Category Archives: Physics

Is Space Real?

I take a walk to the store and can’t help but feel I am moving through something that is more than the atmosphere that rushes by my face as I go. The air itself is contained within the boundaries of the space through which I pass. If I were an astronaut in the vacuum of outer space, I would still have the sense that my motion was through a pre-existing, empty framework of 3-dimensions. Even if I were blind and confined to a wheelchair, I could still have the impression through muscular exertion that I was moving through space to get from my kitchen to my living room ‘over there’. But what is space as a physical thing? Of all the phenomena, forces and particles we study, each is something concrete though generally invisible: a field; a wave; a particle. But space, itself, seems to be none of these. WTF!

Spider web covered with dew drops

Way back in the early 1700s, Sir Isaac Newton proposed that space was an ineffable, eternal framework through which matter passed. It had an absolute and immutable nature. Its geometry pre-existed the matter that occupied it and was not the least bit affected by matter. A clever set of experiments in the 20th century finally demonstrated rather conclusively that there is no pre-existing Newtonian space or geometry ‘beneath’ our physical world. There is no absolute framework of coordinates within which our world is embedded. What had happened was that Albert Einstein developed a new way of thinking about space that essentially denied its existence!

Albert Einstein’s relativity revolution completely overturned our technical understanding of space and showed that the entire concept of dimensional space was something of a myth. In his famous quote he stressed that We entirely shun the vague word ‘space’ of which we must honestly acknowledge we cannot form the slightest conception. In the relativistic world we live in, space has no independent existence. “…[prior-geometry] is built on the a priori, Euclidean [space], the belief in which amounts to something like a superstition“. So what could possibly be a better way of thinking about space than the enormously compelling idea that each of us carries around in our brains, that space is some kind of stage upon which we move?

To understand what Einstein was getting at, you have to completely do away with the idea that space ‘is there’ and we move upon it or through it. Instead, relativity is all about the geometry created by the histories (worldlines) of particles as they move through time. The only real ‘thing’ is the collection of events along each particle’s history. If enough particles are involved, the histories are so numerous they seem like a continuous space. But it is the properties of the events along each history that determine the over-all geometry of the whole shebang and the property we call ‘dimension’, not the other way around.

This figure is an example where the wires (analogous to worldlines) are defining the shape and contours of a dimensional shape. There is nothing about the background (black) space that determines how they bend and curve. In fact, with a bit of mathematics you could specify everything you need to know about the surface of this shape and from the mathematics tell what the shape is, and how many dimensions are required to specify it!

Princeton University physicist Robert Dicke expressed it this way, “The collision between two particles can be used as a definition of a point in [space]…If particles were present in large numbers…collisions could be so numerous as to define an almost continuous trajectory…The empty background of space, of which ones knowledge is only subjective, imposes no dynamical conditions on matter.”

What this means is that so long as a point in space is not occupied by some physical event such as the interaction point of a photon and an electron, it has no effect on a physical process ( a worldline) and is not even observable. It is a mathematical ‘ghost’ that has no effect on matter at all. The interstitial space between the events is simply not there so far as the physical world based upon worldlines is concerned. It is not detectable even by the most sophisticated technology, or any inventions to come. It does not even supply something as basic as the ‘dimension’ for the physical world!

We should also be mindful of another comment by Einstein that “…time and space are modes by which we think and not conditions in which we live“. They are free creations of the human mind, to use one of Einstein’s own expressions. By the way, the 18th century philosopher Immanuel Kant also called the idea of ‘space’ an example of a priori knowledge that we are born with to sort out the world, but it is not necessarily a real aspect of the world outside our senses.

Like a spider web, individual and numerous events along a worldline define the worldline’s shape, yet like the spider web, this web can be thought of as embedded in a larger domain of mathematically-possible events that could represent physical events…but don’t. The distinction between these two kinds of points is what Einstein’s revolutionary idea of relativity provided physicists, and is the mainstay of all successful physical theories since the 1920s. Without it, your GPS-enabled cell phones would not work!

So what are these events? Simply put, according to Physicist Lee Smolin, they are exchanges of information, which are also the interaction points between one particle’s worldline and another particle’s world line. If you think at the atomic level, each time a particle of light interacts with (collides or is emitted by) an electron it generates an event. These events are so numerous the electron’s worldline looks like a continuous line with no gaps between the events. So the shape of one worldline, what we call its history, is a product of innumerable interactions over time with the worldlines of all other objects (photons etc) to which it can be in cause-and-effect contact.

Even though this new idea of space being a myth has gained enormous validity among physicists over the last century, and I can easily speak the language of relativity to describe it, personally, my mind has a hard time really understanding it all. I also use the mathematical theory of quantum mechanics to make phenomenally accurate predictions, but no Physicist really understands why it works, or what it really means.

Next time I want to examine how the history of a particle is more important than the concept of space in Einstein’s relativity, and how this explains the seeming rigidity of the world you perceive and operate within.

Check back here on Thursday, December 15 for the next installment!

Seeing with Mathematics

Our brain uses sensory data to sift for patterns in space and time that help us create a mental model of the world through which we can navigate and stay alive. At some point, this model of the external world becomes our basis for thinking symbolically and mathematically about it.

Mathematics is an amazingly detailed, concise and accurate way of examining the world to state the logical relationships we find there, but many physicists and mathematicians have been astonished about why this is the case. The physicist Eugene Wigner wrote an article about this in 1960 titled ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’. In fact, since the enormous successes of Sir Isaac Newton in mathematically explaining a host of physical phenomena, physicists now accept that mathematics actually serves as a microscope (or telescope!) for describing things and hidden relationships we cannot directly experience. This amazing ability for describing relationships in the world (both real and imagined!) presents us with a new problem.


Mathematics is a symbolic way of describing patterns our world, and sometimes these symbolically-defined descriptions actually look like the things we are studying. For example, the path of a football is a parabola, but the equation representing its path, y(x), is also that of a parabolic curve drawn on a piece of paper. But what happens when the mathematical description takes you to places where you cannot see or confirm the shape of the object?

Mathematics is a tool for understanding the world and symbolically stating its many logical interconnections, but the tool can sometimes be mistaken for the thing itself. Here is a very important example that comes up again and again when physicists try to ‘popularize’ science.

In the late-1940s, physicist Richard Feynman created a new kind of mathematics for making very precise calculations about how light (photons) and charged particles (such as electrons) behave. His famous ‘Feynman Diagrams’ like the one below, are very suggestive of particles moving in space, colliding, and emitting light. This diagram, with time flowing from left to right, shows a quark colliding with an anti-quark, which generates a photon that eventually produces an electron and anti-electron pair.


The problem is that this is not at all a ‘photograph’ of what is actually happening. Instead, this is a tool used for setting up the problem and cranking through the calculation. Nothing more. It is a purely symbolic representation of the actual world! You are not supposed to look at it and say that for the solid lines, ‘particles are like billiard balls moving on a table top’ or that the photon of light they exchange is a ‘wiggly wave traveling through space’. What these objects are in themselves is completely hidden behind this diagram. This is a perfect example of what philosopher Immanuel Kant was talking about back in the 1700s. He said that there is a behind-the-scenes world of noumena where the things-in-themselves (ding-an-sich) exist, but our senses and observations can never really access them directly. The Feynman diagram lets us predict with enormous precision how particles will interact across space and time, but hides completely from view what these particles actually look like.

Another example of how math lets us ‘see’ the world we cannot directly access is the answer to the simple question: What does an electron actually look like?

Since the 1800’s, electricity increasingly runs our civilization, and electricity is merely a measure of the flow of electrons through space inside a wire. Each of us thinks of electrons as tiny, invisible spheres like microscopic marbles that roll through our wires wicked fast, but this is an example of where the human brain has created a cartoon version of reality based upon our ‘common sense’ ideas about microscopic particles of matter. In both physics and mathematics, which are based upon a variety of observations of how electrons behave, it is quite clear that electrons can be thought of as both localized particles and distributed waves that carry the two qualities we call mass and charge. They emit electric fields, but if you try to stuff their properties inside a tiny sphere, that sphere would explode instantly. So it really does not behave like an ordinary kind of particle at all. Also, electrons travel through space as matter waves and so cannot be localized into discrete sphere-like particles. This is seen in the famous Double Slit experiment where electrons produce distinct wave-like interference patterns.


So the bottom line is that we have two completely independent, mathematical ways of visualizing what an electron looks like, particles and matter waves, and each can facilitate highly accurate calculations about how electrons interact, but the two images (particle and wave – localized versus distributed in space) are incompatible with each other, and so we cannot form a single, consistent impression of what an electron looks like.

Next time we will have a look at  Einstein and his ideas about relativity, which completely revolutionized our common-sense understanding of space created by the brain over millions of years of evolution.

Check back here on Tuesday, December 13 for the next installment!


There are at least two basic ways that we create associations. The first is associations in space. The second is associations in time.

Associations in space include recognizing static objects like chairs, trees, cars and people. The reason this works so well is that we live in a world filled with many different kinds of more-or-less fixed objects so that two or more people can agree they have similar attributes.

Associations in time include musical tunes and sounds, or associating one thing (cause) with another thing in the future (effect). For many of these dynamic associations like music, two people with normal hearing senses hear the same sequence of notes in time and can agree that what they heard was a portion of a familiar song, which they may independently be able to name if they have heard it before and made the appropriate associations in memory. But your exact associations related to the song will be different than mine because I associate songs with episodes in my life that you do not also share. Remember, the brain tags everything with patterns of associations unique to the individual.

The human brain is adept at pattern recognition. It can dissect its sensory information and see patterns in space and time that it can then associate with abstract categories such as a chair or a bird, and even specific sub-categories of these if it has been adequately trained (at school, or by reading a book on ornithology!). An upside-down chair seen in the remote distance is recognized as a chair no matter what its orientation in the visual field. A garbled song heard on an iPhone in a loud concert hall, or a particular conversation between two people in a noisy crowd, can also be detected as a pattern in time and recognized. The figure shows some of the brain connection pathways identified in the Human Connectome Project that help to interpret sensory data as patterns in space and time.


Patterns in space let us recognize the many different kinds of objects that fill our world. In the association cortex, once these identifications have been made, they are also sent on to the language centers where they are tagged with words that can be spoken or read. Once this step happens, two individuals can have a meaningful conversation about the world beyond their bodies that the senses can detect. Of course when both people say they have a specific category of objects called Siamese cats, they are most certainly associating that name with slightly different set of events and qualities corresponding to their cat’s personalities , fur patterns, etc..

The next step is even more interesting.

Just as the brain generalizes a collection of associations in space to define the concept of ‘cat’, it can detect patterns in time in the outside world and begin to see how one event leads to another as a rule-of-thumb or a law of nature. If I drop a stone off a tall cliff, it will fall downwards to the valley below. If the sun rises and sets today, it will do so again tomorrow. There are many such patterns of events in time that reoccur with such regularity that they form their own category-in-time much as ‘cat’ and ‘chair’ did in the space context. ‘If I visit a waterhole with lots of animals, there is a good chance that tigers or lions may also be present’. More recently, ‘If I stick my finger in an unprotected electrical outlet, I will probably be electrocuted!’. This perception of relationships is one of cause-and-effect. It has been studied by neurophysiologists, and is due to stimulation of part of the cerebellum and the right hippocampus. These brain regions are both involved with processing durations in time.

Over the centuries and millennia, the patterns in time we have been able to discern about the outside world have become so numerous  we have to write them down in books, and also put our children through longer and longer training periods to master them. This also tells us something very basic about our world.

Instead of being a random collection of events, our physical world contains a basic collection of rules that follow a ‘logical’ If A happens then B happens pattern in time. Physicists call these relationships ‘laws’ and their particular patterns in time and space can be discerned from measurements and observations made of phenomena in the world outside our brains. The brain can also work with these laws symbolically and logically, not by describing them through the usual language centers of the brain, but through a parallel set of centers that make us adept at mathematical reasoning.

In my next blog, I will discuss how mathematics and logic are intertwined and help us think symbolically about our world.

Check back here on Friday, December 9 for the next installment!

Space, Time, and Causality in the Human Brain