Category Archives: Physics

The Minor Storm of May 13, 2024

We had a minor geomagnetic storm on Monday just after the major storm on Saturday that everyone saw. This minor storm launched a CME caused by an X-5.8 solar flare on Friday, but despite early estimates it might rival the major storm, it was a glancing blow to Earth’s magnetic field and caused no aurora over much of the Lower-48 States. Many had hoped they would get to see an aurora in Maryland and other mid-latitude locations but the storm was too week to be seen in most states that had enjoyed the Great Storm of May 10-11.

Nevertheless, my DIY magnetometers did show some life for this Kp=6 event as shown below. This time I had three different magnetometers operating. The top numbers are the 3-hour Kp indices. The red trace is from the Fredricksberg Magnetic Observatory. The black trace is from the RM3100-Arduino system. The blue trace is from the Differential Hall Sensoe system. The green trace os from the Differential Photocell Magnetometer. The two dips marked with ‘Sq’ are the diurnal Sq variations, which were recorded by all magnetometers.

All three designs are described in detail in my book Exploring Space Weather with DIY Magnetometers,

Landscape Dimming During a Total Solar Eclipse

During a solar eclipse, the lansdcape will slowly dim until it is nearly complete darkness along the path of totality. other observers wil see te landscape dim a bit but then brighten to normal intensity. If you didn;t know that an eclipse was going on you might not even notice the dimming, mistaking it for a cloud passing across the sun. The geometric condition for this dimming have to do with the area of exposed solar surface and how this changes as the disk of the moon passes across it. Below is a simple mathematical model for ambient light dimming that you can put to the test the next time a solar eclipse passes over your geographic location.

I have reanalyzed the geometry and defined it in terms of the center-to-center distance, L, between the sun and moon, and their respective radii Rs and Rm as the figure of the upper half-plane of the intersection shows, with the yellow area on the left representing the disk of the sun and the white area on the right the disk of the moon. This problem was previously considered in 2000 by British astronomer David Hughes who used the distance defined by the segment FE, which he called alpha, but L = 1+M-a. The figure shows the moon overlapping the disk of the sun in a lens-shaped zone whose upper half is represented by the area AFDE.


The basic idea is that we want to compute the area of the lunar arc cap AFD by computing the area of the sector BAF and subtracting the triangle BAE from the sector area. That leaves the area of the cap as the left-over area. We perform the same calculation for the solar sector CAE and subtract the triangle CAD from this.  The resulting area of the full lens-shaped overlap region is then

Occulting Area = 2x(AreaAFD + AreaAED).

Because of the geometry, the resulting area should only depend on the center-to-center separation and the radii of the sun and moon. You should not have to specify any angles as part of the final calculation. In the following we will use degree measure for all angles.

The area of the sector of a circle is just A = (Theta/360)piR2 so that gives us the first two relationships:

To simplify the problem, we are only interested in the fraction of the full sun disk that is illuminated. The full sun has an area of pi Rs2, so we divide Am and As by pi Rs2 , and if we define Rs=1.0 and M = Rm/Rs we get:

Although M is fixed by the solar-lunar ratio, we seem to have two angular variables alpha and theta that we also have to specify. We can reduce the number of variables because the geometry gives a relationship between these two angles because they share a common segment length given by h.

so that the EQ-1 for A can be written entirely in terms of the center-to-center distance, L,  and moon-to-sun disk ratio M = Rm/Rs. This is different than the equation used by Hughes, which uses the width of the lens (the distance between the lunar and solar limbs) segment FDE=a as the parameter, which is defined as L = 1+M-a.

During a typical total solar eclipse lasting 4 minutes, we can define L as

L = 1900 – 900*(T/240) arcseconds where T is the elapsed time from First Contact in seconds. Since L is in units of the current solar diameter (1900 asec) we have

EQ 3)          L = 1 – T/480.  

If we program EQ 1, 2, and 3 into an excel spreadsheet we get the following plot for the April 8, 2024 eclipse.

First Contact occurs at 16:40 UT and Fourth Contact occurs at 19:57 UT so the full duration is 197 minutes. During this time L varies from  -(1+M) to +(1+M). For the April 8, 2024 eclipse we have the magnitude M = 1.0566,  so  L varies from -2.0566 (t=0) to +2.0566 (t=197m). As the moon approaches the full 4-minute overlap of the solar disk between L=-0.05 and L=+0.05 (t =97m to t=102m), we reach full eclipse.

We can re-express this in terms of the landscape lighting. The human eye is sensitive to a logarithmic variation in brightness, which astronomers have developed into a ‘scale of magnitudes’. Each magnitude represents the minimum change in brightness that the human eye can discern and is equivalent to a factor change by 2.51-times. The full-disk solar brightness is equal to -26.5m, full moon illumination is  -18.0m on this scale. The disk brightness, S, is proportional to the exposed solar disk area, where E is the solar surface emission in watts/m2 due to the Planck distribution for the solar temperature of T=5770 k.  This results in the formula:

m = -26.5 – 2.5log10(F)

where F is the fraction of the full disk exposed and is equal to Equation 1.  For a sun disk where 90% has been eclipsed, f=0.10 and the dimming is only 2.5log(1/10) = 2.5m. How this translates into how humans perceive ambient lighting is complicated.

The concept of a Just Noticeable Difference is an active research area in psychophysics. In assessing heaviness, for example, the difference between two stimuli of 10 and 11 grams could be detected, but we would not be able to detect the difference between 100 and 101 grams. As the magnitude of the stimuli grow, we need a larger actual difference for detection. The percentage of change remains constant in general. To detect the difference in heaviness, one stimulus would have to be approximately 2 percent heavier than the other; otherwise, we will not be able to spot the difference. Psychologists refer to the percentages that describe the JND as Weber fractions, named after Ernst Weber (1795-1878), a German physiologist whose pioneering research on sensation had a great impact on psychological studies. For example, humans require a 4.8% change in loudness to detect a change; a 7.9% change in brightness is necessary. These values will differ from one person to the next, and from one occasion to the next. However, they do represent generally accurate values.

The minimum perceivable light intensity change is sometimes stated to be 1%, corresponding to +5.0m, but for the Weber Fraction a 7.8% change is required in brightness corresponding to only -2.5log(0.078) = +2.7m. This is compounded by whether the observer is told beforehand that a change is about to happen. If they are not informed, this threshold magnitude dimming could be several magnitudes higher and perhaps closer to the +5.0m value.


Webb Spies Uranus Rings

Webb image of the rings of Uranus. Credit SCIENCE: NASA, ESA, CSA, STScI
IMAGE PROCESSING: Joseph DePasquale (STScI); Source: https://tinyurl.com/mukddzcm

This zoomed-in image of Uranus, captured by Webb’s Near-Infrared Camera (NIRCam) Feb. 6, 2023, reveals stunning views of the planet’s rings. The planet displays a blue hue in this representative-color image, made by combining data from two filters (F140M, F300M) at 1.4 and 3.0 microns, which are shown here as blue and orange, respectively.

What a typical Press Release might tell you.

        Uranus has eleven known rings that contain dark, boulder-sized particles. Although the rings are nearly-perfect circles, they look like ellipses in some pictures because the planet is tilted as we are viewing it and so the rings appear distorted. They appear compressed in the side-to-side direction but are their normal undistorted distance from Uranus in the top-down direction in this image.

The outermost ‘epsilon’ ring is made up of ice boulders several meters across. The other rings are made up mainly of icy chunks darkened by rocks. The rings are thin ( less than 200 meters), narrow (less than 100 km), and dark compared to the rings of other planets. They are actually so dark they reflect about as much light as charcoal. The rings have a temperature of about 77 Kelvin according to U.C. Berkeley astronomers.

Read More!

NASA Press Release: Webb Scores Another Ringed World

Mashable.com. Surprise! Uranus has rings!

Research paper. Thermal emission from uranian ring system

Press Releases and textbook entries depend on scientists interpreting the data they gather to create a better picture of what they are seeing. I am going to show you in this Blog just how some of those numbers and properties are derived from the data astronomers gather. I have created three levels of interpretation and information extraction that pretty nearly match three different education levels and the knowledge about math that goes along with them.

I. Space Cadet (Grades 3-6)

This is the easiest step, and the first one that astronomers use to get a perspective on the sizes of the things they are seeing. In education, it relies on working with simple proportions. The scale bar in the picture tells you how the size of the picture relates to actual physical sizes.

1) Use a millimeter ruler to calculate the diameter of Uranus in kilometers.

2) Place your ruler vertically across the disk of Uranus. Measure the vertical (undistorted) distance from the center of Uranus to the center of the outer ‘Epsilon’ ring. How many kilometers is this ring from the center of Uranus?

3) Compare the size of the Uranus ring system to the orbit of our moon of 385,000 km. Would the moon’s orbit fit inside the ring system or is it bigger?

II. Space Commander (Grades 7-9)

This level of interpretation is a bit more advanced. If you are in Middle School, it works with concepts such as volume, mass, speed and time to extract more information from the data in the image, now that you have completed the previous-level extraction.

1) What is the circumference of the Epsilon ring in kilometers?

2) The rings of Uranus are only about 200 meters thick and no more then 100 km wide, which means their cross-section is that of a skinny rectangle. What is the cross sectional of the area of the Epsilon ring in square-kilometers assuming it is a rectangle with these dimensions?

3) What is the volume of the ring in cubic-kilometers if Volume = Area x Circumference?

4) If the volume of Earth is 1 trillion cubic kilometers, how much volume does the Epsilon ring occupy in units where Earth = 1?

5) With sizes of about 7-meters in diameter, what is the average mass of a single boulder if it is made from ‘dirty ice’ with a density of 2000 kg/m^3?

6) Scientists estimate that there could be as many as 25 billion boulders in the Epsilon ring. From your answer to the previous question, what is the total mass of this ring?

7) [Speed and time] The particles in the Epsilon ring travel at a speed of 10.7 km/s in their orbit around Uranus. How many hours does it take for a boulder to complete one orbit?

III. Junior Scientist (College, Graduate school)

This is a very hard level that requires that you understand how to work with algebraic equations, evaluate them for specific values of their constants and variables, and in physics understand Planck’s Black Body formula. You also need to understand how radiation works as you calculate various properties of a body radiating electromagnetic radiation. Undergraduate physics majors work with this formula as Juniors, and by graduate school it is simply assumed that you know how to apply it in the many different guises in which bodies emit radiation.

The Planck black body formula is given in the frequency domain by

where E is the spectral energy density of the surface in units of Watts/meter^2/Steradians/Hertz and the constants are h = 6.63×10^43 Joules Sec; c = 3.0×10^8 meters/sec and k = 1.38 x 10^-23 Joules/k.

  1. If the temperature of the Epsilon ring material is T=77 k, what is E in the 1.4-micron band of the Webb (F140M) and in the 1.3- millimeter band of the Atacama Large Millimeter Array (ALMA) for a single ring particle?
  2. What does your answer to Question 1 tell you about the visibility of the rings seen by the Webb at 1.4-microns?
  3. If the 1.3-millimeter total flux in the Epsilon ring was measured by ALMA to be 112milliJanskies (Table 3), about how many particles are contained in the Epsilon ring if it consists of dirty ice boulders with a 7-meter diameter? Note: 1 Jansky = 10^-26 watts/m^2/Hz. Assume a distance to Uranus of 1 trillion meters.
  4. If the volume of the Epsilon ring is about 6.4×10^6 cubic kilometers, about how far apart are the boulders in the ring?
  5. From your answer to Question 4, if the relative speeds of the ring boulders are about 1 millimeter/sec (see Henrik Latter), how often will these boulders collide?

So, how did you do?

You may not have gotten all of the answers correct, but the important thing is to appreciate just how astronomers extract valuable information about an object from its image at different wavelengths. Other than visiting the object in person, there is no other way to learn about distant objects than to gather data and follow many different series of steps to extract information about them. Some of these series of steps are pretty simple as you experienced at the Space Cadet-level. Others can be very difficult as you saw at the Junior Scientist-level. What is interesting is that, as our theoretical knowledge improves, we can create new series of steps to extract even more information from the data. Comparing the ring brightness at two or more wavelengths, we can deduce if the boulders are made of pure ice or dark rocks. By studying how the thickness of the ring changes along its circumference relative to the locations of nearby moons, we can study gravity and tidal waves in the ring bodies that tell us about how the density of the ring particles change. Astronomy is just another name for Detective Work but where the ‘crime scene’ is out of reach!

Answers

I.1 Close to 50,700 km.

I.2 Close to 51,000 km radius 102,000 km diameter.

I.3 The moons orbit radius is 385,000 km. The outer Epsilon ring could easily fit inside our Moon’s orbit.

II.1 Circumference is about 2(pi)R, so with R = 51,000 km, the circumference is 320,000 km.

II.2 The cross-section is 100 km long and 200 meters tall so its area is just A = 0.2 km x 100 km = 20 square km.

II.3 Volume = Area x Circumference = (20 km^2)x (3.2×10^5 km) = 6.4 x 10^6 km^3.

II.4 Volume = 6.4 x 10^6 km^3 / 1 trillion km^3 = 0.0000064 Earths.

II.5 Mass = volume x density. A single boulder with a radius of 3.5 meters has a volume of 4/3 pi (3.5)^3 = 179 m^3. Then its mass is 179 m^3 x 2000 kg/m^3 = 359000 kg or 359 tons.

II.6 There are 25 billion of these boulders so their total mass is 25 billion x 359 tons = 9.0×10^15 kg or 9 trillion tons. According to calculations in 1989, the mass of the Epsilon ring is estimated to be closer to 1016 kg or 10 trillion tons [Nature].

II.7 51,000 km/(10.7 km/s) = 8.3 hours.

III.1 Working with the Planck equation is always a bit tricky. The units for B will be Watts/m^2/Str/Hertz. First lets evaluate the equation for its constants h, c and k.

For the Webb infrared band of 1.4-microns, its frequency is 3×10^8/1.4×10^-6 or 7.1×10^13 Hertz. For ALMA the frequency is 231 GHz or 2.31×10^11 Hertz. For a temperature of 77 k, we get B(Webb) = (5.26×10^-9)(5.8×10^-20) = 3.0×10^-28 watts/m^2/Hz/str. For ALMA it will be B(ALMA) = (1.8×10^-16)(6.46) = 1.2×10^-15 Watts/m^2/Hz/str.

III.2 The visibility of the ring by its thermal emission cannot be the cause of its brightness in the Webb F140M band because its black body emission at 1.4 microns is vanishingly small due to the huge exponential factor. It must be caused by reflected visible light from the sun.

III.3 In the ALMA 1.3-millimeter band, the flux density from a black body at a temperature of 77 k is 1.2×10^-15 watts/m^2/Hertz/str. One Jansky unit equals 10^-26 watts/m^2/Hz, so the black body emission in the ALMA band can be re-written as 1.2×10^11 Janskies/str. The angular radius of the boulder at the distance of Uranus ( 1 trillion meters) is given in radians by Q = 3.5 meter/1 trillion meters = 3.5×10^-12 radians. The angular area is then AQ = pi Q^2 = 3.9×10^-23 steradians. Then the black body flux density from this boulder is about S=1.2×10^11 Jy/str x 3.9×10^-23 str so S=4.5×10^-12 Janskies. But ALMA detects a total emission from this ring of about 0.112 Janskies, so the number of emitters is just 0.112 Jy/4.5×10^-12 Jy/boulder = 2.5×10^10 boulders or 25 billion boulders.

III.4 The ring volume is 6.4 x 10^6 cubic kilometers, so each boulder occupies a volume in the ring of about 6.4×10^6 km^3/25×10^9 boulders= 256,000 cubic meters/boulder. The average distance between them is L = V^0.333 = 63 meters.

III.5 Time = distance/speed so 63m/0.001 m/sec = 17.5- hours. The Epsilon particle orbit speed is about 8.3 hours (see II.7), so the particles collide about twice every orbit.

The Big Bang: Explained at the reading level of Genesis.

The universe began with a bang. Can we explain it all as simply as in many religious stories. (Image credit: Shutterstock)

I have often wondered how the modern description of the Big Bang could be written as a story that people at different reading levels would be able to understand, so here are some progressively more complete descriptions beginning with Genesis and their reading level determined by Reliability Formulas.

Genesis (from MIT Bible Gateway)

In the beginning God created the heavens and the earth. Now the earth was formless and empty, darkness was over the surface of the deep, and the Spirit of God was hovering over the waters. And God said, “Let there be light,” and there was light. God saw that the light was good, and he separated the light from the darkness. God called the light “day,” and the darkness he called “night.” And there was evening, and there was morning–the first day. And God said, “Let there be an expanse between the waters to separate water from water.” So God made the expanse and separated the water under the expanse from the water above it. And it was so. God called the expanse “sky.” And there was evening, and there was morning–the second day. And God said, “Let the water under the sky be gathered to one place, and let dry ground appear.” And it was so. God called the dry ground “land,” and the gathered waters he called “seas.” And God saw that it was good. Then God said, “Let the land produce vegetation: seed-bearing plants and trees on the land that bear fruit with seed in it, according to their various kinds.” And it was so. The land produced vegetation: plants bearing seed according to their kinds and trees bearing fruit with seed in it according to their kinds. And God saw that it was good. And there was evening, and there was morning–the third day. And God said, “Let there be lights in the expanse of the sky to separate the day from the night, and let them serve as signs to mark seasons and days and years, and let them be lights in the expanse of the sky to give light on the earth.” And it was so. God made two great lights–the greater light to govern the day and the lesser light to govern the night. He also made the stars. God set them in the expanse of the sky to give light on the earth, to govern the day and the night, and to separate light from darkness. And God saw that it was good.”

The Flesch Reading ease Score gives this an 87.9 ‘easy to read‘ score. Flesch-Kincaid gives this a grade level of 4.5. The Automated Readability Index gives it an index of 4 which is 8-9 year olds in grades 4-5. Amazingly, the scientific content in this story is completely absent and in fact promotes many known misconceptions appropriate to what children under age-5 know about the world.

Can we do at least as well as this story in a 365-word summary that describes the origin of the universe, the origin of the sun, moon and earth, and the appearance of life? Because the reading level of Genesis is only at most Grade-5, can we describe a scientific treatment using only concepts known by the average Fifth-Grader? According to the Next Generation Science Standards, students know about gravity, and scales of time but ideas about atoms and other forces are for Grade 6 and above. The average adult reader can fully comprehend a text with a reading grade level of eight. So if the text has an eighth grade Flesch Kincaid level, its text should be easy to read and accessible by the average US adult. But according to Wylie Communications, half of all US adults read at or below 8th-grade level. The American Academy of Arts and Sciences survey also shows that US adults know about atoms (51%), that the universe began with a Big Bang (41%) and that Earth orbits the sun (76%) so that US adults rank between 5th and 9th internationally in our basic scientific knowledge.

The genesis story splits itself into three distinct parts: The origin of the universe;The origin of stars and planets; and The origin of life and humanity. Only the middle story has detailed observational evidence at every stage. The first and last stories were one-of events for which exact replication and experimentation is impossible.

Because we are 3000 years beyond the writing of Genesis, let’s allow a 400-word limit for each of these three parts and aim at a reading level and science concept level not higher than 7th grade.

First try (497 words):

Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void is, only that it had none of the properties we can easily imagine. It had no dimension, or space or time; energy or mass; color or absence of color. Scientists use their mathematics to imagine it as a Pure Nothingness. Not even the known laws of nature existed.

Part of this Void exploded in a burst of light and energy that expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature that describe how many dimensions exist in space, the existence of four fundamental forces, and how these forces operate through space and time.

At first this energy was purely in the form of gravity, but as the universe cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged and this matter became cold enough that basic elements like hydrogen and helium could form.

But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed so quickly that within a fraction of a second, the space in our universe inflated from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years of further expansion we see only a small fraction of this expanded space today, and we call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.

Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as the universe expanded so that by one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the light from the Big Bang became so cool that it could only be seen as a dull glow of infrared light every where in space. The atoms no longer felt the buffeting forces of this fireball light and had started to congregate under the force of gravity into emmence clouds throughout space. It is from these dark clouds that the first stars would begin to form.

Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter because it is invisible but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than ordinary matter. It prevents galaxies like the Milky Way from flying apart, and clusters of galaxies from dissolving into individual galaxies.

Flesch Reading Ease 60. (Average difficulty); Flesch-Kincaid Grade: 10.2; Automated Readability Index: 11

Second Try (538 words):

Origin of the Universe. Our universe emerged from a timeless and spaceless void. We don’t know what this Void was. We think it had none of the properties we can easily imagine. It had no dimension, or space or time. It had no energy or mass. There was no color to it either blackness or pure white. Scientists use their mathematics to imagine it as a Pure Nothingness. They are pretty sure that not even the known laws of nature existed within this Void.

Part of this Void exploded in a burst of light and energy. Astronomers call this the Big Bang. It  expanded and created both time and space as it evolved in time. This event also locked into existence what we call the Laws of Nature. These Laws describe how many dimensions exist in space. The Laws define the four fundamental forces, and how they operate through space and time.

At first the energy in the Big bang was purely in the form of gravity. But as the universe expanded and cooled, some of this energy crystalized into particles of matter. Eventually, the familiar elementary particles such as electrons and quarks emerged. This matter became cold enough that basic elements like hydrogen and helium could form.

But the speed at which the universe was expanding wasn’t steady in time. Instead this expansion doubled in speed very quickly. Within a fraction of a second, the space in our universe grew from a size smaller than a baseball to something many billions of miles across. After 14 billion years of further expansion we see only a small fraction of this expanded space today. We call it the Observable Universe. But compared to all the space that came out of the Big Bang, our entire Observable Universe is as big as a grain of sand compared to the size of our Earth. The Universe is truly an enormous collection of matter, radiation and energy in its many forms.

Meanwhile, the brilliant ‘fireball’ light from the Big Bang also cooled as
the universe expanded. By one million years after the Big Bang, it was cooler than the light we get from the surface of our own sun. Once this light became this cool, familiar atoms could start to form. As the universe continued to expand and cool, eventually the blinding light from the Big Bang faded into a dull glow of infrared light. At this time, a human would see the universe as completely dark. The atoms no longer felt the buffeting forces of this fireball light. They began to congregate under the force of gravity. Within millions of years, immense clouds began to form throughout space. It is from these dark clouds that the first stars would begin to form.

Mixed in with the ordinary matter of hydrogen and helium atoms was a mysterious new kind of matter. Scientists call this dark matter.  It is invisible to the most powerful telescopes, but it still affects normal matter by its gravity. Dark matter in the universe is five times more common than the ordinary matter we see in stars. It prevents galaxies like the Milky Way from flying apart. It also prevents clusters of galaxies from dissolving into individual galaxies.

Flesch Reading Ease 66.7. (Average difficulty); Flesch-Kincaid Grade: 7.2; Automated Readability Index: 6.6 (11-13 year olds).

Third Try ( 410 words )

Origin of the Universe. Our universe appeared out of a timeless and spaceless void. We don’t know what this Void was. We can’t describe it by its size, its mass or its color.  It wasn’t even ‘dark’  because dark (black) is a color.  Scientists think of it as a Pure Nothing.

Part of this Void exploded in a burst of light and energy. We don’t know why.  Astronomers call this event the rather funny name of the ‘Big Bang’. It  was the birth of our universe. But it wasn’t like a fireworks explosion. Fireworks expand into the sky, which is space that already exists. The Big Bang created space as it went along.  There was nothing for it to expand into. The Big Bang also created  what we call the Laws of Nature. These Laws describe how forces like gravity and matter affect each other.

As the universe expanded and cooled, some of its energy became particles of matter. This is like raindrops condensing from a cloud when the cloud gets cool enough. Over time, these basic particles  formed  elements like hydrogen and helium.

The universe continued to expand. Within the blink of an eye, it grew from a size smaller than a baseball to something many billions of miles across. Today, after 14 billion years  we see only a small piece of this expanded space today. Compared to all the space that came out of the Big Bang, what we see around us is as big as a grain of sand compared to the size of our Earth. The Universe is truly enormous!

After about one million years  the fireball light from the Big Bang became very dim. At this time, a human would see the universe as completely dark. There were, as yet, no stars to light up the sky and the darkness of space. Atoms  began to congregate under the force of gravity. Within millions of years, huge clouds the size of  our entire Milky Way galaxy began to form throughout space. From these dark clouds, the first stars started to appear.

Mixed in with  ordinary matter  was a mysterious new kind of matter. Scientists call this dark matter.  It is invisible to the most powerful telescopes. But it still affects normal matter by its gravity, and that’s a very good thing! Without dark matter,  galaxies like our Milky Way and its billions of stars would fly apart, sending their stars into the dark depths of intergalactic space.

Flesch Reading Ease 73.3. (Fairly easy to read); Flesch-Kincaid Grade: 5.9 (Sixth grade) ; Automated Readability Index: 5.1 (8 – 9 year olds) Fourth to Fifth grade.

Summary.

The Third Try is about as simple and readable a story as I can conjure up, and it comes in at a reading level close to Fourth grade. Scientifically, it works with terms like energy, space, expansion, matter  and gravity, and scales like millions and billions of years. All in all, it is not a bad attempt that reads pretty well, scientifically, and does not mangle some basic ideas. It also has a few ‘gee whiz’ ideas like Nothing, space expansion and dark matter. 

So, what do you think? Leave me a note at my Facebook page!

Next time I will tackle the middle essay about the formation of  stars and planets!

Do Other Dimensions REALLY Exist?

Those of you who have been following physics for the last few decades have no doubt heard about string theory and how it requires that spacetime have 11-dimensions and not the four we are most familiar with (3 for space and 1 for time) . This has been a popular topic of discussion since the 1970s, and has spawned thousands of popularizations and lectures. I have actually written a few of these!

The difficulty is that we never experience even ordinary space directly, and as Einstein noted, space itself is more of a human mental construct than it is a physical feature of our world. When physicists need some additional dimensions to space to model our world, we find ourselves confused as our brains try to fabricate an inner model of what that might mean. The idea of ‘dimension’ is not what you might think. It is just another way of saying that some system you are modeling mathematically needs N numbers to define it uniquely in space and time. For example, economists work in ‘spaces’ where their models use N=4 unique numbers, so their universes are 4-dimensional too!

Space, as a physical idea is just our experience that we only need three numbers to locate a geometric point on Earth. We need its latitude, its longitude and its elevation above the surface of Earth. Two of these numbers are angles, but we can easily convert these angles into meters because the surface of Earth has a fixed radius and forms a sphere. The angles just represents the lengths of arcs on the surface.

Extending this into the solar system and beyond, we only need three numbers to define the location of a planet or a star. If we try to provide four numbers to locate any point in space, that fourth measurement can be replaced in terms of the previous three numbers. Because this minimum number is three, we say that our space is 3-dimensional. Similarly, all of Euclid’s geometry takes place on a flat surface where points are defined by two numbers, so it is a 2-dimensional surface. The figure above shows an example of ordinary 3-d space and its coordinate axis in the Cartesian ‘X, Y, Z’ system. But there are other possible coordinate systems we can use such as spherical (R, theta, phi) or cylindrical (R, theta, h), but they all define points in 3-d space by a unique three-number address. But wait…there’s more!

Three is not enough. Our physical world actually requires a time coordinate to define where objects are because, of course, all objects are in motion or are internally changing. Time is a fourth coordinate that helps us keep track of the complete history of an object as it moves through 3-d space. This path is called a worldline. This is why Einstein’s relativity refers to ‘spacetime’ as the fundamental arena in which all events take place. Spacetime is a 4-dimensional object with three coordinates expressed in terms of meters, and a time coordinate expressed in units of time such as nanoseconds, seconds, years etc. Spacetime is also called a manifold because every point in it can be uniquely defined by four numbers. There are mathematically an infinite number of these points. Because we have yet to find any evidence to the contrary, the manifold of all points in our physical universe, call it M, is just the same as the 4-d spacetime manifold proposed by Einstein’s relativity, call it M4, so in short-hand we can write a symbolic sentence: M = M4.

M4 is not big enough: What you need to keep in mind is that in our 4-dimensional world, we can obviously see that ‘space’ is very different than ‘time’. When physicists talk about our world or our universe having more than 4-dimensions, they also mean that additional coordinates are needed beyond (3-d) space and (1-d) time to keep track of the properties of matter and energy in their new theories. There is nothing about any of these additional coordinates that needs to have the same character as either space or time. All they need to be is numbers defining a 10-dimensional coordinate system. Some physicists, however, do think of these added dimensions as having some kind of space-like attributes.

Structure of extra dimensions in String theory in physics. 3D rendered illustration.

The way that these extra dimensions are added to our world to create the M of our physical universe is that they represent coordinates in a separate kind of space, call it M6, that adjoins our M4. In string theory, this M6 space is vanishingly small. You will not find traces of it in M4, so don’t worry about somehow taking a wrong turn in M4 and suddenly ending up in M6. String theory requires that M6 be a closed, finite manifold present at every point in M4. The size of each of these new dimensions is only 10-33 centimeters, which is why these M6s are called ‘compact’ manifolds. Only quantum particles and fields have access to M6, and this access causes particles to have different characteristics.

So what is M? The complete specification of our manifold can be written as M = M4 x M6. The address of each point in M is now given by, for example, the 4 coordinates (x,y,z,t) to define their location in M4, but to define the location of this point inside one of these compact M6 manifolds you need six additional numbers, which we can write as (a,b,c,d,e,f). The complete specification for points in the M manifold is then (x,y,z,t,a,b,c,d,e,f) or more neatly (x,y,z,t)(a,b,c,d,e,f) where we keep the two manifolds symbolically separate by placing parenthesis to group their respective coordinates.

So the question is, are the coordinates (a,b,c,d,e,f) dimensions of space like (x,y,z), are they more like the dimension of time in M4, or are they something else? As I said earlier, we already know that the time coordinate, t, is not at all like the other three space coordinates in M4, so there is no reason to believe that (a,b,c,d,e,f) should resemble either (x,y,z) or t. In fact, in string theory we already know something about the character of the coordinates in M6.

Very small: String theory proposes that they have a size of about the Planck Length, which is 10-33 centimeters. You can’t get lost in M6 because you always wind up back at your starting point after you have walked 10-33 centimeters!

Periodic: Some or all of these extra dimensions allow for the properties of physical quantities such as fields to have some periodic feature to them. An important quantity is the spin of a particle, which can be either multiples of 1 (called bosons) or 1/2 (called fermions). All elementary particles (electrons, quarks) are fermions, and all force-carrying particles (photons, gluons) are bosons.

Provides a complex topology: The number of times a quantity ‘wraps’ around a periodic extra-dimension, the more mass it has. When M6 is defined by these coordinates, the shapes of the M6 manifolds, called their topology, can have holes in them. String theory requires that these shapes be in a class called Calabi-Yau manifolds in order that the particles and fields resemble our world.

Metric signature: In special relativity, the distance between points in 4-dimensions, dS, is defined by dS2 = dx2 + dy2 + dz2 – c2dt2 where, for instance the symbol dx is the difference in the x coordinates between two points dx = x2 – x1. Notice that the space coordinates enter with a positive sign and the sole time coordinate enters with a negative sign. Physicists write this as the metric signature (+,+,+,-). In string theory, the extra dimensions are added with positive signs to make the string theory models work correctly to get something like dS2 = dx2 + dy2 + dz2 +da2 + db2 + dc2 +dd2 + de2 +df2 – c2dt2. So, the extra dimensions are taken to be space-like even though the maximum distance along any one of these 6 dimensions is only about 10-33 centimeters!

That is the mathematics of it, but do the extra dimensions really, really, reaally exist?

The truth of the matter is that we don’t know! If string theory is found to be incorrect, then there is no obvious reason to have a M6 at all, and so we are left with the M4 universe that we know and love. We cannot investigate the universe at the Planck scale, so the only way to test this idea of extra dimensions is to find that a theory like string theory is correct and accurate. We can then say that, because experiments confirm the predictions of string theory very accurately, there must be something like these M6 manifolds with their additional dimensions beyond the four we can directly measure in M4. On the other hand, it may also be that M6 is just mental ‘scratch paper’ that humans need in order to mathematically describe the particles and fields in our M4 universe, but our universe is actually doing something else entirely!

One important prediction from string theory is that gravity is a force modeled by closed strings in this 10-dimensional manifold. It also has the ability to range far and wide across these additional dimensions while the other three forces are confined to M4. This means that any gravitational interaction takes place in the 10-d arena and we only experience the part of this gravitational field that is in our ‘small’ 4-d universe. In fact, the theory says that this is why gravity is such as weak force because we are only seeing a small part of its full 10-d effects. This allows us to test at least this prediction by string theory.

Supernova 1987A: This supernova produced a pulse of neutrinos measured back on earth through the detection of about 12 neutrinos in the Super Kamiokande Neutrino Detector. These pulses arrived within seconds of the optical burst. Neutrinos are like the Miner’s Canaries and their numbers depend very sentitively on the energy of the collapsing supernova core into a neutron star. These 12 neutrinos matched the energy calculations, but only if the core of the star achieved its temperature by gravitational collapse, and with the energy determined by the action of gravity with little or no leakage into other dimensions. The tests were only able to say that the supernova data are consistent with these extra dimensions being smaller than about 1 angstrom (10-8 cm). So this result is a bit inconclusive.

Gravity waves: In 2017, the LIGO gravity wave detector rang out with the passing gravity wave called GW170817 from the collision between two neutron stars. The added twist was that the collision was also observed by its intense optical outburst. When detailed calculations of the energy in gravity waves and visible light were performed, the energy matched the theory exactly. The theory, based on standard general relativity, does not inlude the diminution of the gravity pulse by leakage of energy outside our M4 spacetime. The conclusion was that on this basis, gravity does not act as though there are extra dimensions! In fact, the gravity wave measurements give an observational estimate for the dimensionality of M4 of D = 4.02 +/-0.07. There is not much uncertainty to hide 6 more dimensions.

So there you have it. Those extra dimensions are probably space-like but their compact character makes them very different than either the huge space-like character of our familiar 3-dimensions to space.

Stay tuned for my next Blog in two weeks where I will be discussing the laatest Webb Space Telescope data!!!

This is Not Your Father’s Universe!

When I was learning astronomy in the 60s and 70s, we were still debating whether Big Bang or Stady State were the most accurate models for our universe. We also wondered about how galaxies like our Milky Way formed, and whether black holes existed. The idea that planets beyond our solar system existed was pure science fiction and no astronomers spent any time trying to predict what they might look like. As someone who has reached the ripe old age of 70, I am amazed how much progress we have made, from the discovery of supermassive black holes and exoplanets, to dark matter and gravitational radiation. The pace of discovery continues to increase, and our theoretical ideas are now getting confirmed or thrown out at record pace. There are still some issues that remain deliciously mysterious. Here are my favorite Seven Mysteries of the Universe!

1-How to Build a Galaxy: In astronomy, we used to think that it would take the universe a long time to build galaxies like our Milky Way, Thanks to the new discoveries by the Webb Space Telescope, we now have a ring-side seat to how this happens, and boy is it a fast process!

The oldest galaxies discovered with the Hubble Space Telescope date back to between 400 and 500 million years after the Big Bang. A few weeks ago, Webb spotted a galaxy that seems to have formed only 300 million years after the Big Bang. Rather than the massive galaxies like the Milky Way, these young galaxies resemble the dwarf galaxies like the Large Magellanic Cloud, perhaps only 1/10 the mass of our galaxy and filled with enormus numbers of massive, luminous stars. The above image from Hubble is a nearby galaxy called M-33 that has a mass of about 50 billion suns. There were lots of these smaller galaxies being formed during the first 300 million years after the Big Bang.

It looks like the universe emerged from the Dark Ages and immediately started building galaxies. In time, these fragments collided and merged to become the more massive galaxies we see around us, so we are only just starting to see how galaxy-building happens. Our Milky Way was formed some 1 billion years after the Big Bang, so the galaxy fragments being spotted by Webb have another 700 million years to go to make bigger things. Back in 2012, Hubble had already discovered the earliest spiral galaxy seen by then; a galaxy called Q2343-BX442, camping out at 3 billion years after the Big Bang. In 2021, an even younger spiral galaxy was spotted, called BRI 1335-0417, seen as it was about 1.4 billon years after the Big Bang.

So we are now watching how galaxies are being formed almost right before our eyes! Previous ideas that I learned about as an undergraduate, in which galaxies are formed ‘top-down’ from large collections of matter that fragment into stars, now seem wrong or incomplete. The better idea is that smaller collections of matter form stars and then merge together to build larger systems – called the ‘bottom-up’ model. This process is very, very fast! Among the smallest of these ‘galaxies’ are things destined to become the globular clusters we see today.

2-Supermassive Black Holes: The most distant and youngest supermassive black hole was discovered in 2021. Called J0313-1806, its light left it to reach us when the universe was only 670 million years old. Its mass, however, is a gargantuan 1.6 BILLION times the mass of our sun. Even if the formation of this black hole started at the end of the Dark Ages ca 100 million years after the Big Bang, it would have to absorb matter at the rate of three suns every year on average. That explains its quasar energy, but still…it is unimaginable how these things can grow so fast! The only working idea is that they started from seed masses about 10,000 the mass of our sun and grew from there. But how were the seed masses formed? This remains a mystery today.

3-The Theory of everything: The next Big Thing that I have been following since the 1960s is the search for what some call the Theory of Everything. Exciting theoretical advancements were made in the 1940s and 1960s to create accurate mathematical models for the three nongravity forces, called the electromagnetic, weak and strong forces. Physicists call this the Standard Model, and every physicist learns its details as students in graduate school. By the early 1980s, string theory was able to add gravity to the mix and go beyond the Standard Model. It appeared that the pursuit of a unified theory had reached its apex. Fifty years later, this expectation has all but collapsed.

Experiments at the Large Hadron Collider continue to show how the universe does not like something called supersymmetry in our low-energy universe. Supersymmetry is a key ingredient to string theory because it lets you change one kind of particle (field) into another, which is a key ingredient to any unified theory. So the simplest versions of string theory rise or fall based on whether supersymmetry exists or not. For over a decade, physicists have tried to find places in the so-called Standard Model where supersymmetry should make its appearance, but it has been a complete no-show. Its not just that this failure is a problem for creating a more elegant theory of how forces works, but it also affects astronomy as well.

https://penntoday.upenn.edu/news/making-sense-string-theory

Personally, when string theory hit the stage in the 1980’s I, like many other astronomers and physicists, thought that we were on the verge of solving this challenge of unifying gravity with the other forces, but this has not been the reality. Even today, I see no promissing solutions to this vexing problem since apparently the data shows that simple string theory is apparently on a wrong theoretical track.

One cheerful note: For neutrinos, the path from theoretical prediction to experimental observation took 25 years. For the Higgs boson, it took 50 years. And for gravitational waves, it took a full 100 years. We may just have to be patient…for another 100 years!

4-Dark Matter: The biggest missing ingredient to the cosmos today is called dark matter. When astronomers ‘weigh’ the universe, they discover that 4.6% of its gravitating ‘stuff’ is in ordinary matter (atoms,. stars, gas, neutron stars etc), but a whopping 24% is in some other ‘stuff’ that only appears by its gravity. It is otherwise completely invisible. Putting this another way, it’s as though four out of every five stars that make up our Milky Way were completely invisible.

Dark matter in Abell 1679.

Because we deeply believe that dark matter must be tracable to a new kind of particle, and because the Standard Model gives us an accounting of all the kinds of elementary particles from which our universe is built, the dark matter particle has to be a part of the Standard Model…but it isn’t!!!! Only by extending the Standard Model to a bigger theory (like string theory) can we logically and mathematically add new kinds of particles to a New Standard Model- one of which would be the dark matter particle. String theory even gives us a perfect candidate called the neutralino! But the LHC experiments have told us for over a decade that there is nothing wrong with the Standard Model and no missing particles. Astronomers say that dark matter is real, but physicists can’t find it….anywhere. Well…maybe not ALL astronomers think it’s real. So the debate continues.

Personally, I had heard about ‘missing mass’ in the 1960s but we were all convinced we would find it in hot gas, dim red dwarf stars or even black holes. I NEVER thought that it would turn out to be something other than ordinary matter in an unusual form. Dark matter is so deeply confounding to me that I worry we will not discover its nature before I, myself, leave this world! Then again, there isnt a single generation of scientists that has had all its known puzzles neatly solved ‘just in time’. I’m just greedy!!!

5- Matter and Antimatter: During the Big Bang, there were equal amounts of matter and anti matter, but then for some reason all the antimatter dissappeared leaving us with only matter to form atoms, stars and galaxies. We don’t know why this happened, and the Standard Model is completely unhelpful in giving us any clues to explain this. But next to dark matter, this is one of the most outstanding mysteries of modern, 21st century cosmology. We have no clue how to account for this fact within the Standard Model, so again like Dark Matter, we see that at cosmological scales, the Standard Model is incomplete.

6- Origin of Time and Space: Understanding the nature of time and space, and trying to make peace with why they exist at all, is the bane of any physicists existence. I have written many blogs on this subject, and have tried to tackle it from many different angles, but in the end they are like jigsaw puzzels with too many missing pieces. Still, it is very exciting to explore where modern physics has taken us, and the many questions such thinking has opened up in surprising corners. My previous blog about ‘What is ‘Now’ is one such line of thinking. Many of the new ideas were not even imagined as little as 30 years ago, so that is a positive thing. We are still learning more about these two subjects and getting better at asking the right questions!

https://iopscience.iop.org/journal/0264-9381/page/Focus-issue-loop-quantum-gravity

7-Consciousness: OK…You know I would get to this eventually, and here it is! Neuroscientists know of lots of medical conditions that can rob us of consciousness including medical anesthesia, but why we have this sense about ourselves that we are a ‘person’ and have volition is a massively hard problem. In fact, consciousness is called the ‘Hard Problem’ in neuroscience..heck…in any science!

https://www.technologynetworks.com/neuroscience/articles/what-if-consciousness-is-not-what-drives-the-human-mind-307159

The ‘Soft Problem’ is how our senses give us a coherant internal model of the world that we can use to navigate the outside world. We know how to solve the Soft Problem, just follow the neurons. We are well on our way to understanding it thanks to high-tech brain imaging scanners and cleverly-designed experiments. The Hard Problem is ‘hard’ because our point-of-view is within the thing we are trying to undertand. Some think that our own ‘wet ware’ is not up to the task of even giving us the intelligence to answer this qustion. It will not be the first time someone has told us about limitations, but usually these are technological ones, and not ones related to limits to what our own brains can provide as a tool.

So there you have it.

My impression is that only Mysteries #1 and #2 will make huge progress. The Theory of Everything is in experimental disarray. For antimatter, there has been no progress, but many ideas. They all involve going outside the Standard Model. Dark matter might be replaced by a modification of gravity at galactic and cosmological scales.

Beyond these ‘superficial’ mysteries, we are left with three deep mysteries. The origin of space, time and consciousness remain our 21st century gift to children of the 22nd century!

Check back here in a few weeks for the next blog!

What is ‘Now’?

What is the duration of the present moment? How is it that this present moment is replaced by ‘the next moment’?

Within every organism, sentient or not, there are thousands of chemical processes that occur with their own characteristic time periods, but these time periods start and stop at different times so that there is no synchronized ‘moment’. Elementary atomic collisions that build up molecules take nanoseconds while cell division takes minutes to hours, and tissue cell lifespans vary from 2 days in the stomach lining to 8 years for fat cells (see Cell Biology). None of these jangled timescales collectively or in isolation create the uniform experience we have of now and its future moments. To find the timescale that corresponds to the Now experience we have to look elsewhere.

It’s all in the mind!

A variety of articles over the  years have identified 2 to 3 seconds as the maximum duration of what most people experience as ‘now’, and what researchers call the ‘specious present’. This is the time required by our brain’s neurological mechanisms to combine the information arriving at our senses with our internal, current model of the ‘outside world’. During this time an enormous amount of neural activity has to happen. Not only does the sensory information have to be integrated together for every object in your visual field and cross connected to the other senses, but dozens of specialized brain regions have to be activated or de-activated to update your world model in a consistent way.

In a previous blog I discussed how important this world model is in creating within you a sense of living in a consistent world with a coherent story. But this process is not fixed in stone. Recent studies by Sebastian Sauer and his colleagues at the Ludwig-Maximilians-Universität in Munich show that mindfulness meditators can significantly increase their sense of ‘now’ so that it is prolonged for up to 20 seconds.

In detail, a neuron discharge lasts about 1 millisecond, but it has to be separated from the next one by about 30 milliseconds before a sequence is perceived, and this seems to be true for all senses. When you see a ‘movie’ it is a succession of still images flashed into your visual cortex at intervals less than 30 milliseconds, giving the illusion of a continuous unbroken scene.  (Dainton: Stanford Encyclopedia of Philosophy, 2017).

The knitting together of these ‘nows’ into a smooth flow-of-time is done by our internal model-building system. It works lightning-fast to connect one static collection of sensory inputs to another set and hold these both in our conscious ‘view’ of the world. This gives us a feeling of the passing of one set of conditions smoothly into another set of conditions that now make up the next ‘Now’. To get from one moment to the next, our brain can play fast-and-loose with the data and interpolate what it needs. For example, it our visual world, the fovea in our retina produces a Blind Spot but you never notice it because there are circuits that interpolate across this spot to fill-in the scenery. The same thing happens in the time dimension with the help of our internal model to make our jagged perceptions in time into a smooth movie experience.

Neurological conditions such as strokes, or psychotropic chemicals can disrupt this process and cause dramatic problems. Many schizophrenic patients stop perceiving time as a flow of  linked events.  These defects in time perception may play a part in the hallucinations and delusions experienced by schizophrenic patients according to some studies. There are other milder aberrations that can affect our sense of the flow-of-time.

Research has also suggested the feeling of awe has the ability to expand one’s perceptions of time availability. Fear also produces time-sense distortion. Time seems to slow down when a person skydives or bungee jumps, or when a person suddenly and unexpectedly senses the presence of a potential predator or mate. Research also indicates that the internal clock, used to time durations in the seconds-to-minutes range, is linked to dopamine function in the basal ganglia. Studies in which children with ADHD are given time estimation tasks shows that time passes very slowly for them.

Because the volume of data is enormous, we cannot hold many of these consecutive Now moments in our consciousness with the same clarity, and so earlier Nows either pass into short-term memory if they have been tagged with some emotional or survival attributes, or fade quickly into complete forgetfulness. You will not remember the complete sensory experience of diving into a swimming pool, but if you were pushed, or were injured, you will remember that specific sequence of moments with remarkable clarity years later!

The model-building aspect of our brain is just another tool it has that is equivalent to its pattern-recognition ability in space. It looks for patterns in time to find correlations which it then uses to build up expectations for ‘what comes next’. Amazingly, when this feature yields more certainty than the evidence of our senses, psychologists like Albert Powers at Yale University say that we experience hallucinations (Fan, 2017). In fact, 5-15% of the population experience auditory hallucinations (songs, voices, sounds) at some time in their lives when the brain literally hears a sound that is not there because it was strongly expected on the basis of other clues. One frequent example is that  people claim to hear the Northern Lights as a crackling fire or a swishing sound, because their visual system creates this expectation and the brain obliges.

This, then, presents us with the neurological experience of Now. It is between 30 milliseconds and several minutes in duration. It includes a recollection of the past which fades away for longer intervals in the past, and includes a sense of the immediate future as our model-making facility extrapolates from our immediate past and fabricates an expectation of what comes next.

Living in a perpetual Now is no fun. The famed psychologist Oliver Sacks describes  a patient, Clive Wearing, with a severe form of amnesia, who was unable to form any new memories that lasted longer than 30 seconds, and became convinced every few minutes that he was fully conscious for the first time. “In some ways, he is not anywhere at all; he has dropped out of space and time altogether. He no longer has any inner narrative; he is not leading a life in the sense that the rest of us do….It is not the remembrance of things past, the “once” that Clive yearns for, or can ever achieve. It is the claiming, the filling, of the present, the now, and this is only possible when he is totally immersed in the successive moments of an act. It is the “now” that bridges the abyss.”

Physical ‘Now’.

This monkeying around with brain states, internal model-making and sensory data creates Now as a phenomenon we experience, but the physical world outside our collective brain population does not operate through its own neural systems to create a Cosmic Now. That would only be the case if, for example, we were literally living inside The Matrix….which I believe we are not. So in terms of physics, the idea of Now does not exist. We even know from relativity that there can be no uniform and simultaneous Now spanning large portions of space or the cosmos. This is a problem that has bedeviled many people across the millennia.

Augustine (in the fourth century) wrote, “What is time? If no one asks me, I know; if I wish to explain, I do not know. … My soul yearns to know this most entangled enigma.” Even Einstein himself noted ‘…that there is something essential about the Now which is just outside the realm of science.’

Both of these statements were made before quantum theory became fully developed. Einstein developed relativity, but this was a theory in which spacetime took the place of space and time individually. If you wanted to define ‘now’ by a set of simultaneous conditions, relativity put the kibosh on that idea because due to the relative motions and accelerations of all Observers, there can be no simultaneous ‘now’ that all Observers can experience. Also, there was no ‘flow of time’ because relativity was a theory of worldlines and complete histories of particles from start to finish (called the boundary conditions of worldlines). Quantum theory, however, showed some new possibilities.

In physics, time is a variable, often represented by the letter t, that is a convenient parameter with which to describe how a system of matter and energy change. The first very puzzling feature of time as a physical variable is that all mathematical representations of physical laws or theories show that time is continuous, smooth and infinitely divisible into smaller intervals. These equations are also ‘timeless’ in that they can be written down on a piece of paper and accurately describe how a system changes from start to finish (based on boundary conditions defined at ‘t=0’) , but the equations show this process as ‘all at once’.

In fact, this perspective is so built into physics that it forms the core of Einstein’s relativity theory in the form of the 4-d spacetime ‘block’. It also appears in quantum mechanics because fundamental equations like Schroedinger’s Equation also offer a timeless view of quantum states.

In all these situations, one endearing feature of our world is actually suppressed and mathematically hidden from view, and that is precisely the feature we call ‘now’.

To describe what things look like Now, you have to dial in to the equations the number t =  t(now). How does nature do that? As discussed by physicist Lee Smolin in his book ‘Time Reborn’, this is the most fundamental experience we have about the physical world as sentient beings, yet it is not represented by any feature in the physical theories we have developed thus far. There is no theory that selects t = t(now) over all the infinite other moments in time.

Perhaps we are looking in the wrong place!

Just as we have seen that what we call ‘space’ is built up like a tapestry from a vast number of quantum events described (we hope!) by quantum gravity, time also seems to be created from a synthesis of elementary events occurring at the quantum scale.   For example, what we call temperature is the result of innumerable collisions among elementary objects such as atoms. Temperature is a measure of the average collision energy of a large collection of particles, but cannot be identified as such at the scale of individual particles. Temperature is a phenomenon that has emerged from the collective properties of thousands or trillions of individual particles.

A system can be described completely by its quantum state – which is a much easier thing to do when you have a dozen atoms than when you have trillions, but the principle is the same. This quantum state describes how the elements of the system are arrayed in 3-d space, but because of Heisenberg’s Uncertainty Principle, the location of a particle at a given speed is spread out rather than localized to a definite position.  But quantum states can also become entangled. For these systems, if you measure one of the particles and detect property P1 then the second particle must have property P2. The crazy thing is that until you measured that property in the first particle, it could have had either property P1 or P2, but after the measurement the distant particle ‘knew’ that it had to have the corresponding property even though this information had to travel faster than light to insure consistency.

An intriguing set of papers by physicist Seth Lloyd at Harvard University in 1984 showed that over time, the quantum states of the member particles become correlated and shared by the larger ensemble. This direction of increasing correlation goes only one way and establishes the ‘Arrow of Time’ on the quantum scale.

One interesting feature of this entanglement idea is that ‘a few minutes ago’, our brain’s quantum state was less correlated with its surroundings and our sensory information than at a later time. This means that the further you go into the past moments, the less correlated they are with the current moment because, for one, the sensory information has to arrive and be processed before it can change our brain’s state. Our sense of Now is the product of how past brain states are correlated with the current state. A big part of this correlating is accomplished, not by sterile quantum entanglement, but by information transmitted through our neural networks and most importantly our internal model of our world – which is a dynamic thing.

If we did not have such an internal model that correlates our sensory information and fabricates an internal story of perception, our sense of Now would be very different because so much of the business of correlating quantum information would not occur very quickly. Instead of a Now measured in seconds, our Now’s would be measured in hours, days or even lifetimes, and be a far more chaotic experience because it would lack a coherent, internal description of our experiences.

This seems to suggest that no two people live in exactly the same Now, but these separate Now experiences can become correlated together as the population of individuals interact with each other and share experiences through the process of correlation. As for the rest of the universe, it exists in an undefined Now state that varies from location to location and is controlled by the speed of light, which is the fastest mode of exchanging information.

Read more:

In my previous blogs, I briefly described how the human brain perceives and models space (Blog 14: Oops one more thing), how Einstein and other physicists dismiss space as an illusion (Blog 10: Relativity and space ), how relativity deals with the concept of space (Blog 12: So what IS space?), what a theory of quantum gravity would have to look like (Blog 13: Quantum Gravity Oh my! ), and along the way why the idea of infinity is not physically real (Blog 11: Is infinity real?) and why space is not nothing (Blog 33: 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 ( Blog 34: Thinking Visually)

I also summarized the nature of space in a wrap-up of why something like a quantum theory for gravity is badly needed because the current theories of quantum mechanics and general relativity are incomplete, but also point the way towards a theory that is truly background-independent and relativistic (Blog 36: Quantum Gravity-Again! ). These considerations describe the emergence of the phenomenon we call ‘space’ but also down play its importance because it is an irrelevant and misleading concept.

Black Holes for Fun and Profit!

Well, astronomers finally did it. Nearly 100 years ago, Albert Einstein’s theory of General Relativity predicted that black holes should exist. Although it took until the 1960’s for someone like physicist John Wheeler to coin the name ‘black hole’ the study of these enigmatic objects became a cottage industry in theoretical physics and astrophysics. In fact, for certain kinds of astronomical phenomena such as quasars and x-ray sources, there was simply no other explanation for how such phenomena could generate so much energy in such an impossibly small volume of space. The existence of black holes was elevated to a certainty during the 1990s as studies of distant galaxies by the Hubble Space Telescope turned in tons of data that clinched the idea that the cores of most if not all galaxies had them. In fact, these black holes contained millions or even billions of times the mass of our sun and were awarded a moniker all their own: supermassive black holes. But there was still one outstanding problem for these versatile engines of gravitational destruction: Not a single one had ever been seen. To understand why, we have to delve rather deeply into what these beasties really are. Hang on to your seats!

               General relativity is the preeminent theory of gravity, but it is completely couched in the language of geometry – in this case the geometry of what is called our 4-dimensional spacetime continuum. You see, in general relativity, what we call space is just a particular feature of the gravitational field of the cosmos within which we are embedded rather seamlessly. This is all well and good, and this perspective has led to the amazing development of the cosmological model called Big Bang theory. Despite this amazing success, it is a theory not without its problems. The problems stem from what happens when you collect enough mass together in a small volume of space so that the geometry of spacetime (e.g. the strength of gravity) becomes enormously curved.

               The very first thing that happens according to the theory is that a condition in spacetime called a Singularity forms. Here, general relativity itself falls apart because density and gravity tend towards infinite conditions. Amazingly according to general relativity, and proved by the late Stephen Hawkins, spacetime immediately develops a zone surrounding the Singularity called an event horizon. For black holes more massive than our sun, the distance in kilometers of this spherical horizon from the Singularity is just 2.9 times the mass of the black hole in multiples of the sun’s mass. For example, if the mass of a supermassive black hole is 6.5 billion times the mass of our sun, its event horizon is at 6.5 billionx2.9 or 19 billion kilometers. Our solar system has a radius of only 8 billion km to Pluto, so this supermassive black hole is over twice the size of our solar system!

               Now the problem with event horizons is that they are one-way. Objects and even light can travel through them from outside the black hole, but once inside they can never return to the outside universe to give a description of what happened. However, it is a misunderstanding to say that black holes ‘suck’ as the modern colloquialism goes. They are simply points of intense gravitational force, and if our sun were replaced by one very gently, our Earth would not even register the event and continue its merry way in its orbit. The astrophysicist’s frustration is that it has never been possible to take a look at what is going on around the event horizon…until April 10, 2019.

               Researchers using the radio telescope interferometer system called the Event Horizon Telescope were able to synthesize an image of the surroundings of the supermassive black hole in the quasar-like galaxy Messier-87 – also known as Virgo A by early radio astronomers after World War II, and located about 55 million light years from Earth. They combined the data from eight radio telescopes scattered from Antarctica to the UK to create one telescope with the effective diameter of the entire Earth. With this, they were able to detect and resolve details at the center of M-87 near the location of a presumed supermassive black hole. This black hole is surrounded by a swirling disk of magnetized matter, which ejects a powerful beam of plasma into intergalactic space. It has been intensively studied for decades and the details of this process always point to a supermassive black hole as the cause.

Beginning in 2016, several petabytes of data were gathered from the Event Horizon Telescope and a massive press conference was convened to announce the first images of the vicinity of the event horizon. Surrounding the black shadow zone containing the event horizon was a clockwise-rotating ring of billion-degree plasma traveling at nearly the speed of light. When the details of this image were compared with supercomputer simulations, the mass of the supermassive black hole could be accurately determined as well as the dynamics of the ring plasma. The round shape of the event horizon was not perfect, which means that it is a rotating Kerr-type black hole. The darkness of the zone indicated that the event horizon did not have a photosphere of hot matter like the surface of our sun, so many competing ideas about this mass could be eliminated. Only the blackness of a black hole and its compact size now remain as the most consistent explanation for what we are ‘seeing’. Over time, astronomers will watch as this ring plasma moves from week to week. The next target for the Event Horizon Telescope is the four million solar mass black hole at the center of the Milky Way called Sgr-A*. Watch this space for more details to come!!

We have truly entered a new world in exploring our universe. Now if someone could only do something about dark matter!!!

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]

 

Thinking Visually

Look at the two images  for a few minutes and let your mind wander.

What impressions do you get from the patterns of light and dark? If I were to tell you that the one at the top is a dark nebula in the constellation Orion, and the one on the bottom is a nebula in the Pleiades star cluster, would that completely define for you what you are experiencing…or is there something more going on?

Chances are that, in the top image you are seeing what looks like the silhouette of the head and shoulders of some human-like figure being lit from behind by a light. You can’t quite put your finger on it, but the image seems vaguely mysterious and perhaps even a bit frightening the more you stare at it.

The image on the bottom evokes something completely different. Perhaps you are connecting the translucence and delicacy with some image of a shroud or silken cloak floating in a breeze. The image seems almost ghost-like in some respects…spiritual

But of course this is rather silly” you might say. “These are interstellar clouds, light-years across and all we are doing is letting our imaginations wander which is not a very scientific thing to do if you want to understand the universe.” This rational response then tempts you to reach for your mouse and click to some other page on the web.

What has happened in that split second is that a battle has been fought between one part of your brain and another. The right side of your brain enjoys looking at things and musing over the patterns that it finds there. Alas, it cannot speak because the language centers of the brain live in the left cerebral hemisphere, and it is here that rules of logic and other ‘scientific’ reasoning tools exist. The left side of your brain is vocal, and talking to you right now. It gets rather upset when it is presented with vague patterns because it can’t understand them and stamp them with a definite emotion the way the right hemisphere can. So it argues you into walking away from this challenge of understanding patterns.

If you can suspend this indignation for a moment or two, you will actually find yourself thinking about space in a way that more nearly resembles how a scientist does, though even some scientists don’t spend much time thinking about space. This indifference has begun to change during the last 20 years, and we are now in the midst of a quiet revolution.

There are three child-like qualities that make for a successful scientist:

Curiosity. This is something that many people seem to outgrow as they get older, or if they maintain it as adults, it is not at the same undiluted strength that it was when they were a child.

Imagination. This is something that also wanes with age but becomes an asset to those that can hang on to even a small vestige of it. It is what ‘Thinking out of the box’ is all about.

Novelty. As a child, everything is new. As an adult we become hopelessly jaded about irrelevant experiences like yet another sunset, yet another meteor shower, yet another eclipse. In some ways we develop an aversion for new experiences preferring the familiarity of the things we have already experienced.

If you wish to understand what space is all about, and explore the patterns hidden in the darker regions of nature, you will have to re-acquaint yourself with that child within you. You will need to pull all the stops out and allow yourself to ‘play’ with nature and the many clues that scientists have uncovered about it. You will need to do more than read books by physicists and astronomers. They speak the language of the left-brain . They can help you to see the logical development of our understanding of space and the Void, but they can not help you internalize this knowledge so that it actually means something to you. For that, you have to engage your right-brain faculties, and this requires that you see the patterns behind the words that physicists and astronomers use. To do that, you will need to think in terms of pictures and other types of images. You will need to bring something to the table to help you make sense of space in a way that you have not been able to before. You will need to expand your internal library of visual imagery to help you find analogues to what physicists and astronomers are trying to describe in words and equations. These visual analogues can be found in many common shapes and patterns, some seen under unusual and evocative circumstances. Here are some evocative images that seem to suggest how space might be put together compliments of  a diatom, the painters Miro and Mondrian, dew on a spider web, and atoms in a tungsten needle tip!

Spider web covered with dew drops

Remember, the right brain uses ALL sensory inputs to search for patterns and to understand them. It even uses imaginary information, dreams, and other free-forms to decode what it is experiencing.  

My book ‘Exploring Quantum Space’ is a guidebook that will give you some of the mental tools you will need to make sense of one of the greatest, and most subtle, discoveries in human history. Space, itself, is far from being ‘nothing’ or merely a container for matter to rattle around within. It is a landscape of hidden patterns and activity that shapes our universe and our destiny. You cannot understand it, or sense the awe and mystery of its existence, by simply reading words and following a logical exposition of ‘ifs and thens’. You also have to experience it through evocative imagery and imagination. Space is such a different medium from anything we have ever had to confront, intellectually, that we need to employ a different strategy if we wish to understand it in a personal way. Once we do this, we will be reconnected with that sense of awe we feel each time we look at the night sky.

My next blog about Nothing introduces some of the other ideas and techniques that scientists use to think about the impossible!