Deconstructing Time part 7 - Mach's Principle

Before we introduce Mach or Relativity, let's step back for a moment and recap what we've covered so far. We began with a Use Case - how do we find coordinates in space-time? This is a Use Case that could be applied to Astronomy, to GPS scenarios, to writing Science Fiction stories or movies and potentially many to other situations.  We explained how we would take an outsider's perspective using what is a essentially an IT methodology for problem solving. Then we began introducing key concepts:

1. Time is inherently connected to motion.
2. Time seems to be constructed of dynamic events.
3. Those events exist within frames of reference - those frames define the parameters for simultaneity for the events within. 
4. Motion occurs (and effects time) not just in our frames of reference but in a cascading chain of ever smaller and ever larger frames - from the subatomic to the universal scale.
5. The universe seems to be comprised of matter, energy and the space in between these elements in motion. Light is not matter but shares wave behavior with matter. Energy, such as light, can be also broken into individual particles just as matter can. 

All of this is a preface to the more complex theories and concepts we're about to explore.  We still perhaps don't understand what time is other than through the abstract event / frame paradigm that's been presented. This is a good point to ask some questions about time again:

• Is it a physical construct or a behavioral manifestation resulting from physical structures?
• Is it merely a human-perceived tool for measuring experience and the physical world around us?
• Is it an absolute, fixed constant of some sort or is it flexible? (if it is a constant is tied to other constants?)
• Lastly, if we were to view events as "time particles," can we say that time exhibits wave behavior?

The final question is interesting in that we might then be able to visualize time in a more robust sense - as spreading ripples or waves rather than straight linear progression (the metaphor Stephen Hawking used was 'Time's Arrows'). We'll come back to this later.

Ernst Mach - better know for defining the speed limit for your jet...

What is Mach's Principle? Well, it was just a handful of pages dedicated to explaining more of an observation or question rather than a theory. The principle goes something like this:

In his book The Science of Mechanics (1893), Ernst Mach put forth the idea that it did not make sense to speak of the acceleration of a mass relative to absolute space. Rather, one would do better to speak of acceleration relative to the distant stars. What this implies is that the inertia of a body here is influenced by matter far distant. A very general statement of Mach's principle is "Local physical laws are determined by the large-scale structure of the universe." 

Here's another description:

Mach’s Principle assumes, among other things, that “a particle’s inertia is due to some (unfortunately unspecified) interaction of that particle with all the other masses in the universe; the local standards of nonacceleration are determined by some average of the motions of all the masses in the universe, [and] all that matters in mechanics is the relative motion of all the masses.” Furthermore, “Mach’s Principle actually implies that not only gravity but all physics should be formulated without reference to preferred inertial frames (artificially defined motion contexts).  It advocates nothing less than the total relativity of physics.  As a result, it even implies interactions between inertia and electromagnetism.”

At this point we also need to introduce another new concept - "Action at a Distance" (sometimes referred to as 'spooky action').

In physics, action at a distance is the nonlocal interaction of objects that are separated in space. This means, potentially, that particles here on Earth could interact with other particles across the galaxy or universe without being constrained by the speed of light. This is also what drives Quantum Entanglement.

Confused yet? no worries - so is everyone else...

So, Mach's Principle effectively opened the door both to Relativity and Quantum physics. How does it relate to our discussion though? As we will see shortly, it introduced the notion of relativity to time as well as to motion. More importantly, though it begins to highlight how in a complex systems view of the universe that there are multiple competing variables that must be considered when calculating exact measures of space-time. Let's say we're talking about a Science Fiction story that needs to come up with a reasonable explanation for how teleportation works. Anytime a character is beamed up to a ship or down to planet there would need to vastly superior ability to locate space-time. With today's military grade version of GPS when can get with inches or centimeters of locating a coordinate. However that's not good enough, two inches too low might mean our character would have his feet "materialize" within solid rock. More exact measurements, down to the micron (one millionth of a meter) level would be needed to make the technology safe (and it would have to be able to compensate for scenarios where the target ground is uneven etc.).

Now it's time to define Relativity, we'll start with Special Relativity:

Einstein's theory of special relativity is fundamentally a theory of measurement. He qualified the theory as "special" because it refers only to uniform velocities (meaning to objects either at rest or moving at a constant speed). In formulating his theory, Einstein dismissed the concept of the "ether," and with it the "idea of absolute rest." Prior to the generation of Einstein's theory of special relativity, physicists had understood motion to occur against a backdrop of absolute rest (the "ether"), with this backdrop acting as a reference point for all motion. In dismissing the concept of this backdrop, Einstein called for a reconsideration of all motion. According to his theory, all motion is relative and every concept that incorporates space and time must be considered in relative terms. This means that there is no constant point of reference against which to measure motion. Measurement of motion is never absolute, but relative to a given position in space and time. 

Special Relativity is based on two key principles:

• The principle of relativity: The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference.
• The principle of the speed of light: The speed of light is the same for all observers, regardless of their motion relative to the light source. (Physicists write this speed using the symbol C.)

Contrary to popular belief, the formula E=MC squared was not published as part of Einstein's Theory of Special Relativity, but was instead published the same year (1905) in a separate paper (Einstein published 4 papers that year).  Of particular interest to Einstein in his development of Special Relativity was the ability to apply a coordinate system to space-time (this will sound familiar as we've already introduced these concepts prior but outside the discussion of Relativity):

An event is a given place at a given time. Einstein, and others, suggested that we should think of space and time as a single entity called space-time. An event is a point p in space-time. To keep track of events we label each by four numbers: p = (t,x,y,z), where t represents the time coordinate and x, y and z represent the space coordinates (assuming a Cartesian coordinate system).

Even physicists have a sense of humor 

Now let's define General Relativity...

There was a serious problem with Special Relativity however, it was artificially constrained on several levels; the most important of which is the fact that it doesn't address acceleration (it handles reference frames at rest or at constant speeds only). The other constraint was the speed of light - C. Einstein has initially sought to help unify his theory with Maxwell's theory of electromagnetism (wave theory) - Maxwell had set C as a constant (that couldn't be surpassed) and Einstein carried that through. However, there was already evidence that this wasn't entirely accurate. The force responsible for the most obvious violations of C and the force responsible in many cases for acceleration was gravity... 

It (General Relativity) states that all physical laws can be formulated so as to be valid for any observer, regardless of the observer's motion. Consequently, due to the equivalence of acceleration and gravitation, in an accelerated reference frame, observations are equivalent to those in a uniform gravitational field.

This led Einstein to redefine the concept of space itself. In contrast to the Euclidean space in which Newton’s laws apply, he proposed that space itself might be curved. The curvature of space, or better space-time, is due to massive objects in it, such as the sun, which warp space around their gravitational centre. In such a space, the motion of objects can be described in terms of geometry rather than in terms of external forces. For example, a planet orbiting the Sun can be thought of as moving along a "straight" trajectory in a curved space that is bent around the Sun.

The most important concept from our perspective in both of these two theories is time dilation (which is referred to as Gravitational time dilation in General Relativity:

Gravitational time dilation is an actual difference of elapsed time between two events as measured by observers differently situated from gravitational masses, in regions of different gravitational potential. The lower the gravitational potential (the closer the clock is to the source of gravitation), the more slowly time passes. Albert Einstein originally predicted this effect in his theory of Special Relativity and it has since been confirmed by tests of general relativity. 

Another way to think of time dilation is this, the faster you travel (now were dealing acceleration), the slower your time progresses as opposed to those you left behind at home.  For science fiction fans, one of the few movies that remain true to this otherwise plot-busting feature of modern physics is the Planet of the Apes. In that plot, astronauts leaving Earth around 1973 travel at near the speed of light for 18 months and end up back on Earth 2,000 years later. Of course, it is unlikely that we'd experience the 'damn dirty ape paradox' if we attempted such a trip.

Apes don't kill apes but they will take over if we leave for a few thousand years...

So, let's recap again what this all means:

1. Several incredible and somewhat intuitive insights, transformed modern physics starting just over a century ago with Mach's Principle. (this isn't to say that other folks like Maxwell didn't provide brilliant insights, but for our investigation Mach's insight was particularly important)
2. This led to the determination that the universe behaves certain common laws yet those laws support relative perspectives of outcomes.
3. The notion of space-time as both a coordinate system and as a curved (multi-dimensional) geometry emerged. 
4. Because of all of this (and more) it was determined that our perception of time is different based upon what reference frame we inhabit. The differences in relative temporal perception are mostly due to the nature of the motion involved (for one or many participants involved).   
5. Gravity, which was a mysterious force before now becomes part of space-time itself under General Relativity and interestingly also seems to exhibit wave behavior. 

It is often said that General Relativity is the last classical theory of Physics as it is the last major one that doesn't involve Quantum mechanics. Relativity takes us much further down the path towards explaining time - but it stops short of doing so adequately.

In our next post, we'll point out why Relativity falls short and introduce some of the foundational concepts of Quantum Mechanics.

copyright 2013, Stephen  Lahanas

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Deconstructing Time part 4 - Introducing Motion

In our last post on Time, we began providing some context to the discussion of time as well as context to where it is that Time actually occurs – e.g. within events and reference frames. For this discussion to really make sense though we need to step back and look at the big picture (actually this is something that will need to occur several times over the course of this series). At some point soon we’ll take a closer look at what Special Relativity, General Relativity and Quantum theory mean and how they relate to time, but for now we're going to spend a few moments discussing Motion. One key element that intersects all of those core theories in physics is the notion of Motion (and of course this applies to Newton's Classic theories as well). Motion and Time are inextricably linked. All of our current perception related to time, and all of our current measurement systems connected to it are “motion-based.”

What does 'Motion-based' mean? Well, let’s list a few examples below:

1. A day is one rotation of the earth.
2. An SI second (the new standard for measuring seconds) is based on the decay of a Cesium atom – that decay is expressed as regular pulsations.
3. A year is a standard orbit of Earth around the Sun.
4. A month is a standard orbit of the Moon around the Earth.
5. A light year is the time it takes a photon of light to travel from one point in space to another. 
6. We travel at roughly 70 miles per hour on the highway on our way to work (e.g. the velocity expressed equals time to cover a distance in continuous motion). 
7. Time flies when you’re having fun. I’ve added this here because there is an important perception consideration for time that appears at least to be related intensity of activities (this as we will see is also motion-related although at first it doesn't seem to be intuitively).
8. The Galactic Year is the time it takes the solar system to orbit around the center of the Milky Way (estimated to be 250 million years or so).
9. Geocentric Coordinate Time (also known as TCG) - This is defined as “a coordinate time standard intended to be used as the independent variable of time for all calculations pertaining to precession, nutation, the Moon, and artificial satellites of the Earth. It is equivalent to the proper time experienced by a clock at rest in a coordinate frame co-moving with the center of the Earth: that is, a clock that performs exactly the same movements as the Earth but is outside the Earth's gravity well. It is therefore not influenced by the gravitational time dilation caused by the Earth.” We will list all formally defined "Time Measurement Systems" 2 posts from now.

Now this last example I included is particularly interesting because it is an international standard already being used to help assign coordinates in 4 dimensional spacetime – it was defined specifically to conform to current theory relating to relativistic space. However, as one can tell from reading the description, it is largely limited to the study of coordinates within our solar system. Another interesting fact is that it is only one of several competing coordinate time systems that have arisen to help astronomers deal with the same Use Case we described in our first post on Time – the ability to locate events within spacetime.

One of the main problems with all of the coordinate systems and even with our current theories on spacetime is the earth-centric perspective we tend to toss in. What does that mean? Well, for the above example we are taking into account planetary motion but not the overall motion of the solar system, the galaxy etc. We touched upon the “taxonomy” of motion context in an earlier post and here it is again (and it actually extends to much lower measurements):

• The earth rotates – motion vector 0
• The earth orbits the sun - motion vector 1
• The solar system travels within its neighborhood in the milky way - motion vector 2
• The milky way itself is rotating – motion vector 3
• The milky way is also hurtling towards the Andromeda galaxy and will collide with in about 25 galaxy years - motion vector 4
• The universe itself is expanding outward at incredible speeds. In fact according to the latest data it is speeding up and some of it even appears to be moving away from us faster than light (1.4 C)!

So, each of these motion contexts listed above has its own velocity, trajectory and mass/gravitational considerations.

There's a whole lot of motion going on around us, do we continue to ignore it?

This taxonomy doesn't include any of the motion that might be occurring on the surface of the planet. That could include walking, riding in a plane, the motion occurring beneath us in Tectonic Plates or even the earth’s core (which is what generates our magnetosphere) or the motion with our bodies or even at the sub-atomic level. There is motion everywhere it is exists at every scale imaginable. More than that though, all of this ‘Contextual Motion’ is occurring along different trajectories. So let’s talk about this in relation to a coordinate system for finding an event in spacetime. The current coordinate systems use four vectors (3 for 3 D space 1 for time t) to locate planetary bodies in space. A scientist might ask the question, where will Saturn’s moon Titan be in ten years on January 10th, 2:00 pm eastern time? Using this type of coordinate system and extrapolating the known orbital behavior of Saturn around the Sun and Titan around Saturn we can plot where it will be at the designated time and date from the perspective of Earth. This works to some degree of precision for the following reasons:

1. It’s still very close to us (from both the galactic and universal perspectives).
2. We are deliberating pegging it to Earth time so using standards based on Earth motion is ok.
3. We assume all other contextual motion will continue moving along the same trajectories they have been so we don't ever bother to factor them in – they become a more or less “absolute” background. The only motion we concern ourselves with is within our own Solar system.

So, if we try to extend this out to a galactic scale we see where the problems will arise almost immediately:

• We’re dealing with massive distances.
• We can’t or shouldn't use Earth focused time scales for managing coordinates.
• Contextual motion becomes very important once we move away from a localized perspective. We can no longer view external motion as an absolute because it in reality it isn't. At the galactic scale it becomes dynamic (and in fact always was even at our scale although that dynamism isn't regularly perceptible by us). 

The problem becomes more immediately noticeable if we decide we need to locate more discrete events – e.g. something smaller than a moon’s orbit – something let’s say like locating the “Peach Orchard” action that occurred on the second day of the Battle Gettysburg (see figure below). This particular event also has the distinction of having occurred in the past rather than the present or future. The diagram illustrates rough Geo-spatial coordinates and major arcs of movement but without topology (altitude) . It wouldn't be too much of a stretch to add topology and clock readings (taken by observers of the battle) next to the movements in the diagram although we cannot be sure how precise that the clock readings are. The real question we need to ask ourselves is this; would the 4-vector coordinates for this reference frame and set of events (the location in Gettysburg and the time the action started and when it finished) be sufficient to actually locate the timespace where the battle occurred?

We know where it occurred and when it occurred, but would this be enough to find the actual event?

The timespace described by the 4 vector coordinates could be logically correct  once we add the missing information – we have represented the location and duration within the context of Earth movement. But what really happened since the battle took place – did the earth travel around and around in the same timespace ‘groove’ for 150 years or did it travel in its orbital groove trajectory across multiple layers of contextual motion – most of which was not moving in exact alignment with our movement? I’m afraid it was the latter. The Earth we’re standing on now isn't moving across an absolute background (what Newton called Absolute Space) – we have moved a phenomenal distance across space in multiple directions simultaneously. Isn't that impossible? Well, maybe not. If we were to express each layer of contextual motion as a distinct dimension then it becomes feasible to track motion across as many as may be involved by simply adding more vectors. The level of accuracy in determining the coordinates we wish to achieve will be dictated largely by how many vectors we choose to apply to the calculations. Of course, there will be a point where adding more vectors becomes counter-productive (we could see that coming close to approximating issues associated with quantum physics).

You might be asking yourselves why folks in the scientific community haven’t been viewing these issues in this manner; here why:

1. For most of the past century we were still assimilating and validating the core premises of relativity and quantum mechanics – it was a lot to digest. We've also become obsessed as to why those three theories don't match up rather than challenging the underlying premises of all 3. The theories have become "institutionalized" - we experienced 30 years or so of radical conceptual expansion which ended in the 1930's (for the core theories) and then settled in around those core theories rather than taking them to the next level.
2. It’s only recently that we've begun looking further into space and decided to look for tiny objects like planets.
3. It’s hard for people residing on Earth not to view the Universe from Earth’s perspective – and it wasn't that long ago that most people thought that Earth was the center of the Universe.
4. It’s a lot easier to make math work if 1 – the formulas are simpler, and 2 there is a fixed reference point to compare to. And science currently rewards the least complicated theories and formulas. The problem with that of course is that some aspects of nature are complicated.

This last point is particularly interesting. For those of you who have read anything about Special Relativity you will probably recall thought experiments such as at the observers on the train platform watching the lightning bolt hit from different perspectives. We tend to construct of all these scenarios as 2 observers in relative motion to one another or to an observer stationary in relation to another. The thing is when we construct it that way we leave out all of the potential contextual motion that may be occurring (or complex event scenarios). Perhaps the limited set of variables is OK to determine whether time dilation or other relativistic phenomenon is occurring or not, but is it sufficient to predict truly accurate event coordinates? Maybe not...

We will explore that and Relativity, Quantum Mechanics and Mach's Principle in our next post. The thing is - in order to understand Time - we have to tackle almost all of Modern Physics.

copyright 2013, Stephen Lahanas

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