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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.

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  • $\begingroup$ As far as I understand it, wormholes don't work that way. They don't accelerate you across space, rather, they make the distance between two points in space shorter. $\endgroup$
    – Arkenstein XII
    Sep 10, 2019 at 20:50
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    $\begingroup$ I've read recently that they actually make the trip longer. However that may be, I don't want FTL and a real-time wormhole is as good as my universe gets. I do know that wormholes don't work by accelerating you across space. The race which built them placed machinery in there that lets you travel near lightspeed. I did not mention this as I considered it irrelevant for the question. $\endgroup$
    – TheDyingOfLight
    Sep 10, 2019 at 21:06
  • $\begingroup$ Very good indicator. However, she should NOT bother to check CMBR. She should instead set her equipment to scan all possible frequencies for any communication signals. Discovering peak of CMBR in somewhat unusual place... $\endgroup$
    – Shadow1024
    Sep 11, 2019 at 5:39
  • $\begingroup$ Why would she measure CMBR? If she's not expecting to travel through time, you'll have to justify that. For that matter, why would she have the instrumentation to do it? $\endgroup$
    – Separatrix
    Sep 11, 2019 at 7:20

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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.

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  • $\begingroup$ Thanks, this is exactly the answer I was looking for. The second part was only supposed to be answered if the CMB idea wasn't viable. +10 $\endgroup$
    – TheDyingOfLight
    Sep 11, 2019 at 7:49
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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.

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.

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.

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  • $\begingroup$ But if I do that I#ll have FTL and no time dilation. This is not what I want. $\endgroup$
    – TheDyingOfLight
    Sep 10, 2019 at 22:05
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    $\begingroup$ @Renan At a distance of 570 million lightyears, the Milky Way Galaxy will not be visible to the naked eye. $\endgroup$
    – Arkenstein XII
    Sep 10, 2019 at 23:09
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    $\begingroup$ @ArkensteinXII As specified in the question that the shuttle may have instruments capable of measuring accurately the temperature of the cosmic microwave background, it's not unreasonable to assume that there is the equipment to see galaxies not visible with the naked eye and compute from those observations. +1 $\endgroup$
    – Angry Muppet
    Sep 11, 2019 at 1:00
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    $\begingroup$ @Chickensarenotcows First, measuring the temperature of the CMBR requires a very different instrument than resolving the magellanic clouds from significantly outside of our local supercluster. Second, I was simply pointing out that Renan's statement that the naked eye would be sufficient was not the case. $\endgroup$
    – Arkenstein XII
    Sep 11, 2019 at 3:35
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    $\begingroup$ @Nosajimiki if this were instant teleportation I would agree, but the protagonist is moving closee to tthe speed of light. Light will beat her to the destination, so she will be seeing the LMC with just a few million years lag. $\endgroup$
    – The Square-Cube Law
    Sep 11, 2019 at 17:52
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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.

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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.

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  • $\begingroup$ I actually like this a lot as she would very likely attempt to observe distant galaxies to get a fix on her position. Then she realises that their density is lower than it should be and runs the CMB temperature experiment to confirm this. Is this plausable? $\endgroup$
    – TheDyingOfLight
    Sep 11, 2019 at 17:09
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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.

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    $\begingroup$ I don't think that there would be any familiar stars or galaxies for that matter in the sky. 570 million lightyears are even outside of our Laniakea Supercluster. $\endgroup$
    – TheDyingOfLight
    Sep 10, 2019 at 21:27
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    $\begingroup$ The stars will be unfamiliar, but the Galaxies may be recognizable. Since many galaxies can be seen from billions of LY away with good instruments, you could use them as your reference frame. $\endgroup$
    – Nosajimiki
    Sep 11, 2019 at 17:28
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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.

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    $\begingroup$ Those are indeed her first questions, however she realises that she hast traveled forward in time while attempting to answer these. The issue for her is that there won't be a home, even if she returns to Earth. After all, more than a billion years will have passed. Would you call Earth during the Hadean Eon "home"? $\endgroup$
    – TheDyingOfLight
    Sep 11, 2019 at 7:44
  • $\begingroup$ @TheDyingOfLight, so her navigation equipment will give that away more directly than anything else. Location comes first, relative location gives relative time. $\endgroup$
    – Separatrix
    Sep 11, 2019 at 7:56
  • $\begingroup$ Will she be able to figure out where she is with greater precision than "not in Kansas anymore"? She is outside the local Supercluster, so there won't be any familiar constellations. $\endgroup$
    – TheDyingOfLight
    Sep 11, 2019 at 8:16
  • $\begingroup$ @TheDyingOfLight, that depends on what equipment you give her. You could possibly justify it on an exploratory vessel, let the story needs drive the technology. $\endgroup$
    – Separatrix
    Sep 11, 2019 at 8:18

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