Energy of the Vacuum Black Hole Artwork: NaturPhilosophie with AI

Zero Point Energy and The Vacuum of Space

Zero Point Energy - The Energy of the Vacuum and Black Holes Artwork: NaturPhilosophie with AIAccording to whom you ask, Zero Point Energy can do everything… or nothing at all.  But what is it?  Something that pervades all of space, albeit on a microscale?  The kinetic energy a molecule does retain, even when cooled down to absolute zero?  And could it offer us a source of unlimited energy? 

A Dive into Quantum Mechanics

To begin to understand the concept of Zero Point Energy (ZPE) or vacuum energy, we need to use a bit of Quantum Mechanics.

First of all, it would appear that our Universe has its very own equivalents in the way of minimum sized building blocks.

The kind of matter you cannot cut down any further.

The stuff that is no longer divisible.

Indivisible, Divisible…

No longer divisible.

That is what the Ancient Greeks precisely meant by ‘atomos’.

The hydrogen atom, photographed in 2013 by AMOLF (The Netherlands)

Although as it happened, some time later, it turned out that scientists discovered that you could divide an atom into protons, neutrons and electrons.

Later still, they discovered that those protons and neutrons could in fact be divided further down into another category of particles, the quarks.

Anyway, currently, physicists believe these are the fundamental particles that make the Universe.  And that is that…

They believe electrons and quarks are not divisible.

Although many theories out there contemplate even smaller units, and even more fundamental particles beneath those.

Uncertainties in Measurements

A humoristic cartoon showing a character looking at a map of Heisenberg Department of Physics. The map points to a dot and the legend reads "You Are Probably Here." Cartoon: ChaseIn Quantum Mechanics, the most basic and indivisible thing is not simply one thing.

Rather, it always comes as a pair of complementary attributes.

If you’ve heard about Heisenberg’s Uncertainty Principle, you already know that we can measure the momentum (or speed) of a particle or what its position is, at the same time, with only so much certainty:

\Delta x \Delta p \ge \frac{h} {4 \pi}

For instance…  Say you want to measure the speed and location of an object.  You can only do this as well as your instruments will allow.

Assuming your stopwatch and ruler are only accurate up to a second and up to a millimeter, respectively, you know you can only get so accurate in your measurements with those devices.

Reducing the minimum uncertainty in a physical measurement, with an ultra accurate ruler and an ultra accurate stopwatch. Artwork: NaturPhilosophie with AIIf you want to reduce the uncertainty of a value and obtain a better, more precise measurement, you will need to buy a more expensive and more accurate apparatus.

On a limited budget, however, buying a more accurate ruler means you will have to contend with a cheaper stopwatch, or vice versa.

The uncertainty is the accuracy of the measurement.

It is a boundary to our knowledge – a boundary beyond which science cannot go.

Conjugate Pairs

The uncertainty is not based on the size or the energy of the particle.  Rather, it is based on the product of the two attributes which are conjugate pairs.

Like momentum and position.

When it comes to the Uncertainty Principle, it is as if the Universe afforded us a minimum uncertainty for measuring these two paired attributes (speed and position).

And this represents a type of fundamental value.

Planck Constant, a Fundamental Value

An infographic explaining Planck's Constant That minimum value is Planck’s constant, aka h, expressed in terms of

energy \times frequency ,

mass \times speed \times position

 The same value works for a number of other paired quantities, like

energy \times time

Consequently, we can only know so accurately how much energy a particle has, by sacrificing how accurately we can time it.

Motorway Parable Artwork: NaturPhilosophie with AI
People don’t live on motorways, they live in cities. But vehicles with one or more passengers do drive through motorways connecting cities, so motorways only have people on it at specific locations or specific times, but they are not always strictly-speaking ’empty’ of people. The same idea goes for particles, even in the most vacuuous parts of the Universe…

As a result of this head-scratching state of affairs, we cannot ever say for sure that the position measurement of a particle is zero.

Even if nothing is there, there is always that uncertain value of energy at any given instant.

A bit like a motorway has no permanent residents, and yet a lot of traffic always circulates through it.

Classical Physics and Absolute Zero

Classical Physics predicts the presence of Zero Point Energy (ZPE), and here we look at the notion of Absolute Zero.

An animation showing the random nature of the motion of particles in an ideal gas.
In an ideal gas, the motion pattern of particles typically consists of random fluctuations in a particle’s position inside a fluid sub-domain, called the Brownian motion. (Animation: Wikipedia)

The kinetic theory of gases is a simple classical model of the thermodynamic behaviour of gases.

It treats a gas as being composed of numerous particles, too small to see even with a microscope, which are constantly in random motion.  Their collisions with each other and with the walls of their container are used to explain physical properties of the gas.  For example, the relationship between its temperature, pressure and volume.

Brownian Motion: The 2D random walk of a gas particle  Note. Real gas molecules can move in all directions, not just to neighbors like on a chessboard.  Source: MIT

Heat and temperature indicate the random kinetic motion of particles inside a system.

Theoretically, we can cool things down by leaching all that random motion out of it.

If you leach it all out, your system will be at Absolute Zero, which is -273 °Celsius or -460 Farenheit, or simply 0 K using the absolute Kelvin scale.

Scientific experiments have involved cooling helium to temperatures of less than a billionth of a Kelvin, using laser cooling, although reaching the limit of Absolute Zero has not yet been achieved.

Nevertheless, it is this residual energy that is known as the Zero Point Energy, and it is a direct consequence of the Uncertainty Principle.

Is Zero Point Energy the kinetic energy a molecule somehow retains even at a temperature of 0 K?

Absolute Zero has weird theoretical properties, like that of having no entropy.

Of course, that notion seems to fly in the face of Heisenberg’s Uncertainty Principle, because if your particle had no energy, no momentum, then it would follow that we cannot tell where it is.  It would have no position, or vice-versa.

(Let’s be honest, we’re not too sure about the photon…)

The key to the Uncertainty Principle is to embrace its sheer nebulousness.

According to Quantum Mechanics, the particle truly was in all those possible foggy positions until the very act of its observation or measurement collapses it into a more certain state.  Again, this is not just valid for position and momentum, but for any of those conjugate pairs we discussed.

That is the weird thing about the Quantum World.  The really SHOCKING thing about Quantum Mechanics!

Zero Point Energy

In this context, we must get used to the idea the uncertainty is real – a fundamental universal minimum, not something that derives primarily from our own observational limitations.

Zero Point Energy gets its name after Absolute Zero – the lowest temperature point at which the enthalpy and entropy of a cooled ideal gas attain their minimum values – and the idea that even perfectly frozen atoms retain some kinetic motion, and thus energy.

Nature abhors a vacuum.
Horror vacui.

Random Fluctuations on a Hypothetical Sea of Virtual Particles - Dirac Sea Artwork: NaturPhilosophie with AIWe could apply this to all sorts of energetic phenomena with fluctuating fields, and call this zero-point, which is where vacuum energy comes from.

Things are not what they seem.

We could imagine the Zero Point Energy field (ZPF) as an endlessly large sea where we, and all the matter around us, are submerged.  Physicists call it the “physical vacuum”.  Yet, it’s anything but a void.

The Zero Point Energy represents a sharing of the uncertainty in position and in momentum.  The energy associated with the uncertainty in momentum gives the Zero Point Energy.

The Physical Vacuum of Space

Space is rich in activity and full of energy.

Even in the emptiest recesses of space, far far away from any planet or even any galaxy, with only one hydrogen atom per cubic metre, there are still billions of photons and neutrinos pouring through it at any moment in time.  (Remember the motorway junction analogy?)  In other words, it’s not a real vacuum.

Vacuum fluctuations are predicted by Quantum Mechanics – a branch of Physics started by Bohr, Einstein and Heisenberg.  Space perpertually vibrates and “fluctuates”.

Space is quantized and virtual or temporary particles are plentiful.

Virtual Particles and Quantum Fluctuations

These virtual particles, popping in and out of existence all the time, are important because they are what you and I, and everything else around us, are mostly made of.

An animated computer model showing the theoretically predicted quantum fluctuations of the physical vacuum.
Vacuum fluctuations are already predicted by classical theory. Source: Wikipedia

Although it is impossible to be certain what spacetime looks like at very small scales, there is no particular reason why its distribution should be entirely smooth.

In a quantum theory of gravity, spacetime would consist of many small, ever-changing regions in which space and time are not definite, but fluctuate in a foam-like manner – the quantum foam.

And again, therein lies the crux of the matter.

As it does turn out, the “vacuum”… is not empty!  And if it’s not devoid of particles, it follows that there must be untapped energy there.

Both theory and experiment agree on that.

Virtual particles are more likely to become real near the boundary of charged particles, or even near the nuclei of atoms.

Those particles often have physical properties that would not normally exist in a stable form.  They pop up in opposite pairs and they annihilate together.

Scientists do not yet understand why.

But it could be said that Zero Point Energy makes up a particle’s atmosphere – a virtual particle cloud.

Turns out Things May Not be Immutable…

Things we think of as constant and immutable at that higher atomic layer of reality, beneath the chemical layer, but above the subatomic particle realm, may not be so constant as we had imagined.

Run-of-the-mill characteristics of particles, like having a positive mass, are no longer guaranteed.  So, you might have a pair of particles that had a positive mass and a negative mass, instead of a positive charge and a negative charge.

Such particles are shifting in and out of existence.

Existing one moment.  Annihilating the next.

Everywhere in the Universe.  All of the time.

A Quick Ripple on a Hypothetical Sea

Think of it as creating small ripples on that sea of virtual particles, with given heights and frequencies.

So, we do not have a complete absence of water, just a local negative compared to the norm.

Our reality, the reality we do experience, from the atomic level and above, floats on top of that sea – the Dirac sea.

The Dirac Sea is a theoretical model of the electron vacuum imagined as an infinite sea of electrons with negative energy, or positrons.

A Physics diagram showing the transitions of particles and antiparticles between energy states.
The Dirac sea for a massive particle Source: Wikipedia

It might bob up and down only a few centimetres here or there, at the surface.  But the ocean of space below it is still kilometres deep, and not a vacuum devoid of mass and energy.

Beyond this, our understanding gets into some muddy waters…

And anyway, what does it all have to do with black holes?

Evaporation of Black Holes

The first image of a Black Hole. Image: NASA (2023)
The first ever photograph of a black hole, at the centre of M87 Source: Event Horizon Telescope, NASA (2019)

Now, the question is: Why do black holes lose mass over time… since nothing, not even light, can escape the pull of their gravity?

An essential part to understanding how a black hole loses mass, is to look at its event horizon – a theoretical demarcation between events and their causal relationships.

Basically, black holes can evaporate by losing virtual particles at their event horizon.  This appears to be counter-intuitive because we know that once electromagnetic radiation is inside that event horizon, it cannot escape.

Actually, the bigger the black hole and the bigger the event horizon, the slower this process goes.

The radiation temperature is inversely proportional to the black hole’s mass, so micro black holes are predicted to be larger emitters of radiation than larger ones, and dissipate faster per their mass.

The reason for this is that black holes are not the source of those virtual particles.

As it turns out, OUR own regular old run-of-the-mill spacetime is.

Pair Formations on the Event Horizon

An infographic explaining how Hawking Radiation works at the event horizon of a black hole. Inside the black hole, nothing can escape. At the event horizon, out-in and in-out pairs annihilate outside the black hole, creating two real positive energy photons (and taking the energy out of the black hole via the virtual particles that fall in).
Hawking Radiation explained Source: BlackHoleCam

There is no greater amount of virtual particle pair formation than at the surface of an event horizon.

But tiny black holes with tiny event horizons, have very sharp gradients in gravity, compared to bigger ones.

If one of the particles in the pair is even 1 nanometre (nm, 10-9 m or 1 billionth of a metre) closer to the black hole than its twin, there will be a vastly higher pull of gravity onto it.

What it means is as follows.

Negative Mass and the Pull of Gravity

If two particles pop up, one on each side of the event horizon, one of the particles may fall back inside the black hole.  This particle will have a negative mass.

The negative mass particle is pulled down, while its positive mass twin manages to escape the pull of gravity.

Those particles are thus unable to recombine and annihilate.

At the same time, the black hole loses a little mass.

Most of the time, however, the particles are close enough together to annihilate, even if one of them experiences a stronger gravity pull than its twin.  But the sharper the tidal difference in gravity, the likelier it is to happen.

When one of those virtual particles does not annihilate with the other, it sticks around and becomes real.

Right here is one of the hypothetical ways we could use to extract energy out of the vacuum of space: by letting it get ripped out of black holes.

Hawking Radiation

The Penrose diagram of the evaporating black hole in the vacuum. Source: ResearchGate

Anyway, the process whereby the mass evaporates from a black hole is called Hawking radiation.

As physicist Stephen Hawking theorized in 1974, black holes radiate small numbers of particles – mainly photons.

This process can lead to the black hole shrinking over time, ultimately vanishing completely.

However, it is a staggeringly slow process

Our Sun has a mass of M = 2.0 × 1030 kg.  So, it would take about 1067 years for a black hole of 1 solar mass to evaporate.  A lot longer than the 14 billion years (1.4×1010 years) our Universe has existed!

But for another black hole of 1011 kg, the evaporation time is 2.6×109 years.

In fact, any primordial black hole of sufficiently low mass will evaporate to near the Planck mass within the lifetime of the Universe.

Micro Black Holes

A graph showing the Constraints on the dark matter fraction comprised of primordial black holes of a given mass. Constraints derived with more and less conservative assumptions are shown in dark and light green, respectively. Projected sensitivity for future cosmic probes are shown with green dashed lines. Existing constraints come from the gamma-ray background [70], microlensing observations of M31 with HSC [71, 72], microlensing observations of the Milky Way with MACHO/EROS [73-75], supernovae lensing [76], dynamical heating of dwarf galaxies [77-81], wide binary stars [82, 83], X-ray binaries [84], CMB distortions from accreting plasma in early universe [85, 86], and disk stability constraints [87]. Dashed lines show the projected sensitivity of a Rubin LSST microlensing survey of the Galactic Bulge [19], a dedicated Roman microlensing survey of M31, and a future MeV gamma-ray facility [88, 89]. Figure adapted from [7, 19].
Constraints on the Dark Matter Fraction comprised of Primordial Black Holes of a given mass.  Source: ResearchGate
Micro black holes or primordial black holes are non-baryonic, near collision-less and stable.

They have non-relativistic velocities, and were formed very early on after the Big Bang.

Small black holes emit more radiation and die quicker.

Their radius changes linearly with their mass.

A diagram for the equation of the Schwarzschild radius. Source: HyperPhysicsThis is given by the Schwarzschild radius, which corresponds effectively to the radius of the event horizon of the black hole:

R_{SCH} = \frac{2M_{BH}G}{c^2}

where c is the speed of light.

And according to the equation of Hawking Radiation,

T_H = \frac {\hbar c^3}{8 \pi G k_B M_{BH}}

where ħ is the reduced Planck constant,

G is the gravitational constant,

and kB is the Boltzmann constant.

For example, a protonsized black hole the could give out an extraordinary GigaWatt of power.  And that just there is 109 Watts.

One thousand million Watts!

That kind of gigawatt-powered micro black hole would still weigh an astounding 560 Megatons, and have a lifetime of 480 billion years.  Thirty-five times the age of our Universe as we understand it.

Turns out Size really Does Matter…

A diagram showing the formation of a primordial black hole.
Primordial Black Hole Formation. Source: Wikipedia

The concept of hypothetical tiny black holes was developed by Hawking who conjectured that the minimum mass required for a black hole to form would be about 10-8 kg – a value of the same order of magnitude as Planck’s mass.

Here we are back to the idea of tiny fluctuations in our Universe.

At this scale, the Planck scale, the predictions of the Standard Model, quantum field theory and General Relativity are not expected to apply.

Instead, the effects of Quantum Gravity are expected to dominate.

Between the Devil and the Dirac Sea

'A Small Ripple on the Hypothetical Dirac Sea of Virtual Particles' Artwork: NaturPhilosophie with AIUnder experimentally achievable conditions for gravitational systems, however, the effect is too small to be observed directly.

Indeed Hawking radiation is expected to be so faint as to being many orders of magnitude below our best telescopes’ detecting threshold.

Besides, that is where Einstein’s Relativity runs into Quantum Mechanics, and both theories do not agree.  Astrophysicists are not sure that black holes really are point-like singularities at their core.

We do not know how deep that sea of particles is,
we do not know how dense matter really is.

At some point, the amount of energy radiating out of a black hole at any given instant might rise so high that it peaked, because you could not get any more virtual pairs, popping out of that ever smaller volume, to keep up.

Effectively, the virtual particle well run dry, or the water can only come out so fast.  Still, we don’t know how deep the well is because General Relativity and Quantum Physics do not agree.

The Casimir Effect

So, how do you stick a paddlewheel in this hypothetical ocean of virtual particles and harness its energy?

How can we channel Zero Point Energy to produce electricity?

A newspaper article in the New York Times reports the first confirmation of the Casimir effect in the lab, as discovered by Lamoreaux et al. at Los Alamos (January 21, 1997).The discovery of the Casimir effect was the breakthrough for the mechanical theory of forces.  It was since confirmed many times over in the lab.

Although other phenomena may be attributed to the action of quantum fluctuations, none of them offers such compelling evidence for the existence of ZPE (Zero Point Energy).

In this age of climate upheaval, we often wonder where to find a clean and abundant supply of truly sustainable energy.

The answer might lie in the great emptiness around us.