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22-September-2011 / quantumsniper1

A bunch of quantum – Part ONE

What does a dead cat have to do with Quantum Theory?

(Article, 3,829 words. Est. 20 mins reading time. Maybe need 2 cups of tea for this one!)

The mystery of Quantum Theory is to understand what happened to Schrodinger’s Cat

Mention the phrase “Quantum Physics” in casual conversation, and most people react with stunned reverence and awe ….

OR …

…. they arrogantly suggest “who cares?”, (which comically exposes their secret inferiority complex on the subject).

Well, to answer the question of who cares, I say :   “I DO ! ”

And if you want to know why, you should be prepared to look deep into yourself, because the conclusions we will draw from the quantum realm are gonna “mess with your head, Baby”

…. And if they didn’t mess with your head in some way; Well, I reckon you just should’ve paid closer attention.

My recommendation to you for reading this article is : TAKE YOUR TIME, but DON’T give up ploughing through. If something appears too confusing to begin with, come back to it the next day.  I promise; the subject matter itself CAN be understood if you keep pushing yourself.

Reading Hint:  At certain points during this explanation, I will ask you to “TRUST THIS”.  When you see that phrase, you don’t have to just screw up your nose in frustration and mumble “Well, I dont believe that blah-blah can be such-and-such…“.  Nor do you need to point out the rigors of linguistic logic to me and say “this is just a fallacy of Argumentum Ad Verecundiam

I understand. If you had the time, you would just  go out and correctly add up the maths OR accurately carry out the experiments for yourself and you would SEE the proof before your very own eyes. But since I presume you don’t have the time, then you’ll just have to trust me for now.

 So;  TRUST THIS:     1 + 1 = 2   Right ? No arguments so far ?  Good !

Let’s start with some quick basics.  The baby stuff.

Of Sir Isaac Newton, and Billiard Balls

From the time of publication of Isaac Newton’s Principia Mathematica in 1687, until about a hundred years ago, scientists believed they knew just about everything they needed to know to unravel the mysteries of the universe.

The three “Laws of Motion” derived by Newton were good enough to mathematically describe the movement of nearly every detectable thing  in the visible universe from sand grains and apples, through to battleships, volcanoes, planets and stars.

Newton’s Laws of Motion:

First law: The velocity of a body remains constant unless the body is acted upon by an external force.[3][4][5]

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Second law: The acceleration (a) of a body is parallel and directly proportional to the net force (F) and inversely proportional to the mass (m)                                                    Thus;            F = ma

_

Third law: The mutual forces of action and reaction between two bodies are equal, opposite and collinear.

Watch the video below and see how each of Newton’s Laws relates to everyday motion:


(Thanks to http://www.youtube.com/user/AllusiveConceptions for claymation)

TRUST THIS.   These laws, particularly F = ma  have worked for scientists and engineers for well over 300 years.  If the law wasn’t true, apples wouldn’t fall, cars or planes wouldn’t work, and your bicycle wouldn’t stay upright.

Through Classical History, up until 1900, these clear, precise, predictable laws governed and described everything in the physical world.  The maths was simple. There were no real surprises.

Centuries of this Newtonian Physics led to a very ‘deterministic’ view of the known universe.  Random Chance was thought to be irrelevant to core science. It was widely believed that (in keeping with the level of technology of the time) the complex universe itself operated like some giant wind-up clock with its own gears and levers. It simply ‘unraveled’ or ‘unwound’ according to fixed unchanging rules.

Marie Curie

Since ancient Greece, it was understood that the world was composed of tiny hard indivisible “Atoma” (gk) or “Atoms”, which were like sub-microscopic rocks, ball-bearings, or billiard balls.

When Madame Marie Curie was awarded the Nobel Prize in Physics in 1903 for her work (carried out with her husband) in discovering and isolating the radioactive elements of Polonium (Po) and Radium (Ra), the science community realized there was a lot more going on in the tiny world of atoms.

Great credit goes to Curie for her tenacity with her radiation studies, because in 1911, she again won a Nobel Prize (This time for Chemistry).  These prizes spurred huge interest in fields of study relating to atomic and sub-atomic particles.

By discovering that the atoms in materials like elements can go through some form of radioactive  decay, Curie turned chemistry and physics theories upside down. “Radiation” did not make sense and was unable to be explained using the maths and science of the time.

Like most scientific discoveries through history, its NOT what makes sense, its what DOESN’T make sense when experiments are carried out, that leads to the biggest most interesting realizations about the world.

I’d Ruther(Ford) not be Bohr’d

Earnest Rutherford was, at around 1912, experimenting with positively charged Alpha Particles (later discovered to be the nuclei of Helium (He).  In experiments conducted at McGill University in Canada, he essentially enclosed a lump of radioactive Uranium (U) inside a heavy Lead (Pb) box, and drilled a hole in one side so that the radioactive particles could escape.  He used this box like a “radioactive gun”.

All you need to know about these particles of radiation is that —

(a)  Alpha Particles have a (+) positive charge; and

(b)  as with magnetism – when a Positive meets a Positive – it causes the charges to repel

(c)  ; and Note for later (because its not so relevant for Rutherford) electrons have a negative (-) charge;

Rutherford essentially used STATISTICS to work out that – based on the number of bounce-backs, versus the number of  straight or only slightly-deflected particles, – these atoms in the gold foil (known to be about 4 gold atoms thick) were NOT fully solid like ball bearings, but were, in fact, “mostly empty” but with a VERY VERY tiny hard positively charged nucleus.

Since the gold foil, itself, doesnt fall apart, he conjectured that the nucleus of each atom in the gold foil must be “held together” and somehow suspended (in the centre) of some even-tinier shared electrons which were probably orbiting these hard tiny nuclei .

TRUST THIS.   In regard to the video we just saw, the nuclei and the electrons are NOT “to scale” in that depiction. It is important to appreciate both the size and scale of these particles.

_

How much space in atoms? How small are the nuclei?

I’m glad you asked. Because it means you’re thinking about what you’re reading so far. Now for the answer:

We don’t want to discuss the size and composition of electrons any further just at this moment. , (but just to hint: they are MUCH smaller still! than the nucleus).

Problems with Newtonian physics and Classical theory

Rutherford’s model of the Atom was a breakthrough from the past, because his experiments showed that the Atom was a small heavy nucleus surrounded by, or “orbited” by electrons. But the picture was not yet complete.

In order to give credence to his work, Rutherford had to support and build on the knowledge of the past to explain his Model of the Atom, its nucleus and electrons.  Unfortunately, this created some problems:

First Problem:  Thermodynamics

Rutherford’s fairly simple Model of the Atom and his experiments clashed with widely-accepted scientific beliefs that had been developed in the 18th and 19th centuries, known as the Laws of Thermodynamics.

Without getting too distracted by thermodynamics as a side-topic. Thermodynamics proponents today (which includes virtually all of the world’s mainstream scientists), hold that the total energy in a closed system (like an Atom, or a Gas Tank, or a Universe) must remain EQUAL no matter what happens to it, or what state its in, even though small parts of that system may flow or vary internally.

Nevertheless, Entropy (also known as “The arrow of time”) will cause all things to move from ORDER to DIS-ORDER over time.  If the energy in a System DIDN’T remain the same, of course, then the universe might allow such things as perpetual motion machines. (Which it apparently doesn’t)

(You may Click here if you need a quick explanation of Thermodynamics (2 mins))

Second Problem:  Staying faithful to Newton’s Laws (and their derivations) 

Unfortunately, Rutherford’s experiments and his new description of the atom as being a tiny dense core surrounded by a ‘cloud’ of electrons, did not seem to make sense in terms of Newton’s classical formulas.

For instance, his formula for Force

F = ma                  (Force = Mass x Acceleration)

… nor with the formula for Acceleration

Formula for Acceleration
         (Acceleration = CHANGE in Velocity over ELAPSED Time) *

* …  note the Triangle symbol (greek capital Delta) in the formula meaning “Change In”

… nor did the motion of electrons around the nucleus seem to accord with standard formulas for CIRCULAR (also known as “Centripetal”) motion. For instance, the primary formula for Centripetal Acceleration derived from the previous two formulas;

          (Centripetal Acceleration  =  the SQUARE of Velocity over Radius LENGTH)

_

So; Newtonian Physics AS A DISCIPLINE had a major problem. The reliable straight-forward formulas for motion that had been used for a couple of centuries was unable to provide a complete explanation for Rutherford’s description of the atom.

Bohr’s atomic model: Quantum Energy States

In 1912, Niels Bohr, a brilliant young graduate, worked with Rutherford in the lab to look for a solution.

It took a few years after Rutherford’s experiments, but eventually Bohr began to flesh out a newer, more coherent picture of the Atom.  For his contribution, in 1925, Bohr also won the Nobel Prize for Physics.

What he did was to create a Model (or description) of the simplest atom known to science; The Hydrogen (H) Atom.  Hydrogen is comprised of only ONE Proton and ONE Electron.

In this new atomic model, Bohr determined that:

1.   Electrons, (which he understood to be like small negatively charged particles/balls) MUST be in motion; AND

2.  Electrons were probably traveling in a CIRCULAR path around an atomic nucleus of Protons (which is positively charged).

(NOTE: If the electrons weren’t in motion around the atom, the Positive Proton would attract the negative Electron (just like in Magnetism), and the atom would collapse on itself.);  AND

3.  When Electrons are in orbits around the atomic nucleus, they only EXIST at SPECIFIC discrete levels around that nucleus. Those levels are what we now call “quantum energy states”.  This also meant that, BETWEEN these specific energy levels, there was actually NOTHING.

TRUST THIS:  This idea of “Nothing being there”, versus “being there” is very important in quantum physics. So, keep it in mind for later when we meet Schrodinger’s Cat.  Because when we shrink things down to sub-atomic size, things become really weird compared to what we’re accustomed to in everyday life.

_


(Again, note that the protons and electrons are NOT to scale!)

Over the rainbow; The Emission Spectrum

Before Bohr’s Model of the Atom became the accepted doctrine, it was presumed that the electrons should theoretically orbit ANYWHERE around an atomic nucleus.

So; How did Bohr come to this conclusion that there were only very specific energy states or energy levels?

In his experiments, Bohr found that when he burned hydrogen gas, and shone the resulting light through a prism, certain bands of coloured light seemed to appear and be brighter than the surrounding light.

Let’s say (for example) we were looking at simple hydrogen which was “stable”. By which I mean the hydrogen is at room temperature, and is not being excited due to being heated up.  In that situation, electrons orbiting the hydrogen nucleus will happily stay in their ‘stable’ orbits. No emission spectral lines appear.

But IF energy is added to the system in the form of heat such as from infra-red light PHOTONS (note I didn’t say PROTONS) then certain colours (or “wavelengths”) of light energy will be ABSORBED by the hydrogen atoms. This causes orbiting electrons to “jump orbit” to a higher energy level.

Of course, it’s not the electrons that jump to higher orbits that we see in the above video (because that would be an ABSORPTION Spectrum, where electrons absorb certain light wavelengths, and sharp lines would be missing from the rainbow).

The lines seen in the video occur when the unstable hydrogen COOLS and the electrons are falling back into their normal stable orbit. By doing so they re-EMIT that centripetal energy as photons of specific light colours / wavelengths as they “cool”.

When looking at different chemical elements and substances, Bohr found different but SPECIFIC wavelengths / frequencies (or colours) would be emitted depending upon WHICH substance or element was being “excited”.

Emission Spectra became thought of as “fingerprints” or “D.N.A” for different elements. And today, this system is still being used by astronomers in radio telescopes to determine what elements can be found in distant stars, and by chemists using gas spectrometers to find out what substances are present in chemical samples.

Head to Head Comparison. Light v. Matter

As early as 1678  (Christian Huygens ‘Treatise On Light’) wrote that since light reflected and refracted through glass, mirrors and water surfaces etc, it must be some kind of vibrating wave. Presumably, if the nature of all material THINGS was assumed to be some kind of hard tiny particle, then light was seen to be different because it could propagate or pass through objects like water and glass.

Even Isaac Newton himself believed that light was different from normal matter, and that it consisted of some kind of “corpuscles”. In other words he accepted that light as being some kind of hybrid matter-particle, and that it acted as a wave.

So. What exactly is “Matter” (particles)?

…  And how is it different from “Light” (waves)?

To do this, we need to look closely at the respective physical properties of both light and matter.

As a candidate for comparison to LIGHT (photons), let us take the ELECTRON (matter particle). The electron was a natural choice as a “Matter/Material” thing for comparison because it had (just 27 years before De Broglie) been discovered by J.J. Thomson in 1897 and the measurements done by Thomson on the electron’s properties were seen to be reliable.

Both Photons and Electrons were known to be extremely small. Also, both were sub-atomic. The electron, for instance, was recognized as being about 2,000 times smaller than an Atom. Remember that the simple Hydrogen Atom, is only comprised of one PRoton (not pHoton), and one Electron.

 

PHOTON
(light / energy wave)
ELECTRON
(a matter-like particle)
MASS
-nil-
REST MASS Fixed at 
9.10938291(40)×10−31 kg
ELECTRIC CHARGE
-nil-
Negative
SPEED
CONSTANT SPEED (‘c’) of 
299,792.458 kilometres per 
second throughout the
universe.
Variable, depending
upon force exerted 
on it


Louis De Broglie:  The Wave / Particle Duality

Unfortunately, even with the progress made by Bohr’s model of the atom, scientists still only had a partial explanation of the inner workings of the atom.

In 1924, a french nobleman and aspiring scientist, Count Louis-Victor De Broglie, suggested that all discrete objects in the known world vibrated like “waves” as well.

In truth, De Broglie didn’t initially prove this claim by experimentation. He simply ‘made it up’ as an assumption for his University doctoral thesis to research and apply existing equations and formulas for his research into Energy and circular motion of sub-atomic particles.

What was his big idea? Well, essentially, he claimed that everything in the universe ‘vibrates like a wave’.

 So;  TRUST THIS:  By “everything”, I mean all matter and energy including small particles like atoms and electrons, as well as more massive objects like billiard balls, Me & You, and even planets. Everything possesses a ‘Wave Function’.  However, based on his formulas, the vibrating wavelength of any objects larger than sub-atomic particles was so small as to have no real effect in everyday living.

For our readers this is, perhaps, the beginning of the “descent into weirdness” for many people who study and try to make sense of quantum physics. In our daily lives, we simply do not see everything around us ‘vibrating’ or having some kind of wave motion.

[Next section re-edited in Oct-2015]

As we’ll see below, De Broglie’s incredible assumption of “Wave-Particle Duality” made in 1924, actually turned out to be correct because it was found that Electrons (accepted to be a “material” thing) did, indeed, possess a wave-like property just the same as Photons (always understood  to be non-particle-like, ElectroMagnetic waves including X-Rays, radio, light, unltra-violet and infra-red).

The proof came in the form of two independent sets of experimenters carried out about three years after De Broglie received his Nobel. Lets briefly look at these below –

Electrons: Particles that act like waves

These two simple experiments involved a process called “electron diffraction”. This involved shooting electrons (these are “PARTICLES”, remember) at very thin materials like crystals and metals to see what kind of patterns the electrons would make on the other side.

The first experimenters were Davisson & Germer working out of Bell Labs. The second experimenter was G.P Thomson (yes, he was the son of the previously famous J.J. Thomson) working out of the University of Aberdeen.

Both experimenters shot high energy ELECTRONS through either a crystalline grid or thin metal foil.

The atoms that make up a thin metal foil, or a crystal, join together in a very regular structures, or lattice-like patterns. The shape of these patterns depends on the material itself. These grid-like “diffraction patterns” in the material might be Hexagons, Squares, Triangles. Helixes; all kinds of shapes.

So; the point of the experiments was to see what kind of interesting “shadow patterns” occur when you shoot electrons through these ‘Diffraction Gratings’, these crystalline lattices, or other thin pieces of metal.

As we just saw in the video above, when shooting the ELECTRONS. (Particles of matter, remember), through graphite (which is made of carbon, which is what diamonds are made of) we can see ring-like patterns appearing.

Similarly, you can easily see PHOTONS (which are ElectroMagnetic waves, remember) being used as either X-Rays or visible Laser light to see the shadowy “diffraction patterns” cast from a helix-shape.

So, to summarize so far: We can see that

  • IF X-Ray photons, and
  • Electron particles,

…can both scatter and diffract like waves patterns, then ELECTRON (which are seen as particles of “matter”, must mean that alll MATTER also possess De-Broglie wave-like properties!

Despite the success of De-Broglie’s idea, however, the concept of a “Wave-Particle Duality”, took quite a while to be accepted by the science community. It wasn’t until 1937 that the (a) Davisson & Germer, and (b) Thomsom experiments led to them being awarded the Physics Prize by the Nobel Committee.

[- end of Oct-2015 edits]

So, why are orbital positions of electrons FIXED?

From the work of De Broglie, we come to understand that “everything is waves” and “everything vibrates”.

In scientific terms this means that all matter possesses a “De Broglie Wave Function”, which includes the properties of both “frequency” and “wavelength”)

TRUST THIS:  You needn’t baulk here just because there are some equations. Just Relax! You are NOT being asked to do any calculations. Just take a minute or two to look quietly at the symbols in the equations and see for yourself the simple general relationships between the properties quantified in DeBroglie’s Wave Function.

_

The famous equations for the DeBroglie WAVE FUNCTION are as follows:

\lambda = \frac{h}{p}                           and                           f = \frac{E}{h}

The symbols in the equations are deciphered as follows:

the “wavelength” = (~\lambda~)  ………  and/or the “frequency” = (~f~)

… are equal to the “momentum” = (~p~) ………    and/or the “kinetic energy” = (~E~)

… as a numerical function of “Planck’s constant” = (~h~)

If electrons were, by themselves, just minding their own business traveling in a straight line and not orbiting a nucleus, a full single De Broglie wavelength (n) including one peak and one trough would be n = 1. In the diagram below left you can see some flat wavelengths. Similarly, we can also see n=2,  n=3 and n=4 full wavelengths further below left.

Now if we were to wrap a wavelengths in a circular manner around a central point (say, the nucleus of an atom), these full wavelengths (or “Standing Waves”) as shown in the diagram immediately below right can only exist at fixed energy levels.

So, in the Hydrogen atom, the radius of orbit of the electron in a ground state , n=1, has a circumference of one standing wave. The radius of the first excited state, n=2, has a circumference of two standing waves. Because of this, an electron’s orbit cannot decay because it is constrained by its standing wave forms.

TRUST THIS: Whilst the diagrams we use for now give only a 2D (two-dimensional) representation, we can use them for the time being to get a basic understanding. A truer understanding needs to be visualized in 3D, 4D … and maybe even higher.

In the next diagram below, which also shows an electron “orbiting” a nucleus, NOTICE that there is a notch breaking the smoothness of the wave pattern / function. In other words, this is actually a hypothetical picture of a dis-allowed orbit; or incomplete standing wave pattern around a nucleus.

This is because electrons MUST exhibit a perfectly formed Standing Wave around a nucleus, where the radii of the circumferences must ALSO equal a multiple of the electron’s de Broglie wavelength. This second diagram therefore demonstrates that the radius (a) below needs be either larger or smaller to permit the full unbroken standing wave pattern.  It also shows why (in the in-between energy levels) there can be “nothing”.

In summary, you therefore MUST have fixed discrete orbits at SET distances of FULL MULTIPLES of the wavelength. No fractions or partial waves are allowed for the electron to exist in these orbits.
(Thanks to http://dev.physicslab.org/Document.aspx?doctype=3&filename=AtomicNuclear_deBroglieMatterWaves.xml for the diagrams)

=======//========

Last thoughts for today:

This is a good time to take a break from all this hard core scientific thinking.

Stay Tuned to QunatumSniper for the final instalment on this topic. “A Bunch of Quantum – Part TWO

Up to this point, we have only just started the descent into what I call the “weird part” of quantum physics. In the next and final instalment, we’ll find out what happens to that darned cat.

And then, perhaps, we will start to see how quantum theory has spawned an entire set of incredible possibilities (that are slowly being turned into fact), which theories sound more like philosophy and science-fiction than science fact.

These will include Time Travel, Parallel Universes, String Theory, and (a) 10-Dimensional multiverse and even The Matrix (like in the movie of the same name).

Here below is a teaser that summarizes what we’ve learnt today, and blends in to the next conceptual leap in quantum theory: “The Heisenberg Uncertainty Principle”.

When Part TWO is published, (soon … I have some politics topics I want to publish blog about), the reader should re-visit this Part ONE, because I may have modified it, and prettied it up a bit.

Please don’t hesitate to let me know if you find any section of this article too difficult to read.

– QuantumSniper

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