Tag Archives: Black Holes

Quantum Gravity – Again!

In my previous blogs, I briefly described how the human brain perceives and models space (Oops one more thing), how Einstein and other physicists dismiss space as an illusion (Relativity and space ), how relativity deals with the concept of space (So what IS space?), what a theory of quantum gravity would have to look like (Quantum Gravity Oh my! ), and along the way why the idea of infinity is not physically real (Is infinity real?) and why space is not nothing (Thinking about Nothing).  I even discussed how it is important to ‘think visually’ when trying to model the universe such as the ‘strings’ and ‘loops’ used by physicists as an analog to space (Thinking Visually)

And still these blogs do not exhaust the scope of either the idea of space itself or the research in progress to get to the bottom of our experience of it.

This essay, based on a talk I gave at the Belmont Astronomical Society on October 5, 2017 will try to cover some of these other ideas and approaches that are loosely believed to be a part of a future theory of quantum gravity.

What is quantum gravity?

It is the basic idea that the two great theories of physics, Quantum Mechanics and General Relativity are incompatible with each other and do not actually deal with the same ingredients to the world: space(time) and matter. Quantum gravity is a hypothetical theory that unifies these two great ideas into a single language, revealing answers to some of the deepest questions we know how to ask about the physical world. It truly is the Holy Grail of physics.

Why do we need quantum gravity at all?

Quantum mechanics is a theory that describes matter and fields embedded in a pre-existing spacetime that has no physical effect on these fields other than to provide coordinates for describing where they are in time and space. It is said to be a background-dependent theory. General relativity is only a theory of space(time) and does not describe matter’s essence at all. It describes how matter affects the geometry of spacetime and how spacetime affects the motion of matter, but does so in purely ‘classical’ terms. Most importantly, general relativity says there is no pre-existing spacetime at all. It is called a background-independent theory. Quantum gravity is an overarching background-independent theory that accounts for the quantum nature of matter and also the quantum nature of spacetime at scales where these effects are important, called the Planck scale where the smallest unit of space is 10^-33 cm and the smallest unit of time is 10^-43 seconds.

We need quantum gravity because calculations in quantum mechanics are plagued by ‘infinities’ that come about because QM assumes space(time) is infinitely divisible into smaller units of length. When physical processes and field intensities are summed over smaller and smaller lengths to build up a prediction, the infinitesimally small units lead to infinitely large contributions which ‘blow up’ the calculations unless some mathematical method called ‘renormalization’ is used. But the gravitational field escribed by general relativity cannot be renormalized to eliminate its infinities. Only by placing a lower limit ‘cutoff’ to space(time) as quantum gravity does is this problem eliminated and all calculations become finite.

We need quantum gravity because black holes do not possess infinite entropy. The surface area of a black hole, called its event horizon, is related to its entropy, which is a measure of the amount of information that is contained inside the horizon. A single bit of information is encoded on the horizon as an area 2-Planck lengths squared. According to the holographic principle, the surface of a black hole, its 2-d surface area, encodes all the information found in the encompassed 3-d volume, so that means that the spacetime interior of a black hole has to be quantized and cannot be infinitely divisible otherwise the holographic principle would be invalid and the horizon of the black hole would have to encode an infinite amount of information and have an infinite entropy.

We also need quantum gravity because it is believed that any fundamental theory of our physical world has to be background-independent as general relativity shows that spacetime is. That means that quantum mechanics is currently an incomplete theory because it still requires the scaffolding of a pre-existing spacetime and does not ‘create’ this scaffolding from within itself the way that general relativity does.

So what is the big picture?

Historically, Newton gave us space and time as eternally absolute and fixed prerequisites to our world that were defined once and for all before we even started to describe forces and motion. The second great school of thought at that time was developed by Gottfrid Leibnitz. He said that time and space have no meaning in themselves but only as properties defined by the relationships between bodies. Einstein’s relativity and its experimental vindication has proven that Newton’s Absolute Space and Time are completely false, and replaced them by Leibnitz’s relativity principle. Einstein even said on numerous occasions that space is an imaginary construct that we take for granted in an almost mythical way. Space has no independent existence apart from its emergence out of the relationships between physical bodies. This relationship is so intimate that in general relativity, material bodies define the spacetime geometry itself as a dynamical solution to his famous relativistic equation for gravity.

How does the experience of space emerge?

In general relativity, the only thing that matters are the events along a particle’s worldline, also called its history. These events encode the relationships between bodies, and are created by the intersections of other worldlines from other particles. This network of fundamental worldlines contains all the information you need to describe the global geometry of this network of events and worldlines. It is only the geometry of these worldlines that matters to physical phenomena in the universe.

The wireframe head in this illustration is an analog to worldliness linking together to create a geometry. The black ‘void’ contains no geometric or dimensional information and any points in it do not interact with any worldline that makes up the network. That is why ‘space’ is a myth and the only thing that determine the structure of our 4-d spacetime are the worldliness.

General relativity describes how the geometry of these worldlines creates a 4-dimensional spacetime. These worldlines represent matter particles and general relativity describes how these matter particles create the curvature in the worldlines among the entire system of particles, and thereby creates space and time. The ‘empty’ mathematical points between the worldlines have no physical meaning because they are not connected to events among any of the physical worldlines, which is why Einstein said that the background space in which the worldlines seem to be embedded does not actually exist! When we look out into ‘space’ we are looking along the worldlines of light rays. We are not looking through a pre-existing space. This means we are not seeing ‘things in space’ we are seeing processes in time along a particle’s history!

There are two major quantum gravity theories being worked on today.

String theory says that particles are 1-dimensional loops of ‘something’ that are defined in a 10-dimensional spacetime of which 4 dimensions are the Big Ones we see around us. The others are compact and through their geometric symmetries define the properties of the particles themselves. It is an approach to quantum gravity that has several problems.

 

This figure is an imaginative rendering of a ‘string’.

First it assumes that spacetime already exists for the strings to move within. It is a background-dependent theory in the same spirit as Newton’s Absolute Space and Time. Secondly, string theory is only a theory of matter and its quantum properties at the Planck scales, but in fact the scale of a string depends on a single parameter called the string tension. If the tension is small, then these string ‘loops’ are thousands of times bigger than the Planck scale, and there is no constraint on what the actual value of the tension should be. It is an adjustable parameter.

This figure is an imaginative rendering of a ‘loop’

Loop Quantum Gravity is purely a theory of spacetime and does not treat the matter covered by quantum mechanics. It is a background-independent theory that is able to exactly calculate the answers to many problems in gravitation theory, unlike string theory which has to sneak up on the answers by summing an infinite number of alternate possibilities. LQG arrives at the answer ‘2.0’ in one step as an exact answer while for example string theory has to sum the sequence 1+1/2+1/4+1/8+1/16 +…. To get to 2.000.

LQG works with elementary spacetime ingredients called nodes and edges to create spin networks and spin foam. Like a magnetic field line that carries magnetic flux, these edges act like the field lines to space and carry quantized areas 1 Planck length squared. By summing over the number of nodes in a spin network region, each node carries a quantum unit of space volume. These nodes are related to each other in a network of intersecting lines called a spin network, which for very large networks begins to look like a snapshot of space seen at a specific instant. The change of one network into another is called a spin foam and it is the antecedent to 4-d spacetime. There is no physical meaning to the nodes and edges themselves just as there is no physical meaning to the 1-d loops than make up strings in string theory. . They are pure mathematical constructs.

So far, the best idea is that LQG forms the bedrock for string theory. String theory looks at spacetime and matter far above the Planck scale, and this is where the properties of matter particles make their appearance. LQG creates the background of spacetime that strings move through. However there is a major problem. LQG predicts that the cosmological constant must be negative and small, which is what is astronomically observed, while string theory says that the cosmological constant is large and positive. Also, although LQG can reconstruct the large 4-d spacetime that we live in, it does not seem to have have any room for the additional 6 dimensions required by string theory to create the properties of the particles we observe. One possibility is that these extra dimensions are not space-like at all but merely ‘bookkeeping’ tools that physicists have to use which will eventually be replaced in the future by a fully 4-d theory of strings.

Another approach still in its infancy is Causal Set Theory. Like LQG it is a background-independent theory of spacetime. It starts with a collection of points that are linked together by only one guiding principle, that pairs of points are ordered by cause-and-effect. This defines how these points are ordered in time, but this is the only organizing principle for points in the set. What investigators have found is that such sets create from within themselves the physical concepts of distance and time and lead to relativistic spacetimes. Causal Sets and the nodes in LQG spin networks may be related to each other.

Another exciting discovery that relates to how the elements of quantum spacetime create spacetime involves the Holographic Principle connected with quantum entanglement.

The Holographic Principle states that all the information and relationships found in a 3-d volume are ‘encoded’ on a 2-d surface screen that surrounds this volume. This means that relationships among the surface elements are reflected in the behavior of the interior physics. Recently it was discovered that if you use quantum entanglement to connect two points on the surface, the corresponding points in the interior become linked together as a physical unit. If you turn off the entanglement on the surface the interior points become unconnected and the interior space dissolves into unrelated points. The amount of entanglement can be directly related to how physically close the points are, and so this is how a unified geometry for spacetime inside the 3-d ‘bulk’ can arise from unconnected points linked together by quantum entanglement.

 

Additional Reading:

Exploring Quantum Space  [My book at Amazon.com]

Quantum Entanglement and quantum spacetime [Mark Raamsdonk]

Background-independence  [Lee Smolin]

Holographic Principle [ Jack Ng]

Causal Sets: The self-organizing universe [Scientific American]

 

The First Billion Years

When we think about the Big Bang we tend only to look at the first few instants when we think all of the mysterious and exciting action occurred. But actually, the first BILLION years are the real stars of this story!

My books ‘Eternity:A Users Guide’ and ‘Cosmic History I and II’ provide a more thorough, and ‘twitterized’, timeline of the universe from the Big Bang to the literal end of time if you are interested in the whole story as we know it today. You can also look at a massive computer simulation developed by Harvard and MIT cosmologists in 2014.

What we understand today is not merely based on theoretical expectations. Thanks to specific observations during the last decade, we have actually discovered distant objects that help us probe critical moments during this span of time.

Infancy

By the end of the first 10 minutes after the Big Bang, the universe was filled with a cooling plasma of hydrogen and helium nuclei and electrons – too hot to come together to form neutral atoms at seething temperatures over 100 million Celsius. The traces that we do see of the fireball light from the Big Bang are called the cosmic background radiation, and astronomers have been studying it since the 1960s. Today, the temperature is 2.726 kelvins, but at one part in 100,000 there are irregularities in its temperature across the entire sky detected by the COBE, WMAP and Planck satellites and shown below. These irregularities are the gravitational fingerprints of vast clusters of galaxies that formed in the infant universe after several more billion years.

By 379,000 years, matter had cooled down to the point where electrons could bond with atomic nuclei to form neutral atoms of hydrogen and helium. For the first time in cosmic history, matter could go its own way and no longer be affected by the fireball radiation, which used to blast these assembled atoms apart faster than they could form. If you were living at this time, it would look like you were standing inside the surface of a vast dull-red star steadily fading to black as the universe continued to expand, and the gas steadily cooled over the millennia. No matter where you stood in the universe at this time, all you would see around you is  this dull-red glow across the sky.

6 million years – By this time, the cosmic gas has cooled to the point that its temperature was only 500 kelvins (440 F). At these temperatures, it no longer emits any  visible light. The universe is now fully in what astronomers call The Cosmic Dark Ages. If you were there and looking around, you would see nothing but an inky blackness no matter where you looked! With infrared eyes, however, you would see the cosmos filled by a glow spanning the entire sky.

20 million years – The hydrogen-helium gas that exists all across the universe is starting to feel the gravity effects of dark matter, which has started to form large clumps and vast spiders-web-like networks spanning the entire cosmos, with a mass of several trillion times the mass of our sun. As the cold, primordial gas falls into these gravity wells, it forms what will later become the halos of modern-day galaxies. All of this hidden under a cloak of complete darkness because there was as yet no physical objects in existence to light things up. Only detailed supercomputer simulations can reveal what occurred during this time.

The First Stars

100 million years – Once the universe got cold enough, large gas clouds stopped being controlled by their internal pressure, and gravity started to take the upper hand. First the vast collections of matter destined to become the haloes of galaxies formed. Then, or at about the same time, the first generation of stars appeared in the universe. These Population III stars made from nearly transparent hydrogen and helium gas were so massive, they lived for only a few million years before detonating as supernova. As the universe becomes polluted with heavier elements from billions of supernovae, collapsing clouds become more opaque to their own radiation, and so the collapse process stops when much less matter has formed into the infant stars. Instead of only producing massive Population III stars with 100 times our sun’s mass, numerous stars with masses of 50, 20 and 5 times our sun’s form with increasing frequency. Even smaller stars like our own sun begin to appear by the trillions. Most of this activity is occurring in what will eventually become the halo stars in modern galaxies like the Milky Way. The vast networks of dark matter became illuminated from within as stars and galaxies began to form.

200 million years – The oldest known star in our Milky Way called SM0313 formed about this time. This star contains almost no iron — less than one ten millionth of the iron found in our own Sun. It is located 6000 light years from Earth. Another star called the Methusela Star is located about 190 light years from Earth and was formed about the same time as SM0313.

The First Quasars and Black Holes

300 million years The most distant known ‘quasar’ is called APM 8279+5255, and contains traces of the element iron. This means that at about this time after the Big Bang, some objects are powered by  enormous black holes that steadily consume a surrounding disk of gas and dust. For APM 8279+5255, the mass of this black hole is about 20 billion times more massive than the Sun. Astronomers do not know how a black hole this massive could gave formed so soon after the Big Bang. A dimple division shows that a 20 billion solar mass black hole forming in 300 million years would require a growth rate higher than 60 solar masses a year!

The First Galaxies

400 million years – The cold primordial matter becomes clumpy under the action of its own gravity. These clumps have masses of perhaps a few billion times our sun or less, and over time this material starts to collapse locally into even smaller clouds that become mini-galaxies where intense episodes of star formation activity are playing out.

This image shows the position of the most distant galaxy discovered so far with the Hubble Space Telescope. The remote galaxy GN-z11 shown in the inset is actually ablaze with bright young blue stars. They look red in this image because the wavelengths of light have been stretched by the expansion of the universe to longer, redder wavelengths. Like the images of so many other young galaxies, we cannot see individual stars, but their irregular shapes show that the stars they contain are spread out in irregular clumps within their host galaxy, possibly because they are from separate, merging clouds whose collisions have triggered the star-forming activity we see.

Although it is hard work, astronomers can detect the faint reddish traces of dozens of other infant galaxies such as MACS0647-JD, UDFj-39546284 and EGSY-2008532660. These are all  small dwarf galaxies over 100 times less massive than our Milky Way. They are all undergoing intense star forming activity between 400 and 600 million years after the Big Bang.

The Gamma-Ray Burst Era begins about 630 million years after the Big Bang. Gamma-ray bursts are caused by very massive stars, perhaps 50 to 100 times our own sun’s mass, that explode as hypernovae and form a single black hole, so we know that these kinds of stars were already forming and dying by this time. Today from ‘across the universe’ we see these events occur about once each day!

800 million years – The quasar ULAS J1120+0641 is another young case of a supermassive black hole that has formed, and by this time is eating its surrounding gas and stars at a prodigious rate. The mass of this black hole is about 2 billion times the mass of our sun, and like others is probably the result of frequent galaxy mergers and rapid eating of surrounding matter.

Also at around this time we encounter the Himiko Lyman Alpha Blob; one of the most massive objects ever discovered in the early universe.  It is 55,000 light-years across, which is half of the diameter of the Milky Way. Objects like Himiko are probably powered by an embedded galaxy that is producing young massive stars at a phenomenal rate of 500 solar masses per year or more.

Again the most brilliant objects we can see from a time about 900 million years after the big bang includes galaxies like SDSS J0100+2802 with a luminosity 420 trillion times that of our own Sun. It is powered by a supermassive black hole  12 billion times the mass of our sun.

The Re-Ionization Era

960 million years – By this time, massive stars in what astronomers call ‘Population III’ are being born by the billions across the entire universe. These massive stars emit almost all of their light in the ultraviolet part of the visible spectrum. There are now so many intense sources of ultraviolet radiation in the universe that all of the remaining hydrogen gas becomes ionized. Astronomers call this the Reionization Era. Within a few hundred million years, only dwarf galaxy-sized blobs of gas still remain and are being quickly evaporated. We can still see the ghosts of these clouds in the light from very distant galaxies. The galaxy SSA22-HCM1 is the brightest of the objects called ‘Lyman-alpha emitters’. It may be producing new stars at a rate of 40 solar masses per year and enormous amounts of ultraviolet light. The galaxy HDF 4-473.0 also spotted at this age is only 7,000 light years across. It has an estimated star formation rate of 13 solar masses per year.

1 billion years First by twos and threes, then by dozens and hundreds, clusters of galaxies begin to form as the gravity of matter pulls the clumps of galaxy-forming matter together. This clustering is speeded up by the additional gravity provided by dark matter. In a universe without dark matter, the number of clusters of galaxies would be dramatically smaller.

Clusters of Galaxies Form

Proto-galaxy cluster AZTEC-3 consists of 5 smaller galaxy-like clumps of matter, each forming stars at a prodigious rate. We now begin to see how some of the small clumps in this cluster are falling together and interacting, eventually to become a larger galaxy-sized system. This process of cluster formation is now beginning in earnest as more and more of these ancient clumps fall together under a widening umbrella of gravity. Astronomers are discovering more objects like AzTEC-3, which is the most distant known progenitor to modern elliptical galaxies. By 2.2 billion years after the Big Bang, it appears that half of all the massive elliptical galaxies we see around us today have already formed by this time.

Thanks to the birth and violent deaths of generations of massive Population III stars, the universe is now flooded with heavy elements such as iron, oxygen, carbon and nitrogen: The building blocks for life. But also elements like silicon, iron and uranium which help to build rocky planets and heat their interiors. The light from the quasar J033829.31+002156.3 can be studied in detail and shows that by this time, element-building through supernova explosions of Population III stars has produced lots of carbon, nitrogen and silicon. The earliest planets and life forms based upon these elements now have a chance to appear in the universe. Amazingly, we have already spotted such an ancient world!

Earliest Planets Form

At 1 billion years after the Big Bang, the oldest known planet PSR B1620-26 b has already formed. Located in the globular cluster Messier-4, about 12,400 light-years from Earth, it bears the unofficial nicknames “Methuselah” and “The Genesis Planet” because of its extreme age. The planet is in orbit around the two very old stars: A dense white dwarf and a neutron star. The planet has a mass of 2.5 times that of Jupiter, and orbits at a distance a little greater than the distance between Uranus and our own Sun. Each orbit of the planet takes about 100 years.

Wonders to Come!

Although the Hubble Space Telescope strains at its capabilities to see objects at this early stage in cosmic history, the launch of NASA’s Webb Space Telescope will uncover not dozens but thousands of these young pre-galactic objects with its optimized design. Within the next decade, we will have a virtually complete understanding of what happened during and after the Cosmic Dark Ages when the earliest possible sources of light could have formed, and one can only marvel at what new discoveries will turn up.

What an amazing time in which to be alive!

Check back here on Wednesday, May 24 for my next topic!