How to figure out that you traveled 570 million years into the future while in space on a small shuttle craft?

Question

I want a character to get sucked into what she thinks is an FTL-wormhole-gate. While it turns out that the gate is indeed a traversable wormhole, it does not allow for FTL travel. The gate transports her at a velocity of ca. 0.9999999999 c over a distance of 570 million lightyears (outside of the Laniakea Supercluster). Due to relativistic time dilation, she only experiences a few seconds of subjective time and believes to have discovered a way to transverse the universe faster than light. (This is completely unrelated to the issue at hand and should not be included in any answers. It is just to give some context.)

How could she realistically figure out how much time has passed during her trip? My idea was that she measures the temperature of the cosmic microwave background, learns that it is colder than it is supposed to be and calculates that she, in fact, has traveled 570 million years in time as well.

Is this a realistic way of figuring out that she has traveled into the future? Are there any easier/more realistic ways? She is driving in a distant systems Kuiper-Belt on a small scouting shuttle with a lot of instruments but almost no delta-vee left.

Answer 1

Answering only the first question: Yes, it is a realistic way.

Precision may be questionable however (so, she will figure out she is a few hundred million years ahead in time, but won't be sure whether it's 500M or 600M, if we presume present-day understanding of CMB, universe expansion and all the relevant stuff, and Planck-level precision of measurement. With future tech, she certainly can have precision under a million years.

So, you want to measure CMB. It would be useless to observe its patterns, as you won't know what those are in your new position, and those change on the scale of 100 thousand years anyway. So the only thing you can use is CMB temperature. Fortunately for you, we know how that behaves. $$ T_{CMB}(t)=\frac{T_{CMB}(0)}{a(t)}, $$ where $T_{CMB}(0)$ is the present-day temperature, $T_{CMB}(t)$ is temperature you want to measure, and $a(t)$ is the scale factor (defined to be 1 at the present day). To properly describe how $a$ changes over time you would need to integrate Friedmann equation. Which is something your hero would do, but I'm too lazy for that. Fortunately, there is a good enough proportionality: in the current dark-energy-dominated era $$ a(t) \propto exp(Ht), $$ where $H$ is the Hubble constant. Plugging in $H=70km*s^{-1}*Mpc^{-1}$ and $t=570My$, we get $$ a(t) \approx 1.042 $$ That means, as the first approximation, CMB temperature would drop by about 4%, or 0.11K. That's certainly a noticeable and measurable change even with present-day (if state of the art) detectors.

The problem with precision in our day arises from the uncertainty about Hubble constant. For example, we have two values ($67.66 m*s^{-1}*Mpc^{-1}$ and $74.03 m*s^{-1}*Mpc^{-1}$) which are supposed to have precision of less than 2%, but you can see that they differ way more. So far this discrepancy wasn't resolved. There is also the issue of Hubble constant not being really constant. We know it changes over time, we know it changes not by much on smaller time scale, but we don't really know how it would change. All this factored in, you can have precision of about $\pm100My$ or so with current data. On the other hand, it is certainly not a stretch to say that even in 10 years, this would be improved to $\pm10My$, and with whatever future technology and science you have, precision can be plausibly at least a couple orders better.

Answer 2

You have a few conceptual problems here.

If you have to cover 570 million light years at 0.9999999999c, time dilation will habe a factor of 0.00014141979198682754. You can use this calculator to find out, just multiply your input by 100 because the calculator uses percentages.

0.00014 of 570,000,000 years is about 79,800 years. That's 12 orders of magnitude more time than what you want.

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A wormhole that long will have its mouths existing in different eras (as seen from Earth) due to relativity and them accelerating at different speeds relative to us. You could just have the gate be a wormhole of medium to small exotic region and stop worrying about speeds.

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Once at the destination, check the position of the Large Magellanic Cloud. It's orbital period around the Milky Way is about 1.6 billion years, so it will have completed about ⅓ of its orbit. This will stand out glaringly in a galactic map.

Answer 3

In the moment before her shuttle entered the gateway, its sensors recorded light coming from the other end and created a snapshot of star positions. The light captured in that snapshot started its journey through the gate 570 million years prior to the moment she entered the gateway.

Comparing that snapshot to sensor reading from the moment she emerged from the gateway on the other side, she would be able to see that things had changed dramatically while she was travelling. In fact, more than a billion years of celestial movement would be evident from that comparison.

Answer 4

Here is a link to a somewhat similar question:

How would an astronaut conclude he's on Earth, but 600 million years in the future?1

And you may note that my answer includes another method of telling that they have reached a distant future and the universe is noticibly older.

Answer 5

Star Position

In that time the stellar map would had changed noticeably. The board computer wouldn't recognize his position and a estimate of time passed could be obtained comparing your map and the actual position of diferent constellations at the point you emerged from the wormhole.

Answer 6

If she's 570 million LY from home, she has bigger immediate problems than what time it is.

Like where she is, and how to get back.

Whatever instruments she has that will allow her to plot location, her biggest immediate problem, will also indicate that time dilation effect. But having been sucked through a wormhole, working out the date is the least of your worries. That will be noticed only if she has instruments capable of locating herself and if she has such instruments, the shifting locations of various large bodies relative to each other will indicate the temporal effects of her journey.

Ultimately however, her first thoughts will be "where am I" followed by "how do I get home", and not "have I missed my date". Discovering she's missed dinner is going to be fallout from finding out where she is.