<p class="MsoNormal"><span style="font-size: 1rem;">The ways described in my last post titled "</span><a href="https://www.steemstem.io/#!/@emperorhassy/particle-physics-the-1575818004" target="_blank">The Search for Order and the Classification of Particles</a><span style="font-size: 1rem;">", for classifying particles were immensely helpful – interactions could be
predicted. But like the Periodic Table in Mendeleev’s day, there was no underpinning
</span><i style="font-size: 1rem;">theory</i><span style="font-size: 1rem;"> or </span><i style="font-size: 1rem;">model</i><span style="font-size: 1rem;"> of particles which explained </span><i style="font-size: 1rem;">why</i><span style="font-size: 1rem;"> the
patterns existed.</span><br></p><p class="MsoNormal"><span lang="">Then a revolutionary new theory was suggested
to explain the ‘threeness’ referred to opposite: the heavy particles (baryons)
might in fact be simple combinations of <i>three</i> <i>smaller</i> <i>particles</i>.
This theory required a startling idea, that <i>electric</i> <i>charge</i> <i>has</i>
<i>to be subdivided into thirds</i>: the new particles could have charges of
1/3 or 2/3 of the electronic charge.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">At the time, very few physicists believed in
the real existence of these hypothetical particles, at first not even the
American physicist Murray Gell-Mann born 1929), who suggested the new particles
and named them <b>quarks</b>.<o:p></o:p></span></p><p class="MsoNormal" style="text-align: center; "><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1576253967/wifufxwaf8wonwt4atij.png" data-filename="wifufxwaf8wonwt4atij" style="width: 527.5px;"><span lang=""><br></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Top_antitop_quark_event.svg" target="_blank"><sup>Top antitop quark event. Raeky, public domain </sup></a><span lang=""><br></span></p><p class="MsoNormal"><span lang="">This theory was later supported by experiments
in which individual protons were bombarded by very energetic electrons. Just as
the Geiger-Marsden alpha particle bombardment experiment showed that the atom
has a small central mass, so these experiments showed that the density of a
proton was not uniform, suggesting that it was made up of even smaller masses.
These turned out to be the quarks. <o:p></o:p></span></p><h2><span lang="">The quark model of hadrons<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The original simple quark model said that
there were three quarks. These are now called the up, down and strange quarks.
They are summarised in the <b>table below</b>. As well as having fractional
charge, quarks also have fractional baryon number.<o:p></o:p></span></p><p class="MsoNormal"><span lang=""><b>The first quarks</b></span></p><p class="MsoNormal"><br></p><table class="table table-bordered"><tbody><tr><td>Quark<br></td><td>Symbol<br></td><td>Charge/e<br></td><td>Baryon num.<br></td><td>Strangeness<br></td></tr><tr><td>Up<br></td><td>u<br></td><td>+2/3<br></td><td>+1/3</td><td>0</td></tr><tr><td>Down</td><td>d</td><td>-1/3</td><td>+1/3</td><td>0</td></tr><tr><td>Strange</td><td>s</td><td>-1/3</td><td>+1/3</td><td>-1</td></tr></tbody></table><p class="MsoNormal"><span style="font-size: 1rem;">The </span><span style="font-size: 1rem;">table below</span><span style="font-size: 1rem;"> shows how these basic
quarks are arranged in the most common baryons: protons and neutrons. The
combination of fractional charges on the quarks explains why protons are
positive and neutrons have no net charge.</span><br></p><p class="MsoNormal"><span lang=""><b>Quarks in protons and neutrons</b></span></p><table class="table table-bordered"><tbody><tr><td><br></td><td>Proton<br></td><td>u</td><td>u</td><td>d</td><td>Neutron</td><td>u</td><td>d</td><td>d</td></tr><tr><td>Charge<br></td><td>+1</td><td>+2/3</td><td>+2/3</td><td>-1/3</td><td>0</td><td>+2/3</td><td>-1/3</td><td>-1/3</td></tr><tr><td>Baryon no<br></td><td>+1</td><td>+1/3</td><td>+1/3<br></td><td>+1/3<br></td><td>+1<br></td><td>+1/3</td><td>+1/3<br></td><td>+1/3<br></td></tr><tr><td>Strangeness</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td><td>0</td></tr></tbody></table><p class="MsoNormal"><span style="font-size: 1.714rem; font-weight: bold;"><br></span></p><p class="MsoNormal"><span style="font-size: 1.714rem; font-weight: bold;">ANTIQUARKS</span><br></p><p class="MsoNormal"><span lang="">But of course, quarks must have antiquarks,
and these were needed to explain the existence of mesons (the middleweight
hadrons). There are also three original antiquarks. In antiquarks, charge and
strangeness have swapped over compared with the corresponding quarks. Antiquarks combine to produce the antiproton
and the antineutron – and shows how a neutral particle can have an antiparticle
version.<o:p></o:p></span></p><h2><span lang="">QUARKS IN BARYONS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Note that all baryons are made of quarks and
all antibaryons are made of antiquarks. The baryon number of a quark is +1/3
and of the antiquark -1/3, which explains why the baryon numbers are either +1
or -1 for these particles.<o:p></o:p></span></p><h2><span lang="">QUARKS AND ANTIQUARKS MAKE MESONS<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The significant difference between mesons and
baryons (both are types of hadrons) is that mesons have baryon number 0. This
is because mesons are made up of a quark and an antiquark, whose baryon
contribution always cancels out.</span><span lang=""> π- is the </span><span lang="">antiparticle
of the </span><span lang="">π<sup>+</sup></span><span lang="">: what was a quark in the
particle has become an antiquark in the antiparticle, and vice versa. It also shows
that some particles are their own antiparticles – changing an <i>up quark</i>
for the <i>up antiquark</i> and vice versa makes no difference to the </span><span lang="">π</span><span lang="">°.<o:p></o:p></span></p><h2><span lang="">WHY SINGLE QUARKS DON’T EXIST<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Quarks are ‘invisible’: they never appear on
their own. Whenever there is enough energy to pull apart a pair of quarks in a
pion, the energy is always enough to create two more quarks, which combine to
form another pion. So all we see – and all we get – are pions.<o:p></o:p></span></p><h2><span lang="">AND ANOTHER THING… COLOUR<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Some combinations of quarks might seem
possible – but have never been found to exist. To explain this yet another
property has been given to the hard-working quark: colour (or colour charge).
The rule is that only colourless (or white) combinations can exist. Just as
white light can be created by mixing red, green and blue (the primary colours)
so baryons can be made with only a combination of three quarks that produce a
colourless result. So a proton has a <i>blue up</i>, a <i>red up</i> and a <i>green
down</i> quark. A quark can carry any colour, so that an up quark can be red,
blue or green. The figure below shows quark colour combinations
for the proton and the neutron.</span></p><p class="MsoNormal"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang=""><o:p></o:p></span></p><p class="MsoNormal"><div style="text-align: center;"><a href="https://commons.wikimedia.org/wiki/File:Proton_quark_structure.svg" target="_blank" style="background-color: rgb(255, 255, 255); font-size: 1rem;"><sup>Three colored balls (symbolizing quarks). Jacek rybak, CC BY-SA 4.0</sup></a></div><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1576254329/zqq68flesf24ol7leqzk.png" data-filename="zqq68flesf24ol7leqzk" style="width: 480px; float: left;" class="note-float-left"><span lang=""><o:p><br></o:p></span></p><div><br></div><p class="MsoNormal"><span lang="">But how can a two-quark object like a meson
manage to become colourless? Think about white light combinations: these can be
made using secondary colours, e.g. yellow. Yellow is red plus green (or white
minus blue). Yellow is often called ‘minus blue’. So antiquarks are needed –
each carrying a ‘secondary’ colour, here called antiblue, antired or antigreen.
Mesons are made from a quark and an antiquark, so that for example a </span><span lang="">π</span><span lang="">° meson can exist with a <i>blue up</i> quark and an <i>antiblue up</i>
antiquark. Antibaryons contain only antiquarks with anticolours.</span></p><h2><span lang="">THE REALLY FUNDAMENTAL PATTERN (POSSIBLY)<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">After accepting the quark model in the late 1960s,
physicists noticed a new kind of symmetry – this time between <i>leptons</i>
and quarks. Leptons contain no quarks (they are indivisible), and everything
else does, so it makes sense to think of leptons and quarks as the basic, really
fundamental building block of matter. The table below shows the pattern of
leptons and quarks known by 1974 (omitting antiparticles).<o:p></o:p></span></p><p class="MsoNormal"><b>Lepton and quark families known about in
1974</b></p><table class="table table-bordered"><tbody><tr><td>Leptons<br></td><td><br></td><td><br></td><td>Quarks<br></td><td><br></td><td><br></td></tr><tr><td>Q = -1<br></td><td>e<sup style="font-size: 10.5px;">-</sup><br></td><td>μ<sup style="font-size: 10.5px;">-</sup><br></td><td>u</td><td>?</td><td>Q = +2/3</td></tr><tr><td>Q = 0<br></td><td>v<sub style="font-size: 10.5px;">e</sub><br></td><td><span lang="">v</span><sub style="font-size: 10.5px;"><span lang="">μ</span></sub><br></td><td>d</td><td>s</td><td>Q = -1/3</td></tr></tbody></table><p class="MsoNormal"><span lang="" style="font-size: 1rem;">The pattern suggested that a quark should
exist in the gap above the strange (s) quark. It was expected to have a charge
of +2/3, and theory predicted that hadrons containing this quark should have
masses of about 3 GeV/c<sup>2</sup>. Late in 1974, two laboratories announced
the discovery of two new heavy hadrons, the J and psi (</span><span lang="" style="font-size: 1rem;">Ψ</span><span lang="" style="font-size: 1rem;">) particles. They turned out to be the same particle, with a mass of
3.1 GeV/c<sup>2</sup>. Confusingly but appropriately, it is called the J/</span><span lang="" style="font-size: 1rem;">Ψ</span><span lang="" style="font-size: 1rem;">.</span><br></p><h2><span style="font-size: 1.714rem;">CHARM ENTERS PHYSICS</span><br></h2><p class="MsoNormal"><span lang="">Physicists then realised that the new particle
was a heavy meson containing the predicted missing quark, carrying yet another
conserved quantity called <b>charm</b>. The J/</span><span lang="">Ψ</span><span lang=""> consists of two charmed quarks, one the antiquark of the other (c</span><span lang="">ċ</span><span lang="">). The new J/</span><span lang="">Ψ</span><span lang=""> particle was predicted,
but in the search for it, evidence was found for a particle that was not
predicted at all. This was a new lepton – but an amazingly massive one, twice
as heavy as a proton. This third kind of lepton was named the <b>tau</b> </span><span lang="">τ</span><span lang="">.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">This discovery ruined the existing pattern
between leptons and quarks and if the lepton-quark pattern was to be preserved
it meant that yet another pair of quarks should exist. Quarks are never found
alone, they have to be found indirectly – by finding particles with properties
and interactions that could only exist if they carry the properties of their
component quarks. Physicists named the new quarks <b>top</b> and <b>bottom</b>
from their positions in the table and had to invent two new conserved quantities,
<b>topness</b> and <b>bottomness</b>.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Top and bottom quarks were predicted to be
much more massive than other quarks, and so should produce equally massive
combinations. Such particles need a great deal of energy to be created, and the
new proton synchrotron opened in 1975 at Columbia University (New York State)
with an energy of 30 GeV very soon found a new massive particle that was a combination
of a bottom quark and an antibottom quark. This b meson was named the <b>upsilon</b>,
<b>Y</b>. It has a mass of 9.5 GeV/c<sup>2</sup>.</span></p><p class="MsoNormal"><span lang=""><o:p></o:p></span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1576254888/bq5bdjwclyhgdpmarvao.png" data-filename="bq5bdjwclyhgdpmarvao" style="width: 158px; float: left;" class="note-float-left"><span lang=""><br></span></p><div style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Hadron_colors.svg" target="_blank"><sup>All types of hadrons have zero total color charge. TimothyRias, CC BY-SA 3.0</sup></a><br></div><p class="MsoNormal"><span lang=""><o:p><br></o:p></span></p><h2><span lang="">THE SEARCH FOR THE TOP QUARK<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The missing piece of the jigsaw was the top quark.
It was predicted to have a mass of more than 90 GeV/c<sup>2</sup>, twenty times
as massive as a bottom quark. A particle containing a top quark would have a
mass greater than this. The energy needed to produce such a massive particle is
available when protons are made to collide with antiprotons in powerful synchrotrons.
This was possible in the 1800 GeV Tevatron collider at Fermilab (Chicago, USA),
and in April 1994 evidence for the existence of the top quark was announced. Experiments
in March 1995 matched a mass of about 175 GeV/c<sup>2</sup> for the top quark. In
2011, when the Tevatron collider at Fermilab has stopped functioning, the Large
Hadron Collider at CERN, with a center-of-mass energy 7 TeV became the only accelerator
that produces top quark.<a href="sourcehttps://en.wikipedia.org/wiki/Top_quark" target="_blank"><sup>source</sup></a><o:p></o:p></span></p><h2><span lang="">Units of mass and energy in particle physics<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Obeying the laws of relativity, the mass of a particle varies with its speed. This means that we have to use the value of its mass when it is not moving, its rest mass. The principle of relativity also requires that mass and energy are equivalent, linked by the Einstein formula E = mc<sup style="font-size: 10.5px;">2</sup>. In fact, particle physicists measure mass in energy units.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Investigations usually involve charged particles which are accelerated by high voltages and gain mass-energy as they accelerate. It is convenient for particle physicists to measure energy and therefore mass in terms of an electrical unit, namely the <b>electronvolt</b>, eV.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">One electronvolt, 1 eV, is the energy gained by a particle carrying the electronic charge e = 1.6 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 10.5px;">-19</sup> C when it moves through a potential difference of 1 V.<o:p></o:p></span></p><h4 align="center" style="text-align: center;"><span lang="">1 eV = 1.6 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">-19</sup> C </span><span lang="">×</span><span lang=""> 1 JC<sup style="font-size: 11.2455px;">-1</sup><o:p></o:p></span></h4><h4 align="center" style="text-align: center;"><span lang="">= 1.6 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">-19</sup> J<o:p></o:p></span></h4><h4 align="center" style="text-align: center;"><span lang="">And 1 J = 6.25 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">18</sup> eV<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The mass of a proton is 1.6726 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 10.5px;">-27</sup> kg. In energy units, this is equivalent to:<o:p></o:p></span></p><h4 align="center" style="text-align: center;"><span lang="">E<sub style="font-size: 11.2455px;">p</sub> = m<sub style="font-size: 11.2455px;">p</sub>c<sup style="font-size: 11.2455px;">2</sup> = 1.6726 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">-27</sup> </span><span lang="">×</span><span lang=""> (3 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">8</sup>)<sup style="font-size: 11.2455px;">2</sup> J<o:p></o:p></span></h4><h4 align="center" style="text-align: center;"><span lang="">= 1.5053 </span><span lang="">×</span><span lang=""> 10<sup style="font-size: 11.2455px;">-10</sup> J<o:p></o:p></span></h4><h3><span lang="">REST MASS IN GeV/c<sup style="font-size: 13.44px;">2</sup><o:p></o:p></span></h3><p class="MsoNormal"><span lang="">The mass-energy of a proton is about 10<sup style="font-size: 10.5px;">9</sup> eV, or 1 GeV, a nice easy number to work with. We need to be careful with this unfamiliar set of units. For example, from the Einstein formula we have:<o:p></o:p></span></p><h4 align="center" style="text-align: center;"><span lang="">m = E/c<sup style="font-size: 11.2455px;">2</sup><o:p></o:p></span></h4><p><span lang="">so we can put</span></p><h4 align="center" style="text-align: center;"><span lang="">m = Energy in eV / (light speed)<sup style="font-size: 11.2455px;">2</sup><o:p></o:p></span></h4><h4 align="center" style="text-align: center;"><span lang="">= GeV / c<sup style="font-size: 11.2455px;">2</sup><o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Thus the rest mass of a proton m<sub style="font-size: 10.5px;">p</sub> is written as 1, with units GeV/c<sup style="font-size: 10.5px;">2</sup>, or:<o:p></o:p></span></p><p><span lang=""></span></p><h4 align="center" style="text-align: center;"><span lang="">m<sub style="font-size: 11.2455px;">p</sub> = 1 GeV/c<sup style="font-size: 11.2455px;">2</sup> =1 GeV c<sup style="font-size: 11.2455px;">-2</sup></span></h4><h2><span lang="">THE AMAZING IMPLICATIONS OF UNCERTAINTY PRINCIPLE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">The uncertainty principle (explained vividly
below) has some amazing consequences for particle physics. It implies that a
quantum of energy can exist for a very short time, <i>provided that the product
of energy and time is less than the value of the Planck constant, that is, if </i></span><i><span lang="">Δ</span><span lang="">E</span></i><i><span lang="">Δ</span><span lang="">T < h/4</span></i><i><span lang="">π</span><span lang="">.</span></i><span lang=""><o:p></o:p></span></p><p class="MsoNormal"><span lang="">This also applies to matter, since energy and
matter are equivalent. So particles could also exist for very small times.
These particles, called <b>virtual</b> <b>particles</b>, can be produced
without breaking the law of conservation of mass-energy. The significance of
this feature of the uncertainty principle is seen as fundamental to a description
of the nature of matter, as it exists now and in the early stages of the
Universe. <o:p></o:p></span></p><h2 align="center" style="text-align:center"><span lang="">THE UNCERTAINTY
PRINCIPLE<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">At the heart of particle physics is the idea
of an uncertainty throughout nature, though not the everyday physical
uncertainty caused by imprecise measurements or the use of techniques that
cannot measure every factor in a complex situation.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">In 1927, the German physicist Werner
Heisenberg (1901-1976) showed that there was an inbuilt uncertainty in the
ability to measure the state of any small particle, such as an electron or a
photon, however accurate the instrumentation. His <b>uncertainty</b> <b>principle</b>
has since been developed beyond the simple problem of measurement into a
statement about the fundamental nature of the Universe.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Heisenberg imagined an experiment to measure
the momentum and position of, say, an electron. One way of doing this would be
to use an ‘imaginary microscope’ that could see the electron. This could only
happen if a photon hit the electron and bounced back into the eyepiece. But the
photon carries momentum and by its interaction with the electron would exchange
some (unknown) fraction of its momentum, so that the electron would no longer have
its original momentum.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">You could try to make this uncertainty in the
momentum very small by using a photon of very small momentum. But a photon is
also a wave that extends over space, having a characteristic wavelength </span><span lang="">λ.
</span><span lang="">The position of the electron would not be determined to an
accuracy better than the value of </span><span lang="">λ</span><span lang="">, and the
smaller its momentum the larger is the wavelength of the photon. This means
that by using a low momentum (low-energy) photon we improve our knowledge of
the electron’s momentum, but lose accuracy in determining its position.</span></p><p class="MsoNormal"><img src="https://res.cloudinary.com/drrz8xekm/image/upload/v1576255504/x4amyfsjwctijlcnnmla.png" data-filename="x4amyfsjwctijlcnnmla" style="width: 396px; float: left;" class="note-float-left"><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal" style="text-align: center; "><a href="https://commons.wikimedia.org/wiki/File:Heisenberg_gamma_ray_microscope.svg" target="_blank"><sup>Heisenberg's gamma-ray microscope for locating an electron (shown in blue). The incoming gamma ray (shown in green) is scattered by the electron up into the microscope's aperture angle θ. parri - Wikimedia commons, CC BY-SA 3.0</sup></a><span lang=""><o:p><br></o:p></span></p><p class="MsoNormal"><span lang="">The incoming photon has momentum h/</span><span lang="">λ</span><span lang="">, where </span><span lang="">λ</span><span lang=""> is its wavelength and h
is the Planck constant, value 6.6 </span><span lang="">×</span><span lang=""> 10<sup>-34</sup>
Js. The photon could transfer all this momentum to the electron. Thus the collision
has produced an uncertainty in the electron’s momentum of:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">p = h/</span><span lang="">λ</span><span lang=""><o:p></o:p></span></h4><p class="MsoNormal"><span lang="">As explained above, the uncertainty </span><span lang="">Δx</span><span lang=""> in the position of the electron is of the order of the light
wavelength, so we can put </span><span lang="">Δ</span><span lang="">x = </span><span lang="">λ</span><span lang="">. Multiplying both these uncertainties gives:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">ΔpΔx = (h/λ) λ = h<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">This represents the best possible accuracy. In
practice, we must accept that the uncertainty is always greater, so we write:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">ΔpΔx ≥ h [1]<o:p></o:p></span></h4><h2><span lang="">The momentum-position formula. <o:p></o:p></span></h2><p class="MsoNormal"><span lang="">This is Heisenberg’s simple treatment of the
uncertainty principle. A fuller derivation gives:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">ΔpΔx ≥ h/4π<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">The uncertainty is not due to any method of
measurement, but is in the nature of the moving object, whether a photon, an
electron, a spaceship or anything else.<o:p></o:p></span></p><h2><span lang="">Uncertainty in energy and time<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">There is also an uncertainty in the energy of
a photon or an electron; both have a wave and a particle aspect. The energy E
of a photon of frequency f, for example, is given by E = hf.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Now think about trying to measure this energy
by measuring the frequency. Suppose our frequency measurer is able to identify
one wave (as above) and so measure to an accuracy of 1 Hz, and we try to
measure the frequency of a 1 000 Hz wave.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">In 1 second we can say, f = (1000 ± 1) Hz. The
uncertainty in the result is </span><span lang="">Δ</span><span lang="">f = 1. We can do
better by taking a reading for a longer time, say 20 s, so that we measure 20 000
wavelengths.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Then the result could be put as (20 000 ±
1)/20. This gives an uncertainty </span><span lang="">Δ</span><span lang="">f = 1/20.<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">So for </span><span lang="">Δ</span><span lang="">t = 1, </span><span lang="">Δ</span><span lang="">f = 1. For </span><span lang="">Δ</span><span lang="">t = 20, </span><span lang="">Δ</span><span lang="">f = 1/20.<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">In both cases: </span><span lang="">Δ</span><span lang="">f</span><span lang="">Δ</span><span lang="">t = 1 [2]<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">This is true, however accurate the measurement.
Now, both photons and particles are wavelike, with energy and frequency linked
by E = hf. So we can write:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">f = </span><span lang="">Δ</span><span lang="">E/h<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">and from equation 2:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">f</span><span lang="">Δ</span><span lang="">t = </span><span lang="">Δ</span><span lang="">E</span><span lang="">Δt</span><span lang="">/h = 1<o:p></o:p></span></h4><h4 align="center" style="text-align:center"><span lang="">giving: </span><span lang="">Δ</span><span lang="">E</span><span lang="">Δ</span><span lang="">t = h<o:p></o:p></span></h4><p class="MsoNormal"><span lang="">Again, this is the best possible result, so in
general we have an <i>uncertainty</i> <i>principle</i> involving energy and
time that says:<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">E</span><span lang="">Δ</span><span lang="">t ≥ h [3]<o:p></o:p></span></h4><h2><span lang="">The energy-time formula<o:p></o:p></span></h2><p class="MsoNormal"><span lang="">Again, a more accurate relationship is<o:p></o:p></span></p><h4 align="center" style="text-align:center"><span lang="">Δ</span><span lang="">E</span><span lang="">Δ</span><span lang="">t ≥ h/4 π <o:p></o:p></span></h4><p class="MsoNormal"><span lang="">This means that if we wish to measure energy
accurately we must take a long time to do the measuring.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Till next time, I remain @emperorhassy.<o:p></o:p></span></p><p class="MsoNormal"><span lang="">Thanks for reading.<o:p></o:p></span></p><h2><span lang="">REFERENCES<o:p></o:p></span></h2><p class="MsoNormal"><a href="https://www.learner.org/courses/physics/unit/text.html?unit=1&secNum=5" target="_blank">https://www.learner.org/courses/physics/unit/text.html?unit=1&secNum=5</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://phy.duke.edu/~kolena/modern/hansen.html" target="_blank">https://phy.duke.edu/~kolena/modern/hansen.html</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://www.livescience.com/64687-why-top-quark-so-heavy.html" target="_blank">https://www.livescience.com/64687-why-top-quark-so-heavy.html</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://www.britannica.com/biography/Murray-Gell-Mann" target="_blank">https://www.britannica.com/biography/Murray-Gell-Mann</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Murray_Gell-Mann" target="_blank">https://en.wikipedia.org/wiki/Murray_Gell-Mann</a><span lang=""> </span></p><p class="MsoNormal"><a href="http://www.nucl.phys.tohoku.ac.jp/sansha/2011/lecture_files/PART-II.quark_model.pdf" target="_blank">http://www.nucl.phys.tohoku.ac.jp/sansha/2011/lecture_files/PART-II.quark_model.pdf</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://www.s-cool.co.uk/a-level/physics/particle-classification-and-interactions/revise-it/the-quark-model-of-hadrons" target="_blank">https://www.s-cool.co.uk/a-level/physics/particle-classification-and-interactions/revise-it/the-quark-model-of-hadrons</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Quark_model" target="_blank">https://en.wikipedia.org/wiki/Quark_model</a><span lang=""> </span></p><p>
</p><p class="MsoNormal"><a href="https://revisionscience.com/a2-level-level-revision/physics-level-revision/particles-radiation-quantum-phenomena/quarks-antiquarks" target="_blank">https://revisionscience.com/a2-level-level-revision/physics-level-revision/particles-radiation-quantum-phenomena/quarks-antiquarks</a><span lang=""> </span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Quark" target="_blank">https://en.wikipedia.org/wiki/Quark</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://www.britannica.com/science/antiquark" target="_blank">https://www.britannica.com/science/antiquark</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Baryon" target="_blank">https://en.wikipedia.org/wiki/Baryon</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/List_of_baryons" target="_blank">https://en.wikipedia.org/wiki/List_of_baryons</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/List_of_mesons" target="_blank">https://en.wikipedia.org/wiki/List_of_mesons</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://en.wikipedia.org/wiki/Meson" target="_blank">https://en.wikipedia.org/wiki/Meson</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://www.britannica.com/science/subatomic-particle/Quarks-and-antiquarks" target="_blank">https://www.britannica.com/science/subatomic-particle/Quarks-and-antiquarks</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://www.researchgate.net/publication/329715575_Quarks_Do_Not_Exist_Everything_is_made_up_of_only_positrons_and_electrons" target="_blank">https://www.researchgate.net/publication/329715575_Quarks_Do_Not_Exist_Everything_is_made_up_of_only_positrons_and_electrons</a><span lang=""><br></span></p><p class="MsoNormal"><a href="https://medium.com/starts-with-a-bang/there-are-no-free-quarks-ddec8cb831ea" target="_blank">https://medium.com/starts-with-a-bang/there-are-no-free-quarks-ddec8cb831ea</a><span lang=""><br></span></p><p class="MsoNormal"><span lang=""><br></span></p>