I think a lot of people assume that this means you couldn't go more than a few (~100) light-years in your lifetime... But this is not actually correct. Counter-intuitively you can theorically go any number of light-years (essentially) in your lifetime, as long as you are able to approach the speed of light because when you do so the distance is dilated and hence you're covering far more ground within your reference frame (of course you'd be in the deep future from the perspective of anyone in our normal reference frame).
As long as we are talking about how far you can go in one lifetime, how would human body react in a spaceship with that much mass? Wouldn't the gravity crush any humans to death. 10% of the sun's mass is more than 30,000 times earth's mass. Add to that the fact that the diameter is only 620 m, and the gravity becomes 1.4e13 g.
If we could somehow make it into a donut planet we could presumably sit in the middle of it experiencing no acceleration. Would the time dilation effects still occur then?
I don't think so. As I understand it, gravity and acceleration are equivalent, if you aren't experiencing any acceleration then time dilation won't occur. (Assuming we are not traveling near the speed of light)
One of the more mindbending things to wrap your head around is that gravity isn't a force (i.e doesn't not cause acceleration in the F=Ma sense.). You're simply on a path through spacetime warped by gravity.
Think about it: when you are in free fall you feel 0 acceleration. You appear to be accelerating relative to the ground-- but you're actually motionless in an "inertial reference frame". (Similar to how the astronauts on the ISS don't "feel" acceleration despite accelerating rapidly relative to the earth.)
The "force" of gravity is often modeled as "gravity pulling you down" and the ground "pushing you back up". This works mathematically, but isn't quite logically consistent.
In reality, on the ground you're in a region of warped spacetime, so you feel constant upward acceleration despite not actually accelerating. (Thinking of this another way, standing on earth feels identical to being in a far away spaceship accelerating at 9.8 m/s².)
This is also why time "speeds up" near more massive objects. (Separate from "acceleration".)
We're so used to gravity this it doesn't seem weird. But when you consider the fact free-fall is when you're not accelerating... well pondering that from many angles is what ultimately led Einstein to his model of relativity.
(This is me trying to condense what could be a 10 minute explanation into a few sentences, so apologies if it's not particularly clear.)
You are far away from the masses. We are alive because we only experience 1g on earth. 10g is enough to kill a human. I don't even know what 14,000,000,000,000g would do, but I imagine we would get added to the neutron star.
Welllll…combination of that and angular momentum. Combined with the masses of the sun, and the moon, the other planets, and all the other masses of the universe.
Fortunately, orbits factor in, too. Everything that orbits is essentially in free fall, wellll…until they get tooo eliptical and the oscillating accelerations get really noticeable.
And it all affects time. Time is a bunch of wibbly-wobbly…stuff.
(( Ok, ok: Matt Smith might not have been that wordy as The Doctor. ))
I know this is true, but I never got my head around this, maybe someone can help.
So if a photon is emitted from the sun, it's passing earth immediately? Then why does sunlight need 7 or 8 minutes to get to earth?
And let's say, i travel one light-year at the speed of light, that should be instantaneous, right? The odometer would show 1 light-year, my watch would should 0 seconds and some decimals. How much would I have aged by the end of the journey?
If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth? Odometer would still show one light year?
And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?
> So if a photon is emitted from the sun, it's passing earth immediately? Then why does sunlight need 7 or 8 minutes to get to earth?
From the photon's perspective, it passes earth immediately. From our perspective, it takes 7 or 8 minutes.
> And let's say, i travel one light-year at the speed of light, that should be instantaneous, right? The odometer would show 1 light-year, my watch would should 0 seconds and some decimals. How much would I have aged by the end of the journey?
You would have aged as much as your watch says you would have aged. Zero seconds.
>If I travelled at one percent of speed of light, same distance, i suppose 100 years would elapse for me, how much would elapse on earth?
I don't know how to do the math, but a very, very long time would have passed on earth.
> And what if I left earth at 50percent of light speed , traveled 1 light-year away and did a turn and came back to earth at same speed. For me, it would be 1 year, but if I had a twin brother who was waiting on earth, would i now be a year younger than him? And how is this possible?
Yes, you would be younger than him, and it's possible because that's just how relativity and time dilation work. It's even practically measurable in "real" life: http://www.leapsecond.com/great2005/tour/
> Is travelling at the speed of light, actually travelling a a fraction of the speed of time?
This is probably one of the more counter-intuitive simple calculations you can do in physics.
In special relativity, distance is given by:
ds^2 = dx^2 + dy^2 + dz^2 - (c^2)dt^2
if X is your total distance in space, you have:
dX^2 = dx^2 + dy^2 + dz^2
Which is just the standard Pythagorean theorem of Euclidean geometry.
Further, your velocity is given by dX/dt. If you are traveling at the speed of light, you have:
dX/dt=c
From which you can derive
dX^2 = (c^2) dt^2
dX^2 - (c^2) dt^2 = 0
ds^2 = 0
In other words, the "distance" light travels in space time is 0.
> just curious... does "time" have a "speed" ?
It is not clear how to parse this question. Traditional "speed" is defined as distance over time. We can give this meaning for time itself by realizing that there is no single notion of time in relativity. As such, you could consider the line parallel to the time axis in the coordinate system of observer A. Since dt=0 in the coordinates of observer A, the speed of this line is not well defined. However, we could consider the coordinates of observer B. Assuming B is moving relative to A, he would see this line as being slanted, with both a time component, and a space component. As such, B could compute the speed of this line as dX'/dt', where X' is the total displacement along B's 3 spatial dimensions, and dt' is the displacement in B's time dimension. As such, B could meaningfully answer "what is the speed of A's time". Assuming I didn't mess up on the math, dX'/dt' turns out to be the velocity of A relative to B. This is a curious result that I have never seen before, but I can't really see any physical significance to it.
B could also compute dt/dt', where t' is the time axis in B's coordinate system. This computation seems more useful as it gives a direct measure of time dilation. Unsurprisingly, it also works out to be the Lorentz factor.
In special relativity, you have two notions of time:
- Time relative to an observer: Designating a non-accelerating massive object ("observer"), you get a coordinate system which assigns a time and distance to each event (point in spacetime). In this coordinate system, the observer moves along the time axis.
- Proper time: For an object taking any path through spacetime, you can measure the "subjective" time which has passed between two points on its trajectory.
The two notions coincide along the path of an observer: For each second of subjective time, the observer moves one second along the time axis in its coordinate system. Observer time moves at one second per second, if you will.
What you usually call "velocity" is distance/time in the coordinate system of some observer. For massive objects, this is always smaller than the speed of light.
If you want, you can define another notion of speed, to illustrate the original commenter's point: distance in some coordinate system per proper time. This can be arbitrarily high, because at high velocities the proper/experienced time becomes shorter.
To get back to the speed of time: If you measure coordinate distance per proper time, it is only natural to also measure coordinate time per proper time. If you take earth as the observer and follow a spaceship, this is earth time per spaceship time. For a fast spaceship, time on board passes slower than on earth (time dilation), so reciprocally, the spaceship moves through (earth) time faster than 1s/s.
(Unfortunately, the notion of proper time becomes useless for massless particles moving at the speed of light: proper time along their trajectory is constant. They "do not experience time".)
I know this might seem like a joke answer but I love it because it's the truest answer.
The 'speed of light' is nothing but a coefficient between seconds and meters (or in general, between units of time and units of distance and is equal to 1 in any sensible measurement system) since the spacetime in GR is unified
It can be said that everything is traveling through spacetime "at c (the speed of light)". The math works out such that the faster you move through space, the slower you move through time and vice versa.
The faster you move through space, the faster you move through time as well, actually! That's because distance in spacetime is defined with a negative sign for time periods. The profound statement is now that the subjective time (which can be measured by a clock moving along with you) matches the theoretically-defined spacetime distance (which is constructed to be invariant under Lorentz transformations).
Another one would be cause and effect, if that had already happened it means it must happen again... and so whatever he does there it will succeed in setting events in motion again... Interesting bit would have been how it all started.
> And let's say, i travel one light-year at the speed of light, that should be instantaneous, right?
Time slows down for the faster moving particles. And by time slowing down we mean all the particles in your body equally all start to move slower and more sluggishly in sync.
This is because it takes more energy to accelerate a particle as it approaches the speed of light. So if you had a pendulum clock moving almost at the speed of slight, that velocity of the pendulum at rest would be at X m/s, but if the whole system is already moving super fast the extra X m/s would take too much energy. So since the energy is constant the relative speed of the pendulum just becomes much slower.
If you were watching their lives out the window of your spaceship you’d see them in fast forward vv. they’d see you in slow motion. Everything is relative.
The main ”paradox” found by experimention is that the speed of light is a constant, regardless of your velocity. The only way this could be true, if you do a thought experiment, is if time was dialating for you. As for the physical and mathematical “why is this happening”, that’s where Einstein comes in.
It’s an exponential. At 0.5c 100 years to you would be 115 years elasped to an observer, 0.9c 229 years, 0.999c 2,236 years, etc.
> If you were watching their lives out the window of your spaceship you’d see them in fast forward vv. they’d see you in slow motion. Everything is relative.
Both observers, looking at one another, would see the other moving near c. Neither would know who was ‘actually’ moving. Yet, you assume there would not be a symmetry in their respective views of the other’s passage of time.
Explain why.
In simpler terms, a twin in a c-speed rocket could very well assume he was still and the earth was moving away. He should expect to find a younger twin when the earth ‘returned.’ Yet the examples only have the earth twin age, so to speak, and not the rocket twin.
It doesn’t answer your question directly, but the tricky part of a twin paradox is not that the earth twin observes his brother in a slow motion (the space twin also does that, thus a paradox). It’s because a space twin actually changes direction by acceleration at some point B, and at that time he skips over a big part of earth’s timeline. The video above only addresses why it’s NOT the earth twin who changes direction by acceleration, which you’re reasonably questioning. The universe somehow knows who is really “steering” and what remains more or less inertial. The pendulum example at the end may give a hint on why.
Edit: also, the space twin doesn’t have to experience any additional acceleration from the “engines” - looping around some gravity well would work too. E.g. an entire trip could be that the space twin goes to the orbit around the earth, gets slung away by a quickly passing blackhole, loops around a distant blackhole and returns, all in a complete free fall.
The symmetry is broken in your twin example because the travelling twin had to accelerate to depart, accelerate to turn around, and accelerate to stop again at earth.
I asked this in physics when I first heard the twin experiment. The answer comes from more complicated relativity based on acceleration and depends entirely on which reference frame you meet in. If you travel back to earth you age slower, if the twin catches up to you they aged slower....
It's not intuitive but time actually warps and there is no true concept of "simultaneous" in a special relativity world.
This TEDEd video works through the thought experiment, with messages sent from each twin to the other at 1-year interval (in the sender's frame of reference).
because light doesn't experience time, and the closer you get to the speed of light, the less time you experience. So what OP didn't say was that, while YOU can travel many lightyears in your lifetime, everyone you know will long be dead.
Also, it doesn’t take too much acceleration to make that trip. Comfortable earthlike 1g (~ 10m/s/s) is enough to build up a decent speed in a very reasonable time. Energy is the issue though.
It's worse than that. It's not possible with any type of rocket. If you are accelerating by pushing mass in an opposite direction then you'll never build a ship that can accelerate at 1G for years at a time.
Unless we invent a reactionless drive the idea of traveling between solar systems remains a pipe dream.
Yep. At 1g you could literally go to the edge of the visible universe in less than 50 years (assuming you are targeting the edge as defined at time of departure).
It is technically true, but requires all kinds of miracles, not the least of which is avoiding every trace of matter/antimatter between here and there.
Oh, and all light from the universe is now gamma radiation focused intensely ahead of the spacecraft cooking the whole thing.
An atomic nucleus sitting in deep space becomes an apocalyptic collision at 99.99% light speed.
You need to spend equal amounts of energy and time on both acceleration and deceleration. It doesn’t help to go fast if you can’t stop at where you are going.
Check out Pohl Anderson's "Tau Zero" which examines precisely this scenario. A starship using bussard ramjet needs to find an "empty" section of space free of interstellar hydrogen so they can fix their engines and decelerate without getting fried. This requires them to continue accelerating so that time dilation effects will allow the trip within the crew's lifetime. That's the setup, not the plot.
To put it another way, time travel machines are very much theoretically possible, and in fact are “only” an engineering problem (an extremely hard one, however). But, only forward travel is allowed: time travel machine could take you as far forward as its engineering would allow it, but there is no going back.
At 1G constant acceleration (both speeding up and slowing down) you can make it on a short vacation to the Andromeda galaxy and back in a lifetime (or 5 million years from the perspective or Earth).
Time elapsed (in starship's frame of reference, "Proper time")
T = (c/a) * ArcCosh[a*d/(c^2) + 1] (given acceleration and distance)
year = 365.25*24*3600; c = 3E8; a=9.8; d=1.25*1_000_000*(c * year)
from math import acosh
T = (c/a) * acosh(a*d/(c*c) + 1)
print(T/year)
=> 14.3 years each quarter
=> 57 years round trip
The speed at flip would be 99.99999999993978% c - good thing intergalactic space is mostly empty.
Oh, what a shame. I was about to install some rockets on my RV and head off to Andromeda. Guess I don't need to put my newspaper subscription on hold now.
since we are talking insane speeds and energies required to reach them why not just say you are in a bigger ship with more radiation shielding a dozen or so meters of water in the hull and a layer of lead a foot thick aught to stop most of it
FWIW, the Project Rho page I linked to also gives the derivation of the relativistic rocket equation. When I plugged in numbers, assuming an exhaust velocity of the speed of light (ie. impossibly high), I get a mass fraction of about 2,000,000 to reach top speed. Then another 2,000,000 to slow down.
Assuming the fully loaded RV weighs 5 tons, this means at max velocity the rest of the ship weighs 10 megatons, which is 10M cubic meters of water, or a cube 200m on each side.
That sounds like plenty of material, right?
The same Project Rho page links to https://arxiv.org/ftp/physics/papers/0610/0610030.pdf which calculates that at the relatively slow 0.995c "the penetration depth of protons of this energy will be ~40 m in water and ~10 m in titanium".
For 99.99999999993978% c, even 10M cubic meters isn't going to be enough.
They are only theoretically possible if you allow for negative mass and energy--not an engineering problem so much as a "need to find exotic matter"
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
Gp is talking about forward-only time travel though, you don't need anything exotic for that at all, just lots of energy and an efficient way to turn it into thrust.
> They are only theoretically possible if you allow for negative mass and energy--not an engineering problem so much as a "need to find exotic matter"
Basically people ran the EFE "backwards" to see what matter distribution makes the wanted curvature. You get either negative mass-energy or the bubble doesn't travel ftl iirc.
> I think a lot of people assume that this means you couldn't go more than a few (~100) light-years in your lifetime... But this is not actually correct
It his, it just depends on the observer.
An external, stationary observer will never see you go further than 100 light years, but yourself? Assuming you are able to make your ship go any arbitrary speed approaching c, you could be traveling billions of light years.
It's just that when you stop (if you manage to stop), the universe around you will have aged billions of years, while you will only be a few years older.
I assume people know how bad the penalty can be for going merely 10 MPH over the speed limit.
Don't worry about an individual photon except as part of an image in this example.
The light from the source hits the subject and is reflected toward your eyes at the speed of light.
That's why they call it the speed of light, and radio signals do it too between their source & receiver.
So now imagine you could travel faster than the speed of light to a planet a number of light-years away and you are going to get there from here.
Once you leave Earth orbit you will be able to accelerate up to and beyond c in the safest most gradual way directly toward your destination.
While still in orbit you look down on the traffic in your hometown, and everything is still moving at normal speed no matter how far it is down there, since you are a steady distance away from what it is you are looking at.
As you accelerate away from Earth and approach the speed of light itself you're beginning to catch up with the light that was reflected off your home planet quite a bit earlier than the light which is simultaneously being seen by those back in orbit.
So at half c you look out the window and it looks like everyone back in your hometown is moving at half speed. But naturally time marches on down there. You just can't be so sure any more. At that speed if you left 2 years earlier you will only be able to know additional things about your home which happened no more recently than 1 year ago at that point.
Of course you can't communicate with them about this in real time because of how long it takes the radio signal to get back & forth so you don't bother.
You keep going and reach full light speed which finally matches the rate the images are being reflected away from the Earth at, so now look back home and everyone appears to be standing still on Earth, as expected. Even though as far as you know they are still carrying on like normal.
OTOH, approaching the destination planet at the speed of light, that's pretty fast, but you have to realize their alien traffic is actually only moving half as quickly as it looks from your craft, whilst you are speeding so rapidly in their direction. Don't let that fool you, the aliens are only half as advanced as they look.
If you want to really see something, go faster than the speed of light and the planet you are approaching will be moving more than twice as fast as normal, and looking Earthward all you can see would be things moving backwards.
One thing that's happening is that you are always seeing images of these two planets where the light source originated from two different suns.
Once the distances get far enough, it's possible to launch a mission to a destination that actually no longer existed any more for quite some time before launch, only who knew?
In that case the earlier you make your reservations the more unwise it could be.
The distance doesn't dilate; time does. The distance contracts.
E.g., to a photon moving at 1c, the whole universe has a contracted length of 0 meters, and it crosses the whole universe instantly. To us, observers at <1c, the whole universe has a non-contracted length of <a lot> and the photon takes <a long time> to cross the whole universe. By the time the photon's 0-second journey across the entire universe has finished (whatever that means), we're all extremely old. :D This is the time dilation meme of slowly-aging space travelers but taken to the extreme.
So if I was in a space battle and the enemy 'jumps to light speed'(1) to make a quick escape ... they would actually be easier to target with a laser because they 'slow down' from my perspective?
(1) 'light speed' as in the speed of light, not as in a sci-fi context of hyperspace jump/FTL jump.
> E.g., to a photon moving at 1c, the whole universe has a contracted length of 0 meters, and it crosses the whole universe instantly.
Since the universe expands with >1c, I wonder if the photon actually crosses the whole universe. And if not, how it would look like from the prespective of the photon?
It basically depends on your perspective. To someone on earth watching the spaceship speed up to the speed of light, the spaceship looks like its contracting. To the person on the spaceship, the rest of the universe looks like it is approaching the speed of light, and hence, contracting.
I'm pretty sure this doesn't work out because you have to slow down.
So thinking about it, if you are traveling at that speed because of your inertial reference frame it is equivalent that everyone else around you is moving at (or near) the speed of light and they are moving slowly through time. This is the classic twin paradox and there is a resolution to it, which is that you can't instantaneously turn around.[0] Or in our case, we have to turn around to slow down.
It does work out, in fact you could go arbitrarily far in space (and, mandatory, in external time) if you had infinite energy to spend. The acceleration and deceleration phase is almost negligible.
Edit: the faster you go, the slower your own (inertial) time passes. That means the external time passes faster, and the factor grows to infinity the closer you get to C.
In fact, subjectively there is no speed limit. As you go faster, anything around you ages faster, but you yourself won't encounter any speed limit.
But in your inertial reference frame the people on Earth are moving at (near) the speed of light. So they are the ones that should be staying young. Or similarly the planet you are traveling to is actually speeding towards you and you are staying still. This is why the twin paradox is a paradox, because of the reference frames.
You're right that the apparent symmetry is broken by acceleration(s!), and to show that I'd point to Michael Weiss's twin paradox equivalence principle analysis at https://www.desy.de/user/projects/Physics/Relativity/SR/Twin... rather than rewriting it.
There is a subtlety not explicitly raised in the writeup, mainly that in General Relativity metrics do not superpose cleanly, in the sense of getting another solution to the Einstein Field Equations. We do not worry about this in the ultrasimplified twin-paradox model where the spacetime is flat in the sense that the Riemann tensor vanishes everywhere. However, if we want to consider the behaviour of gravitational waves with amplitudes outside of the weak https://en.wikipedia.org/wiki/Linearized_gravity limit, we are in a world of calculational pain.
Physicalizing this subtlety, if our travelling twin is travelling in our neighbourhood of the galaxy, it is probably in for a bumpy ride due to gravitational waves from nearby binary stars https://news.berkeley.edu/2021/02/22/binary-stars-are-all-ar... . We cannot easily extract how bumpy by adding in the uniform pseudogravitational field proposed by Weiss. On the other hand, we probably cannot quantify the effects of gravitational waves at all by simple adapatation of the other strictly Special Relativity analyses at the related Weiss link, https://www.desy.de/user/projects/Physics/Relativity/SR/Twin... (which lists among other the resolution in the minutephysics youtube link you provided above).
You're also right that the problem is one of reference frames. We are not obliged to use that of one twin as the spatial origin. In principle any will do, but some choices have advantages driven by features deliberately excluded from the Special Relativity twin paradox.
Let's consider the "(s!)" tacked on at the end of acceleration. We have not only that of the travelling twin's spacecraft engine, but also that which drives the expansion of the universe.
From within our galaxy we observe a highly spatially homogeneous and isotropic arrangement of extragalactic luminous matter (and cosmic radiation, locally) without distortions in the shapes of distant spiral galaxies that imply a spatially non-flat universe. The metric expansion of this, retaining bulk isotropy, gives us a preferred foliation (Wald's 1984 textbook develops this pp 92-93, but alternatively we could use Weyl's principle). Each twin is free to use a "cosmic fluid" observable (like the dipole-free temperature of the cosmic microwave background, which expands adiabatically), even while accelerating, to determine the https://en.wikipedia.org/wiki/Scale_factor_%28cosmology%29 . For example, each twin could consider the dipole pattern dT/T = v/c where T in the twin's proper time. Each twin can thus determine whether it is the relativistic traveller or not, even if it only wakes up occasionally and only long enough to look at a snapshot of the CMB. The travelling twin thus sees a clear breaking of the Copernican principle along the direction of its travel. Or more precisely, with respect to the bulk flow of matter and radiation in the universe, the non-travelling twin can conclude that it is effectively a Eulerian or comoving observer, while the relativistically-travelling twin cannot.
Moreover, the twins (and any third party) can use "cosmic fluid" observables to determine the scale factor when the twins are together at the start of the travel, and when they (or at least one and the other's remains) are together again at the end.
In this approach there is no paradox at all, there is only the consequences of one twin with a worldline with sections where the proper time is at a higher tilt to the cosmic time than the other twin's. We also avoid the difficulties in attaching a pseudogravitational field to a spacetime where there are gravitational waves of reasonably large amplitude, or relativistic stars and other massive compact objects.
We head into the land of apparent paradox by stripping out evidence of an expanding universe. We must also eliminate evidence of the aging of galaxy clusters through gravitational collapse (including the rate of star formation and the change in abundance of heavy elements). Indeed, we have to arrive in a setting in which neither twin can determine that it has departed from a point at which some reasonable generalization of the Copernican principle applies.
Indeed, the usual formulation of the apparent paradox gets rid of everything but the twins, so that one cannot even use Rindler/Unruh-like observables in flat spacetime, and this really emphasizes the "Special" in Special Relativity.
In that setting, as I said above, relying on the equivalence of being in uniform acceleration (even if it's instantaneous) and being immersed in a uniform (pseudo)gravitational field, is a reasonable way to eliminate the apparent paradox.
There is a related "love triangle" Special Relativity problem where there are three parties: stay-at-home (S), early-outbound-passer (E), and late-inbound-passer (L). None of the parties ever experience any acceleration: they remain eternally in uniform motion, with E & L travelling relativistically.
At our origin, S and E synchronize observe their identical atomic wristwatches coincidentally agree that it is "0". Light-years away, E and L come very close to one another and exchange timestamps showing that coincidentally their identical atomic wristwatches agree. Finally, L and S come very close to one another and compare timestamps from their identical atomic wristwatches. All the wristwatch times are identical to those at the three points in the diagram of the "instant turnaround" version of the twin paradox, we've just turned the travelling twin into two unrelated travellers on different trajectories.
The argument is that this "love triangle" is resolved because E & L are different travellers in uniform motion, so all parties must combine the times acquired in two different reference frames (E's and L's) to compare with the times acquired in S's reference frame. The further argument is that this duplicates the "instant turnaround" version of the twin paradox if we can have the travelling twin change direction without acceleration.
Firstly, we can still solve this with a pseudo-gravitational field popping up at the moment E & L exchange timestamps. It's no more of a coincidence than the identical timestamp when S & E are close.
Secondly, it's not clear that the paradox remains interesting in this case, because there is no expectation that S & L should be the same age when they are close to one another again. They aren't twins. Unless we add in accelerations, there is no way by which S, E, and L could all have been born at close to the same location in spacetime.
Thirdly, it's unclear that there can be an instant turnaround without acceleration. A couple flavours have been explored here and there.
One involves a slingshot around a star to change directions from away to towards the stay-at-home twin. In this picture the travelling twin is always in free-fall. But here we are substituting real gravitation (that of the star) from pseudo-gravitation. We've moved from everywhere-flat Minkowski space -- the spacetime of Special Relativity -- to something closer to Schwarzschild spacetime, which is only asymptotically flat. Moreover, we are using the near region of Schwarzschild to accomplish the slingshot.
Another substitutes the open flat Minkowski space with one in which there is a compact spatial dimension that curls back on it self. A universe with the geometry of a cylinder with infinite height and small circumference, or a torus, or a sphere would do. The cylindrical case has been explored recently : https://doi.org/10.1119/10.0000002 with comparisons to Minkowski space (the spacetime of Special Relativity), §IV (Conclusion) being pithy. Again, I see this as trying to substitute pseudo-geometry with real geometry, an adapted clock-comparison recipe, and a highly privileged frame for the traveller, in order to avoid a non-gravitational acceleration opening the door to a pseudogravitational field arising in the ultrasimplfied and thus strictly Special Relativity problem.
Finally focusing on the latter part of my comment that I'm self-replying to (mostly for my own benefit), we have only done away with one acceleration by the returning twin. We still have the effects from the behaviour of matter in the expanding universe with which to clock S, E and L, removing the remaining paradox if we somehow contrive to have S, E & L expecting to age similarly. If we are abandoning Special Relativity in order to avoid acceleration by the returning without invoking outright magic, why only do it along one spacelike dimension, or by importing a very finely tuned third traveller?
