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Astronomy, Eclipse

The Last Total Solar Eclipse…Ever!

Credit  Luc Viatour  https://Lucnix.be….An email to Viatour Luc would be appreciated too.

Well…The answer is 700 million years from now, but the details are interesting!

Since the dawn of recorded history, humans have had a love-hate relationship with total solar eclipses. For most of human history, these events were feared and taken as omens of the downfall of empires or the end of the world. Only in the last thousand years or so have people settled down and viewed them as the beautiful and bizarre events that they are. By the 19th Century, scientists and artists traveled the world over to capture them with sketches at the telescope eyepiece. Among the first images taken by primitive cameras were those of total solar eclipses.

Predicting total solar eclipses

Today, the physics and mathematics of these events are known with such detail that they can be predicted to within minutes from 2000 BCE to 3000 CE [1]. They can even be used to track the slowing down of earth’s rotation by comparing the predicted time and place with historical observations [2]. But total solar eclipses require a precise geometric circumstance to exist. Our moon has a diameter of 3,475 km at a perigee distance of 363,300 km, while the sun has a diameter of 1.4 million km at a distance of 150 million km. This means that, although the sun has a diameter that is 403 times the moon, it is 412 times farther away so that the apparent size of the dark lunar disk completely covers the blinding disk of the sun in the sky. Depending on the exact timing of the moon in its orbit, this ratio of 403/412 can be made to be exactly equal to 1.00 so that the disk of the moon exactly covers the sun to give the classic total solar eclipse shown in the picture above. But this precise geometric circumstance is not written in stone. In fact, to get a proper prediction far into the fiuture you need a supercomputer!

Earth orbit evolution

Currently the distance from earth to the sun has an average value of 150 million km, but because Earth’s orbit is an ellipse, it varies from 152 million km in July to 147 million km in January. This leads to the ironic circumstance that in the Northern Hemisphere, the sun is actually farthest away from the sun in the summer and closest in the winter! Only the Southern Hemisphere with its reversed seasons gets it right!

For many decades, researchers have modeled the evolution of the orbit of the Moon and Earth with supercomputers and pretty much nailed down what we can expect to happen for the next few billion years. As it turns out, this is a fiendishly difficult calculation because it depends on an exact knowledge of the interiors of the moon and earth, the location of the continents, and the influences of the other planets. The inner solar system is dynamically unstable and displays a chaotic behavior over times of 100 million years or longer. A consequence of this is that even changing the location of Mercury in its orbit by 1 meter today causes a variety of different outcomes in a billion years including its collision with Venus and ejection from the solar system. Earth, however, seems to exist in a remarkably stable gravitational balance such that its orbit changes only insignificantly from what we see today. [3] It will drift outwards from the sun by a few thousand kilometers due to the sun itself losing mass. The sun converts 4 million tons of mass into radiant energy every second and added up over millions of years, this causes the sun’s gravitational hold on Earth to weaken and its orbit to drift outwards by 1.5 cm/year [4].

The outward drift of Earth in its orbit is entirely negligable so we won’t bother including it. We will assume that the average perihelion and aphelion distances will still remain close to 147 and 152 million km. This means that from Earth the angular diameter of the sun from the surface will vary between 1,964 seconds of arc at perihelion to 1,900 seconds of arc at aphelion, where 3600 seconds of arc equals 1 angular degree.

Lunar orbit evolution.

The moon raises ocean and solid-body tides in Earth. The tidal bulge accelerates the moon in its orbit and the orbit of the moon increases over time. The tidal bulge also slows down Earth’s rotation and lengthens the length of its ‘day’.

We know from geologic data that our moon was formed some 4.4 billion years ago and orbited Earth at a distance of only about 30 Earth Radii ( 190,000 km) causing Earth to have a rotation period of about 12 hours in a ‘day’. [5]. Since its formation, it has drifted out to its present distance at a current rate of about 3.8 cm/year based on lunar laser metrology [6]. But this outward drift continues today so that in the future the moon will be even farther from Earth. This means that at some time in the future, the ratio of lunar:solar size and lunar:solar distance will fall below the magic 1.000 needed for a total solar eclipse. The moon will simply be too small in apparent size to perfectly cover the disk of the sun. We can’t predict the exact date when we will see the very, very, very last total solar eclipse from Earths surface, but we can get a pretty good idea what timescales are involved.

Simple Linear Model

Suppose we just used the current perihelion and aphelion distances and then assumed that the moon is moving away from Earth at a constant rate of 3.8 cm/year. If we calculate the angular sizes of the moon and sun from Earth we get the following figure.

Explanation: The orange line is the angular size of the sun viewed from Earth when Earth is closest to the sun (perihelion) and the yellow line is the same calculation from when Earth is farthest from the sun (aphelion). The black line is the angular diameter of the moon at its farthest distance from Earth (apogee) and the green line is for its closest distance to Earth (perigee). What you see is that the lunar curves cross the solar curves and indicate when these two diameters are equal, allowing a total solar eclipse to be viewed. So long as the solar lines are between the two lunar lines, you will have a total solar eclipse.

What this graph says is that 1044 million years ago, the sun at perihelion matched the moons size at apogee when it had the smallest angular size. After this ‘year’ the moons size at apogee was too small to cover the sun at perihelion and so total solar eclipses at lunar apogee ceased to happen when the solar disk was largest at perihelion. Notice that before 1044 million years the lunar lines were above the solar lines. This means that the disk of the moon was always much greater than the disk of the sun at any time in the lunar orbit. In fact, the lunar disk was so big that not only was the disk of the sun covered by the moon but much of the inner corona too. You would still have total solar eclipses before 1044 million years ago, but they would look dramatically different than the ones we see today.

By the time we get to 710 million years ago, the moon at apogee was also too small to cover the sun at aphelion when the solar disk is smallest. Between 1044 and 710 million years ago, the small apogee moon could still cover the sun when the sun was between aphelion and perihelion, but after 710 million years ago, there would never again be a total solar eclipse of the sun when the moon was at apogee. This was before the emergence of multi-cellular life on Earth during the Cambrian Explosion. Only annular eclipses will be viewed from then on during lunar apogee.

Now the second lunar curve in green is more interesting. It shows the angular size of the perigee moon, and it is pretty clear that today (Time-0) the size of the perigee moon is larger that the sun at both perihelion and aphelion. So we get total solar eclipses no matter if Earth is at perihelion or aphelion. However, by 280 million years from now, the moon will start to become smaller than the solar disk at perihelion and so eclipses will stop being total solar eclipses when the sun is closest to earth and the moon is also closest to earth. After 613 million years from now, you will no longer have total solar eclipses for the perigee moon and the smaller aphelion sun. After 613 million years the lunar disk will never again be big enough to completely cover the solar disk. This is the estimate you are likely to find in many popularizations of this Final Event such as a SpaceMath problem at NASA, and NASAs lunar scientst Dr. Richard von Drak.

A More Accurate Calculation.

The previous linear calculation was based on the moon maintaining its outward 3.8 cm/yr motion for the next 600 million years, but detailed supercomputer calculations of the evolution of the Earth-Moon system give a more accurate result. I used the model published in 2021 by Prof. Houraa Daher and her team at the University of Michigan [7], and specifically used their Figure 5a, which gave the past value for the lunar orbit semi-major axis. I also used the 2020 data from the published work by Dr. Bijay Sharma [8] at the National Institute of Technology in India, specifically Figure 7, which gave the recession speed (cm/yr) with lunar semi-major axis. Ideally, both of these data should be derived from the same calculations but unfortunately this was not possible to obtain at the time of this writing. However, if they are both faithful to the same underlying physics, then the results should be consistent.

The application of these detailed models to the lunar size evolution is shown in the next figure.

The straight, linear extrapolations have now been replaced by more realistic curved predctions. Here we see along the black line that at 700 million years ago, the lunar size at apogee matched the solar disk size at perihelion (1952 arc-seconds) , some 300 million years later than the linear model. By 500 million years ago the apogee lunar disk no longer covered the disk of the sun at aphelion, so from this time forward there were no longer any total solar eclipses when the moon was at its farthest apogee distance. This happened around the time of the Cambrian Explosion.

Meanwhile, the green line for the perigee moon shows that it has a disk size greater then the size of the large perihelion sun (1952 arcseconds) disk until 300 million years from today. At this time, the lunar diameter varies from 1718 arcseconds (black line) to 1952 arcseconds (green line) so we can still have total solar eclipses so long as the moon is close to its perigee when the sun passes through one of the lunar ‘nodes’ during the equinoxes. At about 700 million years from now the large perigee moon with a diameter of 1952 arcseconds covers the sun at perihelion, but after this time, its diameter continues to decrease until from this time forward all we ever see are annular eclipses. So this critical ‘date’ is about 80 million years later than the linear model.

By 700 million years from now, the moon will continue to drift away from Earth, but at a slower rate of 3.0 cm/year. Its distance from Earth will have grown from 60.2 Re (384,400 km) to 63.8 Re (407,155 km). The moon will then take 28.4 days to orbit Earth having gained about 26.4 hours since today. This means that the time between one full moon and the next will be 30.7 days instead of the current 29.5 days. Meanwhile, the Earth’s rotation has changed from its current 23h 56m to about 26h 25m as the lunar tides continue to do their work. What this means is that an Earth Year at 700 million years from today will only about 330 days long!

Will there be anyone there to care? Probably not.

Our sun continues to evolve and grow in luminosity so by then it will be about 10% more luminous than it is today.  This means the average global temperature will be 117o F and not the 57o F we enjoy today. By this time, the level of carbon dioxide will have fallen below the level needed to sustain C3 carbon fixation photosynthesis used by trees.  Some plants use the C4 carbon fixation method to persist at carbon dioxide concentrations as low as ten parts per million. However, the long-term trend is for surface plant life to die off altogether. The extinction of plants  will be the demise of almost all animal life since plants are the base of much of the animal food chain on Earth. Climate models suggest that by about this time Earth will be hot enough to cause the slow evaporation of the oceans into the atmosphere. This will be the start of what is called the “moist greenhouse” phase, resulting in a runaway evaporation of the oceans and Earth becoming Venus.  Meanwhile, the current continents will have merged and separated and merged again into yet another supercontinent with its own lethal contribution to global heating and weather [9].

So basically by about 700 million years from now, Earth will be a humid, desert world with no complex living organisms to appreciate total solar eclipses except perhaps extremophile bacteria…and cockroaches?

Have a nice day!

[1] Five Millennium Catalog of Solar eclipses https://eclipse.gsfc.nasa.gov/SEcat5/catkey.html

[2] Ancient eclipses Reveal How Earths Rotation has Changed https://www.space.com/ancient-eclipse-records-earth-rotation-history

[3] Highly Stable Evolution of Earths Future Orbit Despite Chaotic Behaavior of Solar System https://iopscience.iop.org/article/10.1088/0004-637X/811/1/9

[4] https://www.forbes.com/sites/startswithabang/2020/04/09/earth-is-spiraling-away-from-the-sun-for-now-but-will-eventually-crash-into-it/?sh=863220238580

[5] Long-Term Earth-Moon Evolution With High-Level Orbit and Ocean Tide Models https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2021JE006875 figure 6

[6] The moon has been drifting away from Earth for 4.5 billion years. A stunning animation shows how far it has gone. https://www.businessinsider.com/video-moon-drifts-away-earth-4-billion-years-2019-9

[7] Long‐Term Earth‐Moon Evolution With High‐Level Orbit and Ocean Tide Models, https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9285098/

[8] The Past, Present and the Futuristic Earth-Moon Orbital-Global Dynamics – and its habitability – https://www.proquest.com/openview/c945a68d9b4a2354aaea7cf859b776ba/1?pq-origsite=gscholar&cbl=4882998

[9] What if You Traveled One Billion Years into the Future? https://whatifshow.com/what-if-you-traveled-one-billion-years-into-the-future/

Brain Research

Math Anxiety: Origins and Cures

Portrait Of Student With Head Down On Stack Of Books

Someone asks you to perform a simple arithmetic calculation, or perhaps you encounter these while doing your income tax. As a consumer you might want to compare the cost of two products with different sales prices. Or perhaps the tags give  you the same product by two different manufactures who tell you the unit cost, but the products are  in either 12-count or 18-count packages. The odds are very good that along with millions of other adults you will have some trepidation in ‘doing the math’. That’s because math anxiety (MA) is endemic not only among US adults but around the world. It crosses ethnic groups, cultures and continents. According to a recent study of MA[1] 93% of all adults in the US suffer from some level of this condition; internationally and across many cultures, this incidence can be over 40%.  It is reinforced by parents, the news media, and even by teachers using outdated pedagogy– all with devastating consequences, long-term. Like ADHD, you can find yourself somewhere on the Math Anxiety Spectrum. Your location might even change as you advance from childhood to adulthood.

Your Brain on Math

The evolution of our brains over millions of years has prepared it to do many kinds of math but often at an unconscious level. We, along with thousands of other species, have an innate ability to compare quantities and figure which is larger. Some species can even count including chimpanzees, crows, bees and frogs[2]. Our brains come hard-wired at birth to understand addition and subtraction. There are actual brain neurons in the parahippocampal cortex that are only active during addition while others are only active during subtraction[3].They also respond when the instruction is written down symbolically as a word or a symbol (five and three  or 5+3).

Credit: https://anthonybonato.com/2016/04/20/this-is-your-brain-on-mathematics/

The number of brain regions involved in mathematics performance reads like a catalog of nearly half of the cerebral cortex itself. This means that many of these math-activated regions are also used for other purposes in the brain. This is a common feature of brain architecture in that regions are recycled to form other neuronal networks depending on the task at hand.

  • Dorsolateral prefrontal cortex
  • Left inferior parietal lobe
  • Left precentral gyrus
  • Left superior parietal lobe
  • Left supramarginal gyrus
  • Left middle temporal gyrus
  • Insula
  • Middle cingulate cortex
  • Middle frontal gyrus
  • Superior temporal gyrus
  • Inferior frontal gyrus
  • Thalamus
  • Bilateral intraparietal region
  • Dorsal prefrontal region
  • Inferior temporal region

As a brain matures, these regions respond to external experiences but are always influenced by innate survival instincts provided by the limbic system composed of the thalamus and the amygdala. When no previous  negative experiences trigger a limbic response for fight-or-flight, all is well.  Even by the age of 7, children still have an enthusiastic and playful attitude towards math. This attitude unfortunately starts to wane in direct proportion to the number of negative performance tests they experience, which is why MA arises.

A common view shared by many MA students is that, unless I can do math quickly, I must not be very good at it. This is also a pervasive attitude among adults who, despite performing well in grade-school math may still not see themselves ‘good’ at math. Math skills are unlike reading skills because there has evolved over time a massive social permissiveness to being a poor math performer that simply  isn’t found in other academic topics.

Thanks to advances in brain research and mapping, we have a ring-side seat into what brain regions and neuronal circuitries are responsible, not only for handling mathematical problem-solving of increased sophistication, but how this process maps into generating anxiety. There is even a specific brain protein called MAOA that correlates with MA and can be used to spy on your emotional state as you are confronted with different problems.

Math comprehension and execution, like our language centers (Broca and Wernicke Regions) are activated primarily in two main regions: The parietal lobe is involved with calculating and processing numbers; The frontal lobe is involved in recalling numerical knowledge and working memory[3].

The sub-region called the dorsolateral prefrontal cortex is most curious because it is also activated as we regulate our emotions. For example, most children learn how to tone-down their glee at winning a game when they see their friends are mortified at  having lost. In math this region seems to be activated when the individual is keeping track of more than one concept at a time[2]. This region, which in math helps us keep relevant  problem-solving information ‘fresh’ in our working memory,  is also shared by circuits that allow us to suppress selfish behavior, foster commitment in relationships, and inferring the intentions of others, which is called a Theory of Mind. Researchers have proposed that math training not only makes us better at math, but also strengthens our ability to moderate our feelings and our social interactions because of the brains proclivity in  sharing brain regions for other purposes.

The Amygdala Hijack

Brain imaging studies[3] show that individuals with MA, not unexpectedly, activate circuits associated with negative emotional processing (amygdala, prefrontal cortex), the experience of pain (insula), but also areas involved with inhibiting irrelevant information, and conflict processing. The emotional control network is activated even before mathematical performance occurs. MA does its dirty work by literally robbing the individual of resources in its working memory so that they no longer have access to recalling how similar problems were previously solved. In fact, actual physical changes to the brains of MA students were found in the amygdala, the anterior corpus callosum, the right inferior frontal sulcus and the pericallosal sulcus. In particular the right amygdala volume is smaller and more reactive in students with MA[4]. Chronic hyperactivity of the amygdala in response to stress results in cellular atrophy and a decreased ability to regulate negative emotions. This effect continues into adulthood, so repeated negative math experiences in childhood alters the way that adults handle MA in a way that is both cumulative and apparently not easily mitigated in adulthood because it involves physical changes (atrophy) to specific brain regions.

One of the most troubling features of exercising a math skill is that the regions used are also connected via neuronal synapses to  the prefrontal cortex and to the amygdala. The PFC is a vital executive brain region used for synthesizing data symbolically, keeping information present in a ‘working memory’ and forecasting what happens next. This means that getting better at math allows your PFC to be trained to make better decisions about the future. But here is the BIG PROBLEM. The amygdala also watches over this process and stamps it with an emotional context. Under conditions were the stress hormone cortisol is elevated, the amygdala sees your current condition as a fight-or-flight situation and ‘hijacks’ your brain. [5]This immediately shuts down your PFC and flavors your conscious thinking with the survival instinct of wanting to flee the situation. Forget about logic and planning – it’s time to run! Of course this is not possible when working on a difficult math problem, plus the hijack has now robbed you of clear executive thinking, planning and working memory, which only increases the cortisol.

Defeating MA

This cycle of increasing stress can be defeated by first recognizing it is happening   (sweaty palms, rapid heartbeat), using deep slow breathing, and especially clearing your mind of intrusive thoughts. It only takes 90 seconds to defeat this progression. But sometimes, putting yourself in a state where MA cannot get a toe-hold is ‘simply’ a matter of not triggering the Amygdala Hijack in the first place. Here are some recommendations for teachers from researchers who have studied this triggering process.

  • Incorporate math into real-world concepts that students understand.
  • Focus on the fun elements of math like pattern making and a curiosity about numbers, not on rote memorization and theory.
  • Have them see how numbers and data literacy surround them in life from supermarket shopping to predicting future trends.
  • Avoid negative self-talk. Train yourself to have a positive attitude.
  • Consider math as a foreign language that takes practice.
  • Break the vicious downward cycle  of a bad test grade leading to lower self-esteem leading to another bad test grade leading to still-lower self-esteem.
  • Never scold a student for being wrong or having failed to perform a ‘simple’ math task.
  • Never tell your child ‘I was never good at math either’. This tells the child they can succeed in life without knowing math, which is demonstrably false in the 21st century.
  • Find ways to provide alternate student assessments rather than timed tests. This is a major source of stress and a key factor in MA.
  • Investigate ‘mixed-ability’ groupings to avoid placing MA student together, which only reinforces and normalizes  MA through peer-pressure.
  • Make math fun with lots of positive reinforcement. This reduces stress and heart rates and mitigates MA.
  • Have parents read math-related bedtime stories.
  • Encourage understanding not rote memorization. STEM professionals are those who think slowly, creatively and deeply..not necessarily quickly.
  • Display ‘anchor charts’ with examples of work, previous problems or formulas as visual clues to recall previous material.
  • Draw or write down facts or relevant equations before working on a math problem
  • Have students describe the problem to a partner to help articulate their thinking
  • Start the class with a ‘diffuser’ such as sharing a joke, or asking ‘who can tell me something we did in class yesterday?”
  • Focus on how a student got their answer and not on it whether it is right or wrong. If incorrect the student may realize this as they explain the process they used.
  • Allow students to post pictures or written explanations of their methods of solving a problem.
  • Pay attention to the words you use. Instead of ‘this is easy’ say ‘this is like the problem we did yesterday”.
  • Always project a positive, confident attitude to support modeling MA-free behavior and attitudes.

Genetic Predispositions

Here’s some bad news. MA might be genetically inheritable. The epigenetic genome controls how genes are expressed. It represents an additional way that traits and tendencies can be passed on. It is well known that traumas to parents can be passed to children, especially starvation and malnutrition. If the starving mother is pregnant, the epigenome she gives to her fetus can cause childhood difficulties in expressing proteins needed for proper digestion. Epigenetics also seems to explain how stress-related disorders can be inherited. According to a review article by TruDiagnostic published in 2020[6], the amount of cortisol in the brain can be regulated by the inherited epigenetic genome and predispose a child to stress-related behavior. It is not impossible that the same transfer of tendencies might happen that predispose the child to MA.  MA seems to result from an interaction of genetic vulnerability with negative experiences learning math. Only an unkind word from a teacher, parent or social group would be enough to set MA in motion, full-blown.

Researchers have also found that a molecular genetic marker called the monoamine oxidase A gene (MAOA) when not expressed at high enough levels correlates with increased MA especially in girls who are known from other studies to be especially susceptible to MA[7]. However, Zhe Wang at Ohio State finds that genetic factors may only account for about 40% of the individual differences in math performance based on a study of 216 twins “If you have these genetic risk factors for math anxiety and then you have negative experiences in math class, it may make learning that much harder.”[8]

MA causes millions of children, especially girls, to not consider STEM careers. This can relegate them to lower-paying jobs that are less quantitative in skill-set. With manual cash registers, some arithmetic acumen was always required even in low-paying sales jobs. Today, change is made with computerized terminals so low-paying jobs require virtually no math and are free of MA triggers.  However, the consequences of not continuing  math education in adolescence can be potentially disastrous not only reducing their career options but in the actual development of their brains.

A recent study of adolescents in the UK shows that a lack of math education affects adolescent brain development. In the UK, students can elect to end their math education at age 16.  The chemical called gamma-Aminobutyric acid (GABA) is present in the middle front gyrus (MFG), which is a region involved in reasoning and cognitive learning. GABA levels are a predictor of changes in mathematical reasoning as much as 19 months later.  What was found among the older adolescents was that GABA showed a marked reduction[9]. Because this chemical is also involved in brain plasticity and the ability to learn new skills and thinking, this reduction at this critical stage in brain development can have far-reaching impacts into adulthood.

Don’t worry…Be happy

But the good news is the brain is not a static thing. It is very ‘plastic’ when it comes to learning and dealing with new experiences. With patience and a more-supportive classroom environment, students can be shown how to make other associations between math and emotions, but this time ones that mitigate MA.

References

[1] Brain areas associated with numbers and math, 2018, doi.org/10.1016/j.dcn.2017.08.002 

[2] Mental math and the fine-tuning of emotions. Sandra Ackerman, 2017, Dana Foundation Blog, dana.org/article/mental-math-and-the-fine-tuning-of-emotions/

[3] Dorsolateral Prefrontal Cortex, 2013, Simmon Moss,  and Wikipedia [ref 8]

[4] Neurostructural correlate of math anxiety in the brains of children. Karin Kucian et al,   Translational Psychiatry, 2018; 8:273. Doi: 10.1038/s41398-018-0320-6. And www.ncbi.nlm.gov/pmc/articles/PMC6288142/

[5] The stress-learning connection: Manage an Amygdala Hijack in three steps. The Brain Health Magazine, 2022, thebrainhealthmagzine.com/hormones/the-stress-learning-connection-manage-an-amygdala-hijack-in-three-steps/

[6] Epigenetics and Anxiety – The relationship between genes and stress-related disorders, 2020, blog.trudiagnostic.com/epigenetics-and-anxiety/

[7] MAOA-LPR polymorphism and math anxiety: A marker of genetic susceptibility to social influences in girls, 2022, Annals of the New York Academy of Sciences 1516(1), DOI:10.1111/nyas.14814.

[8] Who’s afraid of math? Genetics plays a role but researchers say environment still key, 2014, geneticliteracyproject.org/2014/03/19/genetics-plays-a-role-in-math-anxiety/

[9] www.sciencedaily.com/releases/2021/06/210607161149.htm and DOI:10.1073/pnas.2013155118

Physics

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!!!

NASA, Space Travel

An Old Era Ends-A New One is Born

As the international rush to get to the moon ramps up in the next few years, it is worth noting that, just as we are losing the World War II generation, we are also losing NASA’s early astronaut corps who made the 1960s and 1970’s space exploration possible.

Often called the most significant photo from space in human history, the famous “Earthrise” photo taken by Apollo 8 astronauts on Dec. 24, 1968 never fails to cause an emotional response. 

The Mercury, Gemini and Apollo astronauts are legends who made our current travel to the moon far less of a challenge 50 years later than it would otherwise have been. Since these missions completed their historic work, we have been able to mull over many scenarios for how to do it ‘right’ the next time, and so here we are. We have learned from our successes in science and engineering, but we have also learned from our failure of political nerve to go beyond the gauntlet thrown down by Apollo 17. Now we are in the midst of what appears to be a new Space Race, this time between the open societies of the ‘west’ and the closed and secretive society of China. Meanwhile, amidst this political hubris, the ranks of the Old Guard astronauts continue to thin out each year.

Project Mercury

The first group of astronauts to pass, were the original Project Mercury astronauts at the pionering, and very risky, dawn of NASA (1958-1963): Scott Carpenter, Gordon Cooper, John Glenn, Virgil Grisson, Walter Schirra, Alan Shepard and Donald Slayton. With the passing of John Glen in 2016 at the age of 95, we lost irretrivably our connection to the trials and tribulations of sitting in a ‘tin can’ as big as a telephone booth and eating food out of toothpaste tubes. These were the incredably brave men who sat on top of rockets that had only been tested a handful of times without blowing up!

John Glenn entering the Friendship 7 Mercury capsule on top of the Redstone rocket,

But more than that, these were the faces of NASA that we saw in the news media who made space travel a household word in the early-1960s. This was a HUGE transition in social consciousness because prior to Project Mercury, space travel was pure science fiction. We were a Nation obsessed by the prospects of nuclear war and Soviet spies lurking around every street corner. The adventures of the Mercury astronauts let hundreds of millions of people take a mental vacation and think about more hopeful ties to come. That plus the advent of the Jetsons TV series!

The 14 ‘Group 3’ astronauts selected in 1963 for the Gemini and Apollo manned programs

The second cohort of astronauts were those that flew with Project Gemini between 1963 and 1966. There were ten crewed missions and 16 astronauts, who conducted space walks, dockings and tested out technology and protocols for the Apollo program. Many of them went on to fly in Project Apollo having earned their ‘creds’ with Gemini.

The photo above shows, seated left to right, Edwin Aldrin (33), William Anders (30), Charles Bassett (32), Alan Bean (31), Eugene Cernan (29), and Roger Chaffee (28). Standing left to right are Michael Collins (33), Walter Cunningham (31), Donn Eisele (33), Theodore Freeman (33), Richard Gordon (34), Russell Schweickart (28), David Scott (31) and Clifton Williams (31). Additional astronauts were selected for Gemini: Frank Borman (35), Jim Lovell (35), Thomas Stafford (33), John Young (34), Neil Armstrong (33), and Pete Conrad (33). The ages of this group in 1963 spanned 29 to 35.

Whenever I look at this photo, I see these astronauts as being 10 years older than their actual age. I was a teenager during this time and anyone older than 25 or 30 looked pretty old to me. I guess for these astronauts, a military life, and the dress styles of the narrow-tie, conservative, early-60s does that to you.

NASA Astronaut Edward White floats in zero gravity of space northeast of Hawaii, on June 3, 1965, during the flight of Gemini IV.

At the present time, January 2023, the only survivors of the Mercury and Gemini groups are Edwin Aldrin (92), William Anders (89), Russell Schweickart (88) and David Scott (91). We just lost Walter Cunningham (90).

Finally, we have the Program Apollo astronauts. They were actually drawn from the Project Gemini group, but because of the premature deaths of Roger Chaffee, Ed White, Charles Bassett, and Theodore Freeman, additional astronauts were added to this project: Charles Duke, Harrison Schmitt, Ken Mattingly, Fred Haise, Wally Schirra, Edgar Mitchell, Jack Swigert, James Irwin, Alfred Wordon, James McDivitt, Ronald Evans, and Stuart Roosa.

50th Anniversary, 2019: From left to right: Charlie Duke (Apollo 16), Buzz Aldrin (Apollo 11), Walter Cunningham (Apollo 7), Al Worden (Apollo 15), Rusty Schweickart (Apollo 9), Harrison Schmitt (Apollo 17), Michael Collins (Apollo 11) and Fred Haise (Apollo 13). 
Felix Kunze/The Explorers Club

Each Apollo mission had three astronauts. Two would take the LEM to the surface for a walk-about, while the third astronaut remained behind in the Command Module. A total of 12 Apollo astronauts actually walked on the moon between Apollo 11 and 17: Neil Armstrong, Buzz Aldrin, Pete Conrad, Alan Bean, Alan Shepard, Edgar Mitchell, David Scott, James Irwin, John Young, Charles Duke, Eugene Cernan and Harrison Schmitt. Of these, the survivors by January, 2023 are Buzz Aldrin (92), David Scott (90), Charles Duke (87) and Harrison Schmitt (87).

An excellent view of the Lunar Excursion Module (LEM) “Orion” and Lunar Roving Vehicle (LRV), as photographed by astronaut Charles M. Duke Jr., lunar module pilot, during the first Apollo 16 extravehicular activity (EVA) at the Descartes landing site.

So, the surveying astronauts in January 2023 from the Mercury, Gemini and Apollo programs are, in order of age:

Buzz Aldrin (92: Gemini 12, Apollo 11),

David Scott (90: Gemini 8, Apollo 9, Apollo 15),

William Anders (89: Apollo 8),

Fred Haise (89: Apollo 13),

Russell Schweickart (88: Apollo 9),

Charles Duke (87: Apollo 16)

Harrison Schmitt (87: Apollo 17).

Ken Mattingly (86: Apollo 16, STS-4, STS-51C),

Apollo 17 astronaut Harrison Schmitt on the moon.

We are entering something of a race against time for these survivors to be present for the launch of Artemus III. Artemis III is planned as the first crewed Moon landing mission of the Artemis program. Scheduled for launch in 2025, Artemis III is planned to be the second crewed Artemis mission and the first crewed lunar landing since Apollo 17 in 1972. Buzz Aldrin (92: Gemini 12, Apollo 11) was one of the first astronauts to set foot on the lunar surface, while Harrison Schmitt of Apollo 17 was one of the last. With Buzz Aldrin and David Scott, we even have survivors from the Gemini Program who laid the groundwork for EVAs (Gemini 12) and docking maneuvers (Gemini 8).

The odds are pretty good that many of these Old Guard astronauts will still be with us to see the Artimus III lunar lander called Starship HLS reach the lunar surface, and oh what a celebration it will be at NASA!

Astronomy, Brain Research, Physics

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!

Uncategorized

Silent Earth

Noise pollution is a serious matter that can affect not only how well you sleep at night, but also your health and even psychological state. None of this should surprise you, but as our planet becomes more urbanized, the expanding cloud of man-made noise from jets, traffic and even leaf-blowers can penetrate even remote forests and habitats.

Just out of curiosity, I have created a citizen science project that you can download to your phone from your app store and help me map, not the noisiest places on this planet, but the quietest places. The project can be found by downloading from your store the app called ‘Anecdata’. It will ask you to register by entering an email address, a username and your own private password. Once registered, scroll down the project page and join the one called ‘Silent Earth’. You should also join the Facebook group called ‘The Silent Earth Project’ because I post updates there and tips for taking data, as well as interesting results along the way. https://www.facebook.com/SilentEarthProject

This is what the project banner looks like on your phone

In time, I will be using this blog space to include article of interest on noise pollution and some of our results as we get more areas covered. Here is what you need to do to get going.

Check out the national map by the National Park Service to see how your area ranks https://earthsky.org/earth/map-shows-loudest-quietest-places-in-u-s

Step 1: Tap the bar that says ‘+Observe’ on the project window

Step 2: Tap the bar that says ‘Measure’ and click ‘OK’. Remain quiet for a few seconds.

Step 3: Tap the check boxes that apply to you and your location

Step 4: Tap the ‘save’ tab at the upper right of the screen to record your data.

Don’t be shy!! Make as many measurements as you like but certainly more than one!!! Also, if it seems noisy where you are, say above 50 decibels (dB) walk around your neighborhood or town (or use a bike or car) to find a place that is quieter than what you just measured. Numbers in the 40s are very typical of suburban locations but numbers in the 30s are exceptionally quiet and what you would find in rural locations where there is little traffic, jet, plane or other man-made noises. One of the quietest places I have encountered is deep inside Skyline Caverns in Virginia where readings in the high-20s were encountered!

Brain Research, Physics, Time

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.

Education

Things to do with your Smartphone!

We all have smartphones, but did you know that they are chock-full of sensors that you can access and use to make some amazing measurements?

Here is an example of a few kinds of data provided by an app called Physics Toolbox, which you can get at the Apple or GOOGLE stores.

Sensor data accessed by Physics Toolbox app

Each of these functions leads to a separate screen where the data values are displayed in graphical form. You can even download the data as a .csv file and analyze it yourself. This provides lots of opportunities for teachers to ask their students to collect data and analyze it themselves, rather than using textbook tables with largely made-up numbers!

There are also many different separate apps that specialize in specific kinds of data such as magnetic field strength, sound volume, temperature, acceleration to name just a few.

I have written a guide to smartphone sensors and how to use them, along with dozens of experiments, and a whole section on how to mathematically analyze the data. The guide was written for a program at the Goddard Space Flight Center called the NASA Space Science Education Consortium, so if you know any teachers, students or science-curious tinkerer’s that might be interested in smartphone sensors, send them to this blog page so that I can count the traffic flow to the Guide.

Here is an interview with the folks at ISTE where I talk about smartphone sensors in a bit more detail:

https://www.iste.org/explore/classroom/students-can-do-citizen-science-their-smartphones

OK…here’s the URL for the actual Guide!

http://spacemath.gsfc.nasa.gov/Sensor/SensorsBook.pdf

If you really want to look into using smartphone sensors in a serious way, here are some articles I have written about them that you might also enjoy:

Odenwald, S., 2019. Smartphone Sensors for Citizen Science Applications: Radioactivity and Magnetism. Citizen Science: Theory and Practice, 4(1), p.18. DOI: http://doi.org/10.5334/cstp.158

Odenwald, S., 2018, The Feasibility of Detecting Magnetic Storms With Smartphone Technology, IEEE Access, https://ieeexplore.ieee.org/document/8425973

Astronomy, Physics

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!!!

Biology, cancer

A Life in Remission

In the midst of an active research career in astrophysics, in 2008 I was diagnosed with non-Hodgkins Lymphoma, and my world ended.

For the next eight years I learned to live with the cancer growing slowly within me like some creature out of the infamous ‘Alien’ movie series. Annual tests showed the dozens of affected lymph nodes were very slowly growing in size by the millimeter, but with luck none of them would  turn dangerous for a decade or more. But no one could predict when my cancer would ‘transform’ and become dangerously aggressive, requiring immediate chemotherapy. Actuarial forecasts said that the probability of transformation increased by 5% per year, so that after 10 years I would have a 50/50 chance of my NHL becoming aggressive, but it could happen sooner. …or much later. As a scientist, this uncertain diagnosis was devastating.

A scientist conducts research based on the a priori assumption that they will live to see the end of their work and to publish the results.  I just know you are going to say ‘Well, no one knows when they are going to die’, but among those of us who deal with cancer, these kinds of sentiments seem insensitive and a bit flippant no matter how well-intended.

How does one function when one does not know when the monster will spring out of hiding and put the kibosh on your current work? Many of my projects required several years of work, followed by months of writing-up the results and interacting with referees and journal editors to publish the results. You simply cannot muster the stamina to carry-on your research and deal with referees when you are on a short, emotional leash.

Coping with an uncertain future in research

I immediately began to wean myself away from the rigors of research and instead moved into the area of education where NASA had a huge footprint. I won two grants to develop my SpaceMath@NASA resource, which grew every year to become a significant mathematics resource for educators. I even became known in some circles as Dr. Space Math! This was an intensely therapeutic undertaking for me because could write new math problems and design new math books whenever I chose to on my timetable, and if I literally died tomorrow, I would have left behind a complete archive of fun math resources. It was an open-ended commitment that suited my new frame-of-mind, and still made me feel as though I was contributing, intellectually, to a Greater Good: The education of our children.

As the years began to add up, 5…6..7…8  I started to realize that I might be in this cancer frame-of-mind for the long haul. But by this time my hiatus from research, and my ‘advanced age’ of 64, precluded any re-entry into the level of research I had enjoyed in my earlier years. It was very sad to see this part of my career waste away, but considering I was in my peri-retirement years, perhaps as it is for so many other scientists, this transition was inevitable.

In 2016 my NHL became aggressive after eight years of near-dormancy. I was quickly rushed into a course of immunotherapy with a monthly infusion of Rituximab and Bendemustine for six months. At the end, a PET scan showed in November, 2017 that there wasn’t a sign of  the NHL anywhere, and my oncologist, Dr. Bruce Cheson at MedStar/Georgetown University Hospital in Washington DC pronounced me in remission. For the next two years, if there was no further sign of the NHL, he would consider me cured!

All of a sudden my attitude seemed to change almost literally over-night. I was anxious to start new research projects that, at least for now, could be completed in six months or less including writing up the results and submitting to the Journals. I had been out of my own research area for too long, and besides no astronomer at the age of 65 worries about new research unless they are still employed at a stable faculty or government job…which I was not. But I did have a part-time position at NASA working on citizen science activities. I was also involved in some very fun research trying to determine how well smartphones performed as scientific data-gathering sensors. That was starting to generate a pipeline of short-term projects culminating in several papers every year. But now that I was in remission, I could start to think about more complicated projects to tackle once again.

So I, basically, have come full circle in research having wandered for eight years in the dreary and uncertain desert of non-research work.

It’s good to be back!!