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{{Image|Electromagnetic and weak scattering processes.png|right|150px|''Top'': Scattering of two electromagnetic currents due to motion of charges ''e'' by exchange of a photon &gamma;. ''Bottom'': Scattering of a weak lepton current ''J&thinsp;<sup>ℓ</sup>'' and a weak hadron current ''J&thinsp;<sup>h</sup>'' by exchange of a ''W''-boson.}}
{{subpages}}
{{TOC|right}}
{{TOC|right}}
In the [[Standard Model]] of particle physics, the '''weak interaction''' or '''weak force''' is one of three fundamental interactions, the other two being the ''strong interaction'' (also called the ''color force'') and the [[Maxwell equations|''electromagnetic interaction'']]. [[Gravitation]], the fourth fundamental interaction, is not included in the Standard Model, and its inclusion remains an outstanding issue (for example, an aspect of [[string theory]] and of [[quantum gravity]], or what is called generically the ''grand unified theory (GUT)''<ref name=Robinson/>).
In [[philosophy]] the term '''free will''' refers to consideration of whether an individual has the ability to make decisions or, alternatively, has only the illusion of doing so. The underlying quandary is the idea that science suggests future events are dictated to a great extent, and perhaps entirely, by past events and, inasmuch as the human body is part of the world science describes, its actions also are determined by physical laws and are not affected by human decisions.  


The weak interaction is viewed as an ''exchange force'' mediated by three ''messenger particles'', the [[boson]]s: ''W<sup>+</sup>, W<sup>−</sup>'' and ''Z'', with properties listed below:
There are several approaches to such questions.  One is to limit the abilities of scientific description in a manner that excludes human decisions from its scope. Another is to argue that even if our actions are strictly determined by the past, it doesn’t seem that way to us, and so we have to find an approach to this issue that somehow marries our intuition of independence with the reality of its fictional nature. A third, somewhat legalistic approach, is to suggest that the ‘will’ to do something is quite different from actually doing it, so ‘free will’ can exist even though there may be no freedom of action.
{| class="wikitable" style="margin: 0 auto; text-align:center"
|+Messenger particles
|-
! Interaction field
! Particle name
! Symbol
! Spin
! Range ([[metre (unit)|m]])
! Mass(GeV/''c<sub>0</sub>''<sup>2</sup>)


|-
==Science does not apply==
|style="text-align:left"| Weak field
| Weak bosons
| ''W<sup>+</sup>, W<sup>−</sup>, Z''
| 1
|  &asymp; 10<sup>−17</sup>
| ''M<sub>W</sub>''=80.399±0.023;<ref name=Wboson/> ''M<sub>Z</sub>''=91.1876±0.0021<ref name=Zboson/>
|-


|}
One approach to limiting the applicability of science to our decisions is the examination of the notion of cause and effect.  For example, [[David Hume]] suggested that science did not really deal with causality, but with the correlation of events. So, for example, lighting a match in a certain environment does not ‘’cause’’ an explosion, but is ‘’associated’’ with an explosion.  [[Immanuel Kant]] suggested that the idea of cause and effect is not a fact of nature but an interpretation put on events by the human mind, a ‘programming’ built into our brains.  Assuming this criticism to be true, there may exist classes of events that escape any attempt at cause and effect explanations.


==Decay==
A different way to exempt human decision from the scientific viewpoint is to note that science is a human enterprise.  It involves the human creation of theories to explain certain observations, and moreover, the observations it chooses to attempt to explain are selected, and do not encompass all experience.  For example, we choose to explain phenomena like the [[Higgs boson]] found by elaborate means like a [[hadron collider]], but don’t attempt to explain other phenomena that do not appear amenable to science at this time, often suggesting that they are beneath attention.
The ''W''-boson decay channels are listed below; ''W<sup>−</sup>'' is the charge conjugate of the ''W<sup>+</sup>''
As time progresses, one may choose to believe that science will explain all experience, but that view must be regarded as speculation analogous to predicting the stock market on the basis of past performance.  
{| class="wikitable" style="margin: 0 auto; text-align:center"
|+Primary W<sup>+</sup>-boson decay channels<ref name=Wboson/>
|-
! Products
! Fraction
|-
|style="text-align:left"| <math>e^+\ \nu_e</math>
|(10.75 ± 0.13)%
|-
|style="text-align:left"| <math>\mu^+ \ \nu_\mu </math>
|(10.57 ± 0.15)%
|-
|style="text-align:left"| <math>\tau^+\ \nu_\tau</math>
|(11.25 ± 0.20)%
|-
|style="text-align:left"| <math>c\ \overline s</math>
|(31<sub>−11</sub><sup>+13</sup>)%
|-
|style="text-align:left"| all types of [[hadron]] combined
|(67.6 ± 0.27)%
|-
|}
&emsp;


The ''Z''-boson decay channels are listed below:
Although not explicitly addressing the issue of free will, it may be noted that [[Ludwig Wittgenstein]] argued that the specialized theories of science, as discussed by [[Rudolf Carnap]] for example, inevitably cover only a limited range of experience.  [[Stephen Hawking|Hawking/Mlodinow]] also noted this fact in in their [[model-dependent realism]],<ref name=Hawking/> the observation that reality is covered by a patchwork of theories that are sometimes disjoint and sometimes overlap.
{| class="wikitable" style="margin: 0 auto; text-align:center"
{{quote|“Whatever might be the ultimate goals of some scientists, science, as it is currently practiced, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.”<ref name=Davies/>}}
|+Primary Z-boson decay channels<ref name=Zboson/>
::: —— E.B. Davies <span style="font-size:88%">''Epistemological pluralism'', p. 4</span>
|-
! Products
! Fraction
|-
|style="text-align:left"| <math>e^+\ e^-</math>
|(3.362 ± 0.0042)%
|-
|style="text-align:left"| <math>\mu^+ \ \mu^- </math>
|(3.3662 ± 0.0066)%
|-
|style="text-align:left"| <math>\tau^+\ \tau^-</math>
|(3.3696 ± 0.0083)%
|-
|style="text-align:left"| all types of [[hadron]] combined
|(69.911 ± 0.056)%
|-
|style="text-align:left"| <math>\nu_{e,\mu,\tau} + \overline \nu_{e, \mu, \tau}</math> (undetectable)
|(20.000 ± 0.055)%
|-
|}
These values compare well with theoretical estimates.<ref name=Povh/>


==Weak isospin==
Still another approach to this matter is analysis of the mind-brain connection (more generally, the [[mind-body problem]]). As suggested by Northoff,<ref name=Northoff/>  there is an observer-observation issue involved here. Observing a third-person’s mental activity is a matter for neuroscience, a question of neurons and their interactions through complex networks.  But observing our own mental activity is not possible in this way – it is a matter of subjective experiences. This problem is a version of the measurement-observation interference noticed by Bohr and by Schrodinger in the early days of quantum mechanics. (the measurement of the position of a particle caused the particle to change position in an unknown way.) The suggestion has been made that ‘’complementary’’ descriptions of nature are involved, that may be mutually exclusive approaches, or may be simply different perspectives upon the same reality.
As with electromagnetism where [[electric charge]] serves to couple matter to the field, and with the strong interaction where [[Standard Model|color]] couples matter to the interaction, with the weak interaction it is the ''weak isospin'' that couples matter to the weak interaction. The weak isospin is to be distinguished from [[strong isospin]] that describes the [[hadron]]s as various mulitplets, for example, the proton and neutron as the spin states of a doublet, and the three pions as the three states of a triplet. The coupling constant analogous to the [[fine structure constant]] is:[http://www.amazon.com/gp/reader/9812700560/ref=sib_dp_pt#reader-link Eqs 11.19 - 11.21]
:<math>\frac {g_w^2}{\hbar c_0} = \frac{1}{4 \pi \sqrt 2 } \frac{1}{\hbar c_0} \left( \frac{m_W c_0}{\hbar}\right)^2 G_F \approx \frac{1}{240} \ . </math>
Here ''m<sub>W</sub>'' is the mass of the ''W-''boson, and the ''Fermi coupling constant'', symbol ''G<sub>F</sub>'', is defined in terms of the range of the Yukawa potential ''R<sub>W</sub>'', which is given by:


:<math>f(r)=\frac{\exp(-r/R_W)}{r} \ . </math>
==Science can be accommodated==
The other approach is to argue that we can accommodate our subjective notions of free will with a deterministic reality. One way to do this is to argue that although we cannot do differently, in fact we really don’t want to do differently, and so what we ‘decide’ to do always agrees with what we (in fact) have to do. Our subjective vision of the decision process as ‘voluntary’ is just a conscious concomitant of the unconscious and predetermined move to action.


In terms of ''R<sub>W</sub>'':
==’Will’ ''versus'' ‘action’==
There is growing evidence of the pervasive nature of subconscious thought upon our actions, and the capriciousness of consciousness, which may switch focus from a sip of coffee to the writing of a philosophical exposition without warning. There also is mounting evidence that our consciousness is greatly affected by events in the brain beyond our control. For example, addiction has been related to alteration of the mechanisms in the brain for dopamine production, and withdrawal from addiction requires a reprogramming of this mechanism that is more than a simple act of will. The ‘will’ to overcome addiction can become separated from the ability to execute that will.
{{quote|“Philosophers who distinguish ''freedom of action'' and ''freedom of will'' do so because our success in carrying out our ends depends in part on factors wholly beyond our control. Furthermore, there are always external constraints on the range of options we can meaningfully try to undertake. As the presence or absence of these conditions and constraints are not (usually) our responsibility, it is plausible that the central loci of our responsibility are our choices, or ‘willings’.”[Italics not in original.]<ref name=OConnor/>| Timothy O'Connor |Free Will}}


:<math>G_F = 4\pi \sqrt 2 g_w^2 R_W^2 = 4 \pi \sqrt2 \left(\frac{\hbar} {m_W c_0}\right)^2 g_w^2  \ ,</math>
:<math>G_{\mu} = 1.166 32(4) \times 10^{-5} \ \mathrm{GeV}^{-2} \ . </math>  [http://books.google.com/books?id=TZTNU-zsoCkC&pg=PA85&dq=Fermi+coupling+constant&hl=en&ei=ht1kTuqzAcjniAL736iVCg&sa=X&oi=book_result&ct=result&resnum=6&ved=0CEsQ6AEwBQ#v=onepage&q=Fermi%20coupling%20constant&f=false Paschos]
with
:<math>R_W = \frac {\hbar}{m_W c_0} \approx 2.5 \mathrm {am} \ . </math>


==Importance==
The weak interaction is responsible for the radioactive decay of subatomic particles and initiates hydrogen fusion in stars.
===Beta decay===
(from existing article [[weak force]])
Some radioactive materials undergo a process called [[beta decay]], in which a [[proton]] in the nucleus is converted in a [[neutron]], or a neutron in a proton. However, a proton has a positive [[electric charge]] while a neutron has no charge. So that the law of conservation of electric charge is not violated, another particle with a positive charge (a [[positron]]) is created when a proton changes in a neutron. Positrons are also called beta particles, and hence the name ''beta decay''. In fact, there is another particle which is created together with the positron; this is the elusive [[neutrino]].
On a more fundamental level, both a proton and a neutron consist of three [[quark]]s. In the case of a proton, these are two up quarks and one down quark, while a neutron consists of two down quarks and one up quark. The weak force changes a proton in a neutron by changing an up quark to a down quark and creating another particle, the [[W boson]]. This W boson decays in the positron and neutrino which are emitted during beta decay.
==Peculiarities==
The weak interaction is unique in a number of respects:
# It is the only interaction capable of changing the flavor of [[quark]]s (that is, the changing of one species of quark into another).
# It is the only interaction which violates [[parity (physics)|'''P''' or parity-symmetry]]. It is also the only one which violates [[CP-symmetry|'''CP''' symmetry]].
# Its messenger particles have large masses, a feature explained in the [[Standard Model]] by introduction of the [[Higgs boson]], a massive particle yet to be observed. By contrast, the strong force is mediated by zero mass [[gluon]]s, while the electromagnetic force is mediated by the very small (possibly zero) mass [[photon]]s.
==References==
==References==
{{Reflist|refs=
{{reflist|refs=
 
<ref name=Davies>
<ref name=Povh>
{{cite web |title=Epistemological pluralism |author=E Brian Davies |url=http://philsci-archive.pitt.edu/3083/1/EP3single.doc |work=PhilSci Archive |year=2006 }}
{{cite book  |title=Particles and nuclei: an introduction to the physical concepts |author=Bogdan Povh, Klaus Rith, Christoph Scholz |url=http://books.google.com/books?id=XyW97WGyVbkC&pg=PA155 |pages=pp. 155,156 |chapter=Decays of the ''W'' boson; Decays of the ''Z'' boson |isbn=3540793674 |year=2008 |publisher=Springer}}
</ref>
</ref>


<ref name=Robinson>
<ref name=Hawking>
{{cite book |author=Matthew Robinson|chapter=Chapter 5: Beyond the Standard Model of particle physics |pages =pp. 269 ''ff'' |url=http://books.google.com/books?id=JcvWry8rjTwC&pg=PA269 |title=Symmetry and the Standard Model: Mathematics and Particle Physics |isbn=1441982663 |year=2011 |publisher=Springer}}
{{cite book |author=Hawking SW, Mlodinow L. |title=cited work|isbn=0553805371 |url= http://www.amazon.com/Grand-Design-Stephen-Hawking/dp/0553805371#reader_0553805371 |pages=pp. 42-43 |chapter=Chapter 3: What is reality?}}
</ref>
</ref>


<ref name=Wboson>
<ref name=Northoff>
{{cite web |url=http://pdg.lbl.gov/2011/listings/rpp2011-list-w-boson.pdf |title=W |work=PDG Particle listings  |author=K. Nakamura ''et al.'' |publisher=Particle Data Group |date=June 16, 2011 }}
A rather extended discussion is provided in {{cite book |title=Philosophy of the Brain: The Brain Problem |author=Georg Northoff |url=http://books.google.com/books?id=r0Bf3lLys6AC&printsec=frontcover |publisher=John Benjamins Publishing |isbn=1588114171 |year=2004 |edition=Volume 52 of Advances in Consciousness Research}}
</ref>
</ref>


<ref name=Zboson>
<ref name=OConnor>
{{cite web |url=http://pdg.lbl.gov/2011/listings/rpp2011-list-z-boson.pdf |title=Z |work=PDG Particle listings  |author=K. Nakamura ''et al.'' |publisher=Particle Data Group |date=June 16, 2011 }}
{{cite web |title=Free Will |date=Oct 29, 2010 |author=O'Connor, Timothy |url=http://plato.stanford.edu/archives/sum2011/entries/freewill |work=The Stanford Encyclopedia of Philosophy (Summer 2011 Edition) |editor=Edward N. Zalta, ed}}
</ref>
</ref>


}}
}}
[http://www.ncnr.nist.gov/summerschool/ss09/pdf/Gardner_FP09_01.pdf NIST]
[http://books.google.com/books?id=wJUDIBstnMQC&pg=PA36&dq=gluon+mass&hl=en&ei=a6JbTrrzMJDUiAL__tm5CQ&sa=X&oi=book_result&ct=result&resnum=4&ved=0CDoQ6AEwAw#v=onepage&q=gluon%20mass&f=false McParland]
[http://www.amazon.com/gp/reader/9812387447/ref=sib_dp_srch_pop?v=search-inside&keywords=weak+isospin&go.x=15&go.y=10#reader_9812387447 isospin]
[http://books.google.com/books?id=A15OvAvA7HAC&pg=PA53&dq=right-handed+lepton&hl=en&ei=EPRkTsP1CKrhiALQg-iTCg&sa=X&oi=book_result&ct=result&resnum=4&ved=0CD4Q6AEwAw#v=onepage&q=right-handed%20lepton&f=false coupling]

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In philosophy the term free will refers to consideration of whether an individual has the ability to make decisions or, alternatively, has only the illusion of doing so. The underlying quandary is the idea that science suggests future events are dictated to a great extent, and perhaps entirely, by past events and, inasmuch as the human body is part of the world science describes, its actions also are determined by physical laws and are not affected by human decisions.

There are several approaches to such questions. One is to limit the abilities of scientific description in a manner that excludes human decisions from its scope. Another is to argue that even if our actions are strictly determined by the past, it doesn’t seem that way to us, and so we have to find an approach to this issue that somehow marries our intuition of independence with the reality of its fictional nature. A third, somewhat legalistic approach, is to suggest that the ‘will’ to do something is quite different from actually doing it, so ‘free will’ can exist even though there may be no freedom of action.

Science does not apply

One approach to limiting the applicability of science to our decisions is the examination of the notion of cause and effect. For example, David Hume suggested that science did not really deal with causality, but with the correlation of events. So, for example, lighting a match in a certain environment does not ‘’cause’’ an explosion, but is ‘’associated’’ with an explosion. Immanuel Kant suggested that the idea of cause and effect is not a fact of nature but an interpretation put on events by the human mind, a ‘programming’ built into our brains. Assuming this criticism to be true, there may exist classes of events that escape any attempt at cause and effect explanations.

A different way to exempt human decision from the scientific viewpoint is to note that science is a human enterprise. It involves the human creation of theories to explain certain observations, and moreover, the observations it chooses to attempt to explain are selected, and do not encompass all experience. For example, we choose to explain phenomena like the Higgs boson found by elaborate means like a hadron collider, but don’t attempt to explain other phenomena that do not appear amenable to science at this time, often suggesting that they are beneath attention. As time progresses, one may choose to believe that science will explain all experience, but that view must be regarded as speculation analogous to predicting the stock market on the basis of past performance.

Although not explicitly addressing the issue of free will, it may be noted that Ludwig Wittgenstein argued that the specialized theories of science, as discussed by Rudolf Carnap for example, inevitably cover only a limited range of experience. Hawking/Mlodinow also noted this fact in in their model-dependent realism,[1] the observation that reality is covered by a patchwork of theories that are sometimes disjoint and sometimes overlap.

“Whatever might be the ultimate goals of some scientists, science, as it is currently practiced, depends on multiple overlapping descriptions of the world, each of which has a domain of applicability. In some cases this domain is very large, but in others quite small.”[2]
—— E.B. Davies Epistemological pluralism, p. 4

Still another approach to this matter is analysis of the mind-brain connection (more generally, the mind-body problem). As suggested by Northoff,[3] there is an observer-observation issue involved here. Observing a third-person’s mental activity is a matter for neuroscience, a question of neurons and their interactions through complex networks. But observing our own mental activity is not possible in this way – it is a matter of subjective experiences. This problem is a version of the measurement-observation interference noticed by Bohr and by Schrodinger in the early days of quantum mechanics. (the measurement of the position of a particle caused the particle to change position in an unknown way.) The suggestion has been made that ‘’complementary’’ descriptions of nature are involved, that may be mutually exclusive approaches, or may be simply different perspectives upon the same reality.

Science can be accommodated

The other approach is to argue that we can accommodate our subjective notions of free will with a deterministic reality. One way to do this is to argue that although we cannot do differently, in fact we really don’t want to do differently, and so what we ‘decide’ to do always agrees with what we (in fact) have to do. Our subjective vision of the decision process as ‘voluntary’ is just a conscious concomitant of the unconscious and predetermined move to action.

’Will’ versus ‘action’

There is growing evidence of the pervasive nature of subconscious thought upon our actions, and the capriciousness of consciousness, which may switch focus from a sip of coffee to the writing of a philosophical exposition without warning. There also is mounting evidence that our consciousness is greatly affected by events in the brain beyond our control. For example, addiction has been related to alteration of the mechanisms in the brain for dopamine production, and withdrawal from addiction requires a reprogramming of this mechanism that is more than a simple act of will. The ‘will’ to overcome addiction can become separated from the ability to execute that will.

“Philosophers who distinguish freedom of action and freedom of will do so because our success in carrying out our ends depends in part on factors wholly beyond our control. Furthermore, there are always external constraints on the range of options we can meaningfully try to undertake. As the presence or absence of these conditions and constraints are not (usually) our responsibility, it is plausible that the central loci of our responsibility are our choices, or ‘willings’.”[Italics not in original.][4]

— Timothy O'Connor , Free Will


References

  1. Hawking SW, Mlodinow L.. “Chapter 3: What is reality?”, cited work, pp. 42-43. ISBN 0553805371. 
  2. E Brian Davies (2006). Epistemological pluralism. PhilSci Archive.
  3. A rather extended discussion is provided in Georg Northoff (2004). Philosophy of the Brain: The Brain Problem, Volume 52 of Advances in Consciousness Research. John Benjamins Publishing. ISBN 1588114171. 
  4. O'Connor, Timothy (Oct 29, 2010). Edward N. Zalta, ed:Free Will. The Stanford Encyclopedia of Philosophy (Summer 2011 Edition).