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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Deconstructing Time - part 3: Reference Frames

In our past two posts on time, we began to outline some key concepts, most notably the notion of an “event.” Today we’re going to try to add some more context to the discussion and then talk about “Frames.”

A Contextual Dilemma
Let’s say NASA made a breakthrough in propulsion and in its ability to secure some funding (the real miracle perhaps). A mission is being planned to the nearest star that is believed to have an earth-like planet, Kepler 10b. This star system is approximately 500 light years from Earth. In basic terms, this means that the light that we see today emanating from Kepler 10b is not from that star’s present, but from 500 years in its past. We can somewhat accurately plot where Kepler 10b is now as well as all of its locations along its journey between 500 years ago and its “now.” (because it is travelling on a stable course – at least it has been up to the point we’ve been able to witness in its 500 years ago – who knows – aliens from Alpha Centauri could have blown up the whole star system 200 years ago in their time, there is no way for us to know for sure).

NASA artist conception of Kepler 10b

So, you might be thinking it’s obvious that we would be travelling to the “Now” version of Kepler 10b, right? Well maybe it’s not so obvious. Let’s assume that a propulsion approach better than today’s has been discovered providing us speeds up to 20,000 km/s.  This still doesn't come anywhere close to light speed. At this better yet still sluggish speed, it would take our astronauts more than 16,000 years to arrive at the Kepler 10b star system. This obviously doesn't equate to the Now we just extrapolated for Kepler 10b just a moment ago – the ‘Now’ that is equivalent to the distance it traveled since the light we see on Earth's now was generated (500 years ago).

What if we were able to travel at or close to the speed of light (or faster than light)? According to Special Relativity, if we are travelling at close to the speed of light (say 97% or so) then the actual time it takes to arrive at Kepler 10b is 12 years (in travel time felt by the astronauts). For folks back on Earth, 502 years will have passed. So, which Kepler 10b do we arrive at then if we're travelling that fast(important to know so we’re actually pointed at where/when it will be)? Let’s see if we can guess:

1. It’s not the Kepler 10b from which the original light we were looking at came from.
2. It’s not the Kepler 10b that is in the same instance of Now as Earth is. (this is a complex topic and we will explore it in more depth soon).
3. It’s not the Kepler 10b that it would have taken us 16,000 years to reach. (because we close to light speed)
4. It may be the Kelper 10b roughly 12 years after the point we measured the 500 year light old from Earth and determined when was Kepler's Now (in other words 512 years or 12 years into Kepler 10b's future). Or, it may not be.

The reason that there is some uncertainty relates to the fact that all of our measurements are being generated based on time as defined in Earth or near-Earth contexts. We are also assuming (perhaps incorrectly) that Earth and Kepler 10b are moving away from one another at a constant speed. There are some galaxies that despite universal expansion are moving towards one another.

Why would any of this be important? Well, say we were dealing with a typical Science Fiction scenario where people from Earth were preparing to making a first contact with a race of intelligent beings whom were on the verge of discovering atomic energy. In that situation, showing up even five years too late might be devastating, but it would also be somewhat embarrassing if we showed up several hundred years early as well (to witness the invention of the rifled musket instead).

Events occur within Reference Frames (a two dimensional visualization of a multi-dimensional phenomenon)

The invention of a weapon might be viewed as an event as would be any number of activities involved with traveling between Earth and Kepler 10b. Finding the events (across both time and space and across significant distances in space) is a tricky business. One way to help better understand events and how to locate them is by placing them in the context of Reference Frame.

Here is the Wikipedia definition:

In physics, a frame of reference (or reference frame) may refer to a coordinate system used to represent and measure properties of objects such as their position and orientation. It may also refer to a set of axes used for such representation. 

Alternatively, in relativity, the phrase can be used to refer to the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"). The context may itself include a coordinate system used to represent the observer and phenomenon or phenomena.

The Reference Frame is the timespace box within which an event or events occurs. The box though is not limited to 3 three dimensional geometry as it exists across time and space. In fact, the box really doesn't exist at all except in the context of providing a conceptual grid field that allows us to distinguish events from each other. The other key aspect of a Frame is that it allows us to define the boundary for Simultaneity.

Frames don't always move in the same direction...

Sorry for tossing in another new term so quickly – but it’s a key one that helps us to cement events within frames. Simultaneity is often viewed or described in purely relativistic terms, but here we’re going to view it a bit more broadly. Simultaneity is the Now that corresponds to an event within a frame or frames. Simultaneity is usually restricted by the ability to pass information back and forth between observers at the speed of light, C. In the old days, this represented information that could be seen directly – nowadays it can be a live internet video conference between Dayton, Ohio and Tokyo, Japan. This live conference may be occurring 12 time zones apart and the folks in either city would be sitting in a different calendar day than the participants in the other city. Yet, the event is synchronized through a global agreement on the tracking of Terrestrial time (Greenwich Mean Time - GMT) and communications that are passing across satellites and phone lines at roughly the speed of light. So, even though it may be 6:00 pm in Dayton and 7:00 a.m. tomorrow in Toyko, the meeting is a simultaneous event which occurs in the same reference frame.

This is curious even at our own limited scale here on Earth, isn’t it? The people in Dayton are in effect travelling into tomorrow to attend the meeting and the folks in Toyko are going back in time – strictly speaking. In a larger sense, all of us, in Toyko, Ohio and the rest of the planet are travelling forward through time in a sequential, linear manner. So, we have already proved that time travel does indeed exist, sort of.

But let’s get back to Reference Frames; here’s our definition of what they are:

A Reference Frame is the logical boundary within which an event or events may occur. The Frame exhibits (approximate) Simultaneity for the events and participants within and can be used to provide a coordinate system for tracking events. 

The biggest difference between my definition and that associated with Relativity Theory surrounds the use of the word “Logical.” By adding this we allow much more flexibility to the concept. Let’s say for example someone invented a quantum communications system between Earth and Mars. Instead of each transmission taking 8 minutes to send, the communication would be instantaneous (or worse, a reply might be received before a message was sent – we’ll talk about that eventually).

Thus a news conference with our Mars exploration team could become a simultaneous event occurring within one very large (for us) Reference Frame. Let’s add some other characteristics for Frames while we’re at it:

• Frames can last for indefinite duration.
• Frames can overlap.
• Frames generally exist in the same time phase or phase space (more on that later).
• Frames expand and collapse – there isn’t a fixed grid in timespace – only the potential for one, when potential is realized, frames appear (or more accurately can be discovered).
• Frames are supported under both classical and relativistic physics – they may also be supported by Quantum physics but we may never be able to assign coordinates at that scale.
• Frames are by their nature, multi-dimensional.
• Events can be linked within and across frames through “Continuity Paths.”

In conclusion for today’s post I’d like to leave you all with one key thought – the context of the trip I provided earlier makes it clear that any significant travel into Space is in fact an exercise in both Space and Time travel. Why that’s the case is the topic of our next post.



copyright 2013, Stephen Lahanas

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