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