tag:blogger.com,1999:blog-89207959897604283892018-06-24T12:09:00.425-07:00Math-MathThought provoking notes on Math, Physics and ScienceKen Abbott PhDhttps://plus.google.com/101487824185426724709noreply@blogger.comBlogger220125tag:blogger.com,1999:blog-8920795989760428389.post-15297548369535697792018-06-24T12:06:00.001-07:002018-06-24T12:09:00.354-07:00How to Build 3D Space<font size="4"> <b>How to Build 3D Space</b><br><br> Suppose I have a collection of identical balls. Each has 6 connectors on its surface - 2 red, 2 green and 2 blue. <br><br> Then I have cables that come in 3 varieties, red, green and blue. Red cables can only plug into red connectors, green cables can only plug into green connectors and blue cables can only plug into blue connectors. <br><br> Now I specify a simple constraint: ever ball must have all its connectors filled. <br><br> Bingo - the system is a 3D system.<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-64642590676903214092018-06-22T11:16:00.004-07:002018-06-22T11:16:50.754-07:00The Story Behind Spin Inversion Symmetry (SIS)<font size="4"> <b>The Story Behind Spin Inversion Symmetry (SIS)</b><br><br> SIS says every elementary particle in the Standard Model (except for the Higgs) of spin s has a partner of spin 1/s and vice versa. If you look at the Standard Model you'll realize SIS predicts the existence of 12 new spin 2 particles. But here's the story behind SIS..<br><br> I have no theoretical justification for SIS. But I do have a rather amusing story of how I came up with it. <br><br> I was imagining how you might model a spin 1/2 elementary particle with an everyday object. After a bit of thought I decided on a Mobius strip (strip of paper joined after applying 1 half turn). I figured 1 half turn = spin 1/2. <br><br> Then I made a strip with 4 half turns and discovered it will naturally "flip" into a double thickness Mobius strip (no cutting, folding, etc.) <br><br> In other words a strip with 4 half turns (spin 2) naturally flips into a strip with 1 half turn (spin 1/2) and vice versa. <br><br> So there you have it - a desktop version of SIS. All you need is paper, scissors and a touch of glue!!!!!<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-11756977871094981102018-06-19T07:36:00.003-07:002018-06-19T07:43:58.481-07:00Metrics in Physics - An Unexplored Resource?<font size="4"> <b>Metrics in Physics - An Unexplored Resource?</b><br><br> We could probably do a lot in Physics by simply "tweeking" the metric. <br><br> For example: Special Relativity uses the familiar metric x^2+y^2+z^2-t^2. But this is just one in an infinite family of metrics.. x^q+y^q+z^q-t^q where q=1,2,3,4,... And there are many other metrics. <br><br> Even General Relativity, THE metric theory, modifies the metric using coefficients but still retains q=2 and never even considers changing that!<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-2312315679333436992018-06-16T13:38:00.003-07:002018-06-21T07:46:53.154-07:00The Holographic Principle - An Interesting Example<font size="4"> <b>The Holographic Principle - An Interesting Example</b><br><br> The Holographic Principle talks about regions of space where the surface area is just as important as the volume. So I decided to try and construct a specific example.<br><br> I did. And the result is both simple and elegant.<br><br> Consider objects that have their surface area equal to their volume.<br><br> For a circle of radius r in 2D we have surface area (circumference)= 2*pi*r and volume (area)=pi*r^2. Equating these two gives r=2. Which is the dimension of the space!<br><br> Doing the same for a sphere in 3D we get r=3. Which is the dimension of the space!<br><br> Is this always true? Yes!<br><br> Take a point in n-dimensional Euclidean space (x1,x2,x3,...,xn)<br><br> Then the surface of a sphere of radius r is the set of points with:<br>x1^2+x2^2+x3^2+....+xn^2=r^2<br><br> and the volume consists of all the points with:<br>x1^2+x2^2+x3^2+....+xn^2 less than or equal to r^2<br><br> The volume of the sphere is c(n)*(r^n) and its surface area is n*c(n)*r^(n-1)<br><br> So equating them gives r=n. <br><br> Note that the function c(n) cancels out so its value is not needed, but c(n)=(pi^(n/2))/gamma(1+n/2). Where gamma is the Euler Gamma Function.<br><br> So we can say in general..<br><br> "In n-dimensional Euclidean space a sphere with surface area=volume has radius n"<br><br> The radius of the sphere is equal to the dimension of the space!!!! <br><br> This result is related to the Holographic Principle because it equates surface area and volume.<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-12651463001175407552018-06-15T05:03:00.000-07:002018-06-15T06:34:11.906-07:00CERN - LHC to Get Major Upgrade<font size="4"> <b>CERN - LHC to Get Major Upgrade</b><br><br> CERN has officially begun work on a major upgrade to the Large Hadron Collider (LHC) to boost luminosity. <br><br> When the upgrade is complete in 2026 the LHC be able to collect data at almost 10X its current rate.<br><br> CERN says..<br><br> "The secret to increasing the collision rate is to squeeze the particle beam at the interaction points so that the probability of proton-proton collisions increases. To achieve this, the HL-LHC requires about 130 new magnets, in particular 24 new superconducting focusing quadrupoles to focus the beam and four superconducting dipoles. Both the quadrupoles and dipoles reach a field of about 11.5 tesla, as compared to the 8.3 tesla dipoles currently in use in the LHC. Sixteen brand-new “crab cavities” will also be installed to maximise the overlap of the proton bunches at the collision points. Their function is to tilt the bunches so that they appear to move sideways – just like a crab."<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-56728430660367351392018-06-13T05:35:00.004-07:002018-06-14T05:25:37.752-07:00A Prime Number Conjecture in Binary<font size="4"> <b>A Prime Number Conjecture in Binary</b><br><br> Take any prime number p and write it in binary format. <br><br> From this prime now generate a series of numbers using this simple algorithm:<br><br> You can insert a single digit (0 or 1) anywhere you wish. (But you can't insert a 0 at the beginning because that just gives p unchanged.)<br><br> If p is m digits long in binary you will generate 2*m+1 new binary numbers. (btw: some may are duplicates.)<br><br> CONJECTURE: At least one of these new numbers is prime.<br><br> Let me illustrate the process with a simple example. <br>Take the prime 5, which in binary is 101. It has 3 digits, so we know the algorithm will generate 2*3+1=7 numbers. Here they are (notice the duplicates)..<br><br> 1010=10<br>1011=11<br>1011=11<br>1001=9<br>1101=13<br>1001=9<br>1101=13<br><br> So in this case we've generated two new prime numbers, 11 and 13.<br><br> A note on duplicates: <br>I think you will always get m duplicates. So if these are removed the algorithm generates just m+1 numbers and the conjecture says at least one of these is prime.<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-79857861257529995332018-06-12T06:45:00.002-07:002018-06-13T11:27:46.033-07:00Could General Relativity Fail Completely?<font size="4"> <b>Could General Relativity Fail Completely?</b><br><br> General Relativity sets gravity apart from all other fundamental interactions by claiming it's simply curvature of spacetime. It's not even a force!<br><br> This is why GR can't be reconciled with Quantum Mechanics. <br><br> So here's a strange thought. What if spacetime simply ceased to exist (as we currently know it) in certain circumstances? <br>Then General Relativity would fail completely. <br><br> What might these "certain circumstances" be? <br>I don't know. But a great place to start is the interior of a spinning black hole.<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-6026075946388092672018-06-10T12:36:00.001-07:002018-06-21T07:42:17.860-07:00A Special Sphere in n-Dimensional Space<font size="4"> <b>A Special Sphere in n-Dimensional Space</b><br><br> It's really interesting to consider objects that have their surface area equal to their volume.<br><br> For a circle of radius r in 2D we have surface area (circumference)= 2*pi*r and volume (area)=pi*r^2.<br><br> Equating these two gives r=2. Which is the dimension of the space!<br><br> Doing the same for a sphere in 3D we get r=3. Which is the dimension of the space!<br><br> Is this always true? Yes.<br><br> Take a point in n-dimensional Euclidean space (x1,x2,x3,...,xn)<br><br> Then the surface of a sphere of radius r is the set of points with:<br>x1^2+x2^2+x3^2+....+xn^2=r^2<br><br> and the volume consists of all the points with:<br>x1^2+x2^2+x3^2+....+xn^2 less than or equal to r^2<br><br> The volume of the sphere is c(n)*(r^n) and its surface area is n*c(n)*r^(n-1)<br><br> So equating them gives r=n. <br><br> Note that the function c(n) cancels out so its value is not needed, but c(n)=(pi^(n/2))/gamma(1+n/2). Where gamma is the Euler Gamma Function.<br><br> So we can say in general..<br><br> "In n-dimensional Euclidean space a sphere with surface area=volume has radius n"<br><br> The radius of the sphere is equal to the dimension of the space! I think this is a neat result because it relates the dimension of the space to a certain class of spheres within it. It may also be related to the Holographic Principle because it equates surface area and volume.<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-31108263964529758182018-06-10T08:51:00.001-07:002018-06-11T05:39:13.993-07:00Making Prime Numbers - A Conjecture<font size="4"> <b>Making Prime Numbers - A Conjecture</b><br><br> Take any prime number. You are allowed to insert a single digit (i.e. 0-9) anywhere in the number, including the beginning and end (but we don't count adding a 0 at the beginning of the number because that just gives the original number.)<br><br> Conjecture: This process will always generate at least one new prime number.<br><br> Doing this in binary (base 2) means the only digits I can insert are 0 and 1 and it makes the process very simple. The conjecture of course remains the same.<br><br> If you write a program to test this conjecture I would love to hear about your results.<br><br> <b>Examples in base 10</b><br>503 is prime. I decide to insert 2 before the 3 to get 5023, which is prime. <br>20129 is prime. I decide to insert 5 at the beginning to get 520129, which is prime.<br><br> <b>Example in binary</b><br>Take the number 3 in binary (11), so the process generates 3 new numbers..<br><br> 111=7<br>110=6<br>101=5<br><br> And in this case it has generated two new primes, 5 and 7.<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-16653293482238696792018-06-08T13:02:00.002-07:002018-06-16T13:33:11.276-07:00Sphere in n-Dimensional Space<font size="4"> <b>Sphere in n-Dimensional Space</b><br><br> Here's the elegant result clearly explained. <br><br> Take a point in n-dimensional Euclidean space (x1,x2,x3,...,xn)<br><br> Then the surface of a sphere of radius r is the set of points with:<br>x1^2+x2^2+x3^2+....+xn^2=r^2<br><br> and the volume consists of all the points with:<br>x1^2+x2^2+x3^2+....+xn^2 less than or equal to r^2<br><br> Then the Theorem is simply this..<br><br> "In n-dimensional Euclidean space a sphere with surface area=volume has radius n"<br><br> The radius of the sphere is equal to the dimension of the space!!!! I think this is a neat result because it relates the dimension of the space to a certain class of spheres within it. It also has a "holographic" aspect because it equates surface area and volume.<br><br> If you're interested in the proof it goes like this..<br><br> The volume of the sphere is c(n)*(r^n) and its surface area is n*c(n)*r^(n-1)<br><br> So equating them gives r=n. <br><br> Note that the function c(n) cancels out so its value is not needed, but c(n)=(pi^(n/2))/gamma(1+n/2). Where gamma is the Euler Gamma Function.<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-90306769118018000872018-05-31T11:56:00.003-07:002018-06-15T12:24:22.550-07:00The Day Einstein Got Lucky<font size="4"> <b>The Day Einstein Got Lucky</b><br><br> When physicists describe a moving object they measure its position at different times, and obviously these positions have to be given relative to some reference points. These reference points are called a reference frame. <br><br> Special Relativity showed that the Laws of Physics are independent of the choice of reference frames - when the reference frames are moving with constant velocity. <br><br> It was a huge success. But how could Einstein generalize it? <br><br> Easy.. just do the same thing for reference frames that are accelerating. Makes total sense. <br><br> So Albert went about the usual business that had been so successful before. But then he suddenly realized something. <br><br> On a local basis acceleration is indistinguishable from gravity. Bingo. Albert could do his usual thing with reference frames and describe gravity at the same time.<br><br> A huge bonus!!!!<br><br> So he produced General Relativity. And it was a massive success. That is, until it met Quantum Mechanics. The two did not get along. And still don't.<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-55503140915691786402018-05-30T11:47:00.002-07:002018-05-30T11:47:29.565-07:00Was Einstein Toying With Us?<font size="4"> <b>Was Einstein Toying With Us?</b><br><br> First we invent the idea of a coordinate system. That's very helpful. <br><br> Then we frame all our physics in terms of it. <br><br> But we know that the laws of physics must be covariant - i.e. independent of our choice of coordinate system. <br><br> General Relativity showed that, and that alone would have been a very nice achievement. <br><br> But no, Einstein wove into it a description of gravity - placing gravity in a totally unique position. <br><br> No wonder we can't unify gravity with the rest of physics!!!!!!<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-44463022311426442142018-05-28T11:53:00.001-07:002018-05-29T04:49:36.937-07:00The Fluid Dynamics of Spacetime<font size="4"> <b>The Fluid Dynamics of Spacetime</b><br><br> The unification of the two great theories of the 20th Century - Quantum Mechanic (QM) and General Relativity (GR) - still seems far away.<br><br> Why?<br><br> I think both theories will require major modification before they can be united.<br><br> The modification will be in how they treat spacetime.<br><br> In QM spacetime is a stage on which the action occurs. In GR spacetime is the action!<br><br> That's a massive difference.<br><br> Think of a fluid - at the macro level an excellent description is fluid dynamics - the Navier-Stokes Equations. But at the micro level molecules rule.<br><br> So, the EFE (Einstein Field Equations of General Relativity) are the "Navier-Stokes Equations" of spacetime - an excellent description at the macro level.<br><br> But at the micro level of spacetime we have what? Nobody knows. Our theories are not there yet.<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-81059780565920985322018-05-23T11:37:00.002-07:002018-06-07T06:00:13.286-07:00Fermat's Last Theorem - The Search for a Generalization<font size="4"> <b>Fermat's Last Theorem - The Search for a Generalization</b><br><br> One elegant approach is to write the theorem in the language of metric spaces..<br><br> Let (x1,x2,..,xn) be a point in a n-dimensional vector space.<br><br> Then r^q=|x1|^q+|x2|^q+...+|xn|^q defines a series of metrics for q=1,2,3,.. where r is the distance of the point from the origin and |xi| is the absolute value of xi.<br><br> This allows a generalized version of Fermat's Last Theorem to be written as follows..<br><br> "An integer point (x1,x2,..,xn) is never an integer distance (r) from the origin when q>n"<br><br> It's interesting to note that the generalization holds when the metric parameter (q) exceeds the dimensionality of the space (n).<br><br> The special case of n=2 was proved in 1994 by Andrew Wiles. It was an amazing achievement because mathematicians had been trying to prove it since Fermat first suggested it in 1637.<br><br> But is this generalized version true? <br><br> At first I though it was, but one of my readers pointed out a counter example. And one counter example is all you need to disprove a conjecture! However, I am now investigating ways the conjecture may be modified (or even generalized further) so it still holds.<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-36220081262286282872018-05-21T10:36:00.005-07:002018-05-27T14:50:51.769-07:00When Gravity Fails<font size="4"> <b>When Gravity Fails</b><br><br> Einstein's General Theory of Relativity is now over 100 years old and still remains our best description of gravity. <br><br> But the elegant Tensor form of Einstein's Field Equations (EFE) masks a critical property - they are basically differential equations of derivatives with respect to spacetime i.e. with respect to the x,y,z and t coordinates. <br><br> But, as any mathematician will tell you, derivatives are only valid for "very smooth" functions. Meaning if spacetime becomes "granular" EFE will not apply - for the simple reason that the derivatives are not defined. <br><br> At some point this granularity of spacetime will become apparent - the center of a rotating black hole could be an example. <br><br> So, it's not that you can't solve the EFE in this situation - it's that you can't even write them down!!!!!!!<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-3955578138899220312018-05-18T14:28:00.002-07:002018-05-26T11:51:54.176-07:00The Size of the Universe<font size="4"> <b>The Size of the Universe</b><br><br> It takes light about 100,000 years just to cross our Galaxy. And the Universe contains billions of Galaxies. <br><br> So it's huge, right? <br><br> Maybe, maybe not. <br><br> Suppose the speed of light was changed. So it took a second to cross our Galaxy. Then the Universe would be a much smaller place.<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-25424698359603935932018-05-14T10:34:00.004-07:002018-05-19T14:19:12.049-07:00Taxicab Geometry<font size="4"> <b>Taxicab Geometry</b><br><br> Imagine an integer lattice and the only way to move around is to jump from node to node by horizontal and vertical movements. Diagonal movements are not allowed. <br><br> Think of a Taxicab on the Manhattan street grid. It certainly can't drive diagonally through a block!!!<br><br> So the node point (m,n) is at a distance m+n from the origin (m and n are integers of course) and the metric on the space is therefore d(m,n)=m+n<br><br> A "circle" centered on the origin is a diamond and pi=4 exactly. <br><br> In this grid each node is connected to exactly 4 others and pi=4. Is this just a coincidence or a fundamental result?<br><br> Is there a grid where each node is connected to exactly 3 others? Yes, a hexagonal grid has this. And pi=3. <br><br> <b>The General Case</b> This geometry is not constrained to grids (rectangular, hexagonal or otherwise). So long as the connectivity is correct the whole thing could be a mesh piled in a giant heap on the floor!!! <br><br> There are just two rules: You can only move between nodes along a connection, and the (minimum) number of connections between 2 nodes is the distance between the nodes. <br><br> It's incredibly general. It's topological. It's all about connectivity. Examples: the "rectangular grid" is a mesh with connectivity=4 and the "hexagonal grid" is a mesh with connectivity=3.<br><br> A fun way to imagine this geometry: Think of space as a fishing net. The knots in the net are the points of space, the snippets of reality. And the rope between the knots are the connections. It does not matter how you handle the net - throw it on the ground in a heap if you wish - the topology is unchanged. So reality is unchanged.<br><br> Could we build physics on such a mesh and if so what would it 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-90526161830875499792018-05-12T12:22:00.002-07:002018-05-12T12:24:00.477-07:00Spin Inversion Symmetry<font size="4"> <b>Spin Inversion 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 very deep. The universe is awash in spin-2 bosons and the particles we currently know in the Standard Model are only a fraction of the particles out 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-55035519146538465452018-05-06T08:20:00.004-07:002018-05-21T10:39:50.848-07:00Does Hawking Radiation Exist?<font size="4"> <b>Does Hawking Radiation Exist?</b><br><br> Is it possible that Hawking Radiation does not exist?<br><br> Hawing Radiation from a black hole is supposed to happen when the event horizon separates a pair of virtual particles. One falls into the black hole but the other escapes and appears as radiation.<br><br> Current theories assume space is a continuum, meaning the position of the event horizon can be specified with infinite accuracy. Suppose this was not the case. Suppose the event horizon was fuzzy. Simply not enough resolution to separate a virtual pair of particles. Then there would be no Hawking radiation.<br><br> And let's not forget, Hawking Radiation has never been experimentally verified.<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-8730823160286143902018-05-06T08:04:00.000-07:002018-05-15T06:15:28.521-07:00Are there Laws of Information?<font size="4"> <b>Are there Laws of Information?</b><br><br> Suppose I told you this..<br><br> "I weigh 175 lbs."<br><br> I just gave you some information. But what exactly is information, and can it be defined in a quantitive way to become a key concept in math and physics? Let's look more closely at what I just gave you..<br><br> It removed an uncertainty. Meaning, before you read the statement you were uncertain about my weight. Reading the statement removed your uncertainty. So perhaps information is simply the removal of uncertainty. Great, we've defined information!<br><br> Not so fast..<br><br> I gave you the information by publishing it in a blog. So you were not the only person to receive it, thousands of others did also. Perhaps some of those people were my family. But they already know this, so for them it did not remove an uncertainly. Which means for them it was not information!<br><br> So, our definition is true for some people but not for others. That's a bad definition. We need something better.<br><br> OK, let's forget this whole thing. I regret giving you the information, so I'll just delete it.<br><br> Not so easy. I can delete it from the blog, but thousands have read it and they remember it. I can't delete that. So perhaps we've discovered the first law of information..<br><br> "Once received, information can never be deleted."<br><br> Oh boy, information is getting complex. What kind of stuff is this?<br><br> It gets more interesting. The above statement implies there's some information that's never received. Can this be true? If it's never received, ever, then how do we know it exists? We don't. So perhaps we should restrict our definition of information to information that's received. Then our first law of information gets even simpler..<br><br> "Information can never be deleted."<br><br> Does this mean the information content of the universe is constantly increasing, for the simple reason that information cannot be deleted?<br><br> Let's look more closely at what happened when the above information was received. The person receiving the information scanned it and committed it to memory. So they can recall it anytime they want. We don't know exactly how memory works, but we do know that something must have changed in the brain's neural structure in order to store this information. And no change comes for free, a small amount of energy was required to process and store the information. So perhaps we have a second law of information..<br><br> "Receiving information expends energy."<br><br> This statement is interesting for two reasons. First, it shows there's a relationship between information and energy. Second, it indicates a possible quantitative definition of information.. perhaps we can relate the amount of information in a message to the amount of energy needed to receive the message.<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-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-73232812250062230632018-04-20T06:04:00.000-07:002018-05-16T14:22:07.220-07:00The Nature of Spacetime <font size="4"> <b>The Nature of Spacetime</b><br><br> We tend to think of space as nothing - simply a void with no properties. But General Relativity says otherwise. It says spacetime 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 spacetime as something "tangible", something that provides "resistance to motion". <br><br> So light has difficulty plowing through spacetime.. 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 spacetime 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.com