Category: Science

Physicists use imaginary numbers all of the time to help them describe physical reality, but do they themselves have any physical reality?

We all remember square roots from our high school math classes. You know, since 3 times 3, formally 32 squared, equals 9 that means that the square root of 9 is 3. Some numbers, like 9 have nice round square roots like 3. Other numbers, have square roots that are irrational, that is the number never comes to an end and never repeats itself. The square root of 17 is 4.12310563… for example.

The study of ‘Perfect Squares’ is a branch of number theory in mathematics. (Credit: Socratic)

Negative numbers are a special problem because you’ll remember that a negative number times another negative number gives a positive number. Therefore -3 times -3 is +9, not -9. So what is the square root of -9? Does it even have one?

(By the way, if you’ve always had difficulty imagining why a negative times a negative gives a positive consider this metaphor. Someone films a bathtub while water is draining out of it. That film is then shown running backwards! The water draining out is a negative, running the film backwards is also negative but what you would see is the water rising in the tub. A positive!)

For along time mathematicians simply ignored the possibility of the square root of a negative number. Such things just don’t exist they said. Then a sixteenth century Italian mathematician named Cardan was trying to find two numbers that when added together equal 10 but when multiplied equal 40. The solution he got was:

Cardan himself wrote that his solution was meaningless, fictitious and imaginary. But it worked. It worked so well that mathematicians quickly figured out how to contain the madness as it were.

What they did was to define an imaginary number, i2=-1, not i= √-1, the number i is actually never defined, only its square is. Nevertheless anytime mathematicians came across a √-1 they would replace it with i. So for example √-16=√16*√-1=4*√-1=4i.

If you define the imaginary number i this way mathematicians will consider you poorly educated. (Credit: Wumbo)
This is the proper way to define i. (Credit: Kahn Academy)

Formally the square root of a negative number is called imaginary, like 4i, but a combination of an imaginary number and a real number is called a complex number, 5+4i would be an example where 5 is the real portion and 4 the imaginary part. All complex numbers have a strange counterpart called the complex conjugate where every i has its sign changed, i→-i and -i→i everywhere. Whenever a complex number is multiplied by its complex conjugate the result is always entirely real, for example taking the most basic complex number A+iB where A and B are both real numbers and i2= -1 the complex conjugate would be A-iB and:


The terms in i cancel each other out while the i2 term =-1. Since A and B are both real A2+B2 is totally real. For a time it was thought, or perhaps hoped would be a better word, that imaginary and complex numbers were just mathematical fictions, with no application in the real world. However it was found that the familiar trigonometric functions could be expressed as complex functions.

Physicists meanwhile were starting to use the sin and cos functions to represent waves of varying kinds, light waves, sound waves, alternating current in electrical systems etc. Things got even worse during the development of quantum mechanics when the wave nature of subatomic particles became evident and the solutions ψ(x,t) of the Schrödinger wave equation:

are always complex. It was physicist Max Born who figured a way out of this dilemma when he suggested that ψ itself is not observable, its only when ψ is multiplied by its complex conjugate ψ* giving ψψ*= real that the answer to the Schrödinger equation becomes an observable. Schrödinger himself considered the presence of all those i’s in his equation to be unpleasant writing to a fellow physicist that “ψ is surely a fundamentally real function.” This is where physics has remained now for nearly a century with the solutions to our equations giving complex answers but we only pay attention to the so-called ‘real’ part.

Complex numbers are a bit easier to understand, and are very useful, if you consider them as a 2-dimensional plane. The real part is along the x-axis while the imaginary part becomes the y-axis and the complex number as a whole becomes a vector! (Credit: TeX StackExchange)

Now a group of theoreticians has proposed a thought experiment wherein the reality of imaginary numbers is required and it involves another of quantum mechanics strange properties, quantum entanglement. The basic idea of quantum entanglement is that if you measure the state of two particles those particles are now entangled and even if you separate them the measurement of them as a system must remain the same.

Physicists are currently playing all kinds of games with the particles of light called photons in order to learn more about the phenomenon of quantum entanglement. (Credit: J-Wiki at Wikipedia)

To put it more simply, if you measured a system of two coins and found it to have one head and one tail and then separated them by a great distance. Once separated if you measure one to be a head, then the other must be a tail no matter how far apart they now are. (Mind you the trick is to separate the two particles or coins without breaking the entanglement.) This effect has been both demonstrated and calculated using only the real parts of the wave function ψ.

Einstein considered quantum entanglement to be “spooky action at a distance” but that doesn’t mean it’s not real. (Credit: Quantum Mind)

The new thought experiment starts by making things more complicated. Let’s say I have two entangled particles and send one to a friend in California named Perry and the other to a friend in Florida named Nancy. Another physicist in Illinois also has a pair of entangled particles and sends one to Nancy in Florida and the other to a friend in Massachusetts named Bill. Notice how the second set of particles doesn’t come from me.

Now the question. Are the two particles received by Perry and Bill entangled, keeping in mind that Nancy got one from each of us? Well the only way to get the answer that everyone expects to be correct, remember this experiment hasn’t been performed yet, is by assuming that the imaginary part of the wave function of the entire system has a physical reality.

Euler’s equation, which contains only the five principal constants of mathematics, is often called the most beautiful equation. (Credit: Live Science)

At the moment the paper, which includes physicists Marc-Olivier Renou of the Institute of Photonic Sciences in Spain and Nicolas Gisin at the University of Geneva, is undergoing peer review so these results are preliminary. Also, if the groups thought experiment does survive scrutiny you can bet someone is going to try to perform the experiment for real.

We all feel this way sometimes when we have to work with imaginary numbers! (Credit: Medium)

Imaginary numbers have befuddled both mathematicians and scientists for going on 500 years now and will undoubtedly continue to do so for even longer. The whole thing seems so simple, yet so weird, and trust me if you don’t pay attention you can screw them up so easily. I guess maybe it’s just a little more evidence of how important our imagination is in understanding reality.

Book Review: ‘Prelude to Extinction’ by Andreas Karpf.

Attention all ‘Star Trek’ fans, here’s a book I think you’ll enjoy. Really, ‘Prelude to Extinction’ the first novel by experimental physicist Andreas Karpf reads very much like a good episode of that sci-fi classic. Captain Jack Harrison of the Earth vessel Magellan is absolutely cut from the same cloth as James T. Kirk and his first officer George Palmer and science officer Don Martinez will often remind you of Mister Spock and ‘Bones’ McCoy.

Cover of ‘Prelude to Extinction’ by Andreas Karpf. (Credit: Amazon)

And like an episode of ‘Star Trek’ the story line in ‘Prelude to Extinction’ is as much action-adventure as it is sci-fi. Even so Author Karpf manages to give the star ship Magellan a good hard feel, all the technology is based on extrapolation from present knowledge so you can actually imagine Magellan as a real ship. This is very much like the feel sci-fi fans got when they first traveled aboard the U.S.S. Enterprise back in 1967, deliberately so I’m certain.

Like the starship Enterprise in ‘Star Trek’ the starship Magellan has the feel of a ship that could actually exist. (Credit: Popular Mechanics)

Now don’t get me wrong, ‘Prelude to Extinction’ is not fan fiction. The novel is set in a completely different imaginary reality with completely different characters. It just all feels familiar, Mister Karpf’s style is right out of the style of the original ‘Star Trek’ series and it shows.

When he’s not writing novels Author Andreas Karpf is a Research Project Manager at NYU Center for Urban Science & Progress. (Credit: Twitter)

The story takes place in the year 2124, just a hundred years from now as the first Earth starship Magellan is entering the Epsilon Eridani star system at a distance of a little over 10 light years from our Solar System. Now astronomers know that E Eridani is a bit smaller and cooler than the Sun, and that it has several planets orbiting it. The fourth of those planets, E Eridani D orbits within the star’s ‘habitable zone’ where liquid water can exist and therefore is a potential home for life.

Epsilon Eridani is one of the closest stars to our Sun and the closest with a large solar system, one planet of which could have liquid water on its surface. (Credit: stars.astro.illinois.edu)

In the novel recent observations by telescopes on the Moon have found conflicting evidence for the existence of intelligent life on D. This is the mission of the Magellan, to discover if there is a civilization on E Eridani D.

The Epsilon Eridani star system compared to our own. E Eridani is the closest star that appears to have a planet within the so-called ‘habitable zone’. (Credit: Sci-News.com)

What the crew of the Magellan find is the ruins of a single city, destroyed apparently by violence along with a strange alien artifact in orbit around the planet. It isn’t long thereafter that the Earthlings are caught in the middle of an interstellar war between two much more advanced alien species, a war that could quickly engulf the Earth and all of humanity.

I do have a few problems with ‘Prelude to Extinction’, for one thing there is a dry stretch about one quarter into the book between where the crew are beginning to realize what’s going on and their first meeting with aliens. Then there are the aliens themselves, one species is just too goody-goody while the other are too bloodthirsty, both just a bit too cartoonish. Finally in the battle sequences Captain Harrison comes off as a bit too heroic, so much so he makes Captain Kirk seem like a pansy. 

There were times in ‘Star Trek’ when Captain Kirk was just tooooo heroic. Captain Harrison in ‘Prelude to Extinction’ is often that way as well! (Credit: Neatorama)

‘Prelude to Extinction’ isn’t a profound work of SF that examines humanity’s place in the Universe like ‘Childhood’s End’ or ‘The Foundation Trilogy’. Neither does it try to illustrate how we humans are going to have to learn to live on the new worlds we explore like ‘The Martian.’ No, ‘Prelude to Extinction’ doesn’t pretend to be anything more than an action adventure Sci-Fi novel and in that respect it succeeds. If you’re in the mood for an enjoyable ‘Star Trek style’ story you should check out ‘Prelude to Extinction’ by Andreas Karpf.

Space News for April 2021.

Like the Wright brothers’ first flight, which only went 36 meters, the April 19th flight of the Ingenuity helicopter may not have gone far, but it was the first powered flight by a human built aircraft on another planet. There’s also a lot of other news concerning both manned and robotic spaceflight but I’ll begin with Ingenuity.

The Ingenuity helicopter resting on the Martian surface prior to its first flight. Notice the tracks of the Perseverance rover in front of the ‘copter. This image was taken by Perseverance. (Credit: CNN)

NASA’s newest rover to Mars Perseverance carried the tiny, 1.8 kg, Ingenuity helicopter with it to the red planet as it made its landing back on the 18th of February. Then a little more than a month later on March 28th the rover gently placed the small helicopter on the Martian surface in preparation for its first flight. After taking several days to check out Ingenuity’s system it was decided to carry out one last full spin test of the helicopter’s rotors on April 9th leading to a scheduled first flight on April 11th.

Perseverance deploying the Ingenuity helicopter. (Credit: CNET)

As with any new technology there are always teething problems and during the April 9th test the Ingenuity rotors failed to reach their full spin speed of 2500 RPM. Taking about a week to investigate the problem and transmit a new software package to the helicopter the engineers at NASA’s Jet Propulsion Labouratory (JPL) carried out a more successful test on April 17th. With that final test completed the first flight of Ingenuity was scheduled for the early morning hours of April 19th. To watch a YouTube video of that first flight click on the link provided https://www.youtube.com/watch?v=QfHfQamhimE

The flight plan was deliberately simple; the small helicopter would rise about 3m into the air and hover in place for a few seconds. While hovering Ingenuity would turn 90º, hover for a little while more before descending and landing, as close to it’s takeoff location as possible.

It all went perfectly and the proof of just how successful the test went was provided by a video taken by the Perseverance rover parked just 20m away. With this first, historic flight completed the engineers at JPL went on to conduct two other flights with the longest lasting 80 seconds aloft while traveling 100 meters at a maximum speed of 7.2kph. With three flights completed, two additional flights for the little helicopter remain to be carried out in earl May.

A few facts about Ingenuity and its first flight. (Credit: Phys.org)

Ingenuity after all is a technology demonstrator; it was designed to see if flying on Mars, where the atmosphere is only 1% as dense as here on Earth, was even possible. The helicopter’s creators want to learn everything they can about the problems and possibilities of flight there. Nevertheless during those test flights it is hoped that Ingenuity may prove useful to Perseverance as a reconnaissance aircraft looking for interesting rock formations that Perseverance can then examine close up.

And Perseverance may have a new neighbor on the Martian surface before long as the Chinese space agency has announced plans to send the descent module of their Tianwen 1 space probe for a landing sometime in mid-May. The Tianwen 1 probe, which entered orbit around the red planet in February, consists of a combined orbiter and lander modules and the scientists leading the mission have spend the last two months both checking out the spacecraft and determining exactly where they wanted to target their lander. If successful the Tianwen 1 lander would make China only the second nation to successfully place a robotic probe on the Martian surface.

China’s Tianwen-1 space probe is currently orbiting Mars and preparing to detach and land a small rover. (Credit: Yahoo news UK)

Further out in the Solar System NASA’s Osiris-REx space probe will leave orbit around the asteroid Bennu on May 10th and begin its long journey back to Earth. Osiris-REx has been studying the asteroid for 3 years and back on October 20, 2020 and even made contact with Bennu in a Touch and Go sample collecting maneuver. Currently Osiris-REx is conducting one last flyover of Bennu paying particular attention to the area where it carried out the Touch and Go.

Images taken during Osiris-REx’s Touch and Go landing on the asteroid Bennu. (Credit:NewsBeezer)

You see during that maneuver the spacecraft’s sample gathering arm sank a full 48.8 cm into the asteroid’s surface and when Osiris-REx fired its thrusters to pull away a considerable amount to dust and debris erupted in the asteroid’s low gravity. While no harm was done to Osiris-REx the scientists at JPL were curious as to whether the Touch and Go had altered the surface of Bennu.

Before and after images of the surface of Bennu. Osiris-REx made a nice little divot on the surface. (Credit: NASA)

Turned out the encounter had left a nice scar where Osiris-REx landed, a mark that could last for thousands of years in the airless microgravity of Bennu. Just another example of how the human race is now making a mark not only on our own planet but also throughout the Solar System.

There are a few other brief items that I’ll cover quickly. The final two passengers have been selected for the first fully commercial space flight. As I mentioned in my post of the 17th of March of this year billionaire Jared Isaacman has hired Space X to send him and three ‘guests’ into orbit for a 3-5 day long ‘vacation’. Isaacman wants to use the flight to help publicize his favourite charity, Saint Jude’s Children’s Research Hospital and so for his first companion he choose physician’s assistant Hayley Arceneaux who was herself a cancer patient at St. Jude’s when she was a child.

The two remaining seats on what has been christened the ‘Inspiration 4’ mission will now go to Doctor Sian Proctor and Chris Sembroski. Doctor Proctor is a Geoscientist and space communication expert who was awarded her chance to travel into space by winning a contest sponsored by Isaacman’s e-commerce company Shift 4 payments.

The crew of Inspiration 4 mission. Left to right, Jared Isaacman, Hayley Arceneaux, Sian Proctor and Chris Sembroski. (Credit: Daily Express)

Mister Sembroski was chosen from some 72,000 entries to a fundraising contest benefiting St. Jude’s and will serve as a mission specialist for the flight. Currently the mission, which will launch from pad 39A at the Kennedy Space Center, is scheduled to take off no earlier than September 15 of 2021.

Even while Space X is moving forward with its commercialization of human spaceflight Boeing’s Starliner Space Capsule can’t seem to get off the launch pad, quite literally. The final unmanned test flight of Starliner, officially Orbital Flight Test-2 (OFT-2), had been scheduled for this month but because of technical problems with the capsule’s avionics that launch date will have to be delayed at least a month.

The Boeing Starliner capsule being readied for its second OFT-2 flight. Continuing problems have now delayed that flight until at least August! (Credit: CNET)

Problem is that the launch facilities at Kennedy are booked right through mid-summer. The earliest date possible for Starliner’s unmanned flight is August, which will almost certainly push back the earliest manned test flight, officially Crew Test Flight-1 (CTF-1) currently scheduled for September. Just further delays on a program that seems to be going nowhere.

Oh, and speaking of Space X, the Hawthorn California based company launched it’s third manned mission to the ISS. The mission, officially named Crew-2 by NASA, carried two NASA, one European Space Agency and One Japanese Space Agency astronaut into Low Earth Orbit (LOE) on the 23rd of April. Mission commander Shane Kimbrough along with pilot Megan McArthur rode their Falcon 9 rocket with mission specialists Thomas Pesquet and Akihiko Hoshide to relieve the current Crew-1 astronauts and begin a 6-month tour aboard the ISS. The Crew-1 astronauts are scheduled to return to Earth aboard their Space X dragon capsule on the first of May.

In this image made from NASA video, the SpaceX Crew Dragon spacecraft lifts off for the Crew-2 mission carrying NASA astronauts Shane Kimbrough, Megan McArthur, ESA (European Space Agency) astronaut Thomas Pesquet, and Japan Aerospace Exploration Agency (JAXA) astronaut Akihiko Hoshide from Launch Complex 39A, Friday, April 23, 2021, at the Kennedy Space Center in Cape Canaveral, Fla. (NASA via AP)
The Space X crew 2 astronauts, in black jerseys, join the other astronauts aboard the ISS. These 11 crew members represents the most people in space at the same time since the end of NASA’s shuttle program. (Credit: SpaceNews)

With their third manned mission for NASA in less than a year and the coming launch of their first purely civilian mission Space X is generating quite a lot of excitement. Is this the start of a new age in space with commercial and national agencies working together to explore our solar system?

I’ve gotten my Covid vaccinations. I’m all immunized. How ’bout you? When are you planning on getting your shots?

As I’m writing this post the number of Covid-19 vaccines that have been administered is here in the United States is 218,947,643. President Biden’s initial pledge of 100 million shots in his first 100 days in office has been more than doubled and even his updated pledge of 200 million in 100 days is a safe bet to be exceeded by more than 10%.

As President-elect Joe Biden pledged to administer 100 million vaccine shots into American arms in his first 100 days as President. He ended up more than doubling that goal. (Credit: New York Post)

27.1% of all Americans have now been fully immunized while more than 50% have had at least their first shot. Over the last month an average of about 3 million people per day have received a shot and all Americans over the age of 16 have now been declared eligible to receive their shots. (All of these statistics are courtesy of the Center for Disease Control CDC.)

The drive to get people vaccinated is one of the largest peacetime efforts ever undertaking by federal, state and local governments. (Credit: Beaumont Health)

All of that means that we are reaching a critical turning point in our war against a disease that in only a single year has killed more Americans than any of our wars except the civil war. 570,611 Americans have lost their lives to Covid-19 and 31,950,831, nearly one tenth of our country’s population have been sickened according the Johns Hopkins University Covid-19 resource center.

At its peak the covid pandemic death toll was so high that makeshift morgues had to be used to store all of the dead! (Credit: The New York Times)

If we can only continue to vaccinate people at our current pace we will almost certainly reach ‘herd immunity’ within another month or two. Such an achievement will mean that by mid summer the US can begin to really open up. Restaurants, movie theaters, sporting events, all of the industries that have suffered enormously because of the pandemic will be able to resume near normal operations. Our economy, which has recently shown signs that it is ready, even anxious to get back to business will be able to do just that. Simply put we’ll be able to get our lives back.

Contagious diseases need a lot of potential victims in order to spread. When the majority of a population gets vaccinated the disease is unable to take hold and spread. (Credit: Wikipedia)

There is a bit of bad news mixed in with the good. There have been cases identified of people who have received their vaccinations and nevertheless later tested positive for covid. That’s actually to be expected, during testing that efficacy of the Pfizer and Moderna vaccines were measured at 95%, which is really good, but still means that 5% of those vaccinated could still get the disease. Even so to date no one who has come down with covid after being vaccinated has become seriously ill or required hospitalization. In other words the vaccines not only do a great job at preventing covid, they virtually eliminate serious cases of the disease.

Some of the vaccines developed to combat Covid are very efficient but none are perfect. (Credit: Statista)

Of course the worst news are those cases of blood clots that have developed in a few people who have received the Johnson and Johnson vaccine. The latest information is that 15 people, all women to my knowledge, have shown symptoms of serious blood clotting after receiving the J&J vaccine and one death has occurred. That number of cases is out of the over 8 million people who have received the single shot J&J vaccine so obviously the incidence of blood clots is very rare. Nevertheless the situation was serious enough that the Food and Drug Administration ordered a pause in the administration of the J&J vaccine while the incidents were investigated. After eleven days of data collecting and analysis of the data both the FDA and CDC decided that the benefits of the vaccine far outweighed the potential risks and lifted the pause while adding a warning to women under 50 informing them of the risk of blood clots.

There is evidence for both the Johnson and Johnson and Astrazeneca vaccines causing blood clots, but there is a greater risk of blood clots from taking birth control pills and even worse for smoking! (Credit: Hindustan Times)

After all consider the odds. Out of about 330 million people living in the US more than 31 million have now gotten covid, that’s nearly a 10% chance of getting the disease and more than half a million have died, a 0.17% chance. On the other hand your chance of getting a serious blood clot from the J&J vaccine is .000188% far, far less likely than the risk due to covid. In fact right now about 700 Americans are still dying every day because of covid while only 15 people have gotten sick because of the J&J vaccine. And remember no deaths thus far have been linked to the Pfizer and Moderna vaccines.

So it’s difficult to understand why so many people are still hesitant about getting vaccinated. In fact current polling data suggest that approximately 17% of Americans only plan on getting vaccinated if it’s required while a further 8% refuse to get vaccinated under any circumstances. These numbers are so large that they could pose a risk to the effort to achieve herd immunity.

According to polls vaccine hesitancy is falling as more and more people get inoculated. We need everyone to realize the benefit of immunization however! (Credit: Statista)

Now there have always been people whose fear of having substances they don’t understand directly injected into their bodies makes them resolute ‘antivaxxers’. Then you can add those people who devoutly believe that faith in god is the only healthcare system they need. Finally in our nation’s current political climate we have many people whose distrust of authority has led them to proclaim ‘their right as Americans to not get vaccinated’. As if the freedom to ignore the deaths of a half million of their fellow citizens is somehow enshrined in the Constitution.

If only it were that easy. (Credit: Henry Kotula)

Remember, covid is a virus; it is incapable of understanding ‘liberty’ in any sense of the word. It is neither a democrat nor republican, neither a liberal nor conservative. It is just going to try to infect you and maybe kill you, that’s all it knows how to do! Face facts, you can’t fight a virus with an assault rifle, nor is this just a left wing plot to destroy conservative American culture. Covid is a disease that is presently out of control and vaccines are our best weapon against it!

Sensible people know this, and know how to analyse risk versus reward. (Credit: SBS)

I’m not going to try to argue with those who will never listen. All I can do is to relate my own medical history as testimony. My parents had our whole family inoculated against polio as soon as the vaccines became available. When I joined the US Navy I was vaccinated I don’t know how many times. I’ve been vaccinated against tetanus, shingles, etc, etc, and I get a flu shot every year. None, I repeat none of those vaccines, including the Pfizer covid vaccine I just received my second dose of, have ever done me the slightest harm.

My vaccination card for the Pfizer Covid-19 vaccine! I’m now all immunized, I can get back to my life…What ’bout you! (Credit: R. A. Lawler)

In fact since the vaccines against Measles, Mumps and Rubella weren’t developed until after I had all those diseases Mumps left me with permanent deafness in my right ear! What I wouldn’t give to have been able to take the MMR vaccine, which you’ll recall is falsely alleged to cause autism, and still have my hearing! So if you’re thinking about getting vaccinated but are hesitant please think of the risks. Over a half a million Americans have died because of covid and maybe one person has died because of a vaccine. Repeat that simple fact about ten times AND GO GET VACCINATED!!!

Paleontology News for April 2021. What was the earliest kind of animal and crocodile diversity?

Back when I was in high school all living creatures were still being divided into just two kingdoms, animal and vegetable. Biologists were well aware of the problems that oversimplified scheme caused, fungi were obviously not plants and single celled organisms often had characteristics of both animal and vegetable, or sometimes neither. Some new classification system was needed but the biologists took their time creating one in order to make certain that they got it right.

Wasn’t so long ago that two kingdoms of life were considered to be enough but notice how the pictures on the cover of this book do not include either mushrooms or single celled organisms! (Credit: Amazon.com)

What they finally decided on was a five kingdom division that has in fact made understanding the relationships between the groups much easier. Multi-cellular creatures are now split into three kingdoms, animals, vegetables and fungi while single celled organisms with a cell nucleus, like an amoeba, are grouped into the protista and single celled organisms without a nucleus, the simplest life forms like bacteria are called the monera.

Five major kingdoms of life are now the agreed upon classification system. (Credit: Iberdrola)

So one of the questions that this new classification scheme generates is, what was the first animal? What was the first multi-cellular creature that had to eat other creatures for their energy, as opposed to plants that generate their energy through photosynthesis?

Early evolutionary biologists were quite confident that sponges, members of the phylum Porifera were the earliest animals because they were certainly the simplest. In many ways sponges are nothing more than colonies of identical cells working in unison rather than the cells of most animals who differentiate and grow into separate organs. That means that sponges have no digestive system, circulatory system or nervous systems or even anything like muscles. Each cell moves its body in unison with the other cells near it generating a flow of water through the body of the sponge and then each cell captures and absorbs its own food particles from that water flow.

In many ways sponges are like hollow tubes with openings, on the side in the example. The cells sit inside the tubes waving their flagella to make water flow through the tube and feed off of particles of food that they catch from the water. The cells are all the same, no differentiating into separate organs. (Credit: Evolution News)

However, when biologists first used DNA analysis to estimate mutation rates in order to calculate which phylum came first it wasn’t sponges that looked like the oldest animals but rather another kind of creature known as ‘comb jellies’ or technically the Ctenophora. This discovery came as a considerable surprise because comb jellies are in many ways considerably more sophisticated creatures possessing not only a gut and muscles but even a very primitive nervous system.

Comb Jellies, phylum Ctenophora, are considerably more complex creatures having two layers of cells, inside and outside, a primitive gut, cells designed to provide motion and even the beginnings of a nervous system. (Credit: Britannica)

The idea that comb jellies came first, then sort of devolved into the less complicated sponges before re-evolving for later more advanced creatures, like us, was hard for many biologists to accept. As geneticist Anthony Redmond of Trinity College in Dublin Ireland remarked however. “It may seem unlikely that such complex traits could evolve twice, independently but evolution doesn’t always follow a simple path.”

Geneticist Anthony Redmond is a post-doc at Trinity University in Dublin. Nice work if you can get it! (Credit: Twitter)

Still such surprising, even baffling results should be double if not triple checked. With that in mind Doctor Redmond and his colleagues reexamined the mutation rates for the two phyla with newer models that even take into account the rate of change for amino acids in the most common proteins. What they found was that the greater range of diversity of the comb jellies was caused by a burst of evolution early in their history leading to a false impression of greater age. The sponges, on the other hand have been a much more conservative group of animals whose lack of diversity made them look artificially younger.

A great deal of work is currently ongoing to measure the mutation rates of various types of creature. (Credit: ResearchGate)

These latest results clearly show that sponges are the earliest animals, just as biologists had always thought. They also show the danger in simply counting the number of changes, mutations in a DNA sequence and then using that as a measure of age. A group of animals that quickly diversifies in order to fill a large number of ecological niches can have a burst of evolution that imitates age. Just goes to show that while genetic studies can tell us a lot about the relationships between living things we still have a lot to learn about how to interpret the data they provide.

Another group of animals who are often considered to be very conservative like the sponges are the crocodilians. In some respects the 26 modern species of crocodiles, alligators and gharials all bear a considerable resemblance to each other and together seem to have little changed since the days of the dinosaurs. So much so that they are often, unfairly called living fossils.

There may be 26 different species of Crocodile in the world today but let’s be honest they are all very similar animals. (Credit: Pinterest)

In fact however crocodiles were once a much more diverse and rapidly evolving group of animals, with swift running land dwellers, dolphin like swimmers and even herbivores, yes plant eating crocodiles! Modern crocodiles may be restricted to a narrow range of ecological niches but there was a time when crocodiles made up a large and very diverse group of animals.

Based on fossil footprints from South Korea one extinct species of crocodile could run for short distances on two legs! (Credit: BBC)
There were also species of Crocs that were evolving to resemble dolphins and whales. (Credit: GeoScience)

A recent study by paleontologists at the University of Bristol in the UK illustrated the extent of crocodilian diversity. In a paper in the journal Proceedings of the Royal Society B the researchers, including lead author Doctor Tom Stubbs, detailed the findings gained from examining more than 200 skulls and jaws spanning the entire 230 million year long history of the group. Ancient crocodiles it turns out were another example of how spreading out into a number of different lifestyles led to rapid evolution and wide diversity. Proving once again that experimentation leads to success.

As a kid I always wanted to have a pet alligator but I knew that was a bad idea!!! Such animals, poisonous snakes and etc., are not good pets and anyone who keeps one is harming the animal and maybe themselves. (Credit: WVXU)

Unfortunately only a small portion of that ancient diversity managed to survive past the reign of the dinosaurs. So we are left today with only a narrow picture of what a crocodile can be. Of course the dinosaurs themselves were virtually wiped out 65 million years ago when an asteroid or comet struck the Earth leaving only their fossil remains to tell us their story.

Biologists have succeeded in assembling a synthetic cell in the lab that is fully capable of reproducing itself.

It’s been said that the 19th century was the chemistry century with the development of new sources of energy from coal and oil, new techniques for industrial scale production of metals and other materials as well as the discovery of new explosives like nitro-glycerin and dynamite. The 20th century has been called the physics century because of advances in electronics and nuclear science, radio, X-rays and magnetic resonance imaging.

Over the last two centuries the sciences of Chemistry and Physics have reshaped our world. (Credit: R. A. Lawler)

The 21st century is expected to be the biology century and it’s off to a good start with both rapid DNA sequencing and CRISPR gene editing. One achievement that has been predicted to happen in the next few years is the building of a completely artificial life form and recent developments have taken a large step in making that prediction come true.

Will the 21st Century be Biology’s turn? (Credit: English-Online)

The work began in 2016 at the J. Craig Venter Institute in San Diego, California where a team of biochemists led by Craig Venter succeeded in taking cells of the simple bacteria Mycoplasma and completely removing the cell’s genome. The researchers then inserted an artificially constructed DNA strand into the bacteria that contained only the 473 key genes that they felt were necessary for life. As a comparison the well-known bacteria Escherichia coli has about 4,000 genes.

Let’s be honest, people have been playing god since we first learned how to control fire! Craig Vinter is just the latest in a long line of scientists who narrow minded people like to criticize. (Credit: SlideShare)

The resulting part natural – part artificial, ‘minimum cell’ was designated JCVI-syn3.0 and when the cells were placed in a petri dish with the proper nutrients the bacteria not only survived but grew and multiplied, forming colonies that appeared like any natural kind of bacteria. This result was heralded for giving scientists a clue as to what the earliest, and therefore simplest forms of life may have looked like. At the same time it was hoped that JCVI-syn3.0 could serve as a basic platform for the development of other cells that could be designed to manufacture valuable biochemical substances like insulin or penicillin or some as yet unknown drug.

The process of creating JCVI-syn3.0 the first minimal cell. (Credit: Science)

Upon closer inspection however the daughter cells produced by the original JCVI-syn3.0 cells were malformed and of varying sizes. Something was wrong with the way the cell walls were splitting during reproduction. The colonies of bacteria may have looked fine but microscopically there was a problem.

At this point the Cellular Engineering Group at the National Institute of Standards and Technology (NIST) began investigating JCVI-syn3.0 under the leadership of Elizabeth Strychalski.  The NIST team reinserted genes, one at a time back into the synthetic organism until the bacteria was producing daughter cells both looked and behaved more like the parent cell. In the end they found that 492 genes were required for a true ‘minimal cell’ which they have christened JCVI-syn3A.

The version of a minimal cell developed at NIST is capable of reproducing in a more normal fashion. (Credit: SciTechDaily)

This is itself a tremendous breakthrough; scientists have now determined the fewest number of genes, the smallest amount of inherited information that is needed in order for a living organism to exist and reproduce. Those scientists who are studying the processes by which the primordial soup in the early Earth became alive now have a goal to work towards. If they can figure out how something like JCVI-syn3A came into being then they will have succeeded in explaining how life began on Earth.

The Miller-Urey experiment gave us step one, a lot of work has been done since then on step two and now JCVI-syn3A has shown us what step four has to look like. How long before we have a clear idea of the way life itself began? (Credit: CK-12)

At the same time those researchers who are looking into using microorganisms in large scale manufacturing of drugs or other complex biochemicals now have a test bed to employ in their research. By inserting only those genes into JCVI-syn3A that are needed to enable the organism to produce the desired drug the scientists will possess a bacteria whose only function other than reproduction is to manufacture the chemical we have designed it for.

Many of the drugs we already use, like penicillin come from simpler forms of life. Soon however we will be designed simple cells to manufacture exactly what we want. (Credit: www.nlm.nih.gov)

Now it is true that JCVI-syn3A may not be a totally artificial life form but it is certainly a big step in that direction, and remember the ‘Biology Century’ is only one fifth completed. Who knows what kind of discoveries biologists and biochemists will be making in the next eighty years!

Mathematicians have been in love with Prime Numbers for almost three thousand years. Today they are even defining new classes of primes just to have the fun of studying them.

 We all remember Prime Numbers from our high school math classes. You know, those numbers that can only be evenly divided by themselves and one. For example since the number six can be divided into two times three (6=2×3) it is not a prime number. Seven on the other hand cannot be divided by any number except itself and one so seven is a prime number.

The first 12 whole numbers arranged as prime, left side, or composite, right side. While composite numbers can be arranged as rectangles prime numbers can never be arranged as anything but a straight line! (Credit: Wikipedia)

All non-prime numbers are called composite numbers because they can be broken down into their prime factors. For example again 6 can be broken down into 2×3 while 8 can be broken down into 2x2x2 and 36 is 2x2x3x3.

The number two is the only even prime number since by definition an even number is one that can be divided by two! Also while there are a lot of primes down close to zero; one, two, three, five, seven and eleven for example are all primes, as the numbers get larger the distance between primes gets bigger. For example there are five prime numbers between 1 and 10: 1, 2, 3, 5, and 7. However there are only three prime numbers between 80 and 100: 83, 89 and 97.

One age old technique for finding the prime numbers less than, say 100 is to eliminate the multiples of 2, then eliminate multiples of 3, you’ve already eliminated 4 so move on to multiples of five. Keep doing this for all numbers that you haven’t eliminated and at the end you’re left with only prime numbers. This technique is called the sieve. (Credit: Computer Hope)

Nevertheless it is easy to prove that there are an infinite number of primes, so easy in fact that I’m going to do it right now:

We start by assuming the opposite, that there are only a finite number of primes, N, and prove that assumption doesn’t work. So, if there are a finite number of primes we can designate them as p1, p2, p3…all the way out to pN the last prime. If we have all of the prime numbers we can then multiply all of them to get:

MP=(p1xp2xp3x…pN)

If we now add one we get:

MP+1=(p1xp2xp3x…pN)+1

If we try to divide this number by any of our primes, say p15 we will get a remainder of 1/p15. MP+1 is not evenly divisible by any of our primes! That is only possible if it is itself a prime or if it is composed of primes not in the set we said was complete. Either of these two possibilities breaks our assumption so we have proven that it is not possible even in theory to collect a set of all prime numbers, they must be infinite in number! This proof that there are an infinite number of primes goes all the way back to the Greek mathematician Euclid, often called the father of geometry.

Euclid’s ‘Elements’ are still the basis for the mathematics of geometry and are one of the greatest achievements in the history of mankind. (Credit: Biography Online)

Mathematicians have tried for centuries to see if they could derive a formula that will always give them prime numbers. Many such equations work for a while but to date every one that’s been tried has failed eventually. The one below works for integers up to 79 but fails at 80.

N2-79+1601= Prime Number for N a positive integer < 80.

Another interesting, possible technique for finding primes is called the Prime Numbers Cross discovered by German chemist Peter Plichta where when numbers are arranged in progressive circles of 24 numbers per circle the primes occur on 8 spokes radiating out from the center, but not all numbers on those spokes are prime. (Credit: Beyond the Standard Model Pub)

Another interest thing about primes is that they have a habit of coming in pairs, two odd numbers in a row who both turn out to be prime. There are six such pairs less than 100: 11 and 13, 17 and 19, 29 and 31, 41 and 43, 59 and 61 and 71 and 73. The number of these pairs has recently been proven to be infinite as well but I won’t go into the proof both because it’s too long and because I don’t understand it!

Twin Primes are adjacent odd numbers both of whom are prime. It is known that these twins occur more often than would occur randomly but what, if any significance twin primes have is unknown. But they’re just cool! (Credit: Twitter)

Mathematician love to find new properties of primes that they can study and calculate, and the latest news is about a certain kind of prime that has been christened a ‘digitally delicate prime’. Simply put, digitally delicate primes are multi-digited prime numbers that if you change any one of their digits to any other number the resulting number is no longer prime.

Take the number 294,001, which it turns out is the smallest of all digitally delicate primes. This number is prime but if you change any of it’s six digits to any other number, change the 4 to a 6 for example, and the number you get, 296,001, is no longer prime. Now 294,001 has 6 digits, any one of which can be changed to any of 9 other numbers, the 2 say could be changed to 0 or 1 or 3, 4, 5, 6, 7, 8 or 9! That’s 6×9=54 other numbers, none of which are prime, so you can see that just checking to be certain if a prime is digitally delicate or not can be a lot of work.

Delicate primes were first introduced back in 1978 by mathematicians Murray Klamkin and Paul Erdős.  Erdős in fact not only found a few examples of digitally delicate primes but also proved once again that there are an infinite number of digitally delicate primes.

Why doesn’t the Math Olympics get the media coverage the athletic ones do? Murray Klamkin is well known for the problems he developed for the math games. (Credit: Ebay)

The latest development comes from a mathematician at the University of South Carolina named Michael Filaseta who has described a new class that he calls ‘widely digitally delicate primes’. To get a widely digitally delicate prime you take a digitally delicate prime and add a bunch of zeros out front, taking 294,001 and making it 000,000,294001 for example. Remember from high school if you add a zero in front of a number you don’t really change the number, 09 is still just 9 and 000,000,294,001 is still just 294,001.

Doctor Filaseta wearing the first dozen or so digitally delicate primes. He can’t wear any widely digitally delicate primes because, despite having proven they exist he hasn’t found one yet! (Credit: Quanta Magazine)

But what if you change one of those zeros out front to another number, is 000,000,294,001 still a digitally delicate prime like 294,001 is? No, in fact 010,294,001 is not a prime number so 294,001 may be digitally delicate but it is not widely digitally delicate. Doctor Filaseta has actually not yet succeeded in finding a widely digitally delicate prime, but get this, he has managed to nevertheless prove that one exists somewhere.

If you were thinking right now, what practical applications does any of this arithmetic have, why would anyone bother doing all these calculations? Well for centuries people thought the same thing about prime numbers in general. It’s only in the age of high-speed computers and computer hackers that very large prime numbers have found a use as a means of securing sensitive Internet communications.

On the whole I agree with Sir Arthur. But, as I know he’d agree, physicists wouldn’t be able to get very far without all those mathematical tools the idol worshipers have generated. (Credit: Today in Science History)

But more importantly studying number theory in general advances our knowledge of mathematics and in a very real sense our ability to understand the Universe in which we live depends on our understanding of mathematics. That’s why math is often called the ‘Queen of the Sciences’.

Geologists studying newly discovered structures deep within the Earth’s mantel and core are now considering the possibility that they are the remains of an ancient, alien world buried deep within our own.

Before the Apollo astronauts reached the Moon and succeeded in bringing back a few hundred kilograms of Lunar rocks to be studied here on Earth scientists had proposed two basic concepts as to how the Earth-Moon system ever came into being. The first idea was that the Moon had originally been a part of the Earth. Back when our planet was still forming and was a molten mass of rock it got a little too big and was spinning a little too fast which caused a big chunk to spin off and eventually become the Moon.

Just a few of the Lunar samples brought back by Apollo 11. These and the other rocks collected by the astronauts represented the first opportunity for Earth scientists to actually study material from another world! (Credit: KTLA)
An old idea for the Moon’s origin is that it split off from the early Earth like a daughter cell. Some people even suggested that the place where the split occurred gave rise to the pacific ocean. (Credit: Google Sites)

The other idea couldn’t have been more different. In this theory the Moon was never a part of the Earth, it originally came from somewhere else in the solar system, maybe the asteroid belt. Sent on a wandering path by Jupiter’s gravity or some other cause the Moon eventually came too close to the Earth and got captured by our planet’s gravity.

In the capture theory the Moon was never a part of the Earth. (Credit: Two Flags)

The two theories were so different that geologists thought that once they had some actual Moon rocks to examine they’d certainly be able to choose which theory was correct. It didn’t work out that way because the Lunar rocks brought back by the astronauts looked somewhat like Earth rocks but also like something else. After several years of study a new theory started to form, a more dynamic, even violent scenario for the Moon’s birth.

It works like this, about 4.5 billion years ago the Solar System was just beginning to settle down. The proto-Earth, alone with no Moon, was still a molten mass just starting to cool when another planetoid about the mass of Mars came wandering into our orbit from somewhere else in the Solar System. The collision that resulted between the two bodies must have been cataclysmic and resulted in the Earth absorbing some of the planetoid’s mass while some of the fragments of both bodies coalesced into the Moon. The now destroyed planetoid has even been given the name Theia and the entire concept has come to be known as the Planetary Impact Theory.

In the planetary Impact theory another planetoid named Theia smashes into the early Earth and the debris coalesces into our Moon. (Credit: Discover Magazine)

After the collision the Moon soon cooled into the dead world we see today so that the Lunar rocks can still exhibit some traces of its origin as two bodies. The Earth however is a much more active body, with moving tectonic plates, a liquid core and volcanism to say nothing of the erosive forces of wind and rain. The dynamic forces of geology have built tremendous mountain ranges that have then been washed into the oceans to form sedimentary rocks, an entire class of rock completely unknown on the Moon. Surely any trace of Theia on our planet would have long ago disappeared because of all the changes on Earth over the last 4 billion years.

Or maybe not! Back in my post of 24 June 2020, I discussed how geologists had discovered regions of denser, heavier material deep within the Earth’s mantel. Doyeon Kim, the University of Maryland scientist who led the research found these anomalies by analyzing the vibrations caused by large earthquakes as they passed through the inner regions of the core and mantel. Because these anomalous regions were made of hotter, denser material the seismic vibrations passed through them with a lower velocity and so Doctor Kim christened them Ultra-Low Velocity Zones or (ULVZs). Two of these regions, each hundreds of kilometers deep and thousands across, are known to exist, one beneath West Africa and the other beneath the Hawaiian Islands in the Pacific.

By studying the transmission of Earthquake vibrations as they pass through our planet’s center Dr. Kim was able to discover previously unknown structures deep with the Earth. (Credit: EurekAlert)

Now geologists at Arizona State University led by Ph.D. candidate Qian Yuan have proposed that these huge masses are actually fragments of the planetoid Theia that have managed to remain intact deep inside the Earth for more than four billion years. A paper detailing their hypothesis has been presented at the 52nd Lunar and Planetary Science Conference in March of 2021.

As evidence for their theory the geologists point to not only the ULVZs difference in density but also to certain chemical signatures indicating that the material making up the ULVZs is at least as primitive as the Theia impact. Qian Yuan and his colleagues are now preparing a formal paper to be submitted to the journal Geophysical Research Letters. 

Are the large structures deep within the Earth all that remains of the planet Theia? (Credit: World Today News)

Think of it, NASA and other space agencies are spending billions of dollars to send probes millions of kilometers in order to study alien worlds when there may be immense pieces of another planet just a couple of thousand kilometers beneath out feet. Of course the problem is that’s a couple of thousand kilometers of solid rock you have to get through in order to obtain any samples.

Archaeology news for April 2021.

There have been several exciting discoveries from ancient sites around the world. So rather than wasting any time let’s just get to it.

I’ll start today with the discovery that’s gotten the greatest amount of press coverage, the unearthing of new fragments of the Dead Sea Scrolls. Now everybody knows that the Dead Sea Scrolls are fragments of writings from the Jewish Scriptures, the Christian Olde Testament that have been dated from about the second century BCE to the end of the first century CE. The writings were discovered between the years 1947 and 1956 in a series of eleven caves not far from the shoreline of the Dead Sea in the Khirbet Qumran region of Israel. The writings consist entirely of Jewish religious texts and while most are versions of well-known books from the Olde Testament some of the texts are of works that were completely unknown before their discovery.

A few of the caves where the Dead Sea Scrolls were found. They look like pretty good hiding places to me and the fact that the area is so dry helped to preserve the scrolls! (Credit: Wikipedia)

No one knows exactly who wrote the Dead Sea Scrolls nor how they came to be hidden away in deserted caves so far from any habitation. One of the two main theories is that a small religious sect known from the works of the Jewish historian Josephus as the Essenes wrote the manuscripts at a nearby archaeological site. The problem is that there is no evidence to connect the small settlement to either the scrolls or the Essenes. The other theory is that before the Romans captured the city of Jerusalem and ended a Jewish revolt in 70 CE a group of Jewish patriots managed to escape with a part of the Temple library that they hid in the caves to keep them from being destroyed by the Romans. Again the evidence for this theory is only circumstantial.

Ruins of the nearby settlement dated to the time the scrolls were placed in the caves. Nevertheless there is no evidence connecting these remains to either the scrolls nor the religious group known as the Essenes. (Credit: Sonia Halliday Photo Library)

Every since the discovery of the writings seventy years ago the caves along the Dead Sea have been explored and studied by archaeologists in their desire to not only solve the riddle of who put the scrolls there but also in the hope of finding some more fragments. And in fact the Israel Antiquities Authority has recently announced the discovery of dozens of new fragments that when pieced together were found to come from the books of Zechariah and Nahum in the so-called minor prophets of Jewish scripture.

Some of the better preserved fragments of the Dead Sea Scrolls. (Credit: BBC)

The fragments were found in a cave colourfully named the cave of horrors, not because of any grisly find that had been made there but because of the difficulty of reaching the site. Really, at 80m from the cliff top and at the intersection of two ravines the cave is so hard to reach with modern rappelling equipment that it’s difficult to imagine how first century Jewish patriots fleeing the Romans managed to ever reach the cave’s entrance.

The scroll fragments discovered in the past year however are mostly just tiny pieces that have to be assembled like the pieces of a jigsaw puzzle. (Credit: NBC Los Angeles)

Although the latest writings are plainly fragments of Jewish scripture the language they are written in is Greek showing how important that language was in the Middle East at that time. (In fact did you know that all quotations from the Olde Testament that occur in the New Testament are from a Greek translation of the Jewish scriptures known as the Septuagint.) Also, even though only a few lines of text are able to be reconstructed there are noticeable differences in wording between the new fragments and the same lines as printed in your bible.

The Septuagint is a 1st Century BCE Greek translation of the Olde Testament which is the source of the quotations that appear in the New Testament. (Credit: YouTube)

As hard as it can be to interpret writings from thousands of years ago most archaeological sites contain no writing, making it infinitely more difficult to understand exactly what happened there. A 6,200-year-old Neolithic site that has been unearthed near the town of Potocani in what is now the country of Croatia is a prime example of this.

Discovered in 2007 the site is simply a mass grave, the remains of 41 people, men, women and children aged from about 2 to 50 years old were crammed into a pit only 2 meters in diameter and one meter deep. This was not a quick burial for the victims of some plague however, nearly every skull examined by archaeologists from the University of Zagreb showed at least one blunt force wound at the back of the head. Just as telling, there were no sign of defensive wounds anywhere on the arms or body. These people either did not, or could not fight back against their attackers. The dead in the pit were all murder victims.

The Potocani massacre pit. That’s a lot of bodies stuffed into such a small grave. (Credit: National Geographic)

At first the scientists thought that they might have stumbled upon a massacre from the 20th century, a Nazi execution from WW2 or ethnic cleansing during the breakup of Yugoslavia. The lack of any metal objects like belt buckles or buttons made that seem unlikely however. It was only after carbon 14 dating that the archaeologists realized just how long ago the massacre had occurred.

Examples of the injuries sustained by the victims of the Potocani massacre. (Credit: Live Science)

In order to gain some clue as to why these 41 people had been killed it was decided carry out DNA analysis of the remains. Surprisingly it turned out that while the victims were related to a degree, they were not closely related, in other words they were not all members of the same family. So this atrocity was not a family or clan being wiped out by a rival family or clan. As far as the evidence showed this was a random sample of people living in the area 6,200 years ago who were murdered for some unknown reason.

Evidence from the stone age that our ancestors were already fighting wars is not hard to find! (Credit: Weapons Universe)
And we also know that Otzi the Iceman, discovered frozen in the Alps in 1991, was actually a murder victim from the copper age. The Italian police actually have a file on this case making Otzi the coldest of cold cases. (Credit: Pinterest)

We probably will never know the exact motive for these killings but the researchers speculate that climate change, a long period of either drought or flooding may have led to a squabble over limited resources and these victims were simply the losers of that conflict. In other words the events of 6,200 years ago may not have been all that different from the ideological killings of the 20th century.

For my final story I’d like to just mention a somewhat less violent, more pleasant story. Greek archaeologists working near the ancient city of Olympia, site of the Olympic games in ancient times, have unearthed a 2,500-year-old bronze idol in the shape of a bull. The small statue was found quite by chance, as an observant archaeologist happened to notice one of the horns sticking out of the ground after a heavy rainfall.

Small statue of a Bull discovered at Olympia. (Credit: ABC News)

The researchers believe that the figurine was probably an offering to the god Zeus not only because of the nearby temple to the chief of the gods but also because the bull was a well known sacred symbol of Zeus, the story of the rape of Europa where Zeus disguised himself as a bull comes to mind.

The rape of Europa by Francesco Albani. Zeus is disguised as the bull and this legend gave the continent of Europe it name! (Credit: Artnet)

The figurine has been taken to a labouratory for preservation, as have the fragments of the Dead Sea Scrolls and the remains of the Croatian dead. There they will be studied in the hope that some clue or clues may be discovered to help archaeologists tell us more of the stories of our ancestors.

Is Warp Drive just a dream of Science Fiction? Some theoretical Physicists think it might actually be possible. Set Course Mister Sulu, ahead Warp Factor Two!

Just a few weeks ago I published a post about how several physicists at the Central Astronomical Observatory Pulkovo in Saint Petersburg Russia had published a paper discussing how astronomers might be able to actually discover the existence of wormholes in space. See my post of 10 March 2021. Basically wormholes are shortcuts in higher dimensions that could allow a space traveler to go from one part of the Universe to another faster than a beam of light could in normal, three dimensional space. By using a wormhole you’re not breaking the law against going faster than light, you’re circumventing it!

A wormhole connects two distant regions of normal space by a shortcut through higher dimensions! (Credit: Science News)

Well now physicists Alexey Bobrick and Gianni Martire at Applied Physics have published a paper in the journal Classical and Quantum Gravity that proposes what they consider to be a ‘realistic’ approach to building a warp drive engine that would enable a starship to effectively travel faster than light. Now Bobrick and Martire were not starting from scratch, their work is based upon an idea for using Einstein’s gravitational field equations to warp space first developed by physicist Miguel Alcubierre and which has become known as the Alcubierre drive.

Physicist Miguel Alcubierre originator of a solution to Einstein’s equations that would warp space. (Credit: Facebook)

It was back in 1994 that Alcubierre first published his metric tensor that described a region of space generated around an object, a starship. What the tensor would do would be to contract space to one side of the starship while expanding it to the other. The starship itself would remain inside a ‘bubble’ of flat space while the bubble would then ride the contraction – expansion wave in much the same way as a surfboard rides an ocean wave, the starship inside would be like the surfer. Inside the bubble of flat space everything would behave as in normal space, nothing would move faster than light, it’s the entire bubble, an entire region of space-time that is moving faster than light.

Alcubierre’s metric tensor that allows warping of space around a starship which is traveling in the x direction. (Credit: Wikipedia)
The starship Enterprise, appropriately enough, in warp space. Space-Time in front of the ship is squeezed in tight while space-time in back is stretched out. The ship itself is inside a bubble of local normal space-time! (Credit: Quora)

As you might guess there are some practical problems. The three biggest are number one, in order to generate the warp you need quite a lot of ‘negative energy’. What’s negative energy? Well it’s some type of energy or matter that exhibits a negative gravitational field. The only kind of negative energy we have any idea about at present is the ‘dark energy’ that astronomers believe is causing the expansion of the Universe to increase. In other words, we know next to nothing about negative energy and the idea of using it in a generator is pure speculation at present.

The second problem is that when Alcubierre calculated the amount of negative matter needed to generate a bubble big enough to hold a reasonably sized starship, say 100m or so, he found that it would be greater than the amount of normal matter in the entire known Universe. And if all that wasn’t enough the use of negative energy would allow the formation of closed time-like curves that could be used to travel backward in time, see my post of 17 November 2020.

Closed Time-Like Loops can be generated by massive objects moving close to, but not more than the speed of light and can allow time travel to the past! (Credit: Google Sites)

Needless to say a lot of other physicists have voiced their opinion about the whole concept of the Alcubierre drive, both for and against. The work of Bobrick and Martire is just the latest. In their paper they show how, instead of requiring negative energy an Alcubierre bubble could be generated with a strong gravitational field from normal matter. As you might guess the strength of that field is pretty much that of a black hole. So if you want to get somewhere faster than light can, all you need is a black hole!

If you happen to have a black hole handy you too can build a warp drive generator! (Credit: The Conversation)

Perhaps the biggest problem with the Alcubierre drive along with wormholes and all the other kinds of other weird solutions to Einstein’s equations of General Relativity is that they don’t work with Quantum Mechanics. You see for over a century now we’ve had these two wonderful theories, General Relativity that describes the very large, and Quantum Mechanics that describes the very small and they not only don’t work together they don’t even follow the same mathematical formalism.

Just a few of the problems in trying to solve the puzzle of Quantum Gravity. (Credit: ResearchGate)

The majority of physicists today are of the opinion that when a theory of Quantum Gravity is finally found weird solutions like Alcubierre’s drive or wormholes will simply turn out to be invalid, like faster than light travel is in relativity. Of course it is quite possible that quantum gravity could actually point us in the direction of realistic faster than light travel. So let’s be glad that some of the more daring theorists out there are trying to see how far they can stretch Relativity and Quantum Mechanics.

Scotty I need warp drive now! (Credit: NextBigFutureNow.com)

After all, as the Sci-Fi writer Arthur C. Clarke liked to say. “The only way to find the limits of the possible is to go beyond them to the impossible!”