Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EvaH on 29/10/2020 14:48:22

Satya asks:
If you go straight in the universe, will you go round in a circle and end up in the same place that you started?
What do you think?

That depends on how you define "straight" and "same place"
There are two very reasonable interpretations for which the answer to the question is yes:
• The trivial solution is one in which you define "place" relative to one's self. In this case, I am always "here" and never move from being "here." Instead other things in the universe move relative to me. (in this case the bit about moving in a straight line is not so meaningful.)
• The more meaningful answer is: If we account for gravitational curvature of the spacetime in the universe, then a straight line can be a stable orbit about a massive body. (ie you can go "straight" in a circle around a star). This, however does not account for the motions of that star with respect to other things.

If you go straight in the universe, will you go round in a circle and end up in the same place that you started?
Well I'm going to go so far as to say it depends on your definition of 'go' and for that matter, 'place'.
I think the question is meant to be about the large scale geometry of the universe. So for instance, the surface of Earth is a nonEuclidean 2D surface, and if it was perfectly spherical, you can start anywhere, draw a straight line in any direction on it that never bends left or right, and the line must come back to its starting place. So is the universe like that? It could be, but is generally not considered to be so.
Now about the definition of 'go': If I walk in a straight line on Earth, I will eventually come back to my starting place. But if Earth is expanding by 1% each day, I simple do not walk fast enough to ever get to that point, but if I had a vehicle that can 'go' fast enough, yes, I'd complete the circuit. So the universe has a speed limit, and so no matter how fast you 'go', you're not going to get beyond the event horizon, which is currently about 15 billion light years away. The universe is bigger than that, so not even light can make one circuit. You can't see Earth if you 'look far enough', even if spacetime was closed in a loop.
About the local spacetime curvature of which chiralSPO is speaking. Back to the Earth example, except it isn't a perfect sphere, but has smooth hills and valleys here and there. Now a typical line drawn, never bending locally left or right, will not come back to the starting point except by low probability. The curves in the surface will bend the path left or right, and you'll end up somewhere else after one circumference worth of line drawing. For the same reason, light going anywhere in the universe is deflected this way and that a little bit every time some large mass is passed.
There are places in the universe bent sufficiently that light will come back to its starting point in a short time, but nothing like that in our solar system.

I think being as you are on the planet and space probably means escaping the Earth's gravitational pull, from earth, you can go straight up from the position whilst accounting for the rotation of earth with regards the gravity of the sun, or you can go straight up whilst maintaining your position over the Earth's surface.

If you go straight in the universe, will you go round in a circle and end up in the same place that you started?
The universe is embedded in a 4dimensional spacetime.
As we understand it today, time marches inexorably forward, so you can never return to where you are now in spacetime.

Define straight :)

An absence of lateral acceleration

And what is a 'straight line' in SpaceTime?

Presumably, the track of a vehicle that does not experience lateral acceleration.

There are several definitions, yours as good as anyone else I've seen Alan. In a flat space the shortest path between two points. Or a geodesic, or a world line in Relativity. Or just a definition of light always choosing the shortest path between two points, from which follows that if one follow the light one can't go wrong :)
and in the mean of asking what would happen if you tried to follow that path Satya, we don't know.
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There is one thing though, you can't get back to where you started, as long as we define time as being a arrow always pointing to the future.

So the relativistic question is whether the occupants of a vessel following a beam of light, which describes a geodesic in spacetime, would experience any acceleration perpendicular to the axis of their ship.
Obviously we can't chase a photon from its origin, but we can point our ship to a distant source of photons and see what happens.

Obviously we can't chase a photon from its origin, but we can point our ship to a distant source of photons and see what happens.
Thanks to Einstein & Eddington, we know that photons from a distant star are slightly deflected by passing close to the Sun.
Thanks to Kepler & Newton, we know that comets (and spacecraft) are strongly deflected when passing close to the Sun.
If you were to follow the path of photons back towards their distant star, you would experience extreme lateral accelerations, as the Sun's gravity tries to whip you around in a narrow ellipse, but your rocket engines try to make your spaceship follow an almost straight line towards the star.

Well, there are some other definitions too. I said ' light always choosing the shortest path between two points'. you can also express it as it chooses the path that takes the shortest time, they are not exactly the same, although, ah well. I can't decide on that one. Personally I look at it as a straight line is the one expending no energy, but that's when I naively apply it on what I get from reading about SpaceTime.
This is one definition. https://en.wikipedia.org/wiki/Fermat%27s_principle
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What is thought provoking in it is this " First proposed by the French mathematician Pierre de Fermat in 1662, as a means of explaining the ordinary law of refraction of light, Fermat's principle was initially controversial because it seemed to ascribe knowledge and intent to nature.
Not until the 19th century was it understood that nature's ability to test alternative paths is merely a fundamental property of waves. If points A and B are given, a wavefront expanding from A sweeps all possible ray paths radiating from A, whether they pass through B or not. If the wavefront reaches point B, it sweeps not only the ray path(s) from A to B, but also an infinitude of nearby paths with the same endpoints.
Fermat's principle describes any ray that happens to reach point B; there is no implication that the ray "knew" the quickest path or "intended" to take that path. "
hmm

And here's something funny about it. If we assume that a wavefront 'sweeps' all possible paths. What happens to those ones 'non existing' in a outcome? Do I need to introduce a many worlds scenario in where they too exist? But if they would, somewhere exist, Fermat's principle can't be true, am I right?
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If I am correct there, and Fermat's principle also is correct, they either quench themselves, or, they won't exist? And if I apply that on 'many worlds', where does it leave those?

I smell a (very common) misconception!
Physics is about building mathematical models of phenomena. The wavelet method, many worlds, superposition etc., is a usefully predictive model but doesn't purport to be the "real thing", in particular because it demands that a single photon splits itself to pass through two slits, but all we ever measure in the near field is a whole photon at one or other slit, so it isn't a complete statement of reality and should not be taken too seriously.

In a way it explains everything Alan. Calling it 'models' or 'interpretations', but it doesn't change the facts.

If I want to be cynical, which I most probably is, I would say that without a interpretation statistics are meaningless.

In a way it explains everything Alan. Calling it 'models' or 'interpretations', but it doesn't change the facts.
Predicts most things, but doesn't explain them. A good example is tide tables. You can predict tides several years ahead by fitting sine curves to historic data, without knowing anything about gravity or even looking at the moon. Then you look at the sun and moon and predict the motion of planets from your mathematical model of gravitation but that doesn't explain why inertial and gravitational mass are identical, or why gravity sucks.
I find "interpretations" even less satisfactory than empirical models because they are an attempt to fit your new observations into your old beliefs  that's intellectual vanity, whereas science demands humility.