Flatland, Particle-Wave Duality and Super-Luminal Effects

The animated graphic above shows our 3-D Space plus Time view of the physical world and contrasts it with the very different view of "Flatlanders" who are restricted to 2-D Space plus Time.

This posting explores the possibility that insights from consideration of Flatland may be extended to higher dimensionality and shed light on Particle-Wave Duality and Super-Luminal (faster than light) effects such as those that may be associated with the EPR (Einstein-Podolsky-Rosen) experiments.

This is the second of a series. The first Flatland, Dimensionality, and QM Hidden Variables utilized "Flatland" analogies to explore what Feynman called "quantum weirdness" and Einstein called "spooky action at a distance". In particular, could it be that what we perceive as conflicts between ""particles" and "waves" are due to the limits of our perception to 3-D Space plus Time? If we imagine 4-D Space or higher dimensionality, could that help us better understand the "weirdness" and "spooky" nature of  Quantum Mechanics (QM)? Could we resolve questions about the Nature of the Universe such as deterministic vs probabilistic, discrete vs continuous, brain vs mind, and so on?

ANIMATED GRAPHIC

(a) and (b) in the graphic visualize "Particle-Wave Duality" based on the famous Double-Slit Experiment. In that experiment, sub-atomic objects, such as electrons or photons, act like either particles or waves, depending upon whether or not they are made to pass through a SINGLE or DOUBLE slit. If there is a SINGLE slit, they act like particles. If there is a DOUBLE slit, they act like waves.

(c) in the graphic visualizes "Super-luminal" (faster than the speed of light) effects such as those that may be associated with the Einstein-Podolsky-Rosen experiment. In the EPR experiments, the actions of an experimenter "A" appear to instantly affect the results measured by distant experimenter "B".

In the animation, we start with a 3-D object that is a bent red plastic tube:

(a) The bent tube is dropped into Flatland and lands on a Flatland shape that has a SINGLE-width slit in it. As the slit is too narrow for the bent tube to pass thru in that Horizontal orientation, the bent tube bounces and rotates 90° to a Vertical position and penetrates Flatland, leaving only a portion of a nearly vertical part of the bent tube in Flatland. The Flatlanders explore that part (the  tiny yellow circle) and call it a "PARTICLE". 

(b) The bent tube is dropped into Flatland and lands on a Flatland shape that has a DOUBLE-width slit in it. As the slit is  wide enough for the bent tube to pass thru in that Horizontal orientation, the bent tube lands there and  lies flat in a Horizontal position. The Flatlanders explore that part (the yellow wave) and call it a "WAVE".

Note that a 90° rotation in 3-D Space changes a "PARTICLE-like" object into a "WAVE-like" object for Flatlanders, and vice-versa.

Recall that in the first posting of this series Flatland, Dimensionality, and QM Hidden Variables a 90° rotation in 3-D Space changed the appearance of a Cola can from a CIRCLE to a RECTANGLE as viewed by Flatlanders.

A 90° rotation in  higher-dimension world appears to change the basic form of an object in a lower-dimension world. A PARTICLE appears to be a WAVE, a CIRCLE appears to be a RECTANGLE, and vice-versa.

Although not illustrated in the graphic, it turns out that a 180°rotation in a higher-dimensional world changes an object into its MIRROR-image as viewed in a lower-dimensional world.

(c) A human hand penetrates Flatland and is viewed by Flatlanders as five disconnected small yellow circles (or "PARTICLES"). A Flatland triangle-shape happens to touch the pinky of the human hand and the hand reacts by thrusting out its thumb, which happens to push a Flatland square-shape.

The Flatlanders are amazed that touching one PARTICLE (the pinky) causes a totally disconnected and distant PARTICLE (the thumb) to react "instantly" with no apparent means of communication. If we assume the highest speed of communication within Flatland is slower than the 3-D speed of light, to the Flatlanders this reaction seems to be SUPER-luminal (faster than light).


APPLYING FLATLANDER INSIGHT TO QUANTUM MECHANICS In my recent Dialog with Howard Pattee, we speculated on whether the Universe is actually probabilistic, which is the mainstream scientific view, or deterministic, which is definitely the minority view. I speculated that extending the Flatland scenario beyond 2-D and 3-D Space to 4-D and higher-dimensionality, might support an alternative QM interpretation such as that of David Bohm.


In a future posting, I plan to create an animated graphic that visualizes a 4-D Space world in which what we perceive as a PARTICLE-WAVE duality is actually a single object (Bohm's "pilot wave") as perceived by denizens of 4-D world.

Ira Glickstein 

Flatland, Dimensionality, and QM Hidden Variables

The animated graphic above shows our 3-D Space plus Time view of the physical world and contrasts it with the very different view of "Flatlanders" who are restricted to 2-D Space plus Time. This posting explores the possibility that insights from consideration of Flatland may be extended to higher dimensionality and shed light on what Feynman called "quantum weirdness" and Einstein called "spooky action at a distance".

In particular, could it be that what we perceive as conflicts between "particles" and "waves" are due to the limits of our perception to 3-D Space plus Time? If we imagine 4-D Space or higher dimensionality, could that help us better understand the "weirdness" and "spooky" nature of Quantum Mechanics (QM)? Could we resolve questions about the Nature of the Universe such as deterministic vs probabilistic, discrete vs continuous, brain vs mind, and so on?

ANIMATED GRAPHIC

Things we recognize as the same appear different to Flatlanders: 3-D Space residents recognize a can of cola as being the exact same object (a cylindrical solid) regardless of whether it is upright or on its side. However, when a 3-D can of cola intrudes upon the 2-D Space of Flatlanders, they see it as several different kinds of figures depending upon its orientation.

At the left edge of the graphic, the can is upright, and, to the Flatlanders, it appears as a CIRCLE of CONSTANT DIAMETER. When an identical can of cola is on its side, the Flatlanders first see a LINE as the lower part of the can intrudes upon their 2-D Space. Then, as the can is lowered, the LINE transforms into a NARROW RECTANGLE. As the can is lowered further, the RECTANGLE WIDENS. So, what is it? A CIRCLE? A LINE? A VARIABLE WIDTH RECTANGLE?

To we 3-D Space persons, the can is one, and only one, 3-D object, a CYLINDRICAL SOLID. To the Flatlanders, it is several different 1-D and 2-D objects.

Things we recognize as different appear the same to Flatlanders: Continuing to view the animated graphic, we see that a ball appears to us to be a 3-D SPHERE. To the Flatlanders, it is first a 0-D POINT, then a 2-D CIRCLE OF VARIABLE DIAMETER.

Furthermore, when the 3-D SPHERE intrudes such that the diameter of the Flatlander's 2-D CIRCLE is the same as the diameter of the upright can, they cannot distinguish between the can and the ball!

Things we recognize as a single object appear as multiple objects to Flatlanders: Continuing to view the graphic, when a moving 3-D hand intrudes into the 2-D Space, the Flatlanders see a wide variety of 0-D, 1-D, and 2-D objects. At first, when only three fingertips intrude, they see three POINTS. Then, as the fingers penetrate further, they see four small CIRCLES plus a POINT representing the thumb. Further penetration of the hand, beyond the wrist, yields an OVAL as viewed by Flatlanders.

APPLYING FLATLANDER INSIGHT TO QUANTUM MECHANICS

In my recent Dialog with Howard Pattee, we speculated on whether the Universe is actually probabilistic, which is the mainstream scientific view, or deterministic, which is definitely the minority view. I speculated that extending the Flatland scenario beyond 2-D and 3-D Space to 4-D and higher-dimensionality, might support an alternative QM interpretation such as that of David Bohm. This posting, which advocates what may be termed "Superdeterminism", is my attempt to support this alternate view.

Classical Physics vs Quantum Physics

Classical physicists accepted the view that the Universe is deterministic and this was the view of  Spinoza, Einstein, Bohm, (and it is also what I -Ira- would like to believe :^).

Quantum physicists generally accept the "Copenhagen Interpretation" of QM which is that the Universe is probabilistic. In our discussion, Howard supported the view that the Universe is probabilistic. While I accept the general consensus that the probabilistic interpretation of QM has stood the test of time and correctly predicted and explained the results of all experiments conducted to date, I nevertheless take the other view.

The Double Slit Experiment - Particles vs Waves

The Double Slit Experiment demonstrates that photons (or electrons) behave like particles when only one slit is open, but like waves when there are two slits. This raises the question: Is matter in general, or sub-atomic matter in particular, really waves or really particles, or something else?

Perhaps residents of a 4-D Space world would see matter as a single type of object and understand why we 3-D Space world residents sometimes see a wave and sometimes a particle? (The can of cola in the graphic above, which we in the 3-D Space world recognize as a single object no matter its orientation, is observed by Flatlanders either a circle with a continuous edge -or- as a line or rectangle with discrete edges.)

The EPR Paradox - Locality vs Realism

Einstein believed that the Universe exhibited both "Locality" (the influence of a distant event cannot be transmitted faster than the speed of light) and "Realism" (the value of a measurement exists before the measurement is made). Experiments conducted in the 1980's appear to prove him wrong and indicate that we must choose between "Locality" and "Realism" - we cannot have both!

I believe Einstein, if he had to choose, would pick "Realism" over "Locality", meaning that a distant event could exert an influence faster than the speed of light. However, perhaps residents of a 4-D Space world would see that the 3-D Space world was curled up within the 4-D Space world such that objects that appear distant in 3-D Space are actually much closer in 4-D Space. In the graphic above, the fingers of the hand appear to Flatlanders as unconnected points or circles, but we, in the 3-D Space world see that they are all parts of a single object.

A cornerstone of the mainstream scientific interpretation of QM is Heisenberg's uncertainty principle (1927), which is that it is impossible to exactly measure both the position and momentum of a sub-atomic particle.

In 1935, Einstein, Podolsky, and Rosen published a paper that proposed a thought experiment ("EPR") designed to show that Heisenberg Uncertainty was not correct and that QM, as understood and interpreted at the time, was not complete. The EPR idea was to have an experimenter produce two electrons (or photons) that were "entangled" such that they would fly apart at the same velocity in opposite directions and with opposite momentum.

An experimenter at location A would measure the exact time of arrival (and thus velocity) of particle A and a second experimenter at location B (the exact distance in the opposite direction) would measure the momentum of particle B. Since the particles have the same velocity and opposite momenta, this experiment would yield the exact position and momentum of the particles.

According to Wikipedia:

In his groundbreaking 1964 paper, "On the Einstein Podolsky Rosen paradox", physicist John Stewart Bell presented an analogy (based on spin measurements on pairs of entangled electrons) to EPR's hypothetical paradox. Using their reasoning, he said, a choice of measurement setting here should not affect the outcome of a measurement there (and vice versa). After providing a mathematical formulation of locality and realism based on this, he showed specific cases where this would be inconsistent with the predictions of QM.

In 1982, Alain Aspect performed an experiment that did not turn out well for Einstein's expectations. Aspect (and others) experimentally showed that QM was correct and that Einstein's expectations for both "locality" and "realism" could not be supported. In short, you either had to choose "locality" or "realism", but not both!

Einstein had passed away by the time the EPR experiments overturned his expectations. I believe, given the choice, he would insist upon "realism" and abandon "locality". In other words, he would accept that the action of an experimenter "Alice" at point A could instantaneously affect the results obtained by "Bob" at distant point B! (Please note that the EPR experiments did NOT show that INFORMATION could be transmitted from point A to point B faster than the speed of light, only that the actions of the distant experimenter could influence the results obtained locally.)

"Quantum Non-Locality":  The mainstream view of QM is founded on what Feynman called "quantum weirdness" and Einstein termed "spooky action at a distance". The technical term is "quantum non-locality" which means that microscopic measurements may reveal that sub-atomic "particles" that happen to be far apart in Space may never-the-less be "entangled" such that measurement of the state of one "particle" superluminally (faster than the speed of  light) affects the state of the other, no matter how far away it might be!

According to the mainstream view, the action of an experimenter "Alice" at point A could instantaneously affect the results obtained by "Bob" at distant point B! Despite the apparent "weirdness", Feynman accepts the mainstream view. However, Einstein clung to what is now termed "local realism", which is the view that the Universe has both "Locality" and "Realism".

"Locality" means that an object is DIRECTLY influenced ONLY by its immediate surroundings. Thus, the influence of a distant event will be delayed by a length of Time that is at least the distance multiplied by the speed of light. "Locality" is NOT a property of the mainstream interpretation of QM.

"Realism" means that all objects have a VALUE for any possible measurement and that this value EXISTS PRIOR to the measurement. According to the Schrödinger's cat thought experiment, the Copenhagen Interpretation of QM seems to entail that a cat in a sealed box may be both dead and alive until an experimenter opens the box and looks into it! According to that view, the "collapse of the wave function" requires the intervention of a CONSCIOUSNESS. In other words, the Moon may not exist if no one is currently observing it. "Realism" is NOT a property of the mainstream interpretation of QM.

Superdeterminism

According to Wikipedia:

John Bell discussed "Superdeterminism" in a BBC interview.  

There is a way to escape the inference of superluminal speeds and spooky action at a distance. But it involves absolute determinism in the universe, the complete absence of free will. Suppose the world is super-deterministic, with not just inanimate nature running on behind-the-scenes clockwork, but with our behavior, including our belief that we are free to choose to do one experiment rather than another, absolutely predetermined, including the "decision" by the experimenter to carry out one set of measurements rather than another, the difficulty disappears.  

There is no need for a faster than light signal to tell particle A what measurement has been carried out on particle B, because the universe, including particle A, already "knows" what that measurement, and its outcome, will be.  

Although he [Bell]  acknowledged the loophole, he also argued that it was implausible. Even if the measurements performed are chosen by deterministic random number generators, the choices can be assumed to be "effectively free for the purpose at hand," because the machine's choice is altered by a large number of very small effects. It is unlikely for the hidden variable to be sensitive to all of the same small influences that the random number generator was. 

Superdeterminism has also been criticized because of perceived implications regarding the validity of science itself. For example, Anton Zeilinger has commented: "[W]e always implicitly assume the freedom of the experimentalist... This fundamental assumption is essential to doing science. If this were not true, then, I suggest, it would make no sense at all to ask nature questions in an experiment, since then nature could determine what our questions are, and that could guide our questions such that we arrive at a false picture of nature."

As I read the above objections to Superdeterminism (or as I usually call it "Absolute or Strict Causality") it seems to me that Bell and Zeilinger are wrong to assume that the experimenter is "effectively free" or "we always assume the freedom of the experimentalist". As Bell acknowledges in the quote above, it is well known that what we commonly call a "random" number generator running in a digital computer is actually bit-for-bit DETERMINISTIC. That is, if we repeatedly start the "random" number generator with a given key number, the computer will repeat the exact same sequence of supposedly "random" numbers AND that sequence will pass statistical tests of "randomness"!

We all agree that a digital computer is a discrete, finite, deterministic machine. According to my view, so is the Universe. Yes, the Universe is much, much, much more complex, but it, and all biological organisms within the Universe, including humans, are machines! 


[UPDATE 29 Dec 2013] I have posted a follow-up to this Topic, with a new animated graphic, that extends the Flatland 2-D Space vs our 3-D Space dichotomy into higher dimensionality to further explore implications for our understanding of QM, see Flatland, Particle-Wave Duality and Super-Luminal Effects.

Ira Glickstein

Dialog with Howard Pattee - Part 5 - Flatland and Higher Dimensions

From Gödel, Escher, Bach: An Eternal Golden Braid 
by Douglas Hofstadter.
A 3D block projects three different
letters when illuminated along the three axes.

Howard Pattee's 2008 paper Physical and functional conditions for symbols, codes, and languages is available for download here. I recently re-read it in detail and engaged in what was for me an interesting and rewarding email dialog with Howard.

This is the fifth in a planned multi-part posting that includes portions of our email dialog.

Click for Part 1 - His 2008 Paper

Click for Part 2 - Determinism vs Probability

Click for Part 3 - QM and Chess Analogy

Click for Part 4 - Property Dualism

INTRODUCTION

The following excerpts are from emails from Ira Glickstein to Howard Pattee (Oct 19 11:06 PM, Oct 21 11:56, Oct 23 10:21 PM, Oct 22 12:34 AM) and his replies (Oct 21 3:01 PM, Oct 23 10:21 AM).


[IRA GLICKSTEIN]  Howard, THANKS for your prompt and courteous replies to my questions and critique on your 2008 paper. If I have your permission, I am considering putting a new Topic on my Blog linking to your newly posted 2008 paper and possibly including our recent email dialog. … I think a new Pattee Topic with a specific paper link will be welcomed by your many admirers. So, please let me know how you feel about this "opportunity" :^)

[HOWARD PATTEE]  Ira, You have my permission to publish my more-or-less "scholarly" email discussions with you, but notify or link me to it so I know what's being discussed. …

[IG] Thanks for permission to publish your scholarly replies to my probing response to your 2008 paper. I will certainly link it to you when I publish it …

[HP] Other thoughts. Within a few years 90% of the population will have smartphones, and I estimate that much less than 1% will have any idea of how they work, or even have the background knowledge to understand how they work.

The world is already divided into the very rich and very poor, and all the large financial institutions owned by the rich have proven to be corrupt without help from technology. Technology divides us further into a priesthood of techies (good and evil) and the Luddites. This is now a very unstable situation as we are already experiencing with the NSA/CSS leaks and all the international hacking activities (e.g., Stuxnet and who knows what else?).

Experts say our infrastructure (power, transportation, finance) is at risk. I would say that compared to this technological instability global warming is a minor risk. What do you think? Howard

[IG] Well, as you know, I am a Guest Contributor to the world's most popular climate website. I accept that the mean surface temperature of the Earth has increased since 1880, and that part of that increase is undoubtedly due to human activities such as unprecedented burning of fossil fuels increasing Atmospheric CO2 from about 270 to the current 400 ppmv. However, I am sure the official Intergovernmental Panel on Climate Change (IPCC) has over-estimated the Equilibrium Climate Sensitivity - ECS (how much the surface will warm given a doubling of CO2) by at least a factor of two, and perhaps three. That is why all IPCC warming predictions since their first in 1990 have been on the high side compared to measured temperatures.

That IPCC error explains why temperatures have stabilized over the past 17 years even as CO2 levels continue their rapid rise. Thus, most of the warming is due to Natural Cycles, not under human control. The moderate warming and moderate CO2 increase experienced so far may be net beneficial to human civilization, and, in any case, poses no real danger. (And, even if it does pose a risk, since most of it is due to Natural Cycles we humans cannot control, we really cannot stop it, so we will have to adapt, using TECHNOLOGY.)

So, I agree with you that technological instability IS a greater risk than global warming. Technological instability includes, IMHO, a genetic engineering disaster, nuclear disaster, political chaos disaster due to runaway debt triggering riots and class warfare leading to tyranny, etc. But, the only way we can continue human civilization given the inevitability of Natural Cycles of global warming (and global cooling - see the ice core record of alternating ice ages and warm ages about every 100,000 years) IS adaptation using technology.

Thus, we have to accept the risk of technological instability as the price of survival. Ira

[IG] Howard, you earlier brought up property dualism, where a single Material Substance can have both "physical" and "mental" properties as described in the linked Wikipedia entry. I think of these properties as being different aspects or views of a single material thing, such as continuous vs discrete, finite vs infinite, particles vs waves, energy vs matter, mind vs brain, etc. Thinking about it, I came up with the following analogy to Flatland, …

[HP] Ira: … Your idea of knowledge as projection from higher dimensions is essential. It also shows us that there is no one right answer. Complementary views are necessary, even when they appear contradictory …

[IG] … a 3D cylinder (like a can of soda) intrudes upon the Flatlander's 2D plane of existence. If it approaches slowly and side first, they will initially sense a line segment. Then, as it penetrates further they will sense a long, narrow rectangle. Further penetration will result in a somewhat wider rectangle. On the other hand, if the can approaches end first, they will sense a circle of constant diameter.

[HP] See jacket of Hofstadter's Godel_Escher_Bach [NOTE: Illustrated above] where one block's projections cast three different letters. … I think the earliest example of projection is the allegory of Plato's_Cave. …

[IG] So, what is it? A line, a rectangle, or a circle? …

[HP] Projections from higher dimensions is basic in quantum mechanics where we model the "states of reality" by an infinite dimensional, complex, normed vector space (Hilbert space). A measurement is a projection of this space rotated by the choice of the basis vectors. Nobody agrees on what the "states of reality" means. Read a little of Schlosshauer's Elegance_and_Enigma:   The Quantum Interviews (The Frontiers Collection) Maximilian Schlosshauer ...

[IG] Thinking about aspect dualism further, if the can approaches at an angle, it will appear to the Flatlanders to be in any of a variety of shapes. It could look like a trapezoid, an ellipse, a triangle with one curved side, etc. However, when in circle mode, a cylinder will always have a constant diameter.

If a sphere (ball) approaches their plane of existence, they will initially sense a point, then a small circle, increasing in diameter. However, the sphere will never appear to be an ellipse nor anything containing a sharp angle. Flatlanders distinguish a cylinder from a sphere by it having a variable diameter and by never having a sharp angle.

So, if we humans are stuck (evolved) in a world where sensing 3D plus time is all that is needed to survive and replicate, we will forever be limited in how we sense 4D and higher material objects that intrude upon our 3D solid of existence. Sometimes material objects will appear to be continuous (like the edge if a can when it is in its circle mode in Flatland) and sometimes discrete (like the edge of a can when it is in it's rectangle mode in Flatland. Sometimes the intrusions will seem to us to be particles, sometimes waves, and so on.

But what about material vs "information" (otherwise known as brain vs "mind")? Well, I would say that "information" is an abstraction that may never be absolutely true, and will seldom be absolutely false. The Flatlanders may all agree that an intrusive object of type “C” has multiple modes (line, rectangle, trapezoid, circle, ellipse, and so on) and that it never has the ability to change diameter, and that an intrusive object of type “B” may change diameter but never have sharp angles, and thus correctly call them by different names (which we -but not them- understand to be a can and a ball), but that "information" is a mere abstraction that does not capture the material truth. …

[HP] Many physicists interpret the mathematics of QM as an expression of the statistical information that is just sufficient to give the best predictions. The wave function or a vector in Hilbert space is just a strange kind of potential distribution from which we calculate probabilities of measured events (N.B. Born's_Rule and Gleason's _Theorem appear to rule out determinism). When we get new information from a measurement, the probability distribution is immediately changed ("collapse of the wave function").

Born argued that this is also the case in classical mechanics because empirically it is not deterministic. I agree with Born that all dynamic models should be understood as change of probability distributions in time. …

[IG] Thus we (scientists) gather "information" and come up with ways to measure and distinguish different hyper-dimensional objects that intrude upon our solid of existence, and notice and document and quantify the correspondence between "electrons" or "photons" when in their "particle" mode or in their "wave" mode, but we will never really, really apprehend what these hyper-dimensional objects "really" are!

We know how to convert "matter" to "energy" (nuclear energy) but we will never know what they "really" are.

Like the child (or senior citizen) who knows how to skillfully operate his or her HDTV set and DVR and PC and iPad, but has no real knowledge of radio frequency waves or computers or software, we will forever possess incomplete "information" that is a rough abstraction of real, real, "reality"!

[HP] This should be called Ira's modern view of Plato's Cave-- the Allegory of the iPad. Howard

Ira Glickstein

What is Time? Alan Alda's 2013 "Flame Challenge"

Time - the fourth dimension (2013 Flame Challenge) from Ira Glickstein on Vimeo.

My entry for Alan Alda's 2013 Flame Challenge was submitted last week. It is in the form of a short video  answering the deceptively simple question "What is Time?" (click above to view the video).

Alan Alda is on a mission to help youngsters become interested in science. In conjuction with the Center for Communicating Science at SUNY Stony Brook, he started the Flame Challenge in 2012 with the question "What is Flame?" They received some 800 entries.

I expect they will get even more this year with the question "What is Time?"

ABOUT MY ENTRY

I think I've come up with a unique way of viewing "Time - the fourth dimension".  Due to a strict limit on the length of the video, and the fact that it is aimed at 11-year old students, I have had to greatly simplify the material. This Blog posting includes additional material that will be useful to adult readers and science teachers who wish to know more about my way of viewing Time.

There are three big ideas here:

1. TIME is NOT a clock (any more than Space is a ruler or Heat is a thermometer), nor is it rotation of the Earth or motion or the order of events, etc.  
2. TIME is the fourth dimension, plain and simple. It appears different to us because the whole Universe is speeding along the Time axis at the speed of light.  
3. TIME slows down when we move in Space because nothing can move faster than the speed of light, so any motion in Space must take away from the speed in Time such that the vector sum of the Space and Time velocities exactly equals the speed of light.

WHAT TIME IS NOT

Time is not the tick, tick, tock of a click, click, clock, any more than Space is a ruler or Heat is  a thermometer!

 

Nor is Time the rotation of the Earth on its axis that gives us day and night divided into 24 hours. Nor is it the movement of the tilted Earth in orbit around the Sun that gives us the seasons, nor any other kind of motion. Nor is it the spontaneous decay of certain atoms that give radioactive materials a half-life. Nor is it simply the ordering of events.

WHAT TIME IS

Time, plain and simple, is the fourth dimension, very much like the first three dimensions of Space.

 

The Time dimension appears different to us because you and I and the whole Universe are hurtling along it at very nearly the speed of light as a consequence of the “Big Bang” expansion some 13.7 billion years ago, in which our Universe, along with the dimensions of Space and Time, originated.

Since Time itself originated with the "Big Bang" it may not be meaningful to even ask the question "What happened before the Big Bang?" In any case, we may never know what caused it.

 

The Universe originated as an incredibly energetic and dense point of Energy/Matter that suddenly expanded. During the initial moments of the expansion, it is not clear if there was anything like the sub-atomic and atomic particles of Matter or the radiation of Energy with which we are familiar today. However, when Matter and Energy, as we know it, formed, all particles with mass were expelled along the Time axis, or at very tiny angles with respect to that axis. You and I, along with everyone and everything else, are still moving along or near that dimension at very close to the speed of light, c, which is as fast as anything can go.

 

We do not notice our ultra-rapid travel along the Time dimension as motion because the whole Universe is moving along with us. Therefore, we notice only relative motion between ourselves and other people and between ourselves and other things.

 

For example, people on the equator are happily unaware that they are moving Eastward at about 1,000 miles per hour due to the rotation of the Earth on its axis. Unless you live in one of the polar regions, you are moving Eastward at hundreds of miles per hour. Even if you are on an airplane, travelling  "Westward" from New York to Chicago or Los Angeles at 500 miles per hour, your net velocity is Eastward, due to the rotation of the Earth! We are equally unaware that the whole Earth is speeding along at over 67,000 miles per hour on its orbit around the Sun!
 

WHY TIME CAN BE SLOWED A BIT
 

We live in four-dimensional SpaceTime where everything must move at the speed of light, c, either along the Time axis, along a Space axis, or in a combination of Time and Space at an angle, Θ, to the Time axis. If movement is totally aligned with the Time axis, Θ = 0 and we are said to be “at rest” in Space, and we move along the Time axis at the normal rate (c, about one foot per nanosecond).

 

If we are not "at rest" in Space, Θ > 0, and we move through SpaceTime in a combination of Space and Time such that the vector sum of our Space and Time velocities is exactly c. Since nothing can go faster than c, any movement in Space must slow down our movement in Time. This was recognized over 100 years ago by Lorentz, Minkowski, and Einstein, who use the terms "Dilation of Time" and "Contraction of Space". This is usually expressed in terms of the Lorentz factor:

where c is the velocity of light and v is the velocity of an object in Space.

As an engineer, I found that way of expressing relativistic effects of travel at significant fractions of the speed of light not to be "understandable" from my physical (and perhaps anal) point of view.

After knocking my head against the wall over an inordinate amount of Time, I finally realized that I could get an exactly equivalent Lorentz factor by considering the angle Θ, between the Time axis and the velocity vector of an object through SpaceTime.

[above image modified 12 April 2013]

It turns out that v (the velocity of the object in Space) divided by c is equal to the Sin Θ, and that 1/ϒ, the Lorenz factor, is equal to the Cos Θ.  

WHAT ARE DIMENSIONS?

 

This may sound like a simple question, and the answer is pretty simple, but, just to be sure we are all on the same page (see figure below):

 

0 - A POINT has ZERO dimensions

1 - Drag the point along the FIRST dimension ("x" of Space) and you get a LINE, that has ONE dimension.

2 - Drag the line along the SECOND dimension ("y" of Space) and you get a SQUARE (or rectangle) that has TWO dimensions.

3 - Drag the square along the THIRD dimenson ("z" of Space) and you get a CUBE (or rectangular solid) that has THREE dimensions.

4 - Drag the cube along the FOURTH dimension ("t" of Time) and you get a HYPER-CUBE (or hyper-rectangular solid) that has FOUR dimensions.



 

SUMMARY

When movement is a combination of Time and Space, and the velocity in Space is v, an object is moving through SpaceTime at an angle Θ, such that: v/c = SinΘ, and 1/ϒ (the Lorentz factor) = Cos Θ.

The figure below shows the situation for seven different values for the angle of travel through SpaceTime, from Θ = 0⁰ to Θ = 90⁰ .

Θ = 0⁰  [Sin Θ = 0.0000,  Cos Θ = 1.0000]   AT REST IN SPACE
For an object that is "at rest" in Space, Θ = 0⁰. Even when an object is not moving along the Space axis, it is moving along the Time axis. Since everything in SpaceTime must have a speed of c, an object "at rest" in Space must be moving at speed c in Time. Note that for this condition, v/c = 0 and the Lorentz factor ϒ = 1. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Even the fastest rockets and satellites developed so far go only a tiny, tiny fraction of c. Therefore, for all practical purposes, the angle, Θ, is ≈ 0⁰ (approximately equal to ZERO degrees). For example, the Earth is travelling around the Sun at a speed of 67,000 miles per hour, faster than any rocket, but that is only 0.001 % of the speed of light. At 67,000 miles per hour, v/c =  0.00001 and  Θ = 0.0000017⁰.

Θ = 15⁰ [Sin Θ = 0.2588, Cos Θ = 0.9659]    MOVING 26% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 15⁰. It moves through Space at 26% of c and through Time at 97% of c. Note that for this condition, v/c = 0.2588 and the Lorentz factor ϒ = 0.9659. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 30⁰ [Sin Θ = 0.5000, Cos Θ = 0.8660]   MOVING 50% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 30⁰. It moves through Space at 50% of c and through Time at 87% of c. Note that for this condition, v/c = 0.5000 and the Lorentz factor ϒ = 0.8660. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 45⁰ [Sin Θ = 0.7071, Cos Θ = 0.7071] MOVING 71% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ =45⁰. It moves through Space at 71% of c and through Time at 71% of c. Note that for this condition, v/c = 0.7071 and the Lorentz factor ϒ = 0.7071. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 60⁰ [Sin Θ = 0.8660, Cos Θ = 0.5000] MOVING 87% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 60⁰. It moves through Space at 87% of c and through Time at 50% of c. Note that for this condition, v/c = 0.8660 and the Lorentz factor ϒ = 0.5000. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 75⁰ [Sin Θ = 0.9659, Cos Θ = 0.2558]   MOVING 97% OF c IN SPACE
An object is moving through SpaceTime at an angle of Θ = 75⁰. It moves through Space at 97% of c and through Time at 26% of c. Note that for this condition, v/c = 0.9659 and the Lorentz factor ϒ = 0.2558. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ.

Θ = 90⁰ [Sin Θ = 1.0000, Cos Θ = 0.0000]      TIME STANDS STILL 
Light (and other forms of electro-magnetic radiation) move through SpaceTime at an angle of Θ = 90⁰. Light moves through Space at 100% of c and, therefore, since nothing can go faster than c, Time stands still. Note that for this condition, v/c = 1.0000 and the Lorentz factor ϒ = 0.0000. Note also that, for this case Sin Θ is equal to v/c and Cos Θ is equal to 1/ϒ. Anything with mass cannot achieve this speed in Space because it would take an infinite amount of energy to get it up to this speed in Space.
 
[ADDED 11 March 2013] In response to some skepticism about my contention that the whole known Universe is speeding along the Time dimension at nearly the speed of light, I did more research and found support from Brian Greene, Professor of Physics and Mathematics at Columbia U, who has been featured on the PBS Nova series. He writes:

“Special relativity declares a similar law for all motion: the combined speed of any object’s motion through space and its motion through time is always precisely equal to the speed of light” [Excerpt From: Greene, Brian. “The Fabric of the Cosmos.” Vintage Books, 2007. See http://www.pbs.org/wgbh/nova/physics/fabric-of-cosmos.htm for his PBS series.]

I have provided more detail in the first comment below.

Ira Glickstein