Category Archives: Quantum mechanics

Thought Experiment – Photons up Close

Recently I published a paper on radio frequency photons:  Thought Experiment- Photons at Radio Frequencies in which I described a photon from the time of emission from a radio antenna as it propagated outward until it separated into photons and was later captured by an antenna.   

What I found was that the photon started as a whorl or vortex, if you wish, traveling initially in patterns of counter-rotating fields that eventually became identified as individual photons.  These whorls/vortexes have a specific size (diameter) and energy defined by the frequency of the emission.   A point on the rotating photon describes sinusoidal patterns that fall behind the photon in the classic electromagnetic patterns.   The thought experiment allowed me to calculate the maximum diameter of the photon at 105 mhz to be about 0.9 meters and a visible-light blue photon to have a maximum diameter of 143 nm.

Having learned from that, I decided to do some more thinking about photons in general.  What applies at radio frequencies should also apply to photons of light and higher energies.   It occurs to me that we can learn a lot about photons by experimenting with them at radio frequencies.   We know that radio signals diffract around sharp structures and even exhibit double slit diffraction if passed between sets of tall structures with sharp edges.   I don’t know of any single-photon experiments at radio frequencies but I suspect that the results would be the same; diffraction still occurs in which the photon interferes with itself.  

Having looked at it from a whorl or vortex photon standpoint (as opposed to a wave standpoint), it is easy to imagine a photon nearly 1 meter in diameter passing around both sides of a telephone pole or being pulled around a corner of a building as one edge drags on the sharp edge there.    

The same thing should happen to a red, blue or green photon encountering superfine wires or sharp edges of a razor blade or slit.  

Not having the equipment nor the results of any such experiments at radio frequencies, I’m going to move this into a thought experiment and follow a photon up close, drawing on the earlier radio frequency thought experiment and adding details that agree with what we know about light photons and see where we go.  In this case I’ll consider a 450 nm blue photon.   I mention a blue photon only to help differentiate it from a radio frequency photon in the following discussion.  It doesn’t matter what it is, they should behave the same.

Blue Photon

 by James Tabb  (ripples greatly exaggerated)

A blue photon is emitted when a source (the emitter) such as, for example an electron that changes energy levels from a higher level to a lower one, shedding the excess energy as a photon.     I imagine it like a sudden elastic-like release of energy in which the energy packet moves away instantly to light speed.  If the packet follows Einstein’s equations (see graphic below) for space distortion, then a blue photon is immediately flattened into a disk of 143 nm diameter (see graphic above) because the lengthwise direction shrinks to zero at velocity c.   (This diameter was derived as d = λ/Π from my previous article and depends on the wavelength)

In my description of a radio photon, the energy in the packet is rotating around the perimeter of the packet at c as well as moving away from the emitter at c.   The limit of c in the circular direction also limits the diameter of the packet.

I can picture photons that slosh back and forth left to right or up and down or in elliptical shapes.   All of these shapes and directional sloshing, and rotation are equivalent to various polarization modes – vertical, horizontal, elliptical and circular.   I can also imagine that these shapes/polarizations are created as photons are beaten into these modes while passing though lattices or slits that encourage the photon to go into one mode or the other or to filter out those going in the wrong direction.   I can begin to see that when photons at light wavelengths are thought of as rotating whorls, it becomes easier to think of how this all works.   None of the modes involve back and forth motion because to do so, the portion going backward would never catch up to the forward mode or it would exceed c.   

Now that the photon has been emitted and begins its flight, we are purely in a relativistic mode.  Einsteins equations for space distortion and time dilation tell us that the path in front of the photon shrinks to zero and the time of flight shrinks to zero as well.   This has always raised a troubling problem because we know that some photons take billions of years to fly across the universe and move about 1 nanosecond a foot of travel.  

In order to resolve this problem, I’m now imagining an experiment in which an excellent clock is built into a special photon that starts when the photon is emitted and stops when it arrives. (Good luck reading it, but this is only a thought experiment, so I’m good to go.)  Perhaps the path is a round trip by way of a mirror or some sort of light pipe such that a timer triggered at the start point also stops again when the photon comes back. If the round trip is about 100 feet then you might expect the timer and the photon’s clock to both register about 100 nanoseconds more or less for the trip.

When the experiment is run, the photon’s clock is still zero when it arrives and the other timer does indeed read very close to 100 nanoseconds. The photon seems to have made the trip instantly whereas we measured a definite trip time that turns out to agree with the velocity of c for the photon throughout its trip.  I decided that is the correct outcome based on the time dilation equations of Einstein when using velocity = c. 

So we see that Einstein’s time dilation equation applies to the photon in its reference frame, not ours.  There are nuances here that we should consider for the photon:

(1) Since the distance the photon travels is zero, the time it takes is zero as well.  That is why the photon’s clock does not change.   Therefore, I claim that the space/time jump is instantaneous and therefore the landing point is defined at the moment the photon is created regardless of the distance between the two points.

(2) Since we know that the photon packet cannot go faster than c and by experiment, it does not arrive faster than c, it appears obvious to me that the instantaneous space jump is not completed instantly, only defined and virtually connected.  I visualize that for one brief moment, both ends of the path are (almost) connected; emitter to photon, photon to its destination through a zero length virtual path. The photon does not transfer its energy to the destination at that moment because the path is only a virtual one.

(3) I visualize the photon’s forward path shortened to zero, an effect which has everything forward to it virtually plastered to its nose, like a high powered telescope pulling an image up with infinate zoom capability.   All of space in front of it is distorted into a zero length path looking at a dot, its future landing point.   

(4) The photon immediately moves away from the emitter at light speed. As it does so, the path beside and behind the photon expands to its full length (the distance already traveled, not the total path) with a dot representing the destination and the entire remaining path virtually plastered to its nose.   A zero-length path separates the nose of the photon from the landing point. The path already traveled expands linearly as the photon moves away from the emitter along that path at a velocity of c.

(5) I claim that the photon’s zero-length virtual path is effectively connected all the way through, including all the mediums such as glass, water, vacuum, etc.  However, the photon only experiences the various mediums as the path expands as it moves along.  I make this claim because it explains all of the quantum weird effects that we see described in the literature and thus appears to be verified by experimental results.  My next paper will detail this for the reader.

The landing point only experiences the photon after the entire path is expanded to its full length. In the example, the starting and ending points are 100 feet apart with a mirror in between, but the entire distance between (for the photon) is zero and the time duration (for the photon) is also zero (with maybe a tiny tiny bump when it reverses at the mirror). For one brief instant, the emitter is connected to the photon and the photon to the mirror and back to the timer through two zero-length paths, but it is a virtual connection, not yet actually physically connected.

The mirror and landing point remains virtually attached to the nose of the photon which moves away from the emitter at light speed, c. The photon’s clock does not move and the photon does not age during the trip, but the photon arrives at the timer after 100 nanoseconds (our time) and transfers its energy to the timer’s detector.

(6) I also claim that all the possible paths to the destination are conjoined into one path that is impossibly thin and impossibly narrow, much like a series of plastic light pipes all melted into one path that has been drawn into a single extremely thin fiber.   This is a result of the fact that the distances to every point in the forward path is of zero length, and therefore all the paths are zero distance apart.

In effect the entire path is shrunk to zero length at the time of emission due to a severe warp in space. Zero length implies zero duration for the trip as well, and the photon is in (virtual) contact with the mirror (and also with the finish line) instantly, but the space it is in expands at the rate of c as it moves away from the emitter.

Everything in front of the photon is located as a dot in front of it. It experiences the mirror after 50 nanoseconds of travel time. The reflected photon is still stuck to the finish point as the space behind it expands throughout a second 50 nanosecond time lapse and the finish line timer feels the impact at the correct total 100 nanosecond time while the photons clock never moves.

The major point learned in this thought experiment is that the photon’s path and landing point is perfected at the time it is emitted whether the path is a few inches or a billion light years long due to the relativistic space/time warp. This is a major point in explaining why quantum weirdness is not really weird, as I will discuss later in a followup paper that clarifies the earlier posts on this subject.

Wormhole Concept 

I visualize the photon as entering a sort of wormhole, the difference is that the photon “sees” the entire path through the wormhole but does not crash through to the other side until the wormhole expands to the full length of what I call the “Long Way Around (LWA)” path. Unlike a wormhole, it is not a shortcut as it merely (as I call it) Defines the Path and Destination (DPD).  This concept also applies to any previously described wormhole – see my previous paper, Five Major Problems with Wormholes

Here is the important point: The photon in this wormhole punches through whatever path it takes instantly at the moment of creation and defines the DPD. Every point in the DPD is some measurable LWA distance that is experienced by the photon as the path expands during its transition along the path. The LWA includes any vacuum and non vacuum matter in its path such as glass, water or gas.

So now we have a real basis for explaining why quantum weirdness is not weird at all – it is all a matter of relativity, as I will explain in my followup paper.

Oldtimer

Copyright 2007  - James A. Tabb   (may be reproduced in full with full credits)

Five Major Problems with Wormholes

Five Major Problems with Wormholes 

Wormholes are supposed to be shortcuts from one time and place to another time and place.   For example, drive your spaceship into one end and exit near some other star, perhaps 1000 light years away.   Drive back through and return to earth.  Simple enough.

  

 Wormhole drawing from Wikipedia

If a wormhole is ever created for passage of man or machine by some future civilization, then there will be some major problems to overcome other than the biggie… creating the wormhole in the first place.  I believe this is the first time most, if not all, of these problems have been identified.  

Although the wormhole supposedly bends/warps time and space, there is a fundamental limit to how fast you can get from here to there, no matter how much time and space are warped.   That limit is c and it applies to the Long Way Around (LWA) path length.  First let me tell you why I think so as it is key to the some of the rest of my list of problems.  

A common wormhole is created by every photon that exists.   For example, a photon does a space/time warp from Proxima Centauri (the nearest star to our sun) to our eye.  The distance and time the photon experiences is zero.  It does not age during the trip and the total distance is zero at the moment of creation.   However, it still takes 4.22 years to get here, the time light takes to travel the total distance from that star to ours.     

Einstein’s equations say that the photon traveling at c has a total path length of zero and travel time of zero duration.  I believe that applies to every photon.   However, we know that the photon takes 4.22 light years and travels about 28 trillion miles from that star to our eye as we measure or calculate it.   Even though the path the photon sees is zero length and the time it ages is zero time during the trip, it still does not arrive until the entire 4.22 light years elapses.  

It is my theory that this is because the space/time warp of our photon wormhole connects the emission point on Proxima Centauri and the landing point in our eye only in a virtual sense and only in the first instant of its creation.   

After that first instance, the photon moves away from the emitter at light speed and the path behind it expands as the photon travels along it at c.   The photon’s path to our eye always remains zero length, but it traverses the path at c, leaving an expanded path behind until the entire path is traversed.   The photon never transfers its energy until the entire path is completed at the maximum velocity of c.   

My first wormhole problem is that the time required is no less than the long way around travel time at c.   Anything entering the wormhole is imposibly close to the other end (as for our photon example), but cannot actually get there until the path from the entry point expands behind the object moving at c throughout the entire trip, the LWA, just as it does for the photon wormhole.  

Even if the wormhole spans a time/space warp of 1000 light years, it will still take no less than 1000 years to get from here to there even if the wormhole appears to be of zero length.   The crew of the space ship that manages to get into a wormhole would not age during the trip, a distinct advantage for the crew and the ship’s lifetime.  It would seem to be instantaneous and if it were indeed reversible, then the return trip would be just as fast.  Drive into one end and return immediately and likely not be but a few hours older.   However any companions that were left behind on earth would be dead nearly 2000 years.   All this assumes the problems that follow can be solved.

The second problem is that a wormhole cannot be established before it is created at each end.  If  one end is created today and the other is somehow created on a distant star, the wormhole would not be operable until the second wormhole is created, presumably at least the normal space ship travel time from one construction site to the other, even if the construction crew travels at c.    Unless the wormhole acts like a reversible time machine, a much more difficult arrangement, it will take the same amount of time each way through the wormhole with the arrow of time aging both ways and it cannot begin to be used as a shortcut until both ends are finished.    It would take a very patient civilization to plan for such a feat.

My third problem involves getting into any wormhole that moves you along at light speed.  The nose of the ship would presumably be accelerated to light speed even before the crew compartment made it into the opening.   The result would be powdered spaceship and crew with photons leading the way, larger particles and atoms dragging behind, but no survivors or anything recognizable.  

The fourth problem is getting out of the wormhole.  Let’s say somehow you can get your space ship in and up to speed.   Everything going out the other end arrives there at light speed.   A huge blast of various rays and light burping out the other end, frying anything loitering near the exit.  A great light show, but hardly useful for the crew wanting to get from here to there in a hurry, or their greeting party for that matter.  The wormhole turns out to be a great ray gun! 

My fifth problem involves reversibility.  We assume that entering the wormhole at either end establishes the direction of travel.  However, it appears to me that it is very likely that the arrow of time exists only in the direction of the creation of the wormholes.  That is, from the first wormhole to the second.  Items entering the first one created would be moving in an arrow of time from the earliest time to the latest.   Items trying to enter the second wormhole to come back would be rejected in a smoldering heap or blast of rays.   If that logic is reversed, the problem still exists:  One way only!

Arrow of Time Established? 

I believe this applies to photons and particles in general.  The equations for physics always seem to allow collisions to be reversable and there are no laws that would not allow any set of particle interactions to be reversible.   However, it is my opinion that photons are not reversible for the reasons listed above.  They are zipping through non reversible wormholes.   Energy is transferred from point of creation to some other point where it is absorbed or transferred to another particle and can’t go back though the wormhole as it is a one way street, from first end created to the second end and never the other way around.  That means the arrow of time always moves forward and is never reverseable.  It can be stopped but never reversed.

SuperLumal Transmission?

As a side note, for the reasons listed in the problems listed above, there will be no speedup of communications through a wormhole.  No superlumal transmissions, no advantage over sending it across space the normal way, and very likely, no two way communications.   I hope these revelations do not stop any projects in progress as science will advance no matter what.  8>)  Photon wormholes are the best anyone will be able to do.

Oldtimer

PS – check out my earlier wormhole article

Copyright 2007, James A. Tabb  (may be reproduced with full credits)

 

 

Location or Momentum

Space Guy

Bruster Rockit: Space Guy!                           by Tim Rickard

A key element of quantum mechanics is Heisenberg’s uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction, as so aptly illustrated by Tim Rickard above. 

E = c \, p \!  for a photon, where E is the energy, c is the speed of light and p is the momentum.    So the momentum of a photon is equivalent to the energy of the photon divided by the speed of light or p =  E/c  where E is also related to the frequency of the photon by Planck’s Constant E = hf.   h is Planck’s constant and f is the frequency assigned to the photon.   f is also related to the wavelength of the photon by f = c/λ.  

So E = hc/λ = cp       Therefore    p = h/λ

But we know the values for both h (6.26×10^-34 joules sec.) and for λ if we know the color of the photon.  Usually if we are dealing with coherent light (red laser for example) then we know the wavelength λ very accurately.   Thus we know the momentum very accurately.

There is another factor in this equation – spin angular momentum of the photon which is independent of its frequency.  Spin angular momentum is essentially circular polarization for a photon.  Angular momentum is ±h/2π.   It is the helical momentum of the photon along its flight path.   In order to pin down the momentum we also need to know its angular momentum, but it is a constant that is either spinning one way or the other, no half spins no quarter spins just +h/2π or -h/2π.   

The key for this discussion is that we know the momentum for any photon if we know its wavelength.   p = h/λ and the direction of its spin ±h/2π.   According to Heisenberg’s principle we cannot know the location of the photon if we know its momentum.  Since we do know its momentum we are at a loss to try to pin the location to a particular spot such as through a narrow slot or pinhole.  

Whenever we try to fit a photon through a slot, we are trying to pin down the location as it goes through the slot.  The narrower we make the slot the closer we are trying to pin it down.   Nature resists by causing havoc with our measurements – fuzzy behavior/weird effects.

Pair Production

Pair production is a possible way for nature to slip one by us – putting a photon through both slots simultaneously, thus confounding our measurements completely.   When a photon hits an obstacle such as the thin barrier between the two slots, it melds through the slots around the barrier as in my earlier posts or possibly down-converts to a lower frequency pair of photons (or up-converts to a higher frequency) through pair production (conserving energy by the frequency change).  These pairs recombine on the far side of the barrier through an up (or down) conversion process causing an effective interference due to jiggling in the conversion process. 

Our barrier strip knocks the photon silly, and it responds by splitting up, zipping through the two slits independently, then recombining in a way that looks like interference.

Virtual Photons 

Another type of pair production would be through creation of a virtual photon – a pair with one real and one virtual as also mentioned in an earlier post.   The scenario is the same – barrier knocks photon silly, virtual photon forms, passes through other side, then effectively recombines while interfering with the “real” one.   The original and virtual photons could actually be down converted or up converted photon pairs that recombine by up or down conversion causing interference-like behavior.

In either case, blocking one slit or the other would prevent melding and also prevent pair production as well as the formation of virtual photons.

Pair production through down/up conversion and/or virtual pairs would fit better with particles with mass acting like waves that cause interference when passed through slits.  Even bucky balls and cats could potentially form virtual pairs if moving close to the speed of light.   Well, again, maybe not cats.

 Oldtimer

Quantum Weirdness in Entangled Particles

Entangled Particles

Selecting which atom we use with careful attention to its excitation states can create entangled particles.  Some atoms emit two photons at a time or very closely together, one in one direction, the other in the opposite direction.  These photons also have a property that one spins or is polarized in one direction and the other always spins or is polarized at right angles to the first.  They come in pairs such that if we conduct an experiment on one to determine its orientation, the other’s orientation becomes known at once.   They are “entangled”.

Link to image EPR 

Figure 10 – Entangled Particles   

All of this was involved in a famous dispute between Einstein and Bohr where Einstein devised a series of thought experiments to prove quantum measurement theory defective and Bohr devised answers. 

The weirdness, if you want to call it that, is the premise that the act of measurement of one actually defines both of them and so one might be thousands of miles away when you measure the first and the other instantly is converted, regardless of the distance between them, to the complement of the first.   Action-at-a-distance that occurs faster than the speed of light?

Some would argue (me for instance) that this is more of a hat trick, not unlike where a machine randomly puts a quarter under one hat or the other, and always a nickel under a second one.  You don’t know in advance which contains which.  Does the discovery that one hat has a quarter actually change the other into a nickel or was it always that way?  Some would say that since it is impossible to know what is under each hat, the discovery of the quarter was determined by the act of measuring (lifting the hat) and the other coin only became a nickel at that instant.   Is this action at a distance? 

It is easy to say that the measurement of the first particle only uncovers the true nature of the first particle and the deduction of the nature of the second particle is not a case of weirdness at all.   They were that way at the start.

However, this is a hotly debated subject and many consider this a real effect and a real problem.  That is, they consider the particles (which are called Einstein‑‑ Podolsky‑Rosen (EPR) pairs) to have a happy-go-lucky existence in which the properties are undetermined until measured.   Measure the polarization of one – and the second instantly takes the other polarization.

A useful feature of entangled particles is the notion that you could encrypt data using these particles such that if anyone attempted to intercept and read them somewhere in their path, the act of reading would destroy the message.

So there you have it – Weird behavior at a distance, maybe across the universe.

Next:  Some Random Thoughts About Relativity

Quantum Weirdness for Tilted Glass

  Photons That Hit Tilted Glass

Individual photons directed at tilted glass have an option of being reflected or going through.  They can’t do both because they can’t be divided, or so we are told.  Yet some experiments seem to imply that they sometimes take both paths unless a detector is in place. 

Tilted GlassTilted glass acts like a sort of beam splitter.  It either goes through or bounces off  (or sometimes absorbed). 

QED can easily compute the probability dependent on the angle.  Some go through and some reflect and the angle makes the difference.  You can adjust the angle to get a 50-50 chance of reflect or go through.   

If you use other beam splitters to put the two beams back together you can get an interference pattern, not unlike the one depicted in the double slit experiment.   The beam goes both ways, but one path is longer and so when they come back together, they interfere with each other.

However, if you turn the light down so only one photon at a time goes through you still see the same effect, implying the photons go both ways.   If you leave the single-photon-at-a-time beam on long enough and have a good film in an exceptionally dark room, the outcome will be a well defined interference pattern. 

How can single photons being emitted minutes apart interfere with each other?   How can a photon that can only go one way or the other interfere with itself?   QED cannot explain this quantum weirdness for single photons.  It can predict the pattern but cannot explain it.  Every indication is that when no detectors are present, the individual photons somehow split.

There are some very sophisticated delayed choice experiments involving beam splitters.  There are super fast detectors that can be switched into the photon beam after it goes through the splitter. In other words, spit a photon at the splitter, calculate when it reaches it (about 1 nanosecond per foot of travel) and then switch the detector into the path behind the splitter.

The idea is to try to trick the photon into “thinking” there is no detector so it is ok to split, then turning on the detector at the last moment and try to catch the photon doing something it is not supposed to do, breaking laws along the way.  If it arrived at a detector in the reflected path and was also seen by the detector behind the splitter, some law has been broken and the mystery solved – figure out a new law. You do this randomly. If the photon goes both ways, it can be caught by the detectors.   It never does.

The physics says that if you try to make the measurement, it will disturb the experiment. And so every test seems to verify that fact. Whenever a detector is present there is no interference pattern. Whenever the detector is absent, the pattern reappears.

There is an argument that the photon must go through the glass whole since the photons transmitted through the glass are actually retransmissions within the glass, not the same photon that impacts it.  That argument then says that the other path has to either have had no photon or a whole one also (creation of energy not allowed).   It also says that the photon must retain a whole packet of energy.   Yet single photons seem to interfere with each other.  QED cannot explain why.   I hope to do so.

Next:  Entangled Particles

Polarized Light Weirdness

  Polarized Light Weirdness

Polarized CrystalsThe same weirdness problem arises when we pass light through polarized devices as in the figure at the left.  The devices are calcite crystals in which the light is split into two parts, a horizontal (H) and a vertical (V) channel.  If we try to send individual photons through, they go through only one channel or the other, never through both, and those that come out of the H channel are always horizontally polarized, those that come out of the V channel are always vertically polarized as we might expect.  

It is possible to orient photons to other angles at the input.  One such arrangement is to adjust them polarized so that they are tilted 45 degrees right or left as illustrated in the same figure.   If we orient the input to 45 degrees, tilted right, we get half of the photons coming out the H channel and half out of the V channel, one at a time, but these are always horizontal and vertical polarized, no longer polarized at 45 degrees right.  

Reversed Crystal setupNow comes the weird part.  See the figure at the left.  If we put a second calcite crystal in line with the first one, but reversed so that the H channel output of the first goes into the H channel of the second and the V channel output of the first goes into the V channel of the second, we expect the output to consist of one photon at a time (and it is), but since the first crystal only outputs horizontal or vertical polarized photons we expect only horizontal or vertical polarized photons out of the second crystal.  

 Quantum Weirdness at work.

However, if we test the polarization of the output, we find that the photons coming out are oriented to 45 degrees right, exactly like the input.  Individual photons go in at 45 degrees right at the input, are still individual photons but horizontal or vertical oriented in the middle, but come out oriented 45 degrees right again at the output!  Somehow the two channels combine as if the individual photons go through both channels at the same time, despite rigorous testing that detects only one at a time.  Quantum Weirdness at work. 

The polarization problem, like the double slit problem, is often called a quantum measurement problem.  An often-quoted theory is that the photon does go both ways, but any attempt to detect/measure one of the paths disturbs the photon such that the measurement results in a change in the path of the photon.

My theory reafferms the idea that it does go both ways, but in a manner you would not expect.  We will get to that later.  Next I want to mention  Quantum Weirdness in Glass

Introduction to Quantum Weirdness

Quantum Weirdness 

Quantum Electrodynamics (QED) theory has developed to be the theory that defines almost all of the understanding of our physical universe.    It is the most successful theory of our time to describe the way microscopic, and at least to some extent, macroscopic things work.

Yet there is experimental evidence that all is not right.  Some weird things happen at the photon and atomic level that have yet to be explained.  QED gives the right answers, but does not clear up the strange behavior – some things are simply left hanging on the marvelous words “Quantum Weirdness”.   A few examples of quantum weirdness include the reflection of light from the surface of thick glass by single photons, dependent on the thickness of the glass; the apparent interference of single photons with themselves through two paths in double slit experiments; the reconstruction of a polarized photon in inverted calcite crystals, among others.

This paper introduces some ideas that may explain some of the weirdness.

I want to introduce the subject in a way that appeals to the non-scientist public, but also introduce some ideas about what is going on, ideas that may explain some of the weirdness and include a few thoughts about the speed of light and relativity that should stimulate thought on the subject.  Hopefully a few physicists will look in and not be too annoyed with my thoughts.   This will not be a mathematical treatment other than some basic equations from Einstein that most of us are already familiar with.   The later chapters will be more theoretical, but easily understood if I do it justice.   I will include some experimental diagrams and discussion of results.

First let’s review a few facts about one of our most commonly known quantum objects.   Light is a quantum object.  When you see the light from a light bulb it is likely you do not realize that the light you see comes in very tiny packets called photons that are arriving in really huge numbers.   Your nearby 100 watt bulb emits around 250 billion billion photons a second!  A photon can travel unchanged completely across our universe from some distant star or across a few feet from a nearby lamp.   Once emitted, it continues until it hits something that stops it.  It lives a go-splat existence.

When we read this page, we are intercepting some of the billions of photons of light bouncing off the page, those that come off at just the right angle to illuminate rods in the back of our eyes.    Physicists tell us that photons are tiny bits of massless energy that travel at the speed of light.   These bits are indivisible; you can’t split them up into smaller pieces.   In transit they are invisible.

Here are some tidbits of information you will need to know later:

Every photon of a particular frequency has the same intensity (energy).     

If you make the light brighter, you are just making more photons, not changing the energy of the individual photons.  If you make the light very dim, only a few photons are being emitted.  Reduce intensity enough and you can adjust the source to emit one photon at a time, even minutes or hours apart.

The energy and frequency of blue light is higher than that of red light

The energy of each photon is dependent on the frequency of the light but not dependent on the intensity.   A brighter (more intense) light of a particular color is the result of more photons per second, not higher energy in the photons. 

Maybe I can illustrate some of the above this way.  Bird shot is a very small pellet load for a shotgun.  It is small and used for hunting birds.    If you drop a single bird shot pellet from a porch onto a pie pan below, it would make a small sound when it hit.  It would have a certain energy when it hit and every pellet of that size dropped from the same height would have the same energy.  The sound each makes at impact would have the same intensity.  If you dropped a hundred at a time, the energy of each pellet would be the same, but the combined impact and sound intensity would be much higher and louder.  Similarly all red photons hit your eyes with the same energy.  If you step up the current to the light source, the number that hits your eyes goes up accordingly, so you see a higher brightness as the number hitting the rods in your eye each moment is increased.  

Changing from a red photon (light) to a blue one is somewhat like changing from bird shot to buck shot, a much larger pellet.  The blue photon hits harder, as does the buck shot, no matter where it comes from.   

Regardless of color, if you make a light very dim, you can get it down to one photon at a time, sort of like dropping one pellet at a time.   Getting a photon down to one at a time is a bit tricky, much harder than getting a single pellet to pour out of a barrel of pellets, but not impossible.

Photons, unlike shotgun pellets have no mass, but they still have energy.  This energy is transmitted from whatever emitted it to whatever it finally hits.   Thus the photon is an energy carrier in a hurry, always moving at the speed of light.

Next I’ll tell you a little about an easily duplicated experiment using double slits that can be used to prove that light is a wave but also can be used to prove that light is a particle.  It is a good illustration of quantum weirdness.