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Antievolution.org Discussion Board > From the Panda's Thumb > After the Bar Closes... > The Traveling Twin Takes a Short Cut

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Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 25 2008,22:00    In the other thread it was pointed out that I had strayed completely off topic.  There was even an implicit remark that this was dishonest.  Therefore, I am starting this thread. For those that haven't been following the situation, allow me a quick recap... I had presented my thoughts on the comparative strengths and weaknesses of Mike Gene's and Dembski's methods for inferring design (I feel Mike Gene's is a more honest attempt even if it is weak). This, of course, engendered pejorative remarks about me personally and repeated inquiries about things like who I am (Mike Gene?), my definitions, my opinions and what books I have read. I eventually acquiesced to these requests by indicating Penrose’s The Road to Reality is the type of book I like to read and explained some of my general thoughts.  One of which is that I consider the Twin Paradox to be a geometry problem that is explained by understanding the traveling twin takes a short cut. The last comment (from Doc Bill) was questioning the relationship of this topic to a Biology Forum.  It is at this point that I decided to start this thread and answer that. As some of you know, I am of the opinion that it is possible life is the result of an evolution of living organisms making direct use of interconnected quantum effects be it for photosynthesis (see recent Berkeley Lab discoveries), DNA processing (see A. Patel) or quantum consciousness (see S. Hameroff). The reason I feel quantum effects are interconnected is generally based on the Copenhagen quantum interpretation concerning waveforms and specifically due to Penrose’s derivative interpretation called Objective Reduction (OR). And one of the things that ties it all together is the geometry of our universe.  If the distance in four dimensional space-time is appropriately described by the Minkowskian geometry equation… dl^2 = dx^2 + dy^2 + dz^2 – dt^2 or in a rotated complex dimension view… ds^2 = dt^2 - dx^2 - dy^2 - dz^2 Then it becomes apparent there are different path lengths between two points in four dimensional space-time and the shortest distance is NOT a straight line. The homebody twin takes the straight line path along the time dimension (2 years)… ds = SQRT(2^2 – 0^2 – 0^2 – 0^2) ds = 2 The traveling twin takes a path out and back (1 year, 0.8 light-years both ways)… ds = SQRT(1^2 – 0.8^2 – 0^2 – 0^2)       + SQRT(1^2 – (-0.8)^2 – 0^2 – 0^2) ds = 1.2    [Edited to correct mistake made in rush] The traveling twin path is shorter. The traveling twin takes a short cut. Things that travel at the speed of light take the ultimate short cut in space-time, the path length is always ZERO. This trivializes the explanation of quantum experiments involving Bell’s inequality and Greenberger–Horne–Zeilinger (GHZ) quantum states, at least for light.  The quantum effects are interconnected because the space-time path length between them is zero. To me, this starts to tie everything together, as in “life, universe and everything”. And, yes, that includes Biology.

Lou FCD Posts: 5455 Joined: Jan. 2006 (Permalink) Posted: Jan. 25 2008,22:12    I'm not really interested in patrolling 27 different threads wherein you demonstrate that you have no idea what you're talking about on 27 different subjects ala AFDavey Doodles. Keep it to these two, or if you're done with the other, let me know so I can close it up and you can keep it to this one. -------------- “Why do creationists have such a hard time with commas? Linky“. ~ Steve Story, Legend

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 25 2008,22:13    Hi Creek Belly, In the other thread, you wrote...   Quote I understand Minkowskian geometry, moreover I know when it's applicable. When you gave your example of the traveling twin, I showed that the solution came from both accelerating to +0.8c and -0.8c, you can show that the traveling twin enters a non-inertial reference frame and thus the conflict is resolved. The fact that you're still arguing about physics from special relativity is telling, you need general relativity at least to have any knowledge of gravity. Here's the catch with Minkowskian geometry: space-like separated events are not causally connected in the classical relativistic picture. If you want to argue that they are, you can perform some experiments to test this. The fact that you can flip signs around doesn't mean anything unless there's a physical effect that we can measure. Look, I've been reasonably supportive to the point where I'm genuinely interested in the physics research you present. However, when you say things that are demonstrably false, and chide people for holding on to outdated scientific dogma, I get a little annoyed. You complain that we're arguing from authority (I'm not, I'm arguing from the principles of physics), then you turn around and do exactly that. Man up and show me you know what you're talking about. First point, I agree that I haven't filled in details for things like gravity (which I also view as a geometry problem)  But I think I am starting with a firm foundation of a four dimensional view of space time.  So before we progress to gravity, let's address your other points. As far as showing things are "causally connected" in space-time with experimental data, I give you Quantum Mechanics and countless Bell inequality and GHZ experiments.  Quantum Mechanics and Cosmology do not exist in separate realities. This gets back to the fundamental question of whether or not you truly embrace four dimensional space-time.  If four dimensional space-time is real, than the calculated distance is real too.  If the distance is zero, there is no separation. You say I said something that is demonstrably false.  Besides possibly misapplying terms and my stupid "no acceleration" comment what is demonstrably false about saying the traveling twin takes a short cut?

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 25 2008,22:15    Hi Lou, Thank you for asking.  I think we can close up the other thread.  I copied Creeky Belly's comment here.

Lou FCD Posts: 5455 Joined: Jan. 2006 (Permalink) Posted: Jan. 25 2008,22:20    If anyone cares to see the history of this ... stuff, this thread is a continuation of that thread. -------------- “Why do creationists have such a hard time with commas? Linky“. ~ Steve Story, Legend

pwe Posts: 46 Joined: Sep. 2006 (Permalink) Posted: Jan. 26 2008,04:27    Quote (Thought Provoker @ Jan. 25 2008,22:00) This trivializes the explanation of quantum experiments involving Bell’s inequality and Greenberger–Horne–Zeilinger (GHZ) quantum states, at least for light.  The quantum effects are interconnected because the space-time path length between them is zero. To me, this starts to tie everything together, as in “life, universe and everything”. And, yes, that includes Biology. You don't say? I have a question, though. Which of the twins is Mike Gene and which is William Dembski? - pwe

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 26 2008,10:09    FYI Some other nut on the internet wrote... Quote Historically, physicist R. P. Feynman first pointed out the fact that the Green functions of Schroedinger equations are given as path integrals [2]. Later, he used it as a fundamental tool for quantum electrodynamics, and had a resounding success.  We find the nice exposition of the “physical meaning. ... Let “Minkowski path integral” refer to the usual path integral; integral over paths on ‘real’ space-time, interpreted as a Minkowski space. It is known by physicists that when calculating usual path integrals, the formal replacement of the time variable t by “imaginary time” T = it has good effects, e.g. the degree of divergence is reduced. The procedure of replacement is called Euclideanization. This suggests that the Euclideanized path integrals are more likely to be given a mathematical foundation. The history seems to have proven that. ... However I remark the fact that Euclidean path integral is not ’realistic’, and Minkowskian path integral is the only ’realistic’ path integral, where paths are in the real space-time. In my opinion, the final form of physics should be in Minkowskian formulation. Although mathematical foundation of Minkowskian path integral is an extremely difficult problem, the significance of it must not be underestimated.

Jim_Wynne Posts: 1208 Joined: June 2006 (Permalink) Posted: Jan. 26 2008,10:44    Quote (Thought Provoker @ Jan. 26 2008,10:09) FYI Some other nut on the internet wrote...     Quote Historically, physicist R. P. Feynman first pointed out the fact that the Green functions of Schroedinger equations are given as path integrals [2]. Later, he used it as a fundamental tool for quantum electrodynamics, and had a resounding success.  We find the nice exposition of the “physical meaning. ... Let “Minkowski path integral” refer to the usual path integral; integral over paths on ‘real’ space-time, interpreted as a Minkowski space. It is known by physicists that when calculating usual path integrals, the formal replacement of the time variable t by “imaginary time” T = it has good effects, e.g. the degree of divergence is reduced. The procedure of replacement is called Euclideanization. This suggests that the Euclideanized path integrals are more likely to be given a mathematical foundation. The history seems to have proven that. ... However I remark the fact that Euclidean path integral is not ’realistic’, and Minkowskian path integral is the only ’realistic’ path integral, where paths are in the real space-time. In my opinion, the final form of physics should be in Minkowskian formulation. Although mathematical foundation of Minkowskian path integral is an extremely difficult problem, the significance of it must not be underestimated. We're back in the same smelly miasma as in the other thread. Quotations from learned sources (appeals to authority) don't help anything unless you've demonstrated that you understand the source material.  For example, from your quotation,     Quote Although mathematical foundation of Minkowskian path integral is an extremely difficult problem, the significance of it must not be underestimated. [my bold] You want to accept the conclusion (the significance must not be underestimated) without understanding its antecedent (an extremely difficult problem). Here's what you're trying to get away with: :angry: -------------- Evolution is not about laws but about randomness on happanchance.--Robert Byers, at PT

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 26 2008,19:26    Hi Jim, It is interesting that you chose the Pythagorean Theorem in your attempt to make your point because it was a situation involving this theorem that helped shape the way I approach learning. I was in advanced placement math classes back in the dark ages when I was in High School.  I was surrounded by the straight-A know-it-alls on their way to PhD status. One day the class went on a short field trip to a nearby university having a “math day”.  One on the activities was what passed as a multi-media presentation of Euclidean geometry where it was explained how Euclid would have demonstrated (A + B)^2 = A^2 + 2AB + B^2 with rectangles and squares instead of numbers. The next day the class resumed the study of trigonometry and was given the in-class assignment of proving the Pythagorean Theorem.  The presumption made by the teacher and the rest of the class was that this was to be done using the tools presented in the current chapter.  But the current chapter was basic TRIG which is based on the Pythagorean Theorem.  I was the only one in the class who used Euclidean geometry to do the assignment.  Here we were getting exposed to base foundations and while the know-it-alls could mouth the proper words, work the proper formulas and get the As they really didn’t UNDERSTAND what they were doing.  I did. My mental defect is I am lopsided towards the analytical.  I can solve puzzles quickly.  I tend to be able to debug software systems based on the symptoms alone.  I see the holistic picture.  I understand it.  This ability is at the expense of bypassing irrelevant details, like proper semantics.  I know why and how to do Fourier Transforms but I still have to look up how to spell it.   This is the reason why I went down the path of engineering instead of academia. But back to the point at hand, you feel that I am not demonstrating a complete enough understanding of the subject in order to suffer carrying on a serious discussion with me on it. I will tell you what I am looking for.  I am looking for the weaknesses in the basic understanding I do have.  Am I trying to see the holistic picture enough to make sense of things.  I am not in the position to make a detailed presentation of the mathematical foundation tying together Cosmology and Quantum Mechanics while proposing an explanation for decoherence.  If I could do that, I would probably mathematically model Black Holes for a living, engage Stephen Hawking in debates, discover patterns for aperiodic tilings as a hobby and get knighted for my accomplishments. No, you aren’t arguing from authority, you are arguing from repetition.  You, and others, are restating over and over that I am ignorant and I am wrong without saying where specifically my logic breaks down or what specific assumptions you disagree with. From your comment in the other thread about Henderson-Darling oscillations and reciprocal inversions; I suspect you are familiar with Penrose’s hypotheses even if you disagree with them. What I am trying to provoke, politely ask for and/or beg is to get a critique of how well I understand Penrose’s hypotheses, even it is at a very crude level. For example, a critique could go like… “While Penrose does posit a single wavefunction in space-time his connection, his concept of decoherence is dependent on the existence of quantum gravity which you haven’t addressed.”

rhmc Posts: 340 Joined: Dec. 2007 (Permalink) Posted: Jan. 26 2008,19:33    sorry but that last post puts me in the group that thinks you're full of guano.

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 26 2008,21:29    Hi RMHC, Your comment makes me curious. Do you think I am lying and/or exaggerating? If so, about what? That I am an engineer who is good at solving problems? That the Pythagorean Theorem can be understood with Euclidean geometry? That Sir Roger Penrose was knighted and discovered Penrose Tilings in his spare time? If I am lying about Penrose's view of the universe and Quantum Mechanics, that is what I am trying to get people to tell me. What am I misunderstanding?

blipey Posts: 2061 Joined: June 2006 (Permalink) Posted: Jan. 26 2008,22:25    No.  The guano is the part about not needing to understand the basics.  The basics are the base of understanding anything.  I'm an actor and this sort of thing really ticks me off.  Everyone thinks they can act--you just memorize stuff right?  Right.  There is no foundation and no process to be learned.  Even those with natural talent need to have a firm grasp of the basics to be able to create good work day in and day out as is needed.  Just saying "I'm funny" is no solution to being able to be funny on demand, every time.  Training and attention to the details of your profession are what allow you to be funny, believable, and endearing. That you are able to "holistically realize a solution out of thin air" doesn't score you many points if you have such a blatant disregard for the building blocks of the puzzle's subject matter.  What happens when your intuition is off? Also, the poor analogy of doing Fourier Transforms while not being able to spell it doesn't help your case.  What possible relevance could spelling have to being able to do maths? -------------- But I get the trick question- there isn't any such thing as one molecule of water. -JoeG And scientists rarely test theories. -Gary Gaulin

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 26 2008,23:31    Hi Blipey, You wrote... Quote The guano is the part about not needing to understand the basics. But understanding the basics is what I am doing.  It is the base foundations that I look for, the supporting walls, the pillars. Take your acting as an example.  Surely, in acting you run into the type of people who can tell you the names of all the different techniques and maybe even have been schooled in them, but still don’t understand them.  Going through the motions and mouthing the words does not mean you understand them. Yes, the riggers of training is important for the practitioners, be they actors or scientists.  I am neither an actor nor a scientist.  But that doesn’t keep me from understanding and appreciating either or both. As an actor, would you try to convince me that I am incapable of understanding the need for an actor to be believable just because I don’t know the details of acting techniques? I don’t think I am relying on intuition, I am relying on understanding.  Of course I can only understand what I know.  I know GPS Satellites must adjust their clocks because four-dimensional space-time is real.  I know quantum effects interact non-locally in three dimensional space (e.g. Bell’s inequality, GHZ states, etc).  I know there are different path lengths between two points in four-dimensional space-time.  It is my understanding that the space-time path lengths correspond to varying perceived clock times.  I deduce that the different clock times in the Twin Paradox is due to different path lengths in space-time.  Which is why I think… …the traveling twin takes a short cut. Does my understanding become “guano” because I might not know the proper terminology or I fail to appreciate all the subtleties and techniques needed to reach such a conclusion?

blipey Posts: 2061 Joined: June 2006 (Permalink) Posted: Jan. 27 2008,00:27    Quote Does my understanding become “guano” because I might not know the proper terminology or I fail to appreciate all the subtleties and techniques needed to reach such a conclusion? Most likely, yes.  Understanding is hard without knowing the subtleties and techniques, though I'm sure you wouldn't agree.  There are not many Ramanujans walking around and even he needed to learn the basics to be a contributing member of the mathematical world. Quote would you try to convince me that I am incapable of understanding the need for an actor to be believable just because I don’t know the details of acting techniques? No, I would say that you are incapable of being an actor.  And it is no stretch to say that without knowing the basics and techniques of physics, you are incapable of being a physicist.  Try not to mix the metaphors. -------------- But I get the trick question- there isn't any such thing as one molecule of water. -JoeG And scientists rarely test theories. -Gary Gaulin

blipey Posts: 2061 Joined: June 2006 (Permalink) Posted: Jan. 27 2008,00:35    Quote Of course I can only understand what I know. This is the kind of thing that makes you look like a kook.  This is a waste of type and you only include it for one of the following reasons: 1.  You think it is profound and needs mentioning.  It doesn't; it's a truism.  Most people take it for granted and talk about interesting things. 2.  You think that it helps make your case in some way, or helps people figure out who you are.  It may do the latter, otherwise it is trivial. -------------- But I get the trick question- there isn't any such thing as one molecule of water. -JoeG And scientists rarely test theories. -Gary Gaulin

Bob O'H Posts: 2564 Joined: Oct. 2005 (Permalink) Posted: Jan. 27 2008,01:56    Quote My mental defect is I am lopsided towards the analytical.  I can solve puzzles quickly.  I tend to be able to debug software systems based on the symptoms alone.  I see the holistic picture.  I understand it.  This ability is at the expense of bypassing irrelevant details, like proper semantics. Methinks a bit more attention to relevant details might come in handy.  Things like being able to work out when something is accelerating. Bob -------------- It is fun to dip into the various threads to watch cluelessness at work in the hands of the confident exponent. - Soapy Sam (so say we all)

keiths Posts: 2195 Joined: Jan. 2006 (Permalink) Posted: Jan. 27 2008,08:57    Quote (Thought Provoker @ Jan. 26 2008,23:31) Take your acting as an example.  Surely, in acting you run into the type of people who can tell you the names of all the different techniques and maybe even have been schooled in them, but still don’t understand them.  Going through the motions and mouthing the words does not mean you understand them. That's an excellent description, TP -- of you. "Mouthing the words" without understanding.  Knowing the jargon, with no clue as to what it actually means.  That is you, to a 'T'. Case in point:  for several days now, you've been making a fundamental mistake that completely undermines your position regarding special relativity and the twin paradox.  I've been waiting to see if you would catch your error.  By now it is clear that you never will. You have been claiming, for days, that special relativity is "wrong" and that the Minkowskian geometry of general relativity is needed in order to make sense of the twin paradox: Quote A lot of people think of the Special Relativity answer to the Twins Paradox when they hear "relativity" or "space-time".  That version is so incomplete that I consider it wrong. Quote In his book Penrose explains the Twins Paradox (i.e. Clock Paradox) is a geometry problem. He demonstrates how using the Minkowskian geometry of General Relativity ALL BY ITSELF solves the paradox.  Note, a generalized Twins Paradox problem doesn't include gravity. People feel more comfortable saying and thinking of General Relativity as just a minor upgrade to Special Relativity.  You can even find lots and lots of people with impressive credentials saying just that. Quote Since I am on a roll.  Let me offer you something sure to cause a loud howl from the Group Think mentality that holds court here. The reason for the introductory lesson in Minkowskian geometry and General Relativity is to awaken you to the reality of shortcuts in space-time. Quote Special Relativity is superfluous.  General Relativity is a complete explanation.  Special Relativity no longer needs to be a consideration.  Occam's razor suggests we should discard it.  That is what I am doing. Minkowskian space-time geometry is the appropriate model of our universe, not Euclidean geometry. Quote Minkowskian space-time geometry is the appropriate model of our universe, not Euclidean geometry. Guess what, TP? Minkowskian geometry is the geometry of special relativity, not general relativity.   Without realizing it, you've been using special relativity to resolve the twin paradox, all the while claiming that special relativity is "wrong" and that general relativity is needed to resolve the paradox. Talk about shooting yourself in the foot.  Just pathetic. Knowing you, I suspect that you will try to frame this as a mere "semantic" issue.  You'll try to claim that even if you used the wrong term to describe the geometry of general relativity, you understood the concepts all along. Wrong. Not only have you claimed that Minkowskian geometry is the basis of general relativity, when it actually applies to special relativity, you've also used the mathematics of Minkowskian geometry to analyze the twin paradox: Quote Hmmm, let's do the math… ds^2 = dt^2 - (dx^2 + dy^2 + dz^2) = (1 year)^2 - (0.9 light-years)^2 = 1.0 - 0.81 = 0.19 ds = 0.436 years Quote All I can do is my best. ds = sqrt(dt^2 - dx^2 - dy^2 - dz^2) Quote It is my understanding that the arc length function that matches experimental data like GPS satellites is... ds = SQRT( dt^2 - dx^2 - dy^2 - dz^2) Quote What is your understanding on the significance of Minkowskian goemetry? Did I misapply this equation Penrose presented in The Road to Reality?  (chapter 18 is titled "Minkowskian geometry") ds^2 = dt^2 - dx^2 - dy^2 - dz^2 This is classic.  You tell us that special relativity is wrong, and that it cannot resolve the twin paradox.  Then you proceed to show us (copying Penrose) how special relativity (via Minkowskian geometry) resolves the twin paradox.  And you do all this without realizing that you've shot yourself in the foot.  Wait to go, TP. You've also shown us that you completely misunderstand Penrose's chapter on Minkowskian geometry.   Now do you understand why we've been asking you to set the blogs aside for a while, pick up a book on elementary physics, and really learn it for a change? -------------- And the set of natural numbers is also the set that starts at 0 and goes to the largest number. -- Joe G Please stop putting words into my mouth that don't belong there and thoughts into my mind that don't belong there. -- KF

Jim_Wynne Posts: 1208 Joined: June 2006 (Permalink) Posted: Jan. 27 2008,09:04    [quote=Thought Provoker,Jan. 26 2008,19:26][/quote] Quote My mental defect is I am lopsided towards the analytical.  I can solve puzzles quickly.  I tend to be able to debug software systems based on the symptoms alone.  I see the holistic picture.  I understand it. No, your "mental defect," if you choose to call it that, is being unable to understand why your intuitions don't count when you don't understand the basic ideas. You've demonstrated (to yourself, at least) a facility for problem solving, and having been favorably impressed with your results you've apparently come to believe that you can apply your quasi-Sherlock Holmes methods to every problem that presents itself.  It's a form of narcissism.  Being able to debug software systems by examining symptoms is called "experience."  You don't have it in physics, and can't (or won't) understand why it matters. Quote This is the reason why I went down the path of engineering instead of academia. I'm an engineer too, and I know enough physics to be able to apply what I need in my work, but my knowledge is far from comprehensive.  I understand what I don't know, and don't pretend I know more because I read mass-market books. I'm not interested in trying to solve problems I'm not qualified to understand. Quote But back to the point at hand, you feel that I am not demonstrating a complete enough understanding of the subject in order to suffer carrying on a serious discussion with me on it. I will tell you what I am looking for.  I am looking for the weaknesses in the basic understanding I do have.  Am I trying to see the holistic picture enough to make sense of things.  I am not in the position to make a detailed presentation of the mathematical foundation tying together Cosmology and Quantum Mechanics while proposing an explanation for decoherence.  If I could do that, I would probably mathematically model Black Holes for a living, engage Stephen Hawking in debates, discover patterns for aperiodic tilings as a hobby and get knighted for my accomplishments. No, you're not looking for weaknesses in your understanding; if that were the case we wouldn't be into a second or third thread of people explaining that your weakness lies in basic ignorance.  Amongst a good portion of the ignorant masses your grand pronouncements and liberal use of jargon make it seem like you know what you're talking about, but it's a thin disguise when you're spouting off to people who know better. Quote No, you aren’t arguing from authority, you are arguing from repetition.  You, and others, are restating over and over that I am ignorant and I am wrong without saying where specifically my logic breaks down or what specific assumptions you disagree with. Your logic breaks down because of your ignorance. That's what you need to fix. Until you do, you have no basis for understanding anything anyone tells you with regard to specific errors. You are either too lazy or too impressed with yourself to understand where the problem lies. Thus the repetition.  Just because you refuse to acknowledge the problem doesn't mean that the problem doesn't exist.  It's cognitive dissonance. Quote From your comment in the other thread about Henderson-Darling oscillations and reciprocal inversions; I suspect you are familiar with Penrose’s hypotheses even if you disagree with them. What I am trying to provoke, politely ask for and/or beg is to get a critique of how well I understand Penrose’s hypotheses, even it is at a very crude level. Here's the deal, in a nutshell: if you understood Penrose's hypotheses, you wouldn't need to ask, and if you really understood that you don't understand them, you would seek knowledge rather than forming conclusions and challenging people to refute them.  You're not interested in being proven wrong, and it's transparently disingenuous to try to convince us otherwise. You should stick with TT, where there are plenty of ignorant slobs who'll be duly impressed. -------------- Evolution is not about laws but about randomness on happanchance.--Robert Byers, at PT

Jim_Wynne Posts: 1208 Joined: June 2006 (Permalink) Posted: Jan. 27 2008,10:06    In order to better reflect the actual content of this thread, I think it should be renamed to "Thought Provoker thinks he can take a shortcut." -------------- Evolution is not about laws but about randomness on happanchance.--Robert Byers, at PT

hooligans Posts: 114 Joined: Jan. 2007 (Permalink) Posted: Jan. 27 2008,11:01    Thought P said: Quote One on the activities was what passed as a multi-media presentation of Euclidean geometry where it was explained how Euclid would have demonstrated (A + B)^2 = A^2 + 2AB + B^2 with rectangles and squares instead of numbers. That's the way most math teachers go about it nowadays. Except at our school we teach these concepts at the 8th grade.

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 27 2008,11:44    Hi all, Actually Keiths you are correct on two fronts, in that I now understand Minkowskian geometry is generally considered to be flat not curved and, therefore, is mostly a reformation of special relativity. And you are right in that I will call it a semantics problem because I have been thinking in terms of a flexible Minkowskian geometry that could be either flat or curved. This is something I have come to understand better because of our recent exchanges and why I changed my tune to admitting that you might have caught me misusing the term "General Relativity". Here is something from a CalTech web page titled  What is General Relativity?     Quote We've described the Euclidean (or Euclidean-Mesopotamian :-) metric in two space dimensions: dL^2 = dX^2 + dY^2 and we've discussed at some length the complications that arise with the addition of time to space to give the Minkowski metric (shown here in just one space and one time dimension): dS^2 = c^2 dT^2 - dX^2 What else can we do to our spacetime distance function to make life more interesting (and hopefully solve the problem with Newtonian gravity discussed in the last section)? What if we play around with the form of the Minkowski metric? It turns out that if the spacetime metric is arranged in the right manner, we can get something called spacetime curvature. And that is what the General Theory of Relativity is all about. For example, suppose we add some extra space and time dependence to the Minkowski metric to make a new spacetime distance function dS^2 = gTT(T,X) c^2 dT^2 - gXX(T,X) dX^2 Using differential geometry, taking the right combination of first and second derivatives of gTT(T,X) and gXX(T,X), we could calculate the what is called the curvature tensor Ruv for this choice of spacetime distance function. The subscripts on Ruv are called tensor indices and refer back to the coordinates used in the above metric. The Minkowski metric corresponds to the choice gTT = gXX = 1 and it has Ruv = 0 for all values of the tensor indices. This is why the Minkowski metric is known also as flat spacetime - because the spacetime curvature calculated from this distance function is zero. Now I may be wrong, but from the type of responses I have gotten from the less vocal viewers, I suspect some don't have enough understanding to know which clock runs faster; a clock floating motionless in free space away from any gravity wells or a clock sitting on a planet size chunk of rock which is floating motionless’ in free space (not even rotating). I can use my crude, semantically incorrect view of Minkowskian geometry to realize that a curvature in four-dimensional space-time is going to be described by a matrix simular to how a two dimensional curvature would be described by... Gxx, Gxy Gyx, Gyy Accept instead of 2x2 it would be 4x4. So when calculating path length segments (ds) in curved space-time something that would otherwise traveling straight along the time dimension where... ds = SQRT(dt^2) ...ends up with cross products from the matrix multiplication with something like... ds = SQRT(0.99999*dt^2 - 0.00447*dz^2) So things in gravity wells are like the traveling twin taking a short cut. Therefore, the clock sitting on the rock appears to be running slower compared to the clock floating motionless in free space. Isn't a good thing that the general level of understanding is being increased?  Even though I may be the only one learning something new here (which I doubt).

Lou FCD Posts: 5455 Joined: Jan. 2006 (Permalink) Posted: Jan. 27 2008,13:08    A man groping blindly in the darkness of his self-imposed grave of ignorance, all the while proclaiming himself the light of the world to those holding the candlelight vigil for him. Open the casket, it's locked from the inside. -------------- “Why do creationists have such a hard time with commas? Linky“. ~ Steve Story, Legend

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 27 2008,19:42    Hi All, FYI from the crypt. Starting with standard Minkowskian geometry... ds^2 = dt^2 - dx^2 - dy^2 - dz^2 Converting Cartesian to polar ( dx to r*d(phi) and dy to r*sin(phi)*d(theta) and dz to dr) ds^2 = dt^2 - (r*d(phi))^2 - (r*sin(phi)*d(theta))^2 - dr^2 Allowing for curved space... ds^2 = Gtt*dt^2 - (r*d(phi))^2 - (r*sin(phi)d(theta))^2 - Grr*dr^2 In flat space, Gtt = Grr = 1 In generalized curved space, Gtt = 1/Grr, therefore... ds^2 = Gtt*dt^2 - (r*d(phi))^2 - (r*sin(phi)d(theta))^2 - dr^2 / Gtt The sharper the curve, the smaller the Gtt. In my crude, incorrect semantic way of looking at things, I would have called this curved Minkowskian geometry. However, if Gtt is calculated to be equal to... Gtt = 1 - 2 * G * M / r ...where M is mass and G is the gravitational constant I understand this becomes known as Schwarzschild Geometry. ds^2 = Gtt*dt^2 - (r*d(phi))^2 - (r*sin(phi)d(theta))^2 - dr^2 / Gtt I offer that this equation combines aspects of General Relativity (gravity) with aspects of Special Relativity (flat Minkowskian geometry) in one equation. And we are still calculating paths through four dimensional space-time. So, even if it involves gravity and acceleration, the traveling twin still takes a short cut.

IanBrown_101 Posts: 927 Joined: April 2007 (Permalink) Posted: Jan. 27 2008,19:59    Quote (Thought Provoker @ Jan. 27 2008,17:44) Hi all, Actually Keiths you are correct on two fronts, in that I now understand Minkowskian geometry is generally considered to be flat not curved and, therefore, is mostly a reformation of special relativity. And you are right in tha I will call it a semantics problem because I have been thinking in terms of a flexible Minkowskian geometry that could be either flat or curved. "Hi everyone. You know, X is Y not Z, and a lot of you have been pointing this out to me, but I'm still right because I'm saying X might be Y or Z." Seriously, are you THAT good at doublethink? -------------- I'm not the fastest or the baddest or the fatest. You NEVER seem to address the fact that the grand majority of people supporting Darwinism in these on line forums and blogs are atheists. That doesn't seem to bother you guys in the least. - FtK Roddenberry is my God.

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 27 2008,21:11    Hi Ian,     Quote Seriously, are you THAT good at doublethink? And I suppose you think that is double-ungood right? If it isn't obvious by now, I am not concerned about proper terminology and am focusing on ideas, especially thought provoking ideas. Do you accept the reality of four dimensional space-time? If time is truly just another dimension (albeit complex), wouldn't you agree that paths through it would be of the form... ds^2 = A*dt^2 + B*dx^2 + C*dy^2 + D*dz^2 ...where in non-curved space-time A, B, C and D are either 1 or -1 depending on the orientation of the real and imaginary planes? If the four dimensional geometry is real, doesn't that make the paths real too? Do you disagree that whether you calculate it in Cartesian or Polar, with or without curvature due to gravity, it looks like a clock measures the path length of four dimensional space-time? Now you might be able to reformulate things to map into Euclidean geometry and other assumptions made by Newtonian Physics (e.g. acceleration) but only under "special" circumstance.  Does this detract from our ability to understand and calculate varying path lengths in space-time? Do you doubt the traveling twin takes a short cut? If so, why? If not, then we can move on to the thought provoking implications of things traveling at the speed of light taking the ultimate short cut in four dimensional space-time.

blipey Posts: 2061 Joined: June 2006 (Permalink) Posted: Jan. 28 2008,01:19    Shorter TP: I'm not interested in the peanut butter of LAN jacks but rather on stratifying the brittle lamp shade of provoking vomit. -------------- But I get the trick question- there isn't any such thing as one molecule of water. -JoeG And scientists rarely test theories. -Gary Gaulin

IanBrown_101 Posts: 927 Joined: April 2007 (Permalink) Posted: Jan. 28 2008,04:18    Quote (Thought Provoker @ Jan. 28 2008,03:11) Hi Ian,       Quote Seriously, are you THAT good at doublethink? And I suppose you think that is double-ungood right? If it isn't obvious by now, I am not concerned about proper terminology and am focusing on ideas, especially thought provoking ideas. Do you accept the reality of four dimensional space-time? [Sinp to cut things neither I, nor TP understand] Ok, 1. I, like you, am not qualified to talk about this, so I, unlike you, won't try to discuss the finer points. 2. You are literally admitting "I am making things up, and using proper terms to apply to totally different ideas I pull out of my ass" Why should ANYONE bother talking to you, you freaking psycho? Seriously, what the hell? It would be like me saying I wanted to discuss evolution, then talking non stop about the genesis creation story and calling it evolution. It's not just slightly incorrect, it's total misuse of actual terms. You might as well start talking about how "liberals" are left wing. They aren't, and general relativity and special are't the same which YOU state yourself, so stop calling one the other. Good grief. -------------- I'm not the fastest or the baddest or the fatest. You NEVER seem to address the fact that the grand majority of people supporting Darwinism in these on line forums and blogs are atheists. That doesn't seem to bother you guys in the least. - FtK Roddenberry is my God.

olegt Posts: 1405 Joined: Dec. 2006 (Permalink) Posted: Jan. 28 2008,07:39    I haven't read the previous thread, but if I understand it correctly, TP is arguing something physicists and mathematicians have known for a while: a zigzag path in a spacetime with a metric signature (+,-,-,-) has a shorter length than a straight line.  Duh! -------------- If you are not: Galapagos Finch please Logout »

blipey Posts: 2061 Joined: June 2006 (Permalink) Posted: Jan. 28 2008,08:18    Quote (olegt @ Jan. 28 2008,07:39) I haven't read the previous thread, but if I understand it correctly, TP is arguing something physicists and mathematicians have known for a while: a zigzag path in a spacetime with a metric signature (+,-,-,-) has a shorter length than a straight line.  Duh! OT: olegt, do you have a link to your FTK sig?  Given proper context that could be my new favorite. -------------- But I get the trick question- there isn't any such thing as one molecule of water. -JoeG And scientists rarely test theories. -Gary Gaulin

Thought Provoker Posts: 530 Joined: April 2007 (Permalink) Posted: Jan. 28 2008,13:03    Hi Olegt, Thank you for that simple explanation. I agree, I didn't think it was that difficult. The traveling twin takes a short cut. Would you also state it is obvious that the path length of things moving at the speed of light is ZERO in spacetime with a (+,-,-,-) metric signature? ds^2 = dt^2 - dx^2 - dy^2 - dz^2

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