tag:blogger.com,1999:blog-89207959897604283892018-04-21T08:22:12.544-07:00Ken's CommentsThought provoking notes on Math, Physics and ScienceKen Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comBlogger201125tag:blogger.com,1999:blog-8920795989760428389.post-37554084753306630622018-04-20T10:06:00.001-07:002018-04-20T10:08:27.330-07:00Counting is Not Always Easy<font size="4"> <b>Counting is Not Always Easy</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-bBislgvuTo4/WnnOqzLzO8I/AAAAAAAAHqs/Oi2jtvQH9LsFphMBQO8DllrXAJHtsadUgCLcBGAs/s1600/borromean-rings.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-bBislgvuTo4/WnnOqzLzO8I/AAAAAAAAHqs/Oi2jtvQH9LsFphMBQO8DllrXAJHtsadUgCLcBGAs/s320/borromean-rings.jpg" width="320" height="266" data-original-width="220" data-original-height="183" /></a></div> Counting is not always easy, even for a small number of objects. <br><br> Here are the famous Borromean Rings. How many linkages are there? <br><br> Take any two rings and look at the linkage between them - there is none. <br><br> But you cannot pull these rings apart, so they must be linked. How many linkages are there?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-73232812250062230632018-04-20T06:04:00.000-07:002018-04-21T08:22:12.448-07:00The Nature of Space-Time <font size="4"> <b>The Nature of Space-Time</b><br><br> We tend to think of space as nothing - simply a void with no properties. But General Relativity says otherwise. It says space-time can get up to all sort of tricks!<br><br> Consider the case of light..<br><br> In a vacuum light travels at about 186,000 miles per second. That's incredibly fast, right?<br><br> No, it's incredibly slow.<br><br> For example, it takes light 100,000 years just to cross our Galaxy. And the Universe contains billions of Galaxies.<br><br> So why is light so slow?<br><br> Think of space-time as something "tangible", something that provides "resistance to motion". <br><br> So light has difficulty plowing through space-time.. which is why it's so slow. <br><br> And the situation with objects is even worse. Which is why you have to apply a force to move an object.<br><br> Moving through space-time is like wading through molasses!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-72080601035791818402018-04-11T05:18:00.001-07:002018-04-11T10:30:23.592-07:00The Man Who Counted Beyond Infinity<font size="4"> <b>The Man Who Counted Beyond Infinity</b><br><br> Georg Cantor was a mathematician who proved something quite amazing - there are numbers bigger than infinity! <br><br> He called these numbers "transfinite numbers" and he even developed an arithmetic for working with them. He denoted them by the Hebrew letter "aleph". <br><br> So what did Cantor do?<br><br> He formalized counting. He started with the integers {1,2,3,...} and asked what other sets could be placed in 1-to-1 correspondence with the integers. Instead of just saying there are an infinite amount of integers he denoted the number of integers by aleph0 and developed an arithmetic that in many ways treated aleph0 as a regular number. But he went further..<br><br> He showed that the rational numbers (fractions) could be placed in 1-to-1 correspondence with the integers. So counterintuitively, there are only as many rational numbers as there are integers. Not more!<br><br> But when it comes to irrational numbers, there are many more. He called this number aleph1 and he showed that it was different and bigger than aleph0. He proved that the number of subsets of the set of integers {1,2,3,...} is also aleph1 and he produced this amazing result..<br><br> aleph1=2^aleph0<br><br> He even asked if there was an aleph number between aleph0 and aleph1. <br><br> In his lifetime Cantor was ridiculed, not by the general public, but by his fellow mathematicians!<br><br> Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I. The public celebration of his 70th birthday was canceled because of the war. He died on January 6, 1918 in the sanatorium where he had spent the final year of his life.<br><br> Today Cantor's work is part of any university math curriculum and is regarded as one of the most beautiful pieces of mathematics ever created. It stands apart from most advanced math because you don't need to know much math to understand it. In fact, all you need to know is how to count!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-44390237548168366792018-04-08T12:55:00.001-07:002018-04-11T05:11:09.567-07:00Quantum Mechanical Spin - The most fundamental thing?<font size="4"> <b>Quantum Mechanical Spin - The most fundamental thing?</b><br><br> What do you think it is?<br><br> Mass? Energy? Charge? Time? Dimension?<br><br> <a href="https://4.bp.blogspot.com/-xAzm8G-qcYY/Wspzs_FydAI/AAAAAAAAH5Q/2w8bAx_ecXUsziRi9Q7hZGcMjmpqSRE_gCLcBGAs/s1600/elementary-particles.png" imageanchor="1" ><img border="0" src="https://4.bp.blogspot.com/-xAzm8G-qcYY/Wspzs_FydAI/AAAAAAAAH5Q/2w8bAx_ecXUsziRi9Q7hZGcMjmpqSRE_gCLcBGAs/s400/elementary-particles.png" width="400" height="383" data-original-width="800" data-original-height="765" /></a><br><br> If you look at the list of elementary particles in the Standard Model you'll see that each has a property called spin. There are only a few values.. 0, 1/2, 1 (and the hypothetical graviton - not in the Standard Model - has spin 2). <br><br> Spin divides all elementary particles into two radically different groups. Spin 1/2 particles are Fermions. Spin 0,1,2 particles are Bosons. <br><br> And spin is conserved, there is no known process that can change the spin of an elementary particle.<br><br> So perhaps spin is the most fundamental thing. <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-46017242870169990392018-04-03T12:09:00.005-07:002018-04-04T05:31:44.496-07:00Is String Theory a Dead End? <font size="4"> <b>Is String Theory a Dead End?</b><br><br> Oh sure, it produces some very nice ideas. <br><br> But it requires "multiple dimensions". The last I heard was 26. <br><br> Hey, with 26 free parameters to adjust I could produce some nice results also! <br><br> Suppose multiple dimensions don't exist (even at the Planck level). Suppose all we had was 3. You know, like we currently have.<br><br> Is String Theory taking us down the wrong path?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-48960407092394785282018-04-03T06:56:00.002-07:002018-04-04T06:53:41.608-07:00Why is the Speed of Light so Slow? <font size="4"> <b>Why is the Speed of Light so Slow?</b><br><br> In a vacuum light travels at about 186,000 miles per second. That's incredibly fast, right?<br><br> No, it's incredibly slow.<br><br> For example, it takes light 100,000 years just to cross our Galaxy. And the Universe contains billions of Galaxies.<br><br> So why is light so slow?<br><br> Think of space-time as something "tangible", something that provides "resistance to motion". <br><br> So light has difficulty plowing through space-time.. which is why it's so slow. <br><br> And the situation with objects is even worse. Which is why you have to apply a force to accelerate an object.<br><br> Plowing through space-time is like wading through molasses!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-35402571425516245272018-03-23T06:19:00.005-07:002018-03-29T06:29:12.808-07:00My DNA Shock <font size="4"> <b>My DNA Shock</b><br><br> I did a DNA test and the results totally shocked me! <br><br> So now I'm doing a second test with another company to see if the results agree. <br><br> This time I'm using <a style="text-decoration:underline" href="http://refer.dna.ancestry.com/s/abbottsystems">AncestryDNA</a> <br><br> I'm doing the basic ethnic origin test, not a medical analysis test. They don't do full DNA sequencing - they just sample your DNA at 700,000 points and then check you against their database.<br><br> This lets them find ethnic origin i.e. the region of the world you were most likely from. Plus, they also give you "matches" - people who have very similar DNA and so could be related. This is a powerful tool.<br><br> My AncestryDNA test cost $79, but if you're thinking of doing a test you can get a $10 discount here <a style="text-decoration:underline" href="http://refer.dna.ancestry.com/s/abbottsystems">AncestryDNA - $10 Discount</a>.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-63248295681913385212018-03-21T09:09:00.002-07:002018-04-17T13:15:31.518-07:00Ramanujan - Indian Math Genius <font size="4"> <b>Ramanujan - Indian Math Genius</b><br><br> On 16 January 1913, Srinivasa Ramanujan wrote to G. H. Hardy.<br><br> Ramanujan was a self taught mathematician from a small village in India. He had almost no formal training in mathematics. Hardy was professor of mathematics at Cambridge University and one of the leading mathematicians in the world.<br><br> The letter sent by Ramanujan contained a sampling of theorems he had discovered. Hardy later said, "the theorems defeated me completely; I had never seen anything in the least like them before" and added, "they must be true, because, if they were not true, no one would have the imagination to invent them."<br><br> What happened next would change both their lives. Hardy would later write about Ramanujan in his book "A Mathematician's Apology" and say that working with Ramanujan was the most significant event of his life. <br><br> Ramanujan produced some amazing infinite series, including several for π that converge extraordinarily fast and form the basis of today's computer algorithms used to calculate π. <br><br> His other results involved continued fractions. Ramanujan had a special love of continued fractions and used them to extraordinary effect.<br><br> Hardy worked hard to try and discover how Ramanujan produced his remarkable results. He never found out.<br><br> Ramanujan died on 26 April 1920. He was 32 years old. Hardy died many years later, on 1 December 1947 at the age of 70.<br><br> The Ramanujan story is now part of mathematics legend and his notebooks are still being studied today.<br><br> The movie "The Man Who Knew Infinity" tells the story of Ramanujan with Dev Patel in the lead role.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-63061225972182630382018-03-15T08:55:00.004-07:002018-04-18T12:41:25.914-07:002,500 Years of English History - In 30 Seconds<font size="4"> <b>2,500 Years of English History - In 30 Seconds</b><br><br> This is not exactly math or physics, but I thought my readers would like it, and it does relate to my earlier posts about DNA. In fact, it was my DNA analysis that led me to research this.<br><br> 500 BC<br>The Celts show up from Central Europe and bring the Iron Age. They occupy all of England.<br><br> 500 YEARS LATER<br>The Romans arrive and the Celts scatter to Wales, Scotland, Ireland, and the far tip of Cornwall.<br><br> 500 YEARS LATER<br>After making absolutely sure the Romans have gone the Anglo-Saxons invade.<br><br> 250 YEARS LATER<br>The Viking take a shot, but their invasion and occupation is limited. <br><br> 250 YEARS LATER<br>The Normans mount their famous 1066 invasion and bring the Cross Bow and Garlic. This is the last time England is invaded.<br><br> 1,000 YEARS LATER<br>Ken Abbott does DNA test and discovers he's from the original Celtic invasion.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-47742462782832858812018-03-13T11:48:00.000-07:002018-03-13T12:40:16.613-07:00The Physics of Border Wall Design<font size="4"> <b>The Physics of Border Wall Design</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://2.bp.blogspot.com/-dznEgfn4pz8/Wqgc2UHsHEI/AAAAAAAAHx8/IfzX_hh4GA0SyY7-XCCuNBugqucOQu1egCLcBGAs/s1600/border-wall-prototype1.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://2.bp.blogspot.com/-dznEgfn4pz8/Wqgc2UHsHEI/AAAAAAAAHx8/IfzX_hh4GA0SyY7-XCCuNBugqucOQu1egCLcBGAs/s400/border-wall-prototype1.jpg" width="400" height="300" data-original-width="933" data-original-height="700" /></a></div> A total of 8 Border Wall prototypes are ready for inspection. <br><br> This one features see-through design so each side can see what the other is up to - and pass small packages to each other. 😉😉<br><br> Physicists will note that when completed this design will also act as a 2,000 mile diffraction grating. I'll leave it as an exercise to the reader to calculate the diffraction wavelength. 😉😉 <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-79523174556572845832018-03-13T09:29:00.002-07:002018-04-08T06:14:37.387-07:00Physics - A New Elementary Particle Symmetry?<font size="4"> <b>Physics - A New Elementary Particle Symmetry?</b><br><br> Spin Inversion Symmetry (SIS) is currently a conjecture. <br><br> It says says that every elementary particle of spin s has a dual particle of spin 1/s. Of course, SIS does not apply to the spin 0 Higgs. But it applies to all other elementary particles in the Standard Model and to the graviton.<br><br> For example, applying SIS to the 3 neutrinos (electron neutrino, muon neutrino, tau neutrino), and assuming charge is conserved, we get 3 neutral spin-2 particles. <br><br> Applying SIS to the 3 leptons (electron, muon, tau), and assuming charge is conserved, we get 3 charged spin-2 particles. The photon is interesting. It's spin-1 so the photon is its own dual. The same is true for the W and Z bosons that mediate the weak force, and also for the gluon that mediates the color force.<br><br> SIS is still a hunch.. or conjecture. But if true the implications are amazing.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-25008930004473500962018-03-13T07:04:00.000-07:002018-04-05T07:41:39.736-07:00Could there be 3 Gravitons?<font size="4"> <b>Could there be 3 Gravitons?</b><br><br> Spin Inversion Symmetry (SIS) is currently a conjecture. <br><br> It says says that every elementary particle of spin s has a dual particle of spin 1/s. Of course, SIS does not apply to the spin-0 Higgs Boson. But it applies to all other elementary particles in the Standard Model and to the graviton.<br><br> So, applying SIS to the 3 neutrinos (electron neutrino, muon neutrino, tau neutrino) we get 3 neutral spin-2 bosons. A trio of gravitons! <br><br> It's still a hunch. But if true the implications are amazing!<br><br> Is there a physical principle behind SIS?<br><br> I'm not sure, but here's an interesting model that provides some guidance. Hint: think String Theory and associate one half twist with spin-1/2. <br><br> <a style="text-decoration:underline" href="http://www.math-math.com/2017/12/mobius-strip-strange-surprise.html">A model for SIS</a> <br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-79708065260062797032018-03-10T08:37:00.001-08:002018-04-01T15:19:04.258-07:00Elementary Particles - Spin Inversion Symmetry<font size="4"> <b>Elementary Particles - Spin Inversion Symmetry</b><br><br> At the moment I must call this a conjecture. <br><br> Spin Inversion Symmetry (SIS) says that every elementary particle of spin s has a dual particle of spin 1/s. Of course, SIS does not apply to the spin 0 Higgs. But it applies to all other elementary particles in the Standard Model and the hypothetical graviton.<br><br> So, assuming charge is conserved, the spin 1/2 neutrino has a neutral dual of spin 2. The spin 1 photon is its own dual. And the spin 1/2 electron has a charged spin 2 dual. <br><br> So SIS predicts a slew of new particles. Notice that the neutral spin 2 particles could also explain dark matter. However, as of now I don't have any underlying physics to justify SIS. <br><br> It's still a hunch.. or conjecture. But if true the implications are amazing.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-22077116101189285942018-03-09T11:47:00.001-08:002018-03-27T10:55:20.874-07:00Is General Relativity a Dead End?<font size="4"> <b>Is General Relativity a Dead End?</b><br><br> Don't get me wrong, General Relativity is brilliant. It's probably the greatest insight ever produced by a single individual. And it's built from an amazing observation.. <br><br> That acceleration is locally equivalent to a gravitational field. That's clever to say the least. <br><br> But we can regard an acceleration as a stress on space-time. So what happens in the Quantum limit when the acceleration is truly huge? Does it fracture space-time into discrete units or some underlying fundamental constituents? <br><br> If so that's where GR breaks down. And the rest of GR was a nice macroscopic average. <br><br> And don't forget, GR assumes space-time is a continuum. That's a classical concept which simply cannot be true at very small distances.<br><br> Bottom line: GR has to break down at some point. It's great at making predictions at the classical level. But it cannot move to the future. It's a dead end. An incredibly clever dead end. But a dead end none the less.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-5804941280152229582018-03-09T06:11:00.001-08:002018-03-12T07:04:22.451-07:00Cambridge University - Remembering the Old Cavendish Laboratory<font size="4"> <b>Cambridge University - Remembering the Old Cavendish Laboratory</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-JthdoS76CMI/WqKWHZ9MR2I/AAAAAAAAHw4/O4g1Z4BbxUkPe8LSJrezmfI4vVdyUqnjACLcBGAs/s1600/cavendish-crocodile.jpeg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-JthdoS76CMI/WqKWHZ9MR2I/AAAAAAAAHw4/O4g1Z4BbxUkPe8LSJrezmfI4vVdyUqnjACLcBGAs/s400/cavendish-crocodile.jpeg" width="317" height="400" data-original-width="200" data-original-height="252" /></a></div> When I was doing my physics PhD at Cambridge my office was in the original Cavendish Laboratory on Free School Lane.<br><br> My window overlooked the courtyard which contained Kapitza's magnetics lab. It was built in the courtyard due to lack of space.<br><br> And of course I had a clear view of the famous Crocodile carved into the wall of Kapitza's Lab. He used it to tease Rutherford, "The Crocodile" being Kapitza's pet name for Rutherford.<br><br> The Cavendish moved to its new spacious location in West Cambridge in 1974.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-54516270009563617142018-03-08T14:44:00.002-08:002018-03-09T10:48:08.276-08:00Quantum Gravity and Dark Matter<font size="4"> <b>Quantum Gravity and Dark Matter</b><br><br> At the moment Physics recognizes 4 fundamental forces:<br><br> -The Color Force (mediated by a spin 1 Boson - the Gluon)<br>-The Electromagnetic Force (mediated by a spin 1 Boson - the Photon)<br>-The Weak Force (mediated by 2 spin 1 Bosons - the Z Boson and W Boson)<br>-The Gravitational Force (mediated by the hypothetical spin 2 Boson - the Graviton)<br><br> But if we apply the SIO (Spin Inversion Operator) to the spin 1/2 neutrinos (electron, muon and tau) we get spin 2 neutral particles. Could these be "partners" of the Graviton in a new force that's closely related to gravity. And if these new particles have high mass the new force would have very short range - making it an ideal candidate for "quantum gravity".<br><br> So just as the Electromagnetic force gets extended to the Electroweak force by the addition of new spin 1 mediating particles, so Gravity gets extended to "quantum gravity" by the addition of new spin 2 mediating particles.<br><br> Plus, could these new particles also account for Dark Matter?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-82293065937161986772018-03-05T12:50:00.004-08:002018-03-06T05:08:50.881-08:00Remembering Physicist Otto Frisch<font size="4"> <b>Remembering Physicist Otto Frisch</b><br><br> Otto Frisch was one of the great physicists of the 20th Century. I met Otto at the Cavendish Laboratory. We used to eat "digestive biscuits" together at teatime. <br><br> He was a messy eater and showered crumbs all over the place and I called him out on it, much to my regret. His autobiography is "What Little I Remember". A very humble man. It's worth reading.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-89803844188980147102018-03-03T08:39:00.000-08:002018-03-09T10:49:01.922-08:00Predicting New Gravitons<font size="4"> <b>Predicting New Gravitons</b><br><br> At the moment Physics recognizes 4 fundamental forces:<br><br> -The Color Force (mediated by a spin 1 Boson - the Gluon)<br>-The Electromagnetic Force (mediated by a spin 1 Boson - the Photon)<br>-The Weak Force (mediated by 2 spin 1 Bosons - the Z Boson and W Boson)<br>-The Gravitational Force (mediated by the hypothetical spin 2 Boson - the Graviton)<br><br> But if we apply the SIO (Spin Inversion Operator) to the spin 1/2 neutrinos (electron, muon and tau) we get spin 2 neutral particles. Could these be "partners" of the Graviton in a new force that's closely related to gravity. And if these new particles have high mass the new force would have very short range - making it an ideal candidate for "quantum gravity".<br><br> So just as the Electromagnetic force gets extended to the Electroweak force by the addition of new spin 1 mediating particles, so Gravity gets extended to "quantum gravity" by the addition of new spin 2 mediating particles.<br><br> Plus, could these new particles also account for Dark Matter?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-50081498605538571352018-03-01T12:37:00.005-08:002018-03-12T12:20:02.608-07:00LED Surprise<font size="4"> <b>LED Surprise</b><br><br> An LED (Light Emitting Diode) is just a solid state junction that emits light in response to an applied voltage. <br><br> These junctions can be switched amazingly fast - making them ideal for data transmission. <br><br> So forget Wi-Fi, the talk is now about Li-Fi networks. Li-Fi is short for light fidelity. What an interesting idea.. tiny LED lights transmitting data with massive bandwidth.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-89070667507446802972018-02-28T08:53:00.000-08:002018-03-01T11:24:21.380-08:00Quantum Mechanics - Efimov States Explained<font size="4"> <b>Quantum Mechanics - Efimov States Explained</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://4.bp.blogspot.com/-1sI_yPMpzYs/WpbeZAITh8I/AAAAAAAAHvI/yFaxHpBfjfQMcWVtMwFwPHx_ppdhdX7wACLcBGAs/s1600/borromean-rings.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://4.bp.blogspot.com/-1sI_yPMpzYs/WpbeZAITh8I/AAAAAAAAHvI/yFaxHpBfjfQMcWVtMwFwPHx_ppdhdX7wACLcBGAs/s400/borromean-rings.jpg" width="400" height="333" data-original-width="220" data-original-height="183" /></a></div> The Efimov effect is an effect in quantum mechanics that was predicted by the Russian physicist Vitaly Efimov in 1970. It has only recently been observed.<br><br> So, what is it?<br><br> It's a bound state of 3 identical bosons that happen even if the force between any two of the bosons is not strong enough to cause binding.<br><br> In other words, these states only appear when you have 3 bosons, take any one away and the whole system disappears.<br><br> Efimov States have an infinite series of excited three-body energy levels. <br><br> They are often depicted symbolically by the Borromean rings - no two rings are linked, but all 3 rings are linked!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-16867708545668868252018-02-28T06:46:00.001-08:002018-02-28T10:12:04.781-08:00The Permutahedron<font size="4"> <b>The Permutahedron</b><br><br> <div class="separator" style="clear: both; text-align: center;"><a href="https://1.bp.blogspot.com/-25NFyn5chN8/WpbBH59C6hI/AAAAAAAAHuo/59C28X4JItUMLQCxmj6AjEi3JHCvp6KZwCLcBGAs/s1600/permutahedron.jpg" imageanchor="1" style="clear: left; float: left; margin-bottom: 1em; margin-right: 1em;"><img border="0" src="https://1.bp.blogspot.com/-25NFyn5chN8/WpbBH59C6hI/AAAAAAAAHuo/59C28X4JItUMLQCxmj6AjEi3JHCvp6KZwCLcBGAs/s400/permutahedron.jpg" width="400" height="400" data-original-width="1092" data-original-height="1092" /></a></div> This is the 4-permutahedron. It's a geometric representation of the ways to rearrange the numbers 1,2,3,4.<br><br> Two permutations are connected by an edge if one can be transformed into the other by swapping two consecutive numbers.<br><br> And this is just for 4 numbers, I wonder what the 100-permutahedron would look like?<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-35388690474325916202018-02-25T10:30:00.005-08:002018-03-23T13:51:31.255-07:00Driverless Cars - The Problem<font size="4"> <b>Driverless Cars - The Problem</b><br><br> Oh sure, you'll see driverless cars on the road. A few here and a few there. But they will never happen in a major commercial way for a very simple reason: people love to drive.<br><br> I do. It's a skill that took me a while to learn. I'm proud of my skill and I enjoy using it. A driverless car takes that pleasure away. Can you imagine being in a car that obeys all traffic laws including speed limits? <br><br> That would be incredibly infuriating and amazingly boring.<br><br> But there's a much bigger problem. On todays aggressive roads driverless cars are outright dangerous!!!!!! <br><br> Go ahead, plod along at the 30 mph speed limit while 18 wheeler trucks swerve past you at 55 mph. No thanks.<br><br> Or your driverless car hits and kills an innocent person. While you watch. Because the algorithms were not smart enough to evaluate the situation.<br><br> But there's one good thing about driverless cars - as more come on the road they will put my driving skills to the test in order to avoid them!<br><br> Driverless cars are putting me to sleep. Wake me up when we have driverless national train services.<br><br> You gotta love the driverless car industry - a solution to a problem that doesn't exist.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-84428032169248290312018-02-25T07:25:00.000-08:002018-03-08T07:41:38.769-08:00Difference Calculus - Explained in 5 Minutes <font size="4"> <b>Difference Calculus - Explained in 5 Minutes</b><br><br> Most people have heard of Differential Calculus, but few have heard of Difference Calculus. In the rare times it does get mentioned it's described as an "approximation" to Differential Calculus. That's a pity, because Difference Calculus deserves better!<br><br> So what is it?<br><br> It's easily explained if you remember the definition of a derivative in Differential Calculus. For a function f(x) the derivative df(x)/dx is defined as..<br><br> df(x)/dx=Limit as c approaches 0 of (f(x+c)-f(x))/c<br><br> It turns out that for this limit to exist f(x) has to be a very "well behaved" function. Not all functions are, so df(x)/dx does not exist for many functions. Which means that Differential Calculus cannot be used with these functions.<br><br> Difference Calculus gets around this problem in an incredibly simple way, it just removes the limit from the definition of df(x)/dx to define the "difference" Df(x) as..<br><br> Df(x)=(f(x+c)-f(x))/c<br><br> But this definition is not as simple as it looks. Notice that in the definition of df(x)/dx the c never appears in the result, it's simply used to define the limit. This is not true for Df(x), where c actually appears in the result, and so different choices of c will give different values for Df(x). This is not a bad thing, but it's something that should be noted. To be strictly accurate we should denote the difference as Dcf(x) because it depends on c, but it's usually just denoted by Df(x) and some value of c is assumed.<br><br> Of course, for the case of c=1 we get the simple expression..<br><br> Df(x)=f(x+1)-f(x)<br><br> Let's try an example..<br> The function f(x)=e^x is famous in Differential Calculus because it's equal to its own derivative, df(x)/dx=f(x)<br><br> This is not true in Difference Calculus, because the difference is..<br><br> Df(x)=f(x)*(e^c-1)<br><br> As we noted above, the result depends on c. If we want to get the same result as differential calculus, Df(x)=f(x), we have to use a specific value of c such that..<br><br> (e^c-1)=1 which means c=ln(2)=0.69314718056..<br><br> This is a hint that Difference Calculus has its own properties and is more than just an "approximation" to Differential Calculus.<br><br> For functions of an integer variable, f(n) where n=1,2,3,4,.. the value c=1 is natural and the difference is Df(n)=f(n+1)-f(n)<br><br> Equations involving Df(x) are called difference equations and are the equivalent of differential equations in Differential Calculus. Here's a simple example..<br><br> Df(x)=-2*f(x) for c=1, which is the simple difference equation f(x+1)+f(x)=0<br><br> One solution to this difference equation is f(x)=a*cos(pi*x), where a is an arbitrary constant. So even a very simple difference equation has a "wave-like" solution! This is another hint that Difference Calculus has its own properties distinct from Differential Calculus.<br><br> In Differential Calculus we can define higher order derivatives. Can we do this in Difference Calculus? Yes! For example, the second order difference is just the difference of the first order difference..<br><br> D(Df(x))=(f(x+2*c)-2*f(x+c)+f(x))/(c^2) and for the case of c=1 this is the simple expression f(x+2)-2*f(x+1)+f(x)<br><br> Higher order differences simply use the value of the function at more points. The first order difference uses x and x+1. The second order differences uses x, x+1 and x+2. This continues for higher order differences. <br><br> Difference Calculus has very broad applicability. In fact, I like to think of Differential Calculus as just a special case of Difference Calculus!<br><br> More to explore: "The Theory of Finite Differences" by C. Jordan, first published in Budapest in 1938. This book give a complete mathematical treatment of Difference Calculus.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-32966017874361617672018-02-25T07:09:00.003-08:002018-02-25T07:11:26.502-08:00Plot a Function - Google Plot is Fast and Free<font size="4"> <b>Plot a Function - Google Plot is Fast and Free</b><br><br> Need to plot a function? <br><br> Just punch your request into Google to get an instant plot. The Google plot feature is powerful, fast and free! It's a great way to teach yourself functions, or to make math homework easy!<br><br> Example: to plot the function f(x)=x^2 just enter plot x^2 into Google. Of course, it can also handle more complex functions, for example try 5*(x-4)^2+5 or x^3+(1/x) or try one of my favorites, just enter plot 1/(1+x^2)<br><br> Notice the symbols used by the Google Plot function: x^n means raise x to the power n and of course * is used to denote multiplication.<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comtag:blogger.com,1999:blog-8920795989760428389.post-16122867019395577032018-02-24T08:53:00.001-08:002018-02-25T10:32:30.473-08:00The Problem with General Relativity<font size="4"> <b>The Problem with General Relativity</b><br><br> General Relativity had its 100th birthday in 2015 and is still the #1 way to describe gravity. But change may be on the horizon.<br><br> The theory is probably the most brilliant physics insight ever produced by a single individual. But it can never be correct at the quantum level and must be replaced or seriously modified.<br><br> Totally new thinking is needed, especially concerning space time coordinates and dimension. <br><br> Sorry Albert, but heck, 100 years is a pretty good run!<br><br> </font> Content written and posted by Ken Abbott <a style="text-decoration:underline" href="mailto:abbottsystems@gmail.com">abbottsystems@gmail.com</a><br><br>Ken Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.com