a point particle, is the electron a black hole? Also, one has to say what the massive non-point particles of the Standard Model “have” mass and what that actually means to “have” it. Enter quantum field theory (QFT), the Higgs field/mechanism and the Higgs boson, string theory, etc. However, the way I like to think of this is to imagine the vacuum, or what we usually called “empty space.” Once again our intuition fools us. The vacuum is known not to be empty. So without getting into field theory or S-Matrix, it seems useful to think in relatively simple terms and ask, “What is empty?” and “What is at rest?” How do we draw this distinction, more importantly, why might that be?

Uncertainty

It turns out that if something occurs fast enough, relative to you, it can appear to be stable and constant. Or given the right scenario, an observer might say that it appears there might be universal time intervals occurring at different relative velocities of time evolution in different areas of space. Or it can even appear, to an outside observer, that time as stopped all together for another observer. But these are all just interpretations and observations based on frames of reference and the transfer of information between states, not the actual local states.

There is also the basic premise that one must establish in terms of reality that to observe something is to assume it exists (that everything isn’t an illusion or trick of the eye or observation process). This is where the uncertainty principle comes into play and limits what you can known across different domains based on the transfer of information. You cannot arbitrarily known both the position and momentum of a small particle because you’re required to use a photon to observe it, to transfer information. And it’s through the act of observation that you then either disturb it’s position or you give it momentum.

I’d like to take this same notion and apply it to knowing if something exists or not in the vacuum. If you observe the vacuum, you’re affecting it to say whether it’s there and a vacuum, or if it’s there at it has mass. This most fundamental rule is the transfer of information is itself a tangible mechanism that is part of the system. There is no independent outside observation.

Averaged zero != zero

It’s therefore possible that, relative to the macro, that the micro can appear empty even though it’s not. A zero may not be a zero if it only appears zero on average. Who is to say what it is if different observers in different conditions see something differently? This is not unlike an object seeming to appear solid to the macro when it’s actually mostly “empty” at the micro. Except, now we know that even this picture is inaccurate because that “emptiness” isn’t even what we think it is.

And so we might want to temporarily abandon the concept of empty as a possible state and just hypothetically assume that there is no such thing as empty (for now). The way I like to think of the distinction between vacuum and particle is in terms of:

1. At rest <- mass-energy
2. At !rest <- vacuum-energy

And between these two states there are then one or more boundaries of some sort. But as soon as you draw some sort of boundary, you might determine that you have to assume either a surface area in the case of two dimensions or a volume in the case of three. Otherwise, you’re talking about an infinite or ill defined boundary. You also have to choose whether this state boundary is a gradient or an infinitely discrete separation between the two. And finally, you have to ask yourself if there are boundaries which define either solid states within the boundary, or hollow boundaries.

Determinacy

It is in this determination of the infinitely (or Planck?) discrete separation between the two that I find the question of being at rest to be most fascinating. If all you did was to create an infinitely discrete closed boundary for a 2D circle or a 3D sphere (2-sphere surface area), then we might be free to assume that the circle or sphere is hollow, the inside of which could just be trapped vacuum. Or, the inside of a Standard Model particle with rest mass coud truly be a zero, nothing, truly empty with not even any virtual particles inside the boundary.

Therefore, along this discrete boundary we then see a distinction between vacuum states whereby information either cannot flow across the surface through the interior, due to the boundary, or is somehow changed or filtered by it.

What is a possible model for this vacuum & boundary? Since I am not an educated physicist or mathematician, I cannot create any actual models myself. As of now, the best established model is the Standard Model, based on Yang–Mills gauge theory (QFT). While this is mainly useful for performing calculations and making predictions, it’s also useful for checking against any underlying more fundamental models. As with Newton and the question of gravity, the Standard Model leaves out what the fields actually are (and what gravity is). Are these fields & particles best represented by fundamental vibrating strings, or are they something else?

Look for familiarity

My favourite subject and way of viewing the answer to this question is to look at something we know exists as a mechanism. I like the idea of patterns and repetition. So when we see the golden ratio, circles, pentagons, or other repeating patterns it seems like a pretty good clue. While string are nice oscillatory models, it’s hard to imagine a really large multi-dimensional string being repeated at the macro level. That’s not to say that there isn’t a good theory of everything (TOE) model for a string theory that would be able to accurate represent reality, but I’m not yet convinced that there really are little tiny vibrating strings.

So what really happens we we’re at rest? Consider yourself sitting in a chair at a computer. Our intuition is to say that gravity is pushing us down into our chair. We assume we’re “at rest” even though relative to the Earth, the Sun, and the galactic centre, then we’re not actually at rest. However, assume for a second that there is no invisible force between yourself and the Earth. Instead, for you your future is to simply follow a curvature of space that wants to go towards the centre of the Earth, like falling into curved tube which is somehow blocked. It’s a strange feeling to think that for you, your arrow of time in a sense, is to continually follow this curvature of space, which is itself moving around the Earth, and moving around the Sun, and moving around the galactic centre of the Milky Way galaxy.

One again what we’re really talking about is this distinction between the at rest and !rest vacuum state. We’re talking about moving this boundary, which could just be an infinitely discrete hollow one that somehow distorts the transmission of information. In terms of an array of atoms composed of standard model particles, the collective boundaries of our almost entirely vacuous rest “mass” all want ultimately “appear” to want to evolve in a correlated way, something we call our inertia. In terms of information theory, this doesn’t necessary need to be thought of as an evolution through traditional 3+1 dimensional space-time. Using the holographic principle, one could imagine holographically representing 3+1 evolution using information from a lower dimensional 2+1 hologram.

What might a field actually be?

This still doesn’t really give a clear picture of what these boundaries or fields might actually “be.” So this is what I imagine:

Start with the idea of a black hole. What you have are all these aggregated boundary distinctions (rest & !rest vacuum) falling into a gravity well and further curving space-tine to the point that even light cannot escape. What you get is an event horizon. This is basically a boundary of causality where by no event inside the horizon can be transmitted to an outside observer through the use of an escaping photon, since it cannot escape. For all purposes, an outsider observer might consider the black hole to have a diameter equal to it’s event horizon. However, to an in-falling observer that crosses this event horizon, they will feel nothing when crossing the event horizon. The event horizon is therefore an information barrier giving rise to a complementarity.

The other important thing to consider is that at the event horizon of the black hole, Stephen Hawking predicts that quantum effects will produce a Hawking radiation using a feature of the !rest vacuum not being empty. If this vacuum contains briefly existing at rest “virtual” particles, then there might be interactions between these virtual particles and space-time curvature along this infinitely (or at the Planck scale) discrete event horizon boundary. This would mean that as a virtual particle and anti-particle pop into existence, one of the pair will be on either side of this discrete event horizon boundary. In this configuration, these two virtual particles will therefore not be able to further communicate with each other. One pair partner falls into the black hole where it can annihilate with whatever rest mass (the cause of the curvature) might be waiting.

Information does get out

If they waited long enough, an outside observer would see the black hole evaporate and reduce in mass due to emitting very low Hawking radiation. The problem here is that the black hole has done a great job of thoroughly scrambling up all the information that fell into the black hole, spreading this information out over time. It basically impossible to determine what might have fell into the black hole before it got converted to hawking radiation. The other virtual pair partner actually escapes the black hole, presumably with some random virtual particle momentum giving it either a stable orbit or escape velocity from the black hole. This escaping radiation energy would be Hawking Radiation and the amount of of radiation would depend on the black hole’s age & mass, giving it a temperature. The consequence of this is that the annihilating virtual particle that falls into the black hole conserves energy when it finds an anti-particle, thus returning the rest mass to the !rest vacuum from which it was taken.

But what you can’t have is Hawking radiation leave the black hole while it having taken longer to appear to reduce in mass. So to an outside observer, they need to measure deep-time space-time curvature changes, as a result of the black hole’s mass reduction, in accordance with the emitted Hawking Radiation in order to maintain the perception of energy conservation. It need not be simultaneous annihilation & emission, only that it appears to be to an observer in accordance with the space-time curvature changes, which the observer assumes to be observed mass reduction of the black hole.

Boltzmann’s revenge

Through Hawking radiation and the proposed mechanism of virtual particles along a causal event horizon, we can see a discrete boundary that affects the transmission of information related to the perception of mass, and changes to mass, even with no actual event horizon boundary. What this really is might be best thought as a “firewall” that some some information out but no information in. The only information it lets in is Hawking Radiation and space-time curvature change.

But what might this have to say about the model of at rest & !rest vacuum or this boundary? What I like to consider is that if you were to take a black hole and shrink it down in size, there is reason to expect that it would continue to behave the same (perhaps down to some minimum mass level). This either presumes that you started with a ridiculous large black hole and waited forever for it to evaporate, or if you could create micro black holes through a hypothetical process. As it stands, the only known mechanism for actually forming a macro black hole is through the evolution of stars of sufficient mass that go supernova and form extremely dense neutron stars, who then continue to feed on in-falling matter.

So hypothetically, if you had a mechanism of some kind that could to squeeze the mass of the Earth down to a diameter of 9mm, space-time curvature would cause the inertia of this rest mass to remain confined and form a black hole. You could consider that what you’re doing is squeeze the mass down to a small volume, or you could choose to look at this as actually curving space-time.

So now we can consider how a large stellar black hole evaporates by having a temperature and how a smaller 9mm Earth mass black hole would have a temperature and might evaporate. The larger black hole would have more mass, thus ultimately having a capacity to live longer. More mass inside the event horizon would mean it can then evolve to give off “hotter” Hawking radiation (information). The Earth size black hole on the other hand has less mass, but will evaporate quicker, not living as long and giving off a less “hot” Hawking radiation temperature.

The Zeroth law

However, this assumes that the temperature gradient is such that the Hawking radiation would move from a hotter area (more ordered) to a colder one (less ordered). In addition to not being empty, the vacuum also has a pervasive temperature called the Cosmic Background Radiation (CMB). This is radiation that was emitted at after the presumed Big Bang inflation and the surface of last scattering, when the universe went through a phase transition and because transparent to photons. These photons have been cooling off ever since and they’re currently at a temperature of 2.7K. So, the Hawking Radiation of a small black hole needs to be hotter than 2.7K to then give off this Hawking radiation, lose it’s mass, and be observed to evaporate through the curvature of space-time like the it’s bigger brother/sisters.

As it turns out, the limit where a black hole will have suck temperature is about 0.8% the mass of the Earth, or about the mass of the Moon. Meaning, if you squish the mass of the Earth down to a black hole, it should develop a Hawking radiation temperature greater than 2.7K so that it can evaporate. Consider that the Earth is a cool glass of water and air around it is warmer, it will evaporate and reduce in volume. Now if the temperate of the air was colder than the water, it would freeze. If you take a mass about the size of the Moon (7.34767309 × 10^22 kilograms) and turn it in to the size of a black hole, it would be 0.2mm in diameter. A black hole of this mass would generate a temperature approximately equal to the temperature of the CMB, 2.7K. This would be like an ice cube surrounded by air at the same temperature.

Anything less than this mass would not produce Hawking Radiation with a temperature warmer than the CMB. It would actually take heat away from the CMB through the nature increasing entropy of the universe. This is just like warm bath water being evenly distributed throughout the cold bath tub. Where does that warm CMB go? If the virtual particles themselves were smaller exceedingly brief micro black holes which formed and evaporated quickly enough to average to zero, would they not evaporate by taking in the CMB heat and reducing it?

This would mean that over time, the universe only allows for smaller and smaller black holes to be detected in accordance with the drop in the CMB temperature. Anything smaller than this would eat CMB temperature in an undetectable way, other than the universal CMB drop.

Eventually, the larger black holes would be the last to evaporate bringing everything in equilibrium, potentially through virtual black holes (or premature evaporations that might exist smaller than the Moon’s mass) that take in CMB or Hawking Radiation, spreading it out through every increasing entropy.

“My God Its Full Of Stars”

The other thing I was considering was that if the vacuum were virtual micro black holes quickly forming and evaporating, that they would exist everywhere, including near the boundary of the larger black hole horizons, taking in thermodynamic inclines lower than the CMB temperature. Any fractionally <0.2mm sized black holes (smaller than the mass of the Moon), as well as any virtual micro black holes would be basically undetectable as they gradually reduce the temperature of the CMB through hawking radiation. While at the same time, larger black holes would slowly give off Hawking radiation in a theoretically observable way.

Black holes smaller than the mass of the moon (including micro/virtual black holes) might be converting their mass, virtual or otherwise, to Hawking radiation which then pulls down the CMB temperature. This might have something to do with what creates space-time curvature, dark energy, or dark matter?

I was going to further elaborate about space-time curvature and information theory but I’m going to stop this here for now.

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