tag:blogger.com,1999:blog-11714522.post4756499618534353947..comments2021-11-26T08:43:26.032-08:00Comments on Incinerating Presuppositionalism: Bolt's Pile of Knapp, Pt. 3Bahnsen Burnerhttp://www.blogger.com/profile/11030029491768748360noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-11714522.post-41252572483086032632012-03-12T13:58:38.954-07:002012-03-12T13:58:38.954-07:00Because of gauge invariance all of classical mech...Because of gauge invariance all of classical mechanics, electro-magnetism, special and general relativity and with addition of balanced constants and substitutions, quantum mechanics can be derived regardless of the point of view of an observer. This is justification of the uniformity of nature from modern physics using Noether's theorem. <br /><br />Gauge invariance is a generalization of Noether's theorem from space-time to abstract state vector space. (Nothing in Noether's treatment limited it to space-time.) Consider again the two-dimensional example. In figure 4.1(b), the axes are rotated by an amount The generator of the transformation is , which will be conserved. Early in the twentieth century, another fact about gauge invariance was discovered. If is allowed to vary from point to point in space-time, Schrödinger's time-dependent equation, which we recall is the equation of motion of quantum mechanics, is not gauge invariant. However, if you insert a four-vector field into the equation and ask what that field has to be to make everything nice and gauge invariant, that field is precisely the four-vector potential that leads to Maxwell's equations of electromagnetism! That is, the electromagnetic force turns out to be a fictitious force, like gravity, introduced to preserve the point-of-view invariance of the system. Note that for neutral particles, no new fields need to be introduced to preserve gauge invariance in that case. When depends on the location of the particle in spacetime, we have what is called a local gauge transformation. When it is the same at all points, we have a global gauge transformation. In the case of electromagnetism, is proportional to the electric charge of the particle and so global gauge invariance, or, as I prefer, global point-of-view invariance, leads to the principle of conservation of charge. Also note that is the generator of a rotation in a two-dimensional space This generator is mathematically equivalent to angular momentum, which in quantum mechanics is quantized, that is, takes on discrete values. Thus global gauge invariance in this space will result in charge being quantized. So charge quantization is yet another consequence of point-of-view invariance. Summarizing, we have found that the equations that describe the motion of a charged free particle are not invariant under a local gauge transformation. However, we can make them invariant by adding a term to the canonical momentum that corresponds to the four-vector potential of the electromagnetic field. Thus the electromagnetic fields are introduced to preserve local gauge symmetry. Conservation and quantization of charge follow from global gauge symmetry. Now, we still need to introduce the Lorentz force law, which tells us how to calculate the force on a charged particle in the presence of electric and magnetic fields. This equation is nothing more than a definition of the fields. The electric field E is operationally defined as the force one measures on a charged particle at rest in the presence of other charged particles, per unit charge. More complicated, B is the vector field that leads to a measured force F on a charged particle moving with a velocity v that is perpendicular to the plane of v and B. How do these connect to Maxwell's equations, which are used to calculate the fields for any given charge and current distribution (a current is a moving charge)? In a 1989 paper, physicist Freeman Dyson provided a derivation of Maxwell's equations from the Lorentz force law that he says was first shown to him by Richard Feynman in 1948.6 That is, Maxwell's equations follow from the definition of the electric and magnetic fields. If we assert that Maxwell's equations follow from point-of-view invariance, then the Lorentz law is implied.<br /><br />Stenger, Victor J. (2011-05-19). Fallacy of Fine-Tuning, The: Why the Universe Is Not Designed for Us (Kindle Locations 1135-1153). Prometheus Books. Kindle Edition.Anonymoushttps://www.blogger.com/profile/03469718358131331499noreply@blogger.comtag:blogger.com,1999:blog-11714522.post-51619489502148517682012-03-12T13:40:06.557-07:002012-03-12T13:40:06.557-07:00Victor Stenger refutes WL Craig’s notion that Bord...Victor Stenger refutes WL Craig’s notion that Borde, Guth, and Vilenkin’s work proves existence had a beginning in his book Fallacy of Fine-Tuning<br /><br />The conclusion that Borde and collaborators had proved that the universe had to have a beginning was disputed the same year by University of California–Santa Cruz physicist Anthony Aguirre and Cambridge astronomer Steven Gratton in a paper that Craig ignores.27 <br /><br />Being good scholars, Borde et al. refer to Aguirre and Gratton in their own paper. I contacted Aguirre and Vilenkin, the latter whom I have known professionally for many years. I greatly admire the work of each, which will be referred to often on these pages. I first asked Vilenkin if Craig's statement is accurate. Vilenkin replied: I would say this is basically correct, except the words “absolute beginning” do raise some red flags. The theorem says that if the universe is everywhere expanding (on average), then the histories of most particles cannot be extended to the infinite past. In other words, if we follow the trajectory of some particle to the past, we inevitably come to a point where the assumption of the theorem breaks down—that is, where the universe is no longer expanding. This is true for all particles, except perhaps a set of measure zero. In other words, there may be some (infinitely rare) particles whose histories are infinitely long.28 <br /><br />I sent this to Aguirre, who commented that the “infinitely rare” particles have worldlines [trajectories in space-time] that extend indefinitely into “the past,” and can prevent there being a “time” at which the universe is not expanding/inflating. The fact that they are infinitely rare does not make them unimportant, because they nonetheless thread an infinite physical volume.29 <br /><br />I then asked Vilenkin, “Does your theorem prove that the universe must have had a beginning?” He immediately replied, No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time.30 <br /><br />Vilenkin further explained, For example, Anthony in his work with Gratton, and Carroll and Chen,31 proposed that the universe could be contracting before it started expanding. The boundary then corresponds to the moment (that Anthony referred to as t = 0) between the contraction and expansion phases, when the universe was momentarily static. They postulated in addition that the arrow of time in the contracting part of space-time runs in the opposite way, so that entropy grows in both time directions from t = 0. <br /><br />The problem and its solution are illustrated in figure 6.4. (not shown-cannot paste image) Worldlines of particles are seen emerging from the origin as part of inflation. Borde et al. proved they all had to come from a point, which then was interpreted as the beginning of the universe. Aguirre et al. showed that they can continue through the origin to the negative side of the time axis, allowing for an eternal universe.<br /><br /> I also checked with Caltech cosmologist Sean Carroll, whose recent book From Eternity to Here provides an excellent discussion of many of the problems associated with early universe cosmology.32 Here was his response: I think my answer would be fairly concise: no result derived on the basis of classical spacetime can be used to derive anything truly fundamental, since classical general relativity isn't right. You need to quantize gravity. The BGV [Borde, Guth, Vilenkin] singularity theorem is certainly interesting and important, because it helps us understand where classical GR breaks down, but it doesn't help us decide what to do when it breaks down. Surely there's no need to throw up our hands and declare that this puzzle can't be resolved within a materialist framework. Invoking God to fill this particular gap is just as premature and unwarranted as all the other gaps.33<br /><br />Stenger, Victor J. (2011-05-19). Fallacy of Fine-Tuning, The: Why the Universe Is Not Designed for Us (Kindle Locations 1631-1639).Anonymoushttps://www.blogger.com/profile/03469718358131331499noreply@blogger.comtag:blogger.com,1999:blog-11714522.post-32699291570185634622012-03-12T13:39:50.752-07:002012-03-12T13:39:50.752-07:00Victor Stenger refutes WL Craig’s notion that Bord...Victor Stenger refutes WL Craig’s notion that Borde, Guth, and Vilenkin’s work proves existence had a beginning in his book Fallacy of Fine-Tuning<br /><br />The conclusion that Borde and collaborators had proved that the universe had to have a beginning was disputed the same year by University of California–Santa Cruz physicist Anthony Aguirre and Cambridge astronomer Steven Gratton in a paper that Craig ignores.27 <br /><br />Being good scholars, Borde et al. refer to Aguirre and Gratton in their own paper. I contacted Aguirre and Vilenkin, the latter whom I have known professionally for many years. I greatly admire the work of each, which will be referred to often on these pages. I first asked Vilenkin if Craig's statement is accurate. Vilenkin replied: I would say this is basically correct, except the words “absolute beginning” do raise some red flags. The theorem says that if the universe is everywhere expanding (on average), then the histories of most particles cannot be extended to the infinite past. In other words, if we follow the trajectory of some particle to the past, we inevitably come to a point where the assumption of the theorem breaks down—that is, where the universe is no longer expanding. This is true for all particles, except perhaps a set of measure zero. In other words, there may be some (infinitely rare) particles whose histories are infinitely long.28 <br /><br />I sent this to Aguirre, who commented that the “infinitely rare” particles have worldlines [trajectories in space-time] that extend indefinitely into “the past,” and can prevent there being a “time” at which the universe is not expanding/inflating. The fact that they are infinitely rare does not make them unimportant, because they nonetheless thread an infinite physical volume.29 <br /><br />I then asked Vilenkin, “Does your theorem prove that the universe must have had a beginning?” He immediately replied, No. But it proves that the expansion of the universe must have had a beginning. You can evade the theorem by postulating that the universe was contracting prior to some time.30 <br /><br />Vilenkin further explained, For example, Anthony in his work with Gratton, and Carroll and Chen,31 proposed that the universe could be contracting before it started expanding. The boundary then corresponds to the moment (that Anthony referred to as t = 0) between the contraction and expansion phases, when the universe was momentarily static. They postulated in addition that the arrow of time in the contracting part of space-time runs in the opposite way, so that entropy grows in both time directions from t = 0. <br /><br />The problem and its solution are illustrated in figure 6.4. (not shown-cannot paste image) Worldlines of particles are seen emerging from the origin as part of inflation. Borde et al. proved they all had to come from a point, which then was interpreted as the beginning of the universe. Aguirre et al. showed that they can continue through the origin to the negative side of the time axis, allowing for an eternal universe.<br /><br /> I also checked with Caltech cosmologist Sean Carroll, whose recent book From Eternity to Here provides an excellent discussion of many of the problems associated with early universe cosmology.32 Here was his response: I think my answer would be fairly concise: no result derived on the basis of classical spacetime can be used to derive anything truly fundamental, since classical general relativity isn't right. You need to quantize gravity. The BGV [Borde, Guth, Vilenkin] singularity theorem is certainly interesting and important, because it helps us understand where classical GR breaks down, but it doesn't help us decide what to do when it breaks down. Surely there's no need to throw up our hands and declare that this puzzle can't be resolved within a materialist framework. Invoking God to fill this particular gap is just as premature and unwarranted as all the other gaps.33<br /><br />Stenger, Victor J. (2011-05-19). Fallacy of Fine-Tuning, The: Why the Universe Is Not Designed for Us (Kindle Locations 1631-1639).Anonymoushttps://www.blogger.com/profile/03469718358131331499noreply@blogger.comtag:blogger.com,1999:blog-11714522.post-75318616572073673352010-05-10T03:50:00.144-07:002010-05-10T03:50:00.144-07:00The way that a theist would challenge your view is...The way that a theist would challenge your view is that they would say that you define the Universe in a way that is not consistent with modern science; As scientists generally define the Universe as the space-time continuum. And since space and time are said to come into existence at the formation of the Universe, then the Universe had a cause that was immaterial, timeless, spaceless, and Omnipotent. These attributes being consistent with attributes that are understood to belong to God.<br /><br />Thus, they would say they have evidence that the beginning of the Universe shows there is a God.The Secular Walkhttps://www.blogger.com/profile/08342572056569966450noreply@blogger.comtag:blogger.com,1999:blog-11714522.post-57089969488508078602010-04-20T05:58:45.166-07:002010-04-20T05:58:45.166-07:00Hello again,
A theist would be unwise to appeal t...Hello again,<br /><br />A theist would be unwise to appeal to Guth & co. in defending the view that the universe had a beginning. What the theist claims and what physicists like Alan Guth are claiming, are very different and I'd even say incompatible. The theist says that the universe finds its origin in an act of consciousness - his god essentially *wished* the universe into existence. It's like a magic trick you'd see in a cartoon. By contrast, Guth & co. are saying that the current inflationary occupation of the universe is the result of a mechanistic cause - e.g., an explosion or "big bang" originating from a "singularity." As Guth himself put it:<br /><br />"We observe the expansion of the universe, so we see it flying apart and that certainly makes it look like it came from an initial, hot state, which is the idea behind the big bang."<br /><br />Guth actually has the big bang originating from something which exists - namely "an initial, hot state." If the universe is the sum totality of everything that exists, then that "initial, hot state" is included in that sum total of what exists, even if that's all that existed at the time. I don't see how this challenges my view at all. If you think it does, you'll have to clarify.<br /><br />Also, I would contend that this "initial, hot state" is not an actual infinity, for Guth is identifying it in finite terms. "Initial" as opposed to what? "Hot" as opposed to what? "State" as opposed to what? To say that it is "infinite" would defy the very act of naming it in such a manner. You may want to check out my blog <a href="http://bahnsenburner.blogspot.com/2009/06/demystifying-universality.html" rel="nofollow">Demystifying Universality</a> to get a better understanding of where I'm coming from when it comes to the proper use of concepts in such contexts. It may be helpful.<br /><br />Regards,<br />DawsonBahnsen Burnerhttps://www.blogger.com/profile/11030029491768748360noreply@blogger.comtag:blogger.com,1999:blog-11714522.post-20952604855933424282010-04-18T20:23:48.892-07:002010-04-18T20:23:48.892-07:00Mr. Bethrick, you are often seen articualting that...Mr. Bethrick, you are often seen articualting that the Universe is everything that exists, but this appears to be in error.<br /><br />A Theist would destroy your position by pointing out that the Universe cannot be the totality of existence since the Universe had a beginning.<br /><br />The fact that the Universe had a beginning is scientifically substantiated by the fact that physicists Arvind Borde, Alan Guth, and Alexander Vilenkin showed that this Universe had a beginning since it has a positive average expansion rate. <br /><br />Does this refute your position, or can you provide a defense?The Secular Walkhttps://www.blogger.com/profile/08342572056569966450noreply@blogger.com