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Specifically, I'm considering a situation where:

  • The entire planet, as well as all other bodies in the solar system are sent forward in time fifty years, so it's not possible to notice purely from observing bodies within the solar system (in effect, the rest of the observable universe has changed, but not our solar system)

  • Since the whole solar system is affected, the positions of Earth and the planets/Sun have not changed relative to each other --- only relative to other star systems

  • The astronomy practices and precision of equipment are those of Earth today

  • The Sun and solar system will be in a new location, as though it had continued to move through space for fifty years

What sort of plausible situation would lead an academic to notice something was wrong, in the course of routine observation or research?

My first thought is that you may be able to notice the change in position based on parallax of nearby star systems. However, I don't have a great sense of whether fifty years would make a big enough difference to notice with the precision of today's instruments.

If your solution works for fifty years, would it work for five years? Or six months? And if not, would it work for five hundred?

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    $\begingroup$ What does the phrase "the entire planet, as well as all other bodies in the solar system are sent forward in time fifty years" mean specifically? Are they exactly in the positions where they would have been fifty years from now? If so, then you don't even need astronomical equipment to see that something is very wrong -- any amateur astrologist will notice that "the Moon is in the seventh house and Jupiter aligns with Mars", so to say. You can tell time quite precisely by observing the planets; the astronomer will immediately notice that it's year 2070 instead of 2020. $\endgroup$ – AlexP Jul 14 at 22:59
  • $\begingroup$ Additional clarification added! The solar system as a unit is moving forward in time, so anything observable in our solar system isn't much help. @AlexP $\endgroup$ – lettuce_or_something Jul 14 at 23:04
  • $\begingroup$ Ah, in this case see @Alexander's answer -- binary stars will be suddenly out of whack. $\endgroup$ – AlexP Jul 14 at 23:05
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    $\begingroup$ At that scale you also have to consider the speed of light. Depending on the size of the space that's transported forward in time, it may take a year or more for light from outside that space to reach Earth. That would be at least how long it would take to discover that something has changed. Although that might not affect the how much, only the when. $\endgroup$ – NotThatGuy Jul 15 at 9:26
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    $\begingroup$ @DragandDrop I think that as described, The Voyager probes would likely have been transported along with everything else. If the entire solar system has been transported, that would presumably include the Oort cloud, which Voyager 1 has not yet reached. $\endgroup$ – Darrel Hoffman Jul 15 at 14:56
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This would be noticed rapidly by observations of stars with high proper motions. These are stars that through a combination of being close to us, and moving at high velocity relative to us, move noticeably against the background of more distant stars over the course of a few months. It so happens that there are no stars with high proper motion that are visible to the naked eye, but there are several that are easy to detect with small telescope or binoculars.

The best-known star with high proper motion is Barnard's Star, which is frequently studied as an example of a red dwarf. Almost any professional observations would notice that it was out of place with a five-year jump. Indeed, it's likely to give away any jump of more than a week, since its motion is 10.3 seconds of arc per year, and measurements of its position are taken to an accuracy a tenth of a second of arc or better. Once discrepancies had been noticed, a survey of high proper-motion stars would reveal what had happened within a few weeks. This method works for any period of time.

And that's discounting the Gaia satellite, which is engaged in measuring the positions of about a billion stars to an accuracy of about 20 millionths of a second of arc. Your time jumps would cause its operators to think the satellite had malfunctioned at first, but they'd soon have evidence of what had happened, although accepting it might take a long time.

An alternative explanation might be a glitch in a simulated universe. A way to check that would be to look for glitches in the beam currents of particle accelerators at the right moment. Teleporting particles moving very close to lightspeed, along with everything else, might be tricky.

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    $\begingroup$ Excellent answer, though I would hesitate to say people would realize "soon" that such an unthinkable thing has happened to the entire solar system. $\endgroup$ – Cyrus Jul 15 at 11:16
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    $\begingroup$ I would tend to agree with @Cyrus here, the issue isn't observability of the astronomical discrepancies that would result from such a jump, but the task of managing to convince a rather large number of people that something that quite simply cannot happen given our current understanding of physics had happened. Excellent point about stars with proper motion though, that's likely to be the first thing most astronomers would notice. $\endgroup$ – Austin Hemmelgarn Jul 15 at 11:44
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    $\begingroup$ @Cyrus: the great thing about something this blatant, and where the "impossible" explanation is so simple, is that the hypothesis would be almost immediate. Then it's a question of how you define "realise" -- is it when you first formed the hypothesis, is it when you ran out of competing hypotheses, is it when you started treating your hypothesis as a fact, or is it when you successfully reformulated fundamental physics in line with the new observations that provoked the hypothesis :-) $\endgroup$ – Steve Jessop Jul 15 at 12:47
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    $\begingroup$ @SteveJessop I would expect that divine intervention and a glitch in our simulated universe would be competing hypotheses for these observations. $\endgroup$ – Cyrus Jul 15 at 13:12
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    $\begingroup$ @Cyrus: Spotted a possible way of testing for a simulated universe vs teleportation. $\endgroup$ – John Dallman Jul 15 at 21:37
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Your astronomer has a number of options.

  1. Binary stars. Many binary star offer orbital periods in excess of 50 years. For example, Alpha Centauri A-B pair has orbital period of about 80 years, and Proxima Centauri - about 547,000 years. By observing this system and comparing it to "present", an astronomer may find the amount of time passed with good precision.

  2. Nova/Supernova nebulae. After Nova or Supernova goes off, a fast expanding cloud of gas can be visible from Earth. These nebulae are a short-living phenomenon, they exist on scales of only hundreds and thousand of years. By studying the size of a known nebula, an astronomer can estimate how much time has passed.

  3. Pulsar slowdown. Pulsars are known as a very precise clocks, but they do slow down with time. This is particularly noticeable for young pulsars. For example, Crab Pulsar is known to slow down by 38 nanoseconds per day. With the help of an atomic clock, this slowdown can be measured.

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There are a ton of things we have telescopes pointing at that would definitely notice a 50-year jump. John and Alexander's responses are excellent examples. Here are some more:

  1. Exoplanets: There are dozens of active projects searching for planets orbiting around other stars. All telescopes involved in this kind of research would notice that the incredibly regular periods of all of their exoplanet candidates all shifted at the same time. It won't take long to realize that only a 50-year gap in data could cause these exact shifts in phase to line up across every system.
  2. Pulsars: These neutron stars have extremely precise rotation rates, beating continuously in the night sky every few seconds across a swath of frequencies. Of course, like just about everything in the sky, we're actively measuring a bunch of them. If every pulsar in the sky skipped a beat, it would be a headline immediately, and again, by comparing the different frequencies of the skips, we could calculate that we skipped 50 years. In fact, pulsars might be the most accurate measurement of the skip that we have - you could probably pinpoint the 50-year time difference to within a fraction of a second.
  3. The Expansion of the Universe: The universe is expanding, and that expansion is speeding up. This means that, 50 years from now, some particularly distant objects will be moving away from us much more quickly than they are now. Some current research is probably sensitive enough to pick up on this by measuring the redshift from those distant objects. Again, they'll notice a sudden skip in their data, though they won't be able to pinpoint 50 years as accurately as the exoplanet or pulsar researchers.

I imagine grad students around the world will spend the first few days yelling at their data, wondering if their telescopes malfunctioned or something. As the complaints spread around universities, it will quickly become extremely conspicuous that every project has exactly the same "glitch." I give it a few weeks at most before people figure out what happened.

EDIT: To answer your question,

If your solution works for fifty years, would it work for five years? Or six months? And if not, would it work for five hundred?

the answer is a resounding yes for all of the above (at least for exoplanets and pulsars). Even if you're observing just 2 pulsars whose frequencies aren't multiples of each other, as long as you know their frequencies and phases precisely, you can calculate any length of time. If, for instance, when the skip happens, the first pulsar is at 93.0056 degrees and the second is at 202.4855 degrees, you know exactly what time it must be, because those pulsars will only be in that position once in the history of the universe.

There will probably be some uncertainty in the frequencies, so some other times might give configurations that are "close enough." But we can measure frequency so accurately these days that I'd imagine your calculation would give something like, "we've moved exactly 50 years, or 20 billion and 50 years, or 40 billion and 50 years, and so on." But you can rule out all but the first by noting that Andromeda hasn't crashed into the Milky Way yet.

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There are already a number of very reliable methods in the other answers (and frankly, I'd only posted a comment if I could). I want to offer an answer more directed towards a plot or story element if that is where you want to go with the question:

Comets

Depending on how you define "solar system", there are objects that occasionally visit our solar system (in the sense of roughly the space occupied by our planets' orbits). They often do so periodically and one of such encounters to happen fifty years early would probably cause confusion at first (some people claiming to have found a new object until they realize it's a known comet), but could lead to the theory of having performed a jump in time (which could then easily be proven/made believable with one of the other methods mentioned here).

This method is definitely not the most precise or practical one (it only works if a comet happens to pass by right now) and it needs further definition of your situation (Does everything that orbits our sun jump, even if it is far outside of the solar system? Do we jump in space or just in time - which could also result in a comet's regular orbit to cut through the solar system in an unexpected way?

It does however offer multiple options for story telling (from your astronomer being the one to first recognize the object as C/1905 F1 to the object dramatically colliding with the moon due to its shifted orbit) and allows for a fairly precise guess of the jumped time period, once it is identified.

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Depending on what you mean by the solar system, an early probe like voyager might be 50 years along further than you'd expect and that much harder to detect.

Might make for an interesting first scientific hint.

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The Hulse-Taylor binary

The Hulse-Taylor binary consists of a neutron star and a pulsar in a tight orbit. These two objects emit gravitational waves at a known rate, which causes the period of their orbit to slowly decrease with time. This change in orbital period was the first indirect evidence for the existence of gravitational waves, and netted Hulse & Taylor the 1993 Nobel Prize in Physics.

enter image description here

This is a distinct effect from the slow-down of a pulsar's rotation rate (as mentioned by other answers). Here's how I would imagine things playing out:

  • A significant number of pulsars experience a "glitch", since the 50-year jump will not be an even number of cycles for most of them.

  • Examinations of the Hulse-Taylor binary would then show that the period is decreasing at a much higher rate than one would expect. Further examinations would then be able to estimate the amount of time "skipped", probably to an accuracy of a couple of years.

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Very good answers so far, so just adding two approaches:

Statistics

  • If one star is suddenly at the wrong place / have the wrong brightness fluctuation, that's a measurement error.
  • Two stars? better refine your Gaussian filters.
  • Thousands of small variations registered across the board (local stars, distant galaxies)? Something is deeply, deeply wrong.

Bonus statistical event: according to Wikipedia, "[...] the number of novae discovered in the Milky Way each year [is] about 10." Imagine that ~500 new novae detection events suddenly pop up (or at least their remnants after 50 years or less).

Event Horizon

Time has slowed down around the solar system. That means that incoming photons are accumulating in a bubble around the affected area due to time dilation, not completely akin to a black hole's event horizon, and if the time taken by the jump as experienced by local observers isn't zero these photons will arrive at a rate defined by 50 years divided by the local duration of the jump.

So, if the jump takes, say, one hour - that means that the whole sky will light up with 438,000 times the normal intensity.

As a reference: the Sun is 400,000 times brighter than the full Moon in the sky.

Imagine that kind of brightness difference coming from all directions.

In that case it's safe to assume that every single able-bodied person will notice the event, but a scientist can actually come up with a the correct cause, as several indicators (brightness variance, relative star motion, pulsar rates, etc.) will show the same multiplier value of ~438k.

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  • $\begingroup$ Interesting catch on the accumulation of photons! The (until now not mentioned) actual mechanics of the "time travel" I'm conceiving is an instantaneous restructuring of all matter inside the solar system to match how it existed 50 years ago, so that unfortunately doesn't line up well with my particular story. $\endgroup$ – lettuce_or_something Jul 15 at 21:11
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Ten seconds after this time jump, the first amateur astronomer somewhere on the world says "what the hell where is that asteroid I was just looking at?" One minute later, he has found and identified at least one of Venus, Mars, Jupiter, Saturn at a very odd place. (To anyone who has looked at the skies at night often enough, they just stick out.) From there on, he is texting, telephoning, emailing like crazy.

After one hour, every astronomer in the world who has not set his phone on mute before going to bed will be informed about the exact lenght of that time jump, provided the communication systems (due to GPS malfunction, or sheer overload) are still online.

Everybody will try to find something that hasn´t jumped, and astronomers immediately check positions of nearby stars according to their known proper motion, and pulsars. After another hour, it will be around the world that the rest of the universe is still where it was about three hours ago. And at this point, the plot will turn into a "whodunnit" story. Let´s hope you were very discrete with your time machine setup. ;)

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  • $\begingroup$ You seem to have misunderstood the question. As I read it, the relative positions of everything orbiting the Sun are unchanged, so observations of solar system bodies won't show any changes. $\endgroup$ – John Dallman Jul 15 at 21:40
  • $\begingroup$ @JohnDallman Yea, reading closely, that interpretation makes more sense. I would perhaps have said the solar system is transported into a future "universe". The effect would however be much the same. After one hour, dozens of automatic survey systems will have sent off emails indicating a malfunction, the first astronomer to compare two pictures sees what happend, compares a few more picture, sends out emails, phones his boss at 3 AM, etc. $\endgroup$ – Karl Jul 15 at 22:03
  • $\begingroup$ @John Dallman is correct, although I certainly could have phrased the scenario better. Effectively, I want the discovery to only be possible by observing things outside the solar system, which there are apparently a number of good ways to do! $\endgroup$ – lettuce_or_something Jul 16 at 1:35
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This could be a comment, but is probably too long for one.

What does the OP mean by:

The entire planet, as well as all other bodies in the solar system are sent forward in time fifty years, so it's not possible to notice purely from observing bodies within the solar system (in effect, the rest of the observable universe has changed, but not our solar system)

"All other bodies in the solar system" include the Sun, seven other planets, at least 5 dwarf planets, possibly the hypothetical Planet Nine, about a million known minor planets or asteroids, hundreds of moons of the planets, Thousands of Trans Neptunian objects in the Kuiper Belt, hundreds or thousands of known comets, and the million, billions, or trillions of undiscovered comets believed to be in the Oort Cloud, etc.

If any of the known objects are left behind, sooner or later some astronomer is going to take a look at them and discover that they are not where they used to be. And if astronomers keep looking to see if other know objects are are actually in their predicted positions, they will soon compile a list of which ones are and which ones aren't. And by compiling lists of the latest dated observations of various now missing objects, they will be able to get a good idea for when those objects disappeared.

And it seems to me that the angles between the Sun, the Earth, and another body orbiting the Sun are constantly changing as both the Earth and the other object orbit the Sun with different speeds. The period between successive moments when another body orbiting the Sun happens to be at the same Angle relative to the Sun and the Earth is call its synodic period.

Here is a link to a table of the synodic periods of the other seven planets, and 9 other bodies that orbit the Sun, relative to the Earth.

https://en.wikipedia.org/wiki/Orbital_period#Examples_of_sidereal_and_synodic_periods[1]

Each object has a different synodic period. So try to calculate how much time will pass before an even number of each and every one of those 16 synodic periods passes and all 16 bodies are at the same angles relative to the Sun and Earth as they are this very moment.

Furthermore, a planet will not be in the same direction relative to the background stars after a full synodic period has passed. For each body, there must be a certain number off full synodic periods which will pass before the planet is both in the same angle relative to the Sun and Earth and also in the direction relative to the background stars. So since those other periods for each body are several - probably very many - synodic periods long, The time that it would take for all those 16 orbits and synodic periods to realign and be the same again should be extremely long.

it is my belief that even though the apparent directions to the stars shift very slowly due to their immense distances, the time for such a realignment would be so long that the stars would have shifted their apparent positions so much that the shapes of the constellations would clearly be different. So I believe that the apparent positions at any one moment in time of those 16 bodies listed will never be the same again in the billions of years of future history of the solar system, that it is a unique configuration.

And there are are many other solar system objects beyond the 16 in that list, which are also routinely observed by both amateur and professional astronomers.

And what about bodies that orbit other solar system bodies?

Amateur astronomers often observe the four Galilean moons of Jupiter, perhaps often enough for them to be under constant observation, which might mean that someone would actually see them disappear in real time if they are left behind in the time jump.

A few decades after the Galilean moons were discovered, tables predicting their movements were published. If someone observed their apparent positions, passing into the shadow of Jupiter or other moons, casting shadows on Jupiter, occulting other moons, passing behind Jupiter and emerging from behind Jupiter, etc., etc., and noted the local time using an accurate clock, they could compare those local times with the times predicted for some other location in the published tables. And they they could calculate the difference in local astronomical time between the place where the observations were made and the place where the predictions were made for. And thus they could calculate the difference in longitude between the two places.

This method was first used to find the longitude of places more than 350 years ago.

And there are tens of other moons in the solar system with well predicted orbits. Those other moons will also have to be moved by the super science and technology, or extremely powerful magic, used in the story, in order to keep the Earth humans ignorant of the time jump for as long as possible.

So if the beings (?) who move the solar system forward in time by 50 years move only ten solar system objects and leave the rest behind, it is quite possible that some amateur astronomer will be looking at one of the objects left behind, and will actually see it disappear from view, and/or be making a video recording of it, at the moment it disappears. So moving only ten solar system objects forward in time may result in instant discovery that something strange has happened.

If the one hundred solar systems objects most likely to be observed are moved forward in time it should take longer to discover what has happened.

If the one thousand solar systems objects most likely to be observed are moved forward in time it should take a longer time to discover what has happened.

If the ten thousand solar systems objects most likely to be observed are moved forward in time it should take much longer to discover what has happened.

If the one hundred thousand solar systems objects most likely to be observed are moved forward in time it should take even longer to discover what has happened.

And so on and so on.

If thousands or millions of solar system objects are moved forward in time and space by fifty years, it would be a very complicated operation, especially making certain that all of them are in their proper positions and orbits relative to each other.

So if the objects are moved in time and space individually, the number of objects which are moved instead of being left behind will determine how quickly professional and/or amateur astronomers discover something very strange has happened.

The best way to delay detection of the move in time and space would be to move everything in the solar system.

So I can imagine some sort of time warp field being generated which covered the entire solar system and moved the entire solar system with many millions, billions, trillions, etc. of objects all at once.

One way in which amateur observers help professional astronomers is by observing variable stars and recording their apparent magnitudes, thus keeping track of the lisght curves of many variable stars.

Another way in which amateur observers help professional astronomers is by observing binary stars and recording the position angles of the stars in them, thus keeping track of the changing apparent positions of the stars and providing data for calculating the orbits of the stars.

And the organizations that the amateur astronomers send their reports to will soon be flooded with reports of variable stars suddenly changing their apparent magnitudes and double stars suddenly jumping around in their orbits.

In the 20th century, astronomers often took long exposure photographs of astronomical objects to show details which were too faint to be seen instantly. And if professional and/or amateur astronomers still do that in 2020, all such photographs of other stars, star clusters, and nebulae taken in time periods including the jump should include duplicate and probably overlapping double exposed images of those distant astronomical objects, as the directions to those objects change over 50 years of time.

The OP wrote:

My first thought is that you may be able to notice the change in position based on parallax of nearby star systems. However, I don't have a great sense of whether fifty years would make a big enough difference to notice with the precision of today's instruments.

Proper motion is the astrometric measure of the observed changes in the apparent places of stars or other celestial objects in the sky, as seen from the center of mass of the Solar System, compared to the abstract background of the more distant stars.1

https://en.wikipedia.org/wiki/Proper_motion#:~:text=Proper%20motion%20is%20the%20astrometric,of%20the%20more%20distant%20stars.[2]

Proper motion was suspected by early astronomers (according to Macrobius, AD 400) but a proof was not provided until 1718 by Edmund Halley, who noticed that Sirius, Arcturus and Aldebaran were over half a degree away from the positions charted by the ancient Greek astronomer Hipparchus roughly 1850 years earlier.[23]

https://en.wikipedia.org/wiki/Proper_motion#History[3]

So ancient astronomers using naked eye observations suspected proper motion over a period of centuries.

in 1716 Halley proved that Sirius, Arcturius, and Aldebaran had proper motion equalling about 0.162 arc minutes per year, or about 0.972 arc seconds per year.

So in 50 years they might show a proper motion of about 48.3678 arc seconds. Modern astronomical instruments record angles with a precision of 0.001 arc second or better, so they should be able to record the difference in the positions of Arcturus, Sirus, and Aldebaran in a time jump of only one day.

Barnard's star has the largest known proper motion, moving 10.3 arc seconds per year, which is about 0.028 arc seconds per day and about 0.00117 arc seconds per hour, just about detectable at a precision of 0.001 arc seconds.

https://en.wikipedia.org/wiki/Proper_motion#Examples[4]

The Gaia satellite can measure positions of stars with an accuracy of 20 microsarcseconds, or 0.00002 of an arc second, and thus would be barely able to measure the displacement of Barnard's star in a time jump of one minute, and the displacement of a star with typical proper motion in a time jump of a few months.

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  • $\begingroup$ The "warp field" approach was what I intended with the question. Thanks for the response, some useful links and info in there! $\endgroup$ – lettuce_or_something Jul 16 at 1:32

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