How are Experienced and Observed Mission Elapsed Times defined? (EMET & OMET)

To the question titled What timezone would be used for interstellar travel? this currently unsourced answer currently says in toto:

I suspect any interstellar travel will have relativistic effects (it's a factor of even interplanetary travel), the only reasonable timezones are EMET and OMET -- Experienced and Observed Mission Elapsed Times which would have the departure date as its epoch. UTC would fall somewhere in the middle of these.

While the term mission elapsed time is in widespread use in spaceflight, a quick check failed to turn up specific definitions for these two terms. So I'd like to ask the following:

Questions:

1. How are EMET and OMET defined? Are they for example what two ideal clocks initially set to UTC at the launch site would read if one remained at the launch site and the other remained in the spacecraft? Or is it something different since UTC is said to be between them (see #3).
2. Are these generally recognized and well defined concepts that can be sourced or for which citations exist, or are we witnessing the birth of new space acronyms?
3. How does "UTC would fall somewhere in the middle of these." work exactly? Since it seems that they would be defined in different frames relativisticly separated by a large distance, how could the concept of UTC being in between them be defined much less measured?

I haven't been able to find any references to EMET nor OMET, is it possible to cite a source or two showing that these are recognized and well defined concepts? Also, since (I presume, because again no sources) that each is measured in a different frame.

• Did you search those terms? The top two hits are the linked answer and this question. This makes both the linked answer and this question more than a bit suspect. These are highly nonstandard terms. While it is true that he global navigation satellite systems do have to make their onboard atomic clocks tick at a slightly different rate, the difference is very, very small. – David Hammen Nov 28 '20 at 8:12
• @DavidHammen I saw that coming too! :-) "While the term mission elapsed time is in widespread use in spaceflight, a quick check failed to turn up specific definitions for these two terms." 9 hours ago my search didn't even show the linked answer, but now that there's a follow-up question, it seems google catches on quick! Although milage can vary one location to another and one browser history to another they pop to the top of my results now as well. – uhoh Nov 28 '20 at 8:58

How are EMET and OMET defined?

I understood the answer to be an example of what the timing on an interstellar mission would look like. In other words, the definitions of EMET and OMET are that answer.

Are they for example what two ideal clocks initially set to UTC at the launch site would read if one remained at the launch site and the other remained in the spacecraft?

No. The answer clearly states [bold emphasis mine]:

Experienced and Observed Mission Elapsed Times which would have the departure date as its epoch.

The epoch of UTC is not the departure date of the mission, it is midnight of New Year's Eve after the supposed birth of Jesus Christ. Therefore, UTC and EMET/OMET will differ by at least something like 63777909600 seconds initially.

Are these generally recognized and well defined concepts that can be sourced or for which citations exist, or are we witnessing the birth of new space acronyms?

I understood the answer as an example of what a sensible system would look like. Mission Elapsed Time is what we use today, and at least to me, it seems like a natural extension to continue to use this concept, but account for relativistic effects by explicitly acknowledging the fact that time moves differently at mission control and the spacecraft.

Note that even for missions as short and low velocity as the Apollo missions, the time dilation was on the order of hundreds of microseconds. So, an interstellar mission that would take much longer time and reach much greater velocities will definitely have to deal with time dilation.

How does "UTC would fall somewhere in the middle of these." work exactly? Since it seems that they would be defined in different frames relativisticly separated by a large distance, how could the concept of UTC being in between them be defined much less measured?

Yeah, I didn't understand this one either, especially since both EMET and OMET start with a difference of 0 to each other but a difference of the better part of 100 billion seconds to UTC.

Note that UTC has another undesirable property that was not mentioned so far: it is not smoothly continuous. A minute may have anything between 59 and 61 seconds. The industry I work in uses TAI, not UTC, as the universal time reference for precisely that reason.

• "UTC is not the departure date" very nice! Like a clock I've now been set right :-) – uhoh Nov 28 '20 at 9:08
• I used an implicit conversion when comparing the timezones, but it obviously caused confusion. Hopefully the revised wording makes more sense. – user20636 Nov 28 '20 at 10:19

I think (as with the other answer) that the referenced answer is really defining these terms. The following is an attempt to make sense of these definitions. My definitions below are, I think, compatible with those, but if they are not then I think they make sense in their own right.

Note that I am not quoting sources for these definitions apart from the previous answer: this answer is defining them. I think that's safe as, given the lack of interstellar missions so far, there is not a lot of precedent. There are sources for the actual computations in the example below.

I am going to do the thing I understand as a theoretical physics person, which is to ignore UTC and all its complications: instead I'll just say that the various people involved in the mission have good atomic clocks which measure what a relativity person would call their proper time, and that, at the point the mission starts, these clocks are all in the same place in an inertial frame, at rest with respect to each other and are all set to zero.

I'll also just ignore general relativistic effects, which are likely to be very small for plausible missions (so the clocks can start off on the Earth, for instance).

Clocks and times

There are two clocks:

• the mission clock is travelling on the spacecraft, and is always at rest with respect to the people in the spacecraft;
• the ground clock remains at mission control.

OK, so now there are three (yes) interesting notions of times for events on the mission, which are defined as follows.

• EMET – Experienced Mission Elapsed Time – is the elapsed time (the time since the clocks were synchronized at the start of the mission) as experienced by the people in the spacecraft. It's simply the time read out by the mission clock: in the terminology of relativity it is the proper time experienced by the people in the spacecraft.
• GMET – Ground Mission Elapsed Time – is the elapsed time as experienced by the people on the ground when various events on the mission occur in the ground frame. It is the time read from the ground clock, and it's the proper time experienced by the people on the ground. This is a term I have introduced to avoid talking about UTC.
• OMET – Observed Mission Elapsed Time – is the elapsed time as experienced by people on the ground when they observe various events on the mission occurring. It's also the time read from the ground clock, and is proper time experienced by people on the ground, but it's the time when, for instance, they get the 'one small step for a robot' message when the spacecraft lands on some planet, not when it happened.

A simple example of the difference between GMET and OMET is the landing of Curiosity on Mars: it landed at about 05:17 (this is a time in UTC, I have not converted it to MET) but we did not observe the landing until about 05:31. 05:17 corresponds to both GMET and, very closely, to EMET, while 05:31 corresponds to OMET.

It's clear from special relativity that, for any event which occurs in the spacecraft's frame, $$\mathrm{EMET} \le \mathrm{GMET} \le \mathrm{OMET}$$: the experienced time on the mission is shorter than the time in the ground frame, and this also is generally shorter than the observed ground frame time, since events on the mission take place far away from the people on the ground. This follows from the fact that, in special relativity, the unique longest causal curve between two timelike-separated events is that followed by an inertial observer.

1. I believe that the referenced answer was defining EMET and OMET: this answer certainly does, and additionally defines GMET which serves as a simpler proxy for UTC.
2. I don't think they're generally recognized concepts, and so I dont think there are citations. Given this answer I believe they are now well-defined however.
3. As above, GMET is always between EMET and OMET, although at various points GMET and OMET are the same.

An example

Here I'll use formulae from the John Baez's version of the usenet physics FAQ and in particular the section on the relativistic rocket.

So, the scenario is that there is a fantasy rocket which can accelerate at $$1g$$ indefinitely: it sets out from Earth (with clocks initially synchronized, so all of EMET, GMET and OMET are then zero), accelerates for a year as measured on the rocket (so EMET at that point is 1 year), and then decelerates for a year as measured on the rocket, coming to a halt in Earth's frame with EMET being 2 years. At that point it transmits some message back to Earth: call this event $$E$$. At the event $$E$$ it has travelled

\begin{align} d &= 2\frac{c^2}{a}\left(\cosh \left(\frac{a T}{c}\right) - 1\right)\\ &\approx 1.1\,\mathrm{ly} \end{align}

where $$a$$ is acceleration of the rocket, $$T$$ is the EMET when the rocket starts decelerating (so $$T=1\,\mathrm{y}$$), and $$c$$ is the speed of light.

Given $$T$$ we can then compute $$t$$, the GMET for $$E$$:

\begin{align} t &= 2\frac{c}{a}\sinh\left(\frac{aT}{c}\right)\\ &\approx 2.4\,\mathrm{y} \end{align}

And finally, given $$d$$ and $$t$$, we can compute the OMET for $$E$$ which is $$t + 1.1\,\mathrm{y} = 3.5\mathrm{y}$$: it's the time when the message is received on Earth after travelling from a point $$1.1\,\mathrm{ly}$$ away.

So for $$E$$ we have these times:

\begin{align} \mathrm{EMET}(E) &= 2\,\mathrm{y}\\ \mathrm{GMET}(E) &= 2.4\,\mathrm{y}\\ \mathrm{OMET}(E) &= 3.5\,\mathrm{y} \end{align}

If the rocket then turns around and returns to Earth ad $$E_2$$ we get

\begin{align} \mathrm{EMET}(E_2) &= 4\,\mathrm{y}\\ \mathrm{GMET}(E_2) &= 4.8\,\mathrm{y}\\ \mathrm{OMET}(E_2) &= 4.8\,\mathrm{y} \end{align}

Note that GMET and OMET are now the same as the rocket is on Earth again.

General relativity

The definitions of EMET and OMET will still work in the presence of general relativistic effects. In general there's no useful definition of GMET, since there are no global inertial frames. (It might make sense to use some time coordinate based on, for instance, cosmological time.) The computations will be a lot more complicated: for instance, a mission which orbits a black hole closely will very definitely need to take general relativistic effects into account. In some cases the ordering of the two times can change, and OMET may even have more than one value: I think it's safe to then define OMET as the earliest time at which a distant event is observed.

• Good call on multiple OMETs – user20636 Nov 29 '20 at 14:47