A Quantum Pane In The Glass: Part Two

In quantum physics, you may deduce that those residents of the micro realm, those elementary particles, have some very strange properties bordering on a quasi-free will.  They seemingly have the ability to ‘know’ things about their external world and their relationship to that and make decisions and act accordingly. There are experiments to back this up that include an observation you can make at home to verify this. Look outside your window. What do you see? A very big mystery is what you see, if your window is anything like my window or most windows.

Continued from yesterday’s blog...

CAUSALITY & CERTAINTY vs. PROBABILITY & CHANCE

I need state the obvious here – all photons are identical; the pane of glass in question is obviously identical to itself. Therefore, knowing that and only that, one could only conclude that when photon meets window pane, one and only one outcome is possible.

We, the observer say the photon has such and such a probability of going through, or being reflected from, the pane of glass. If seven out of ten photons go through the glass window, then there’s a 70% probability the next photon will go through. Wrong. As far as that photon is concerned, we, the observer, are irrelevant, and it’s 100% certain to either go through the glass or be reflected by the glass. We can be pretty damn sure that a group of photons won’t gather together in the middle of the glass pane and do an impromptu performance of a Wagnerian opera. There’s no probability involved. It’s one or the other. There’s no superposition of state. The photons aren’t in two places at once – passing through and being reflected.

Another way we can be sure causality is operating, albeit going up one level, is that every time you go to the inside of your window pane looking outside, you see both outside and a faint reflection of you and the interior. Not once in a while; not sometimes 100% outside and no reflection; not sometimes a 100% reflection but you can’t see outside (your window isn’t a mirror after all), but 100% of the time, each and every time, you see both the exterior outside the pane and the interior reflected inside the pane. 

SUMMARY, DISCUSSION & RESOLUTIONS

In summary here, some photons from the inside pass through a pane of glass to the outside; some outside photons pass through that glass to the inside; some photons from the inside reflect off the glass back inside and some outside photons reflect off the glass back outside. The big question is, how does the photon decide what to do? Here comes Ms. Photon heading toward the pane of glass. She has to make up her mind whether to pass on through or reflect back: decisions, decisions. To reflect, or not to reflect, that is the question! IMHO, photons should all go through, or all reflect, from the same pane of clear glass at the same time.

We note from the outset that the glass hasn’t been tinted or polarized – not that that would alter the general picture. What we have here is just an ordinary pane of glass.

Further, no external forces are apparently at work here. Both the photons and the glass are electrically neutral. Gravity plays no role and the strong and the weak nuclear forces are only applicable inside atomic nuclei.

To make a long story shorter, causality rules IMHO! Photons are not in a state of superposition; they are not in two places at the same time. Clearly photons are not in a position to ‘know’ anything. Photons have no decision-making apparatus; they have no consciousness of any kind, no free will to be or not to be. That can be demonstrated by adding a little extra thickness and/or density and/or energy.

But first, one could easily suggest that since even seemingly ‘solid’ stuff is 99.999% empty space, that a photon passing through the glass is passing through that entire void, and a photon reflected has hit a glass molecule and bounced back. One exception to that is that the reflection takes place at the surface of the glass pane, none from the interior of the glass. A second exception would be that reflections off of a solid molecular bit in the mainly empty glass pane would be totally scattered in many directions which is what we don’t see. Basic optics – the angle of incidence equals the angle of reflection. Yet clearly if photons are being reflected, they are bouncing off something. Or, perhaps they are being absorbed by the electrons within the glass matrix and then reemitted, though the photon that’s reemitted might not be the exact same photon – but that’s of no consequence since all photons are identical.    

We note that the greater the thickness or the greater the density the more the pass through to reflection ratio changes. If you look through the exact same pane of glass, but this time edgewise, no photons pass through from one edge to the other edge. The X-ray case study above shows the role of increasing density. Both are an illustration that ultimately things become so thick and/or so dense that while there might not be total reflection, there would be any pass though either. The option for the photon might then be reflection vs. partial penetration. Of course that in itself doesn’t explain the either this or that option the photon takes, at least until such time that it becomes one or the other. In a vacuum it’s 100% pass through and 0% reflection; in the case of a metre thick lump of lead, a light photon will 100% reflect and 0% pass through. Restrictions placed in the photon’s way by density and thickness just tends to confirm an earlier notation that stuff is 99.999% void such that pass through equals boldly going through that void; reflection is a collision with that rare bit of stuff that sometimes gets in your way.

But that’s not the entire story. Thickness is also related to opaqueness though they are not the same thing. Photons can pass through Earth’s entire atmosphere from the fringes of outer space to ground level, yet if you dab a smear of black paint on your pane of glass, well that will strop the photons from passing through albeit black paint is a lot less thick than the Earth’s atmosphere.

Energy plays a role too. X-ray photons are more energetic than visible light photons, which is why X-rays are better for detecting structural flaws (like tooth cavities and bone micro-fractures) which are concealed by external surfaces which are opaque to light.

Air and glass are transparent to light photons, but are generally fairly opaque to the less energetic infrared photons. That’s the general principle or concept behind both the botanical greenhouse and the environmental greenhouse effect, although in the later case not all the components found in air are equally as opaque.

Ultimately invoking variations in properties like density, thickness, energy levels and opaqueness doesn’t totally explain why identical particles, with all other factors being equal too, have this Jekyll and Hyde property whereby some do and some don’t; some will and some won’t.

But we see that while things aren’t totally explained yet, we’re well on the way to determining the real factors that decide the photon’s fate, and it’s not photon’s free will either. 

A Quantum Pane In The Glass: Part One

In quantum physics, you often deduce that those residents of the micro realm, those elementary particles, have some very strange properties bordering on a quasi-free will. They sort of possess a ‘mind’ of their own. They seemingly have the ability to ‘know’ things about their external world and their relationship to that. They make decisions with respect to those relationships and act accordingly. They are not just little inert billiard balls. There are observations to back this up that include an observation you can make at home to verify this. Look outside your window. What do you see? A very big mystery is what you see, if your window is anything like my window or most windows.

Even if you don’t know or understand very much about quantum mechanics, or quantum physics (same difference), you have probably associated it with weirdness. Unlike the certainty and causality domination of your day-in and day-out macro world, the realm of the quantum is centred on probability, chance and randomness where things happen for absolutely no reason at all and identical scenarios will yield different results. One oft given example you can (and have) witnessed – how light (photons) interacts with a common pane of window glass.

GENERAL DESCRIPTION

Here is a common happening that you have experienced at home or in the office or in the car that you probably never gave a second thought to. That unregistered oddity you experienced is seeing the reflection of AND the passing through of light waves (photons) with respect to a pane of glass simultaneously. What’s so odd about that? Well, what’s odd is that light is both passing through and reflecting from the same pane of glass at the same time. Why both? Why not one or the other scenario? What’s odder still, assuming you are inside, is that not only can you see your reflection or the reflection of what’s in your background but what’s also outside and through your own reflection. You see your reflection and the outside image, both superimposed on top of each other. So photons are both passing through the glass (you can see the outside while you are inside) from the outside to the inside and at the same time reflecting from the inside to the inside (you can see the inside from the inside) both happenings at the same spot on the glass.

And if you go outside the reverse is also true. The outside is partly reflected by the glass surface back to you while you are outside looking in while at the same time light photons from the inside are passing through the entire glass so you can see inside your room though you are standing outside, both inside and outside as superimposed images.

Further, the ratio of pass through to reflection also depends on the thickness of the glass, so presumably the photon ‘knows’ in advance what that thickness is and acts accordingly. If all of that doesn’t strike you as odd, nothing will, though it’s so commonplace it probably doesn’t strike you as odd.

OTHER EXAMPLES

This ‘do I or don’t I’ oddity doesn’t just apply to panes of glass. This applies to a wide range of transparent, even translucent stuff. The same pass through vs. reflect back applies for example to your eyeball. Some photons enter your eye and deliver their message; some photons hit the identical spot but are reflected back, but can then hit a mirror and reflect back again this time entering your eye so that you see your eye that reflected in the mirror.

Speaking of eyes, you can ‘see’ an external bright light even with your eyelids shut, yet some of the light is also being reflected off the external surface of your eyelids.

Sunglasses are another obvious example. You can see your reflection in the outer side of the lenses, but clearly the sunglasses let through without any obstruction photons too.

You can see your reflection in still water and the bottom beneath the surface too if the water is pretty clear and the bottom is fairly shallow. This should also apply to say a polished diamond or other similar gemstones or crystal(s).

Another visual example – you see sunlight reflected off of the tops of clouds when in an aircraft that’s flying above them. As you descend through them and land, though the day is now overcast, clearly some sunlight photons are passed through the clouds. It’s the same clouds; and the same sunlight; and the same observer; but differing outcomes. So the pass through vs. reflection enigma applies equally to translucent objects (like clouds) too.

Though this is an obviously visual puzzle, well that in itself is obvious since we can only see visible light photons. However, photons come in a wide range of forms, from ultraviolet to radio; infrared to microwave; gamma rays to X-rays. Presumably this pass through vs. reflection phenomena takes place with non-light photons too. The most obvious example is that radio, TV or cell phone reception tends to be better outside than inside – one reason for your TV aerial or antenna. So, some radio/TV/cell phone photons are reflected off of the outside of your solid building but some pass through too, but this has nothing to do with frequency or wavelength since these transmissions are on a very narrow bandwidth.

In a similar vein, it’s been advocated for decades that the ideal location to do radio astronomy and/or SETI, searching for alien radio signals, is on the far side of the Moon because the Moon’s bulk is 100% opaque to terrestrial and human generated radio signals that just add unwanted noise to the signals the astronomers are looking for.

One clue that the pass through vs. reflection conundrum must be density related, not just thickness related, comes from X-rays. We’ve all seen X-ray photos of the human hand. The bones stand out; the wedding ring more so, but the flesh is visible too though less so. So some X-ray photons were reflected, greater reflection related to the density of the stuff the X-ray photon was hitting. Yet clearly some X-ray photons passed through since the image of the fleshy bits isn’t as strong as the bones and the bones weren’t as solid an image as the ring. Yet it was the exact same X-ray dose that hit all three substances – flesh, bone and metal.  

THE STANDARD SOLUTIONS

The basic postulate postulated by quantum physicists is that the photon pass through vs. reflection anomaly is an anomaly because it all happens for absolutely no reason at all. It’s all random. It’s all probability. Some photons pass through via the luck of the draw; other photons get reflected by that same random luck of the draw. How is that possible given that we have, in the original example, one identical pane of glass with identical photons impacting? Well, if you don’t invoke causality, you can just about get away with anything anomalous.

The other accepted answer is that any one photon is in a superposition of states. It can be in two places at the same time, so it can both reflect, and pass through the pane of glass at the same time. Either that or the photon has awareness of its external surroundings; it has a mind of its own and decides what it wants to do!

Superposition of state has been experimentally demonstrated via the classic quantum double slit experiment whereby particles, like a photon (but any type of particle will do, like an electron) fired one at a time at two parallel slits, will pass through both slits and thus will interfere with itself and cause a classic wave interference pattern on a target board behind the slits. The only logical conclusion has to be that one particle was in two places at the same time. Personally, I find that absurd, but it’s hard to debate hardcore experimental results.

The one flaw I find in that standard pane of glass situation explanation is that if the photon is in two places at the same time, then both the inside reflected image and the external image – the pass through the glass image – should be equally as vivid. Usually the pass through the glass image is the more obvious of the two superimposed images assuming just one light source, say external sunshine, or the reflected image is the stronger, assuming the prime light source is inside, like say at night.

To be continued…

A Voyage To A Black Hole: Part Two

Suicide missions are hardly unknown happenings, so presumably it wouldn’t be too hard to find a volunteer to take a long walk off a short pier and dive into the heart of a Black Hole. Well, let’s trade in the walk and the pier for a spaceship, with our suicidal pilot crewmember willing to boldly go. What might she expect? For that matter what might a chickenhearted outside observer expect to see?

Continued from yesterday’s blog…

Now for the speculation: Let us suppose that our suicidal voyager survives her voyage (curses, foiled again) and gets to play tourist. What will she see or will she see anything at all? Well, yes, she will – see that is. The event horizon is like a one-way mirror. Light can pass through the event horizon into the interior of the Black Hole, but light cannot pass from the interior of the Black Hole through the event horizon to be witnessed by an outside observer. Okay, let there be light, and there was light. Light is energy, so there’s energy inside a Black Hole. It’s also been shown that a Black Hole has entropy, or in other words a temperature. That too is energy. 

There’s matter (mass) inside a Black Hole – obviously, since there’s gravity. Now the big unknown is what kind of matter is that matter? We don’t know. Outside of a Black Hole matter exists in four states – solid, liquid, gas and plasma. The transition from one state of matter to another is called a phase change, as in ice to water to steam. One speculation is that the matter inside a Black Hole undergoes a phase change to something even more solid and denser than, well a dense solid.

We sort of observe this in a Neutron Star, a star extremely massive with extreme gravity, but just short of enough gravity to form an event horizon and turn into a Black Hole. Why is it called a Neutron Star? Well, the gravity is so great that the bits and pieces of the atom, electrons, neutrons and protons are squashed together into one big glob. The positive protons fuse with the negative electrons – these electric charges thus cancelling out – to make neutrons, hence join with the already neutral neutrons, so everything forms into just one huge glob of neutron soup, or a Neutron Star. Rapidly spinning Neutron Stars are also known as Pulsars.

Now if atoms lose all sense of identity, there is no atomic structure, no isotopes, no molecules, no elements, no compounds, no electrons and no protons, then I’d have to define that as a phase transition, but one we don’t witness on Earth. Given the even more extreme gravity inside a Black Hole, would that same phase transition to a neutron soup hold sway, or might there be another beyond that found in Neutron Stars? 

Neutrons are not fundamental particles. A glob of neutron soup is ultimately a glob of quark soup, as quark trios comprise the identity we call a neutron. Neutrons are actually composite particles. However, as quarks are fundamental particles, it’s unlikely they can be crushed or fused together. Electrons too are fundamental, but it is well known – to particle physicists at least – that an isolated neutron will in fairly quick-smart order decay to a proton, an electron and an antineutrino. Reactions are reversible so it is straightforward to create a neutron if the ingredients are brought together with sufficient energy.

Since a Neutron Star is just one coin short of a Black Hole dollar, the inside of a Black Hole could well be akin to a Neutron Star, only slightly more massive. One thing is certain IMHO, the interior will not be matter crushed down to the infinitely small (i.e. – zero volume); the interior will not be infinitely dense.

What lies at the heart of a Black Hole? The traditional answer is a ‘singularity’ – a point of (near) infinite density and (close to) zero volume, matter crushed down to the final, ultimate limit – or maybe not.

Start with a hunk of matter. Keep on keeping on adding more and more and more matter (mass) to it. Your original hunk grows larger, ever denser; its gravity swells in proportion. Finally it’s just a fraction away from achieving Black Hole status – meaning its gravity is so strong not even light can escape from its grasp. It’s that Neutron Star entity.

So you are a thimbleful of salt away from crossing the not-quite-yet a Black Hole to an actual Black Hole boundary. You can (barely) still see your now super-sized hunk of Neutron Star stuff. Now toss in that final thimbleful of stuff onto the hunk. No light now reaches you – you’ve crossed the threshold or boundary and have got a Black Hole. But do you doubt that lurking on the other side of the not-quite-yet a Black Hole to an actual Black Hole boundary, though unseen, you still have that super-sized hunk of stuff, not a singularity, but a really real solid 3-D hunk of stuff? Or, in other words, if the escape velocity of your hunk is 185,999 miles per second, no Black Hole and no singularity, but if it climbs to 186,001 miles per second you have a Black Hole and your hunk morphs into a singularity? A two mile a second difference makes that much difference? I don’t think so.

The other issue though is this really going to be a one-way trip for our boldly going voyager, dead or alive? One of the 64,000 $64,000 questions: Can you pour stuff down a Black Hole indefinitely, or does the Black Hole have a finite capacity and ultimately or eventually will have to spew stuff out the ‘other side’ (i.e. – producing a White Hole) as you keep pouring in more and more and more? I’d wager the conservation relationships and principles of physics and chemistry hold sway here. What goes in ultimately comes out. That doesn’t mean there’s not a temporary holding vessel. Or, in more human terms, you fill what’s empty; you empty what’s full, but in-between those two there’s storage in the stomach and the intestines; the lungs and the bladder.

Let’s adopt that point of view that what goes in, ultimately has to come out.

And so, our intrepid voyager might well exit elsewhere, maybe even elsewhen. The exit could be deemed the opposite of a Black Hole, or a White Hole; the passageway from Black Hole entrance to White Hole exit is that staple of sci-fi, albeit based in the realm of theoretical physics, the Wormhole. That the exit could be elsewhen is based on the theoretical ‘fact’ that a wormhole could be manipulated in such a manner as to allow for time travel. If that’s too far out for you, then a Wormhole elsewhere shouldn’t be. The apt analogy is with an apple. Mr. Worm can crawl around the outside of the apple to get from one side to the other, or Mr. Worm could take a shortcut and worm his way through the apple to get to the other side, or elsewhere.

Now the question arises, is there any observational evidence that White Holes and associated exits exist? Astronomers and cosmologists would argue in the negative, but I’m not convinced. What would be the signature of a White Hole? Well, it would be roughly stellar-sized, not planetary or galactic. It would be vomiting out one heck of a lot of stuff including lots of energy. Does the cosmos contain such beasties? Obvious candidates are quasars – quasi-stellar objects. Quasars are roughly stellar in size, but violently emitting the froth and bubble of nearly an entire galaxy worth of stuff and energy. The other high-energy astrophysical anomaly is gamma ray bursts. They occur way out back of beyond, in the outer fringes of the cosmos, which is all to the good for if a gamma ray burst happened in our stellar neck of the woods, the results would be akin to Kentucky Fried Humans! Still, we don’t know enough squat about them to be able to predict exactly where and when one will happen. So, astronomers who are into studying these cosmic critters are akin to sleeping fireman who never knows when they will be rudely awakened to respond to that rare five-alarm event.

So, in short, we have Black Holes that are your ultimate in garbage disposals; Quasars and gamma ray bursts that are your ultimate in, IMHO, recycling that garbage back into useful cosmic stuff – matter and energy. In other words, they are the exit to the Black Hole’s entrance. 

No matter. Either our boldly going voyager has snuffed it going into a Black Hole; is forever trapped in a Black Hole; or has been turned into a Kentucky Fried Human and vomited back out again via a White Hole quasar or gamma ray burst to become as one with the cosmos. We all started out as starstuff – and so shall we (or what’s left of our remains) all ultimately return to become starstuff again a millennia of millennia from now. 

Singularities: The Heart of Black Holes and the Big Bang

Singularities are fascinating objects and places, yet entirely ‘inaccessible’ in the sense that you can’t actually go there on vacation and send back a postcard, or travel to one on a government grant as a scientific expedition and report back via a peer-reviewed article in a technical scientific journal about the local environment, geography, inhabitants, etc. In a sense singularities are like Heaven in terms of accessibility. You have to rely on intuition or theory or second-hand observations as to what’s what and who’s who.  

Okay, for those readers I’ve already befuddled, I’d better tell you exactly what a singularity is! You’ve all heard of the phrase ‘Black Hole’ and not the one in Calcutta either! I refer to astronomical or cosmic Black Holes. Black Holes are ‘black’ because they have packed inside them so much stuff, so much mass, and hence so much gravity that not even particles of electromagnetic energy (photons) can escape their gravitational clutches. If photons, and that includes visible light photons, are jailed, can not pass go, can not collect $200, then they might as well as, as far as your perception of them is concerned, not exist. If what you don’t see exists, that existence is of no matter (well lots of matter actually). Translated, Black Holes are black because visible light can’t get from them to your eyeball! The absence of light is well, blackness.

So, is a Black Hole just a big lump of stuff, albeit stuff you can’t see? Well, ‘yes’ and ‘no’.  First off, we can ‘see’ Black Holes indirectly because of their gravitational influence on stellar objects we can see. I mean if you see a star whirling around something you can’t see, then the logical interpretation is that the star you can see is in orbit around something you can’t see – i.e. a Black Hole. Well ‘no’, you can’t ‘see’ a Black Hole because light from the Black Hole can’t get away from the crush of that Black Hole’s gravity.

What’s all this got to do with singularities? Well, the stuff composing a Black Hole, all that stuff that clumps together and is the centre of the massive all-encompassing gravity that prohibits the photons to escape the house (Hole) that Jack built is the Black Hole’s singularity. An analogy: The extent of the Black Hole is the extent of the Earth’s outer atmosphere; the singularity is the solid Earth proper. So think of a nebulous outer edge with a solid core of stuff in the middle. The stuff in the middle generates the intense gravity; the nebulous outer edge marks the boundary between gravity below the threshold of light escaping and light not escaping. That boundary is referred to as the ‘event horizon’; the stuff in the middle is the singularity.

Now the idea of a singularity doesn’t stop with the idea behind an astronomical Black Hole. No, a singularity is any concentration of stuff or mass that has such a massive amount of gravity as to prevent photons from leaving the gravitational well or prison so created. What’s the ultimate Black Hole – the Mother of all Black Holes? Well, if bits of our Universe can clump together to form astronomical Black Holes, then our entire Universe, when clumped together and in a relativity tiny state, would have been the Mother of all Black Holes and hence the Mother of all singularities. When was our Universe in such a state? Well, in the beginning!

Our Universe is expanding. That’s verified by direct cosmological observation. Every cluster of galaxies has such astronomically bad ‘body odour’ that every other cluster of galaxies is moving out of the vicinity quick-smart! Well actually you can’t have ‘body odour’ in space, so that’s not the real reason. The real reason is that in the beginning or once upon a time, there was some sort of explosive oomph event that started the expansion process. We call that the ‘Big Bang’ event. At the time of the Big Bang event, our entire Universe had a close encounter with, well, our entire Universe. Our entire Universe was roughly all in the same space at the same time. Translated, if you run the film of an expanding Universe backwards, you eventually get the entire contents of our Universe on collectively very intimate terms. Such a massive collection of stuff, matter, mass, hence gravity, all of the stuffs, matter or mass that the Universe possesses, well let’s just say you’d have the Mother of all singularities – in the Big Bang beginning; or anyway once upon a Big Bang time at least .  

Well surely one didn’t have this Mother of all singularities just sitting around for eons then for no apparent reason go ‘poof’ and thus have an explosive oomph moment which kick-started things off as far as our Universe is concerned. The intense gravity of the Mother of all singularities probably would have muted any oomph to begin with; the birth of our Universe stalled at the onset.

But, let’s throw some momentum into the mix. What’s the opposite of a Big Bang? It’s a Big Crunch! So let’s propose that we have this other universe which, the bits and pieces thereof, under all those mutual gravitational attractions, is slowly, ever so slowly, but ever so surely, coming together. And as it comes together, the contracting velocity gets faster, and faster, and faster. Eventually, you have this massive collection of stuff rushing together to meet at a single point in space and in time at a fantastic velocity. There is such momentum present that the contracting Big Crunch universe just can’t stop on a dime any more than an automobile going a hundred miles an hour can stop with inside of a foot of having the brakes applied. The Big Crunch at the omega point obviously forms the Mother of all Black Holes and singularities, but the sheer momentum of that contracting universe just tears the fabric of things (space and time) apart, and like a glove turning inside-out, the contraction passes through the omega point, spewing its gets out, becoming an alpha point, which is our Big Bang event and the start of our new expanding Universe.

Okay, so we have two sources that have singularities – singularities at the centre of astronomical Black Holes, and the Mother of all singularities residing inside the Mother of all Black Holes, the one that existed at the Big Bang beginning of the Universe.

We of course can’t see a singularity directly (unless you’re willing to take a one-way trip down a Black Hole, but even if you survived that and landed safely on the singularity, you couldn’t ever broadcast back your findings – that speed of light restriction that by definition a Black Hole imparts regarding sending stuff out). So, we have to rely 100% on what theoretical equations predict a singularity to be. Unfortunately, those equations, when pushed to the sorts of mass and gravitational extremes that a singularity would represent, well you get nonsense answers. Translated, if taken at face value, the equations note that the intense gravity crushes the stuff that itself is responsible for that gravity down to a point of zero dimensions and hence infinite density.

The essential problem behind this nonsense is that gravity is represented by Einstein’s Theory of General Relativity which is a classical physics smooth continuum phenomenon. That is, you can have this gravitational value, and that gravitational value, and every possible value in-between. However, tiny objects, which is what a singularity is postulated to be, is in the realm of the quantum, which is a non-continuum phenomena. Think of a staircase. You can be on this step, or the next step, but there is no step in-between the two. That is, you can have this value, or that value, but only certain other values in-between. It’s also like money – you can have a five dollar bill, and a ten dollar bill, but not a six and a third dollar bill, or an eight and three-quarters dollar bill, or even a seven or a nine dollar bill. Money and staircases are non-continuum quantum-like; money and staircases are not a smooth continuum like gravity is.  

So, to adequately come to terms with the really real properties of singularities, you need a theory of quantum gravity. Alas, despite the best efforts of thousands of theoretical physicists over many, many decades, no quantum gravity theory to be had. There’s no quantum gravity dice.

So, let’s abandon that theoretical track and go back to common sense predictions.

Either Black Hole singularities, or the Big Bang singularity, are infinitely dense and have zero volume, or they do not. If they do not (and the alternative defies common sense and is IMHO ridiculous), then singularities have a finite volume and can grow in size as more stuff is added on. You have an original tiny singularity with extremely high, but not infinite density. You keep piling stuff onto it. For a while, the density keeps on increasing, but since it can’t become infinite, there will be a point reached where further increases cease. As more and more stuff continues to be piled on, the only other option is that the size of the singularity must grow. The volume increases, and increases and increases. The upshot is that singularities can reach a size where quantum effects become negligible. Or, in other words, singularities can grow to where they aren’t quantum objects anymore, and while theories of quantum gravity might be still be useful in explaining their properties, it’s probably no longer essential. Singularities have entered the realm of classical physics.

One property of singularities I find interesting is that the stuff that eventually forms the singularity isn’t the same sort of stuff that went down the Black Hole’s throat in the first place. There’s been a phase transition of one kind of stuff to another kind of stuff. You’re quite familiar with phase transitions in your day-to-day life. There’s nothing mysterious about the concept. The most common example is steam or water vapour condensing to liquid water condensing or freezing to ice; ice melting to liquid water hence boiling or evaporating into steam or water vapour.  Apart from your division into solid, liquid and gas, there’s also plasma. Now the sort of matter that composes a singularity is probably something else yet again, a phase transition that only extreme gravity can achieve. That such a new state of matter exists is predicted by the following: If you have an ordinary matter star, and if it should happen to collide with an antimatter star, what you get is one hell of a big Ka-Boom; the annihilation of matter/antimatter into pure energy.  However, say your matter star implodes into a Black Hole with singularity. And say your antimatter star implodes into a Black Hole with singularity. Now have these two Black Holes collide. No Ka-Boom results, just a larger Black Hole! 

Dark Energy: The Ultimate Free Lunch

Science is full of surprising discoveries. One that recently won the Nobel Prize in Physics was the discovery that the Universe is not just expanding, but that expansion rate is accelerating. The cause is a mysterious and unexplained ‘dark energy’ which is ever increasing right along with the accelerating Universe. But if the Universe contains all that is and ever will be, where is this extra ‘dark energy’ coming from and is this creation out of nothing a gross violation of the basic laws and principles of physics? If yes, perhaps there’s an even more surprising alternative.

If you toss a ball into the air, there are two basic forces at work acting on the ball (ignoring atmospheric friction or drag of course but one can pretend there’s no atmosphere). There’s the oomph (kinetic) energy you give the ball in the upwards direction; there’s the gravitational force that pulls on the ball in the opposite direction. There are two outcomes. 

If you toss a ball up into the air, you expect just one thing to happen – the ball will go up; the ball will slow down; the ball will stop; the ball will fall back to the ground. Why? Earth‘s gravity, that’s why.

If your name is Hercules and you really toss that ball up into the air, maybe, just maybe, the ball won’t fall back down to the ground. You have given the ball enough oomph energy to overcome, though not avoid, Earth’s gravitational pull. But, even if it doesn’t fall back to ground level, even if it keeps on going up, up and away for all time, it will still be forever slowing down. Why? Earth’s gravity, that’s why.

In both scenarios the oomph you give the ball can never be enough to enable the ball to escape Earth’s gravity entirely. The ball must slow down. That’s because the gravitational pull of the Earth on the ball (and also the ball on the Earth) extends to infinity. At no point does gravity cut out. You can’t escape gravity though your energy oomph can be enough to prevent its domination – the ball doesn’t have to fall back to Earth.

Now, the absolutely one scenario you would never expect, is that if you toss the ball into the air, even if the ball didn’t fall back down to ground level if it was given really lots and lots of oomph, that the ball would somehow not only fail to slow down but would in fact speed up. If you witnessed that you’d suspect that your mind or vision was faulty. The only way the ball could accelerate away from you is if it had some sort of additional, internal energy supply (like a rocket). Since it doesn’t, it can’t.

Now apply that logic to the Universe as a whole. In the beginning the Big Bang (the explosive event of the creation) gave a certain finite amount of oomph to all the bits and pieces that make up the Universe. And thus the Universe is expanding – a standard scenario when you have an explosion. When a bomb explodes, the result is an expansion of bomb-stuff. Now all those bits and pieces have a certain finite amount of gravity. The Universe as a whole therefore has a certain finite amount of gravity.

And so we have a similar contest as per the ball’s oomph and Earth’s gravity. Now, either the combined universal gravity of all those bits and pieces will be enough to overcome the finite amount of oomph provided by the Big Bang, and the Universe, like the ball, will slow down, stop and reverse direction (becoming a contracting Universe) or the oomph will prove greater than all those combined bits and pieces gravity and the Universe will expand forever, though that expansion rate will slow down over time. The expansion rate may never reach zero, but the gravity of the bits and pieces must drag forever and ever on the overall initial oomph. The Universal expansion will slow down, albeit never to zero. Okay, like the ball and the Earth, it’s pretty much one or the other. You, as per the ball and the Earth, wouldn’t expect the expansion rate of the overall Universe to increase. That defies logic, everyday experience and basic physics.

For the Universe to accelerate, it would have to be supplied with extra energy from outside, but the Universe is everything and contains everything, there is no outside, so where can additional energy come from? It can’t, not without violating one of the most basic of all basic fundamental physical principles – you can change one form of energy into another form, but you can’t create energy from nothing. Wouldn’t it be nice to just snap your fingers; wave a magic wand, and presto, your empty gas tank is now full or your cold house is now snug and warm! You don’t get something from nothing! The common phrase is that “there’s no such thing as a free lunch!”

So the fundamental question cosmologists (astronomers who study the Universe as a whole) were interested in finding out was whether the Universe’s expansion rate was slowing down enough to cause the Universe to grind to a halt and then reverse; or not. There was never any question that the expansion rate was slowing down. It was just a question to what order of magnitude and was it enough to ultimately cause a Big Crunch.

And so it came to pass that two competing teams of astronomers embarked on a study to crunch the deceleration rate numbers; answer that question of whether the Universe will eventually cease expanding and undergo a contraction (like that ball falling back down to Earth) or not (like the ball that Hercules tossed). Nobody on either team would have bet a nickel, far less the family farm, that the answer would be none of the above. Somehow or other, the bits and pieces that make up the Universe gave the middle finger to gravity. The unthinkable became thinkable, in fact, it became fact. The Universe’s expansion rate was accelerating; therefore energy must be being created out of nothing to provide that extra gravity-defying oomph; there was such a thing as a free lunch after all! The mysterious and unknown energy source behind this unexpected phenomenon was termed ‘dark energy’.

There’s little to dispute in terms of observational evidence for the existence of ‘dark energy’, or rather the fact that the expansion rate of the Universe is accelerating. Evidence has gone from strength to strength.

This discovery was so great, and so totally unexpected, that the team leaders were awarded the Nobel Prize in Physics (2011) for it. But, it must be pointed out that the recognition was for the discovery, not for the explanation. There is no explanation. You can’t adequately explain a free lunch! You need extra energy oomph to power up the acceleration rate of the Universe just like you need an extra surge of gasoline to accelerate your car. Where does that extra energy come from and keep on keeping on coming on from? Just calling that addition source ‘dark energy’ provides no explanation for the free lunch it is. There is a fundamental problem here.

How so a free lunch? Well if I have my facts right, the way ‘dark energy’ works is this. Dark energy is an intrinsic property of space that exerts a pressure that causes that space to expand, which in turn creates new space which has ‘dark energy’ as an intrinsic property which results in that space expanding thus creating more space and thus more ‘dark energy’ and so on and so on. More space means more ‘dark energy’ which means more space, etc. It’s creation out of nothing, or, it’s a free lunch. Now this notion of an expanding space alone puts me at odds with the establishment of modern cosmology. We part company here since I remain convinced the Universe is expanding through existing space. But that still leaves the acceleration rate to the expanding Universe, even if through existing space, as an anomaly.

From the Oxford Companion to Cosmology (2008) we have this snippet: “The simplest dark energy model is the cosmological constant*, which maintains a fixed density as the Universe expands. … Thus far the cosmological constant has proven capable of explaining all relevant observational data, and thus is the chosen ingredient of the standard cosmological model.”

What’s wrong with this statement? It postulates a free lunch, that’s what.

Let’s drop down a notch in scale and look at something more familiar.

To illustrate, take a pure ice cube which has a density slightly less than the pure fresh water from which it came (which is why ice cubes float in water). Say the ice cube is one inch by one inch by one inch or one cubic inch in volume. Now double the dimensions to two inches by two inches by two inches. The ice cube is now eight cubic inches in volume. The ice cube has expanded in volume -so far so good. The density of the ice cube hasn’t changed, so you have to account for the creation of the extra seven cubic inches of ice. If you can’t account for the additional seven cubic inches then something is amiss. The alternative is that the original ice cube has expanded, but no additional ice has been added, so the density of the ice cube has decreased – same amount of ice but spread over a greater volume. But that’s equally screwy. You can’t change the density of ice and still have ice. Density is a fixed parameter of the substance we call ice.

Now change the ice to water vapour and you can alter the parameters. One cubic inch of water vapour can expand to eight cubic inches of water vapour. If you don’t add extra water vapour then the density of your original cubic inch of water vapour obviously decreases in the expansion. You have less water molecules per unit of volume than you had originally. Now the Universe is like water vapour. The Universe is not one solid lump like our ice cube; rather it’s zillions of bits and pieces (like water molecules) that occupy and spread throughout an ever expanding volume. The same amount of stuff expanded into a greater volume means of necessity less density. Any high school student knows that.

You cannot have the concept of density without also talking about the density of a something (like the cosmological constant). It’s meaningless to talk about the density of nothing. That something could be matter, energy or more likely a mixture of both since it’s hard to conceive of energy-less matter or matter in an energy-less state. In fact it’s physically impossible.

But note the Oxford phrase above: “the cosmological constant, which maintains a fixed density as the Universe expands” - something’s screwy somewhere.

If we can’t accept creation of this mysterious cosmological constant ‘dark energy’ out of nothing, whatever is driving the accelerating expansion of the Universe (call it ‘dark energy’ if you must) must also be getting thinner and thinner on the ground, but that would be like easing your foot off the accelerator pedal of your car. You car would cease to accelerate and ease back to a constant velocity (in Universe terms a steady expansion rate) or a deceleration (which is what our two teams of cosmologists were trying to measure in the first place). So it’s a Catch-22. We can’t have creation out of nothing (a free lunch) – that is just not acceptable - but without it you can’t have an expanding and ever accelerating Universe which has been experimentally observed.

I used to think that ‘dark energy’ must be a variation on the theme of the vacuum energy, but I couldn’t figure out how to get a free lunch out of the vacuum energy. For the perplexed, the vacuum energy just means that even when you seemingly have nothing, a vacuum, you still have some energy present. Translated, you can’t have an absolute state of nothingness which would be a theoretical temperature of absolute zero. At the micro or quantum scale, since energy and mass are equivalent (Einstein’s famous equation), energy can be converted to mass  – usually a pair of matter-antimatter particles, which annihilate each other quick-smart returning the energy back to the environment that created them in the first place. Mass can be converted to energy. There’s no free lunch. Conservation laws and principles rule the vacuum energy roost.

Has the Universe always been expanding at an ever accelerating rate? No. There are two competing forces at work. Gravity, a pull force, and this ‘dark energy’, a kind of antigravity or push force. Over time, so the story goes, the amount of ‘dark energy’ increases as space expands. But gravity doesn’t increase. The amount of gravity the Universe has now is the amount the Universe had way back when. At the start gravity was king of the hill because there wasn’t that much space, therefore that much ‘dark energy’. However, with every passing second the amount of ‘dark energy’ increased until it finally overran gravity which was standing still or constant. At that point of intersection the acceleration began in earnest. Apparently that was some five or so billion years ago. Prior to that, the Universe was expanding but at a decelerating rate.

There are two related offshoots to this ‘dark energy’ puzzlement. One is the Big Bang itself. Now the standard cosmological model has it that the Big Bang took place in a small space; a very, very, very small space. In fact the space available was something atomic sized. You couldn’t even see our Universe with the unaided eye a micro-second prior to the Big Bang Ka-Boom it was that tiny, yet anything and everything that exists today, existed then in that tiny volume. Now the problem is that when you try to figure out the state of play with the mass of the Universe (gravity) crushed down to the size of an atom, (the realm of the quantum), the equations break down. You have no idea what the state of play was. In a broader context, the physics of gravity (general relativity) cannot be reconciled with the physics of the quantum. Thousand have tried over many decades. They were just banging their heads against a brick wall. To this day, nobody can fit the hand of gravity into the glove of quantum physics. The way I like to put it is that you apparently have two different and incompatible sets of physics software running the cosmos. That’s nuts! That too needs an explanation.

The other – well there’s an awful lot of Universe for just little old us, and an awful lot more was created (that accelerating Universe) in the time it took you to read that. It’s like having a flea housed in Buckingham Palace that’s adding additional rooms on at a rapid rate of knots. For the flea, it’s a lot of wasted space. There’s an awful lot of just about empty space between the planets; between the stars; between the galaxies; between clusters of galaxies, etc. Why do we, and any other extraterrestrial life forms that may exist, need with so much empty space and pretty much worthless real estate, nearly all of which we can’t even reach? That’s nuts. That needs an explanation, like maybe most of the Universe is just visual holographic wallpaper and has no more reality than the images on your bedroom wallpaper. Is the Universe in fact just a simulation; a virtual reality?   

The way to befuddle an artificially (simulated) intelligent ‘life’ form is to give it an unsolvable problem like dividing a number by zero; calculating the square root of a negative number; coming up with the definitive final value of Pi; or solving an unsolvable paradox like something that both is and is not at the same time; how many angels can dance on the head of a pin; or create a spherical cube. The possibilities are numerous and it’s been used many a time in sci-fi plots to demonstrate the superiority of wetware (brains) over software (silicon chips).

But what if we weren’t wetware (any more than the characters in your dreams are), but in reality software – say a simulated being – an artificial intelligence being given unsolvable puzzles to solve like quantum gravity; why is there so much Universe; why are all electrons identical; why ghosts; and how come crop circles; how can dragons and griffins be real creatures without any fossil remains; and how can a viable breeding herd of lake ‘monsters’ exist in Loch Ness for so long without absolute verification, along with other anomalies that make no apparent sense, like why the expansion rate of the Universe is accelerating.

Conclusion: There’s no disputing the observations that the expansion rate of the Universe is accelerating. While that appears to be wildly improbable, a violation of natural law, that is creation from nothing – a free lunch in other words – it’s not difficult to do as a simulation. So, do we live in a simulated Universe as virtual beings?

*The cosmological constant was a concept invented by Einstein. He knew that the Universe should be contracting under its mutual gravity yet he and nearly everyone else knew (or assumed) that the Universe was static. So he needed a constant outward pressure (the cosmological constant) to balance gravity just-so to enable the Universe to be static – unchanging. So, when Einstein learned, along with the rest of the world later on down the track that the Universe wasn’t static but expanding, he called his ad hoc cosmological constant mechanism the greatest blunder of his career in science. However, the concept, though dormant post-Einstein, has never been too far from the minds of those who could resurrect it in a flash if it served their purpose, like explaining the accelerating expansion rate.

The Big Bang’s Tiny Pinprick

Did our massive Universe start off as just a tiny pinprick in size? That’s what the standard cosmological model would have you believe. But to paraphrase a well known Gershwin song from the American opera “Porgy and Bess”, ‘those things that you’re libel, to read in Cosmology’s bible, well it ain’t necessarily so’.

  

Recently, a well known physical scientist made the following comment in an article he wrote: “Everyone knows about the Big Bang. (Well, almost everyone. I receive several e-mails a month from people who simply cannot believe that all existence began as a tiny pinprick).” I took certain umbrage at that since it seemed to imply that if you didn’t accept the ‘tiny pinprick’ you were scientifically illiterate and that the Big Bang (as a tiny pinprick) event was somehow set in stone.  

So I sent him one more email to add to his collection that disputes the ‘tiny pinprick’ version of the Big Bang.

But first, that standard model of the Big Bang suggests that the origin of our Universe was such that not only was all matter and related energy created at that point in time, but that time and space itself were created then. First there was nothing; then there was something; and the transition between the two was something akin to a pinprick of stuff in size popping out of the never-never that rapidly expanded until, 13.7 billion years later the Universe is the now massive size that it is with all the stuff that it contains.

However, I’ll first note that this standard model of cosmology’s origin of our Universe, the Big Bang event (as a tiny pinprick), isn’t universally accepted by all cosmologists. There are many variations on the Big Bang ‘tiny pinprick’ origin theme, from two branes colliding (technically called the Ekpyrotic Universe which is the string theory version – and it’s hardly a pinprick scenario); to an origin via quantum fluctuations arising out of the vacuum energy (which is an alternative pinprick scenario); variations of the Steady State theory of cosmology still kick around which postulates our Universe had no beginning and will have no end (obviously no pinprick there); to (and this is my favorite) the contraction of a previous universe that resulted in a Big Crunch which so warped space and time that the contraction inverted itself back into an expansion and thus kick-starting our Universe (which also wouldn’t be a pinprick event IMHO). So, I sort of object when the standard pinprick model Big Bang event is put forth by people (such as the above physical scientist) as something set in concrete.

As to that pinprick itself, take a tiny pinprick (equivalent to the physics term ‘quantum’) object of very high, but finite density (on the grounds that it is ridiculous to have a zero dimensional object with infinite density – say a Black Hole’s singularity as so often portrayed, but equally applicable to the standard Big Bang concept). If you keep adding stuff to a pinprick sized singularity, the volume might remain constant for a while, while the density keeps increasing, but because density can not ever equal infinity, that progression has to stop somewhere. When it does, the volume of the pinprick singularity has to increase and eventually increase beyond the realm of the pinprick sized that equates to all things quantum. The proof of that pudding as if any were needed is that, if you add stuff to a Black Hole (with its three dimensional ‘solid’ singularity centre and finite density) you get a bigger Black Hole. The singularity inside must have grown a bit. If it keeps on growing, it will eventually grow past the realm of the pinprick quantum. Anyway, it’s that ‘beyond the realm of the quantum’ that I see as the real Big Bang ‘singularity’ or whatever you wish to call it (to be honest I still like the term coined by Ralph Alpher and  George Gamow in the late 40’s  - ‘Ylem’ – their term for the sort of cosmic egg our Universe started out from).

Now cosmologists can’t observe any closer back in time than to about 380,000 years after the Big Bang event. It’s only then that electromagnetic radiation (i.e. – that which enables us to observe) was able to escape through the expanding and cooling plasma soup, in much the same way that a photon (the particle associated with electromagnetic radiation) at the core of our Sun takes a very, very long time to work its way up to the Sun’s surface, but once there, it shoots off into space quick-smart. Thus, as far as cosmologists are concerned, anything prior to 380,000 years post Big Bang is beyond the realm of observation and hence pure theory – mathematical equations that may have bugger all to do with an accurate reflection of what’s what. 

The General Relativity equations that govern the Big Bang event break down at the presumed pinprick quantum level. Or, the equations covering quantum pinprick sized events break down under extreme gravity; two sides of the same coin. That’s because General Relativity covers gravity, and gravity is a continuous force. That is, you can have this value of gravity, or that value of gravity, and all values in-between. However, pinprick sized quantum events are not continuous. You can have this value, or that value, but only selected values in-between, if any. A useful analogy is a book. You have the first page, through to say page 100, but while you can have page 50, you can’t have page 49.5 or page 50.1 or page 99.9. Put another way, when it comes to gravity, you can be half-pregnant; in quantum physics, it’s either this or that, no half-pregnancies allowed.

Translated, gravity and pinprick quantum events can not be meshed. What ones needs is a theory of quantum gravity to adequately come to terms with the sort of extreme gravitational conditions coupled with the extremely tiny sizes that the standard model of cosmology puts forth. Alas, there is no theory yet to hand of quantum gravity despite the best efforts over many decades by the finest intellects in theoretical physics. So, there’s no actual meshing between the quantum and gravity and thus I suggest perhaps that in actual reality, gravitational (General Relativity) and quantum equations, well they break down well in advance of the extreme Big Bang conditions so postulated by the standard model, losing all semblance of accuracy. Equations are ultimately theoretical representations and don’t always reflect Mother Nature’s reality, especially when they push the boundaries of the envelope, and the conditions postulated at the time of the Big Bang certainly do push the envelope. 

As to those theoretical equations, General Relativity, quantum or otherwise, and the faith some physical scientists put in them, well let’s just point out that the history of physics is littered with discrepancies between theory (the equations) and reality (the observations). An obvious example is the value of the vacuum energy – theory has it as 120 orders of magnitude greater than experimental observation! You don’t have to understand the ins and outs of what the vacuum energy is; the important point is the massive discrepancy between the equations and the reality.  Then there was the ‘ultraviolet catastrophe’ where classical equations totally failed to explain certain phenomena by their prediction of logically absolute nonsense, which ultimately resulted questioning those classical equations resulting in the beginnings of the transition of classical physics to quantum mechanics in order to come to terms with that classical failure. But, speaking of quantum mechanics, that field is also full of sleight-of-hand parlor tricks like renormalization to deal with the many variations of infinities that kept cropping up in the solutions to the newly formed quantum equations.  You could fill entire books on things that were once considered impossible because the equations said so, yet are now commonplace, like breaking the sound barrier. So, I just don’t put that much faith in what equations predict in the absence of any observational backup.

Now the evidence for a Big Bang event (which happened way before anyone was around to actually observe it and take measurements) rests with observations billions of years after the fact. Observations strongly suggest that our Universe is expanding. It is increasing in volume. So, what happens when you run the expanding Universe clock backwards? The Universe would be getting smaller and smaller. Take that to its logical extreme and you end up with the Universe having to start out as a massive (extreme gravity) object crammed down to a pinprick in size. But, should one take that running the clock backwards to such an extreme, or should one stop well short of that?

Now by analogy, one can think of blowing up a balloon and calculate the expanding mathematical relationships. Then one can run those equations backward – a contracting balloon. But it would be wrong to extrapolate backwards to where the contracting balloon becomes a dimensionless point (or at least a quantum sized tiny pinprick), though you could have of course done it – in theory. But, it would be a case of where theory wouldn’t reflect reality.

One obvious standard model proof-of-the-pudding tactic is to try to get closer than 380,000 years after the actual time of the Big Bang event in order to sort out what’s what. Now the detection of gravitational waves could narrow that post Big Bang interval to a time way closer to the event itself. However, the technical challenges are quite considerable and downright daunting. While that hasn’t stopped scientists from trying to detect the gravitational waves that would have been part and parcel of the Big Bang event, translated, don’t hold your breath waiting for immediate results, but please do stay tuned. 

One other bit of evidence that points towards the relatively pinprick micro-origin to our Universe is the concept of ‘inflation’ – that’s a super-sudden ultra-extra expansion oomph to our Big Bang event. While that concept of ‘inflation’ helps solve many cosmological problems, from magnetic monopoles (the lack thereof) to the overall flatness of the cosmos,  some cosmologists consider ‘inflation’ a bit of an ad hoc add-on, and also that there is no such thing as THE inflation model, rather there are several versions floating around, each with their own champions. Thus, ‘inflation’ is not proof-positive that the standard model is the be-all-and-end-all. If it were, the textbooks would be definitive and cosmologists would be out of a job. The textbooks are not definitive and cosmologists remain gainfully employed. The standard model of the pinprick Big Bang remains the leading contender, but it’s not the only game in town. I’m playing a different game!

Personally I think that anyone who believes based on pure abstract mathematical theory that the observable universe, far less our entire Universe can be squeezed into a volume or space that’s atomic sized or less (i.e. – that pinprick) is living in cloud cuckoo-land. Now readers well versed in cosmology have got to believe what they’ve got to believe, but I see no compelling evidence that the Big Bang was an actual quantum pinprick event. It was far more likely to have been, IMHO, a macro event. So, if you don’t go along with the pinprick model, I personally don’t consider you scientifically illiterate.

In summation, the origin of the Universe is still a very fluid one and I’ll bet dimes to donuts that any similarity between a cosmology textbook published in 2011 will be not only be out of date by 2031, but be viewed as quaintly as Lowell’s books on the canals of Mars are today.

Infinities, Like Diamonds, Are Forever

I get rather irritated by the rather loose use of ‘infinity’ by physicists and science writers. At least I assume its ‘loose’ as I can see very few cases where an actual infinity can exist, other than in cases of mathematical abstractions, puzzles and paradoxes. I really assume they mean in most cases ultra tiny or extremely large, and not literally infinity as in infinitely large or small. Let’s examine the case for infinity applying to time, temperature, space or volume, density, velocity, matter and energy, and gravity.

“Ben Casey” was one of the better known and more profound of dramatic TV shows.  The introduction to each episode went as follows: “Man – Woman – Birth – Death – Infinity”. Well, of course the use of the word ‘infinity’ applies only as long as man and woman get their act together, which, in all probability, won’t really be forever and ever, amen. But what you can forgive in a TV show isn’t in the same league when infinity is misused by those who should know better.

Infinity, at one end of the scale, is akin to forever and ever, amen. There is no end; there is no limit. On the other end of the scale is something more familiar to us – zero. Zero is infinitely small. So, what of the various concepts that surround us in our life, our Universe, and in our everything – can they be infinite?

Time: Time apparently comes in quantum sized bits. That is, you can’t have an interval of zero time. The smallest allowable time span, while incredibly short, isn’t zero, and is known as a Planck-Wheeler time unit. Can time be infinitely long? As long as there is change, there is time (which is rate of change), and as long as there is quantum activity in the vacuum energy there is change. That just means that if you had the ability to magnify the microscopic by many orders of magnitude, right down to the quantum level, you’d witness constant activity as virtual particles get created out of the vacuum energy and ultimately annihilate and return their borrowed energy required for their creation back to the vacuum energy.

If our Universe had a beginning, which apparently it did (the Big Bang event) and should our Universe finally stop expanding and reverse direction and ultimately all come together in the mother of all Black Holes and go ‘poof’, then clearly time, as far as our Universe is concerned, is finite, time sandwiched between the Alpha and the Omega. But, if our Universe has always been and always will be (as it would be in the ‘Steady State’ model of our Universe), or if our Universe continues to expand, ever expand, and expand some more without end, or if our Universe is one of an endless number, a cyclic or oscillating Universe that goes boom, expands, stops, contracts, goes ‘poof’, but the ‘poof’ creates another bang, etc. then time is infinitely long, even if our Universe exists for a finite segment within that infinity.

Temperature: Despite reading a comment in one of the books by the renowned astrophysicist Stephen Hawking that at the time of the Big Bang event, the temperature of the embryo Universe was infinite, you can not have an infinitely hot temperature. Temperature is the measurement of the average motion of matter’s particles. The faster they move or vibrate, the hotter things are. So, infinitely hot would imply that matter, or rather the fundamental particles that make up matter, were moving infinitely fast. But infinitely fast would mean faster than the speed of light, which is a no-no. If the Universe started off with an infinitely high temperature, then no matter how much the Universe expanded, it would remain at an infinitely high temperature, because any infinity that’s diluted, divided by a finite number, is still infinity. Since our Universe isn’t currently infinitely hot, it couldn’t have been infinitely hot at anytime in the past. 

An infinitely small temperature would have to be absolute zero of course. However, absolute zero is unobtainable again because of quantum fluctuations in the vacuum energy. In physics, the lowest possible energy state isn’t ever zero because that would violate the Heisenberg Uncertainty Principle which states that it is fundamentally impossible to know both the exact location and the precise velocity simultaneously. At absolute zero, the particle wouldn’t have any motion; thus its location and its velocity would be precisely known. That’s not allowed. Since the Universe has an overall finite temperature, as it expands, it continues to cool. But, no matter how much the Universe expands, it can’t cool down to absolutely nothing.

Space or Volume: If there was a Big Bang event, a location in space and time where our Universe is defined as having a beginning, then clearly the Universe had then, has now, and will always have a finite size, albeit expanding, ever expanding. Of course, if it keeps expanding for an infinite amount of time, then after an infinite amount of time our Universe would have an infinite volume. It’s also possible that our Universe, itself finite in volume, could exist in a larger infinite sea of space. In contrast to the Big Bang scenario, a rival theory, the ‘Steady State’ type of universe where new matter is constantly being created, could be infinite in volume. As new matter is constantly being created, assuming the ‘Steady State’ universe has always been and always will be, it would need infinite space to accommodate it all. Alas, the ‘Steady State’ theory hasn’t been viable, except to a few never-say-die true believers, for decades. However, there could be a Multiverse that could, in theory, be comprised of an infinite number of individual universes, of which our Universe is but one, in which case the Multiverse space or volume would have to be infinite. A finite Multiverse (a finite number of universes) wouldn’t need an infinite amount of space, but that doesn’t preclude a finite Multiverse existing within an infinite amount of space.

Density: Density can not be infinitely small – zero – because of quantum fluctuations in the vacuum energy. Virtual particles are always popping into and out of existence in the vacuum energy. As long as you have ‘stuff’ you must have density. The concept of absolutely nothing would have zero density, but it’s not possible to achieve a state of absolutely nothing.

Density on the other end of the scale can not be infinitely large, as is frequently claimed for Black Hole singularities or the state of the Universe at the time of the Big Bang event. You’d need infinite mass to achieve infinite density and clearly neither a Black Hole, nor our Universe has infinite mass. It would also seemingly have an infinite amount of energy to expand a Universe from a singularity point of presumed infinite density, and since there isn’t an infinite amount of mass in our Universe, there can’t be an infinite amount of energy, as matter and energy are two sides of the same coin as per Einstein’s most famous equation. It’s often stated in more colourful language that mass is just frozen energy. 

Either the Big Bang event singularity (and Black Hole singularities by analogy) was infinitely dense and had zero volume, or it was not. If they (Big Bang and Black Hole singularities) do not have infinite densities and zero volumes (and the alternative are really quite ridiculous), then singularities have a finite density and a finite volume and can grow in size as more stuff is added on. The upshot is that singularities can reach a size where quantum effects are negligible. Or, in other words, singularities aren’t of necessity quantum objects. To explain the importance here is that in the realm of the singularity as is currently accepted, one needs both the classical physics of gravity, and the quantum physics of the microscopic, to adequately describe the properties of any singularity. Unfortunately, there’s as of yet, no accepted theory of quantum gravity. Despite the lack of a theory of quantum gravity, you will usually read that the Big Bang event started off as an infinitely dense object of zero dimensions – a singularity. The origin of our Universe was a quantum event since the size of the singularity was within the realm of the quantum. I maintain that while as one extrapolates backwards in time towards the Big Bang event, the Universe gets smaller and smaller, it does not even reach the stage where the Universe becomes so tiny that for all practical purposes it has infinite density (that’s where the gravity comes in) and zero volume (where quantum physics rule).   

Velocity: Velocity can of course appear to be infinitely small – zero – but only relative to some other object. You may be standing still relative to the Earth’s surface, but the Earth is rotating on its axis and revolving around the sun, which in turn is moving relative to other stars, etc. However, at the quantum level, those quantum fluctuations, the quantum jitters, that never ending seething activity in the vacuum energy, means that even a rock stilling apparently still on the ground is actually vibrating. In addition, the rock is expanding and contracting as the daily temperature waxes and wanes. So, appearances are deceiving here. You can’t in fact have zero velocity, and in fact having an absolute zero velocity again violates the Heisenberg Uncertainty Principle. The closest you could achieve is a thought experiment where the Universe consists of one, and only one elementary particle. There’s nothing else to measure its velocity relative to, well, something else – there is no something else.   

Velocity can’t be infinitely fast as you’d have to break the light speed barrier. On the other hand, you can travel faster than the speed of light (superluminal) if that was your natural state to begin with, but hypothetical faster-than-light particles (tachyons) haven’t ever been detected, and there is no reason to believe they would travel infinitely fast even if they did exist. Anything that travelled infinitely fast in a finite Universe would be everywhere in every Planck-Wheeler unit of time. Translated, the entire Universe could consist of just one particle!

Matter and Energy: Since matter equals energy, and energy equals matter, by considering one, we consider both. Temperature is a form of energy, and we’ve already seen that temperature can neither be infinitely large nor small (zero). Further, one can’t have an infinite amount of matter without an infinite amount of space to put it in. Since we take stock in the Big Bang model of our Universe, and since that model dictates a finite volume, albeit an expanding one, it’s still finite and so the matter contained within must be finite, and therefore so is the energy content of the Universe.

And you can’t have zero matter and/or energy for reasons which should be pretty apparent by now.

Gravity: Although gravity is the weakest of the four known physical forces, it most certainly acts over long distances. Even though the pull of gravity weakens with increasing distance, it never reaches the infinitely minimum – zero. As long as there is so much as two fundamental bits of matter in the Universe, gravity will never equal zero. It’s probably nonsense to talk of gravity if there was only one elementary particle in the cosmos, since gravity is an attractive force between two or more bits of matter.

Further, because it is the amount of matter in our Universe which determines the overall gravitational quota of the Universe, and because that amount of matter is finite, that quota of gravity must be finite, even if all that matter were lumped together at one time and in one place.

Further reading in infinities:

Barrow, John D.; The Infinite Book: A Short Guide to the Boundless, Timeless and Endless; Vintage, London; 2005:

Clegg, Brian; Infinity: The Quest to Think the Unthinkable; Carroll & Graf, N.Y.; 2003: