In this entry I continue to examine Chris Bolt’s reaction to my post on The Uniformity of Nature. At this time I would like to take a look at Bolt’s defense of the Christian “account for” the uniformity of nature.
The Christian “Answer”
The Christian “answer” to the question “why is nature uniform?” is to assert the existence of a supernatural conscious being which allegedly
The Christian “Answer”
The Christian “answer” to the question “why is nature uniform?” is to assert the existence of a supernatural conscious being which allegedly
has created the universe in which we live (Gen. 1:1, Col. 1:16), and who sovereignly maintains it as we find it to be (Heb. 1:3)… This God has a plan for his creation (Eph. 1:11), not the least part of which is revealing himself to it (Rom. 1:19-20). Part of this revelation involves creating and sustaining the universe in such a way that his creatures are able to learn about it and function within it (Gen. 8:22). (Brian Knapp, “Induction and the Unbeliever,” The Portable Presuppositionalist, p. 132)
In my post I developed a detailed critique of this view, pointing out that – instead of “accounting for” the uniformity of nature – it simply moves the problem back. It does so by characterizing – without evidence or even a good argument – the uniformity of nature as a product of prior causation, thus invoking one of the natural laws for which it is supposed to provide contextual justification in the first place. I interacted with the potential response to this problem which apologists may raise in their defense against it, namely that the Christian god does not affect the uniformity of nature by making use of “natural causality,” but does so instead by using “supernatural causality,” and pointed out that this nonetheless assumes uniformity – if nothing else, the uniformity of the supernatural.
Rather than interacting directly with any of the points I raise in response this potential objection, Bolt sought to turn the spotlight on me. For instance, he writes:
Rather than interacting directly with any of the points I raise in response this potential objection, Bolt sought to turn the spotlight on me. For instance, he writes:
Mr. Bethrick is not satisfied with the answer provided by Christians for why nature is uniform.
No one should be “satisfied with the answer provided by Christians for why nature is uniform” if a concern for truth is a minimum criterion. The “answer” which Christianity provides for this question cannot be true. This is because the Christian answer presupposes the primacy of consciousness, which is a false metaphysics. Truth presupposes the primacy of existence, not the primacy of consciousness, and this should be easy to recognize for any honest thinker. The primacy of existence is the principle that the objects of consciousness exist independent of the conscious activity by which we are aware of those objects. A statement is true when it maintains fidelity to the natures of the objects which we perceive and/or consider – i.e., to that which exists independent of our consciousness. To say that statement X is true is to say that it corresponds to the state of affairs to which it refers apart from the wishes, preferences, ignorance, commands, imaginations or emotions of the subject of consciousness. If we say that New York City has seven million inhabitants, we are saying that this is the case regardless of anyone’s conscious activity, that this is the case independent of consciousness. It is the case whether anyone agrees, has no idea, prefers a different number, loves New York City, hates New York City, wishes it did not exist, imagines fewer people live there, etc., and truth recognizes that facts are what they are independent of such conscious activity. Thus truth presupposes the primacy of existence. But Christianity assumes the primacy of consciousness (see here and here), which directly contradicts the primacy of existence, and thus the Christian account for the uniformity of nature presupposes the primacy of consciousness. Thus it is inherently opposed to the metaphysical basis of truth.
Bolt says that I
Bolt says that I
attempt… to restrict the actions of God to being essentially natural causes. By “natural law” Bethrick means “the law of identity applies”. The Christian is not committed to this Objectivist idea that natural law is essentially identity applied to action. Such an idea is inconsistent with the Christian worldview since there are actions God has taken which may be identified but have nothing to do with anything natural (e.g. the exchange of love between the Persons of the Trinity).
But notice the point which I did raise in my blog. By claiming that the uniformity of nature is caused by some action performed by the Christian god (it “created” and “sustains” the world as we find it to be), the Christian answer clearly characterizes the uniformity of nature as the result of some prior cause, and thus invokes the law of causality, a natural law, and in the very sense which Bolt himself has denied. In fact, assumption of the very sense of causality which Bolt has denied is inescapable for the Christian “account for” the uniformity of nature, since it in fact names the actions by which its god allegedly affected uniformity in nature: by means of “creating” and “sustaining.” Just by naming these actions, presuppositionalists tacitly admit that the law of identity does in fact apply to action – in particular to the actions which they claim their god has performed – since they could not do this if those actions did not have identity – i.e., if the law of identity did not apply to action.
Bolt announces that the Christian worldview “is not committed” to the fact that actions do in fact have identity, but instead must prefer the view that actions are indistinct from each other and from anything else. That is the only alternative possible here: either action has identity, in which case the law of identity does in fact apply to action; or, the law of identity does not apply to action, and therefore actions are not distinguishable from anything else, and thus the very concept ‘action’ and any other concepts specifying one action as opposed to another (or anything else) is meaningless.
While I agree with Bolt that the idea that action has identity is in fact “inconsistent with the Christian worldview,” Bolt still attributes specific kinds of actions to his god, borrowing concepts such as “exchange” and “love” from the realm in which actions do have identity to apply in a context which denies identity to action, while failing to explain how he can name actions if the law of identity does not apply to them. Thus, in order to distance his god from the “natural,” Bolt sacrifices the law of identity, and consequently every affirmation he makes about his god acting in one way or another commits the fallacy of the stolen concept. A god which is not subject to natural law would be a god without identity performing actions which have no identity, and thus could not be distinguished from something that is not a god. And yet Christians speak of their god as if it were “unique,” which could only mean that the law of identity applies.
In my post, I had asked:
Bolt announces that the Christian worldview “is not committed” to the fact that actions do in fact have identity, but instead must prefer the view that actions are indistinct from each other and from anything else. That is the only alternative possible here: either action has identity, in which case the law of identity does in fact apply to action; or, the law of identity does not apply to action, and therefore actions are not distinguishable from anything else, and thus the very concept ‘action’ and any other concepts specifying one action as opposed to another (or anything else) is meaningless.
While I agree with Bolt that the idea that action has identity is in fact “inconsistent with the Christian worldview,” Bolt still attributes specific kinds of actions to his god, borrowing concepts such as “exchange” and “love” from the realm in which actions do have identity to apply in a context which denies identity to action, while failing to explain how he can name actions if the law of identity does not apply to them. Thus, in order to distance his god from the “natural,” Bolt sacrifices the law of identity, and consequently every affirmation he makes about his god acting in one way or another commits the fallacy of the stolen concept. A god which is not subject to natural law would be a god without identity performing actions which have no identity, and thus could not be distinguished from something that is not a god. And yet Christians speak of their god as if it were “unique,” which could only mean that the law of identity applies.
In my post, I had asked:
what exactly is ‘supernatural causality,’ and how is it different from natural causality?
While Bolt does repeat this question of mine in his reaction to my post, it is important to note that he does not answer it. He does not deny the applicability of the notion of “supernatural causality” within the context of his god-belief, but he does not tell us what could possibly be different about the category of actions which his god is supposedly capable of performing vis-à-vis those actions which happen in the natural (i.e., actual) realm. Instead of taking the opportunity to educate us about his position, he chooses to complain:
If Bethrick does not know what “supernatural” means as opposed to “natural” then I am at a loss as to why he constantly uses the words in his own writings.
I certainly know what I mean by “supernatural” (I have explored it in great detail here), but I expect that Bolt would object to my understanding and criticisms. So I don’t think it would be very helpful for Bolt’s interests to leave definitions of his worldview’s key terms up to me. Christians use the term “supernatural” to characterize their god and other beings associated with the imaginary realm of their god-belief, and as a critic of Christianity, I reserve the right to use the term when referring to the Christian god, just as Christians do. Unfortunately, Christians typically hesitate to put a clear definition to this enigmatic term, especially one which they can defend consistently. Notice that Bolt himself does not take the opportunity to define it for the record. The question is: Why not?
Bolt says that
Bolt says that
Reality involves much more than matter in motion.
How does Bolt know this? What other than “matter in motion” exists? Now, before Bolt confuses me with those who do affirm that “only matter in motion exists” (a claim which I have never affirmed or endorsed), as an Objectivist I affirm that existence exists, and only existence exists. Since reality is the realm of existence, reality is only that which exists, and it is fundamentally distinct from what any individual happens to imagine.
Bolt supposes that the claim that “God is transcendental and real offends me. On the contrary, it amuses me. It’s in the same league as a child who believes that the stories he reads in Harry Potter are true. It’s quite a fantasy, but typically the avid fan of the Harry Potter series eventually grows up.
Since Bolt claims that his god is transcendental and real, my question for him is: by what means does he have awareness of this “transcendental and real” god, if not by means of his own imagination? Christians typically describe their god as having no corporeal body, being invisible, beyond the limits of human perception, etc. But clearly Bolt must have awareness of this being, does he not? It is supposed to exist independent of his own psychology, right? As such, can he identify any means of awareness by which he has awareness of his god which cannot be confused with the internal explorations of the imagination?
In the past, Bolt has affirmed what Reformed Christians call the “sensus divinitatus,” but it is unclear how the believer can securely distinguish between this alleged faculty and his own imagination. Moreover, believers who appeal to the “sensus divinitatus” often affirm contradictory positions and exhibit noteworthy difficulty when it comes to explaining how they cannot be deceived by this mystical apparatus (for instance, see here and here). To make matters worse, when asked if it is possible for the Christian god to communicate with believers through the “sensus divinitatus” and believers still get the message from their god wrong, Bolt openly admitted, “Yes, this is the case” (see Bolt’s 10 Oct. 2009 comment in this blog). So the theistic approach here, far from producing a convincing case that the uniformity of nature is a product of a supernatural consciousness, offers no bankable promises at all on these matters.
Bolt confirms my suspicions that the Christian “account for” the uniformity of nature does in fact assume the primacy of consciousness when he claims:
Bolt supposes that the claim that “God is transcendental and real offends me. On the contrary, it amuses me. It’s in the same league as a child who believes that the stories he reads in Harry Potter are true. It’s quite a fantasy, but typically the avid fan of the Harry Potter series eventually grows up.
Since Bolt claims that his god is transcendental and real, my question for him is: by what means does he have awareness of this “transcendental and real” god, if not by means of his own imagination? Christians typically describe their god as having no corporeal body, being invisible, beyond the limits of human perception, etc. But clearly Bolt must have awareness of this being, does he not? It is supposed to exist independent of his own psychology, right? As such, can he identify any means of awareness by which he has awareness of his god which cannot be confused with the internal explorations of the imagination?
In the past, Bolt has affirmed what Reformed Christians call the “sensus divinitatus,” but it is unclear how the believer can securely distinguish between this alleged faculty and his own imagination. Moreover, believers who appeal to the “sensus divinitatus” often affirm contradictory positions and exhibit noteworthy difficulty when it comes to explaining how they cannot be deceived by this mystical apparatus (for instance, see here and here). To make matters worse, when asked if it is possible for the Christian god to communicate with believers through the “sensus divinitatus” and believers still get the message from their god wrong, Bolt openly admitted, “Yes, this is the case” (see Bolt’s 10 Oct. 2009 comment in this blog). So the theistic approach here, far from producing a convincing case that the uniformity of nature is a product of a supernatural consciousness, offers no bankable promises at all on these matters.
Bolt confirms my suspicions that the Christian “account for” the uniformity of nature does in fact assume the primacy of consciousness when he claims:
Nature is uniform because God created and controls it as mentioned in Knapp’s article…
All we have here is a statement of faith, a bald assertion which is supposed to be accepted as if it were true without question or contention, requiring the utmost credulity that any individual can summon up. Bolt provides no argument for the claim that his god “created” nature, let alone for the premise that nature needed something “outside” of it to make it uniform. He just asserts his theistic view, demands that non-theists present elaborate arguments for theirs, and when they do, he dismisses them as if their inadequacy were self-evident (for he does not explain why they’re so insufficient).
Bolt expresses the opinion that
Bolt expresses the opinion that
Labeling this explanation “supernatural causation” does not change the fact that it is an answer with no apparent problems.
But several problems with this “answer” were in fact pointed out in my post. Note that Bolt does not reject the label “supernatural causation” in referring to his god’s alleged creative and controlling activity which is said to result in nature being uniform. Thus he openly accepts the premise that his god affects uniformity in nature through some kind of action. But this in itself implies uniformity – even if it is uniformity merely on the supernatural level – for which Bolt provides no account or justification. Bolt completely ignores this problem, thus confirming that Knapp only succeeds in moving the initial problem back rather than resolving it. This is on top of his failure to (a) validate his assumption that nature is not inherently uniform; (b) justify the notion of “supernatural” in the first place, and (c) address my questions about metaphysical primacy.
Bolt suggested that we compare my position on the uniformity of nature to that of the Christian worldview. But if Bolt really wants such a comparison, why didn’t he speak to my questions pertaining to metaphysical primacy? The answer to this should be obvious: the Christian cannot deal with the issue of metaphysical primacy consistently. While the Objectivist view holds explicitly that the objects which exist in the world are what they are independent of consciousness (and therefore that the uniformity of nature is not a product of conscious activity), the Christian worldview explicitly characterizes the world as a creation of consciousness and the identities of the objects which exist within it as subject to the ruling consciousness’ personal whims. In short, Objectivism maintains fidelity to the objective understanding of nature, while Christianity affirms a subjective view of nature.
We will delve deeper into the problems of the Christian position as it pertains to the uniformity of nature in my next installment of this series. For now, consider Bolt’s following statement:
Bolt suggested that we compare my position on the uniformity of nature to that of the Christian worldview. But if Bolt really wants such a comparison, why didn’t he speak to my questions pertaining to metaphysical primacy? The answer to this should be obvious: the Christian cannot deal with the issue of metaphysical primacy consistently. While the Objectivist view holds explicitly that the objects which exist in the world are what they are independent of consciousness (and therefore that the uniformity of nature is not a product of conscious activity), the Christian worldview explicitly characterizes the world as a creation of consciousness and the identities of the objects which exist within it as subject to the ruling consciousness’ personal whims. In short, Objectivism maintains fidelity to the objective understanding of nature, while Christianity affirms a subjective view of nature.
We will delve deeper into the problems of the Christian position as it pertains to the uniformity of nature in my next installment of this series. For now, consider Bolt’s following statement:
Mr. Bethrick has failed to answer why nature is uniform but Knapp is not after this answer at this point.
Bolt’s statement that I have “failed to answer why nature is uniform” is patently false, as we saw above. I did in fact give an answer to this question, namely that nature is inherently uniform independent of conscious activity by virtue of the fact that it exists. Bolt cannot say that I “failed” to answer this question; even he himself acknowledged earlier that I answered it by interpreting me to have affirmed the view that nature “just is” uniform. How has he forgotten this so quickly? It may simply be the case that he does not like my answer (which is irrelevant; whether he likes or dislikes a position is no indication of whether or not it is true), but he has not shown that it cannot be the case that nature is inherently uniform. He may wish that there’s some supernatural cause for nature’s uniformity, but a wish is not to be confused with fact. He may imagine that there’s some supernatural being which compels nature to be uniform through some conscious activity, but again imagination is not reality.
Stay tuned!
by Dawson Bethrick
Stay tuned!
by Dawson Bethrick
Mr. Bethrick, you are often seen articualting that the Universe is everything that exists, but this appears to be in error.
ReplyDeleteA Theist would destroy your position by pointing out that the Universe cannot be the totality of existence since the Universe had a beginning.
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.
Does this refute your position, or can you provide a defense?
Hello again,
ReplyDeleteA 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:
"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."
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.
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 Demystifying Universality 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.
Regards,
Dawson
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.
ReplyDeleteThus, they would say they have evidence that the beginning of the Universe shows there is a God.
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
ReplyDeleteThe 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
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
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
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
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.
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.
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
Stenger, Victor J. (2011-05-19). Fallacy of Fine-Tuning, The: Why the Universe Is Not Designed for Us (Kindle Locations 1631-1639).
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
ReplyDeleteThe 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
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
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
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
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.
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.
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
Stenger, Victor J. (2011-05-19). Fallacy of Fine-Tuning, The: Why the Universe Is Not Designed for Us (Kindle Locations 1631-1639).
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.
ReplyDeleteGauge 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.
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.