What would life be like for an Earth-like planet that orbited a star like that? What about spaceflight (e.g. from a planet to a moon) within that solar system? And what would the rest of the universe look like to them?
The rest of the universe would look quite different, though. Stars "ahead" of the solar system - in the path of its motion - would be noticeably blue-tinted and clumped together. Stars behind the system would be red-shifted. There are some great visualizations at [0].
[0] https://math.ucr.edu/home/baez/physics/Relativity/SR/Spacesh...
Stars might pass through their lifecycle in a matter of weeks. Constellations might deform over days.
But ya, you'd have to be going really #*$&#@ fast.
In the frame of the planet orbiting the hypervelocity star, the rest of the universe is moving at 0.5c, so the planet would measure all clocks in the rest of the universe to be running slower by a factor of 1/sqrt(1-0.5^2) = 1.15. Astronomers on this planet would measure stellar lifecycles (and every other physical process) to proceed slower, not faster.
You have it backwards (easy to do with such a thought experiment!). The direction of time dialation originally stated was correct. Clocks on a body moving at ludicrous speeds will be slower (to the observers present, who are able to look at those clocks) than clocks on a body not moving at ludicrous speeds. Which is to say, if you did a loop around the galaxy at light speed (hypothetical, of course) and came back to Earth and compared your clock with a terrestrial clock, your clock would be waaaay behind, and you would be younger than the people you left behind. This effect is measurable and provable even in the orbit of our own planet (albeit, at a miniscule scale). And so while your time did in fact move more slowly, the overall effect is that you time travelled into the future because everyone else was moving much faster. This of course assumes that you are able to escape intact, which is most unlikely (again, this is just a thought experiment, for argument's sake).
In your defense, I know how easy it is to get turned around in such a thought experiment. Theoretically speaking from the perspective of the par-luminal traveller, it's easy to think "my clock moves slower, so am I slower?" In a way, yes, you are! Your reality moves slower relative to theirs, and for those not travelling at light speed time passes more quickly relative to your time. Objectively speaking, a human lifecycle on a very fast moving planet will equate to many, many lifecycles on a slow moving planet, if all other things are equal. And so while you are truly travelling much faster, your time moves slower, relatively speaking.
Remember as a kid being told about a hypothetical traveller that enters a black hole, and at one point they become a long spaghetti string and then simply freeze in time? That's because they are moving much faster than us, and from the outside looking in they appear to be frozen. The light emitted from their mass is but an echo. They have moved far beyond the light that we see. From the inside looking out, the universe would move much faster.
Again, this is an extreme example used for clarification, but it might not be as extreme as you think. Consider a solar system that gets caught within the grasp of a black hole. Initially the tidal forces tear it apart, but over eons that mass might begin acting like a normal solar system again, and harbor life once more.
If you are travelling fast in a straight line, you will observe the clocks in the entire universe around you running slower. Every clock you watch through a telescope on your ship will be running slow. The entire universe around you will be moving in slow motion.
However, everyone else observing you speeding by in your ship will observe your clocks running slow. They will observe you moving in slow motion.
This is an apparent paradox - in fact, it is the quite famous twin paradox.
The resolution is that this only holds for non-accelerated motion. Flying in a loop around the galaxy requires not just high speed but also a constant acceleration, giving you the additional effects of general relativity, which complicates the situation by quite a lot, but resolves the paradox.
However, an inhabitant on a star moving at relativistic speed through the universe still falls under the original case - the inhabitants on the star will see the rest of the universe moving in slow motion, while the rest of the universe will see them also moving in slow motion.
Very interesting response! Thank you for that. I do see why my comment was misleading now. If you don't mind, could you clarify a few things? I'm just really interested in the subject.
I understand your point about travelling in a straight line: If a traveller were to travel at the speed of light speed away from a theoretical stationary point then both the observers at the stationary point and the observer within the travelling vessel would appear to eachother as frozen (assuming the traveller had equipment to measure the place they left from), because light wouldn't be able to catch up in either direction. That makes sense. When I said "From the inside looking out, the universe would move much faster" I shouldn't have used the term "looking out", that was definitely misleading now that you've mentioned it.
> However, an inhabitant on a star moving at relativistic speed through the universe still falls under the original case - the inhabitants on the star will see the rest of the universe moving in slow motion, while the rest of the universe will see them also moving in slow motion.
Your last statement got me thinking... so let's say there are two equally sized vessels that are somehow able to communicate instantaneously (for arguments sake, let's say the travellers are immortal wizards who have a telepathic link).
Let's say that one of the vessels is caught in the orbit of a black hole and is travelling at nearly the speed of light, and is constantly accellerating as it gets closer to the singularity (ignoring that tidal forces would destroy the vessel, because of it's wizard shielding).
The other vessel is lacadaisically making it's way around a star the size of our own. And let's say that the star and the black hole are slowly drifting away from eachother.
My question is this: Will the wizard inside of the vessel travelling around the black hole age more slowly than the wizard travelling around the normal star? Keep in mind that they will never meet (i.e. never share the same world line), but they do still have a telepathic link and can compare their clocks.
We talk about the "speed of light" being a constant, but this is misleading. The "speed of light" is actually the "speed of causality". Breaking the speed of light, with some theoretical instant communication, would be breaking causality.
In the earlier example, if those two stars each had an emergency beacon that sent you an instant message just as they exploded, you would receive both simultaneously. But the person travelling past you would be very confused about how that could happen, since he clearly observed them exploding at different times.
I do understand what you're saying, and while I agree that observations differ based on the location of the observers, there's one thing that still baffles me. Quantum entanglement.
Let's say that we replace the wizards in my example with a pair of entangled particles, and in fact, for this thought experiment let's pretend that humans and "observers" don't even exist anymore - there is noone left in the universe to observe what is happening anywhere.
Wouldn't our current understanding state that the wave function would be identical between the particles regardless of where those particles are located in spacetime? In effect, wouldn't the wavefunction be "happening at the same time"? Mind you, I'm not suggesting that the particles are communicating, simply that their waveforms are identical. It's really baffling to me that one particle could be in an area subjected to massive gravitational distortion while the other is not (a completely different world line), and yet they are always in sync. Thoughts?
I've read that as well, and I concur that popular opinion states that quantumly linked particles do not appear to violate causality, because we don't believe they are actually communicating at all, let alone communicating faster than light.
The way I interpreted this claim is that those particals are more akin to a deterministic algorithm, which is to say, once you set it free it will always result in the same answer based on the seed. I'm still very confused though about how those particles could remain in sync in vastly different spacetimes. That to me, is a flaw in the conjecture, and one that cannot be tested. We've based our understanding of quantum entanglement only upon that which we can observe, and so we truly don't know if a quantumly entangled particle will be "behind" if it is in a denser gravitational field. It's unprovable, because even if we were to travel into that spacetime, we could not escape to share the results with other observers.
Thank you again for your input. Your argument forced me to mentally reconcile "observable reality" from "actual reality", and that was a fun and intriguing thought experiment, albiet probably pointless since none of it can be proven. Our observations do not define reality, they only measure it to the best of our ability. And most of the time when we measure reality, apparently we fuck it up (i.e. breaking quantum links, or just having incorrect assumptions).
No. When you go fast time slows. Thus the rest of the universe appears to be going faster.
So if you fly away on a spaceship at relativistic speed, then people observing you will see you moving slowly. However, if you observe them from your ship, you will think it is they who are moving slowly.
When he returns all of his friends have aged 50 years. But he has only aged 1 year.
So you see, his friends were aging 50x faster.
Assuming the planet miraculously hung around for the ride, after the initial acceleration, it would be no different then what we experience here on earth.
Remember that everything is relative and perspective is key. A question about speed depends on who you’re asking.
To us, the other star and it’s planets are traveling at near light speeds away from us. To that stars system, it’s Earth that’s traveling at near light speed away from them.
Space flight would be the same and so would gravity and time. To them, nothing changes within their stars system because it’s all within the same reference frame.
I guess the night sky would be the main difference for people on that planet. They’d see the galaxy they left behind as red shifted and anything they’re speeding towards as blue shifted.
Since they’ve left the galaxy and was red shifted, they probably wouldn’t see as many stars with their naked eyes.
This has always bothered me a bit, everything being relative. You can validly say that we're the ones moving at near light speed and those stars we're talking about are actually the stationary objects; there's literally no way to tell the difference.
Couldn't you say the same thing about the earth and the sun? Why do we insist that we are moving around the sun, and not the other way around if everything is relative? Well I understand the reason actually, and it seems that there is good reason to believe one interpretation of relative motion is the correct one, conforming to physics.. and the other view of relative motion isn't actually what's happening in reality.
A planet orbiting the sun is accelerating toward the sun.
How do we know that the sun isn't orbiting the fixed earth, and accelerating toward the earth? Everything would look _exactly_ the same to everyone.
Yes, the math works out much easier and more neatly, so that is likely what is happening in reality. But from a purely relativistic framework.. you can consider any point in space the frame of reference, and all motion relative to that "fixed" point.
It makes me think that relativity is actually describing a more subjective experience, rather than the objective reality where we "know" the earth orbits around the sun.
Well, yes.. because Einstein's theory beautifully makes all the math work out, explaining one interpretation of motion as the real one. But what it did at the same time was show that there is no "fixed grid" of space independent of the objects themselves. Which is what leads to my uneasy feeling of how we ever can say one interpretation is more real than another -- i admit it may just be a nonsensical perspective.
As for what all physicists mean by relativity in general... I can highly recommend this old series from the National Science Foundation:
That wouldn't work out. You can take the earth as a fixed point and describe the Sun's motion relative to it, and it would be perfectly valid, but it wouldn't look as the Sun orbiting the Earth in any kind of almost constant speed elliptical orbit, it would look like a very different kind of motion.
So yes, it is correct to say that the sun revolves around the earth or the other stars are stationary while the sun is moving.
So while both relative views are equally true, the laws of physics (or at least mathematics) don't seem to hold both those views with equal esteem.
However with the introduction of the mathematics of general relativity by einstein in 1915; we can prefer whatever reference frame we like and we get the same correct predictions. Predictions that are more accurate than Newton's.
Technically, the earth doesn't rotate around the sun either -- they both rotate around the center of mass of the solar system, which happens to be very close the the center of the sun, so it looks like everything rotates around the sun.
Clearly you aren't aware of what the principle of general relativity is. It is not a good idea to argue about a topic where you lack basic knowledge.
Try to express the trajectories relative to earth of other planets in our solar system and you will quickly understand why we use a heliocentric model.
Because it makes the math easier - that's all. If you fix your frame of reference to the Sun, the orbits of all other bodies become almost perfectly elliptical. If you try to pin the reference frame to any other body, you end up with complicated curves. But they model the same thing[0]. So the whole thing about "Earth orbits the Sun" is that it gives same results, but is much easier to work with.
Technically, for the easy math, the point you're after is the barycenter[1] of the Solar System - the center of mass, which, per Newton's First Law, can be used to center the reference frame, because it's not accelerating[3]. As it turns out, the barycenter of the Solar System spends most of the time within the volume of the Sun[2], and otherwise is very close to it. So for most calculations, you may just as well pin the reference frame to the Sun.
And then, when you fix your sights at the barycenter, you'll notice the movement of celestial bodies fall out pretty much straight from joining Newton's Second Law with the Law of Universal Gravitation - m₁a₁ = Gm₁m₂/r². Your model simplifies - you now realize the movement of celestial bodies is governed by the same laws movement on Earth is, and all the complexity of geocentric model was caused by needless coordinate transformation, due to a bad choice of the reference frame.
Also worth noting that historically, humans have developed the geocentric model to a very impressive level of precision - to the point that the "upstart" heliocentric model initially was worse at predicting movement of planets. It took some extra insights for the heliocentric model to beat the old ones[5] - and only then Newton came along, and people connected the effect with the cause.
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[0] - If I recall correctly, if you were to take the path of a planet in a geocentric model and do a Fourier transform on it - that mathematical operation which represents a function of time as a possibly infinite sum of sine waves - you'd notice that the path of your planet is essentially a sum of two periodic functions. One would correspond to the movement of Earth around the Sun, the other to the movement of the planet around the Sun. This would give you a strong hint that your model is needlessly complicated, and can be recreated using much simpler curves.
[1] - https://en.wikipedia.org/wiki/Barycenter
[2] - https://en.wikipedia.org/wiki/Barycenter#/media/File:Solar_s...
[3] - Only forces from outside the considered system could cause it to move, which we're by definition not considering when talking about our system in isolation. And besides, they add up to negligible amounts anyway. Nice thing about forces in our reality scaling like 1/r^2 or worse[4] is that they very quickly add up to nothing with distance, which makes it easy for us to treat systems as isolated in calculations, and have the results match up to reality with extreme accuracy.
[4] - https://en.wikipedia.org/wiki/Inverse-square_law applies to gravity and electromagnetism; weak and strong forces drop much faster with distance.
[5] - Like using ellipses instead of circles as the fundamental curve, because your competition that used circles moving on circles could just keep adding circles - they were doing a Fourier transform without knowing it, and each circle added a frequency component, increasing the accuracy of approximating the actual ellipse.
It actually annoys me that we still teach kids that the Earth revolves around the Sun and the ancients with their silly earth-centric system were wrong. Just the math is (kinda [1]) simpler, thats all.
First, its a lie. And second it breeds contempt for the ancients that said and discovered many great things. I dont mind telling them that heliocentism is a great (amazing) approximation. But I really dont appreciate how from K-University previous work that has been outdone is dismissed [2]
[1] the higher order terms are sill there in the heliocentric system, they're just smaller in magnitude.
[2] Another example is atomism and how the physicists who rejected it are mocked in undergrad classes. Those guys were bloody titans and their models and methods are the cornerstone of modern engineering (try designing a bridge w/out continuum mechanics but using MD)
I wonder if this will work on trying to talk yourself out of a speeding ticket?
Edit: according to [0], you would have to be driving at 30855km/h (2237mph) to see a red semaphore as green, which comes up to ~3 millionths of c.
[0] http://www.astronomy.ohio-state.edu/~ryden/ast143/ps3_soln.p...
As sibling comments describe, any planetary orbits that happen to survive would continue operating as usual, but if they were outside the heliosphere they would be subjected to interstellar gas traveling at half light speed in the other direction.
As such in a cosmic void planets around such stars would be fine. Though it seems extremely unlike for such planets to exist.
It's negligible compared to our sun. All this from the top of my head (so double check if you really care ;) but our sun in winter at surface level is roughly about 100W/m^2 and in summer about 1kW/m^2.
To make this comparison more concrete, maybe we could consider how much alpha particle energy is present inside of a nuclear reactor running at peak energy output. I'd be surprised if it was as much as 1 W/m^2.
Next solar wind actually becomes significant protection at those densities. It varies significantly and simulating what happens gets complicated, but it shouldn’t be ignored at those densities.
Anyway, the outer fringes of earths atmosphere for example is almost exclusively Hydrogen and Helium as it gets sorted by atomic weight. Free neutrons decay in a matter of minutes and therefore would almost entirely end up as more hydrogen. What’s a much larger risk is stripping the atmosphere off of any planet.
The outer fringes of the Earth's atmosphere are hydrogen, but the density there is so low that these cosmic ray particles would be unlikely to interact there. Also, the neutrons here are FAST neutrons (the (n,p) reaction on 14N is a fast neutron reaction) so they are traveling at very high, if not relativistic, speed, and would not have time to decay before they react (or are thermalized and become irrelevant to 14C generation from 14N).
As to the density of earths hydrogen, that’s a function of earths atmosphere. Under sustained bombardment, assuming the planet kept an atmosphere, it’s going to have significantly less nitrogen in the upper atmosphere as that’s destroyed by collisions with relativistic hydrogen/helium.