Physics people. Let's assume that we live in a closed universe (in which you travel far enough in any direction and end up back where you started). Picture two observers Alice and Bob, both in inertial reference frames and traveling past each other, each measuring the other's velocity to be close to c (and theirs to be 0, obviously) as depicted. On one particular 'pass', when they're both next to each other, they synchronise their clocks and continue on their way. The next time they meet each other, both will claim that more time has elapsed on their own clock, but they cannot both be correct, thus we have a paradox. Does this mean that we cannot live in a closed universe or is there another solution?
>>7652676
>synchronise their clocks
whooops
>>7652676
Think about this.
How do they synchronize their clocks?
What is the physical method of determining synchronisity?
>>7652676
those names seem familiar
>>7652682
British English spelling
>>7652684
This is just a thought experiment, I don't think that there's anything physically stopping them doing that. But for argument's sake, when they pass they both set their clocks to 12 o'clock.
>>7652690
lol dude its not the spelling i was talking about
>>7652696
haha good. Another way to think of it is, when they pass, they both start a stopwatch...
>>7652676
Openin gstatement
>Physics people. Let's assume that we live in a closed universe (in which you travel far enough in any direction and end up back where you started).
Closing statement
>Does this mean that we can live in a closed universe or is there another solution?
Your problem assumes we live in a closed universe only to prove we live in a closed universe. That's as stupid as saying "imagine if we lived in a universe where everything is purple, if I look up I see purple. Does that mean everything in our universe is purple?"
Sage in all fields
>>7652705
Typo, was meant to be "Does this mean that we CAN'T live in a closed universe or is there another solution?". But I'm sure that's pretty obvious to most...
>>7652705
>Openin gstatement
>>7652676
To reach this state, both clocks have had to accelerate. Acceleration slows down the time, not the relative velocity itself, because I just made that up to avoid thinking about it.
>>7652722
maybe, but once we're in this position, the situation still stands, they'll both think that their clock should measure more time passing that the other person's, but this can't physically be possible
>>7652693
It does matter. The method for defining synchronicity is important.
For example, how do three stationary people, separated by large distances, synchronize their clocks? Relativity should not enter into this, they are in inertial reference frames, all velocities are 0.
>>7652740
'People' are just an illustrative tool in the situation. As mentioned before, imagine that when they pass at their closest distance (an arbitrarily small distance if you like), they both press start on a stopwatch, and the next time they reach that point, they both take a (fleeting) glance at the other person's stopwatch. Shouldn't be any physical problems here, synchronizing clocks is used all the time in relativity textbooks (i.e. it can in principle be done).
>>7652740
"When we both cross line 'L', we both press start on our stopwatches and when we pass it again, we both look at the other person's stopwatch"
>>7652778
whoops top-right two arrows should be pointing the other way
>>7652778
Because when you say look, you imply light passes between them instantaneously
Draw the light rays, if they are moving 99% c it would take them a long time to find out that the other person crossed the line.
>>7652786
I did say that when they pass they can be arbitrarily close. So close that the time it takes for the light to travel to the other person would tend to zero, which is good enough.
>>7652786
Stop being retarded about an irrelevant point.
OP is right. If the universe had a flat metric, and was essentially a cube with opposite sides identified, then we could do the experiment that OP describes. As they pass, they start their clocks. When they pass again, they stop them. Their clocks must read the same then.
>>7652826
>>7652816
See, because it does matter
It does not matter how close they pass each other.
For example, assume your closed flat universe is 1 light second long. That means you can represent it as a closed loop with circumfrence of 1 light second. The stationary person is sitting at a point on the line, we will call x0. He sees the person travelling at 99% of c and starts his watch. The person travelling doesn't even see the person until he has travelled 99% of the entire distance necessary. At which point he starts his stop watch. He doesn't see how much time has passed until his second full rotation is almost complete.
>>7652826
It seems that they must be the same, just by the symmetry of the problem, but still special relativity is telling us that they'll be different so where's the flaw? Relativity or the assumption that we live in a closed universe?
>>7652715
weak and underaged
>>7652867
The whole point of relativity is that there's no "stationary" person. There's no ether and this "issue" is all very pedantic.
To the guy flying around the circle, he is stationary and the "stationary" guy is flying round the circle.
>>7652875
> Gr8 b7 m9
Heey, physics bachelor student?? I guess.
This problem comes from the fact that you have studied special relativity, however special relativity does not cover the whole picture. Because there are other things happening when for example you accelerate. Take a course in general relativity and you'll understand.
>>7652891
>The whole point of relativity is that there's no "stationary" person.
No, and I wish people would stop repeating this.
A functionally, spatially stationary object, can exist, we just can't resolve what or if it is. This is ignoring particulate movement or whatnot.
>>7652913
>A functionally, spatially stationary object, can exist, we just can't resolve what or if it is.
i wish all the highschoolers would leave already
>>7652909
I'm a 4th year MSci student and I'm studying general relativity. There's no acceleration in this problem, just two inertial reference frames so it's my understanding that special relativity is all that's necessary.
>>7652913
stationary relative to what? The only thing that matters is relative velocities (in the absence of gravitational fields/acceleration)
>>7652913
Ever heard of the Michelson-Morley experiment?
>>7652921
new anon here, I understand that there is no acceleration in the problem. OP also assumes that the universe is closed, which mean this circumference >>7652867 is expanding. It's actually expanding faster than light (so the circle would turn into a hyperbola) and alice and bob would never pass each other unless they accelerate to speed faster than the speed of light relative to each other. This is mathematically equivalent to time traveling, and I believe this resolves the apparent paradox.
TL;DR The universe is too big to know for sure. Maybe some older lifeforms can tell us what their experiments concluded when the universe was small enough to not expand faster than c.
>>7652924
The universe itself.
If space is quantized to a grid-like structure, then only two states can exist. Moving, and not moving. It has nothing to do with being relative to anything beyond that's it's necessarily part of a binary relationship.
Whether it's completely and absolutely not moving, or if space is or isn't like I described above, is irrelevant. There can exist a state where motion (translation through space) is so trivial it might as well be stationary. You just, as of yet, couldn't ever know if something was or wasn't.
>>7652935
You may well be correct for our universe. It's interesting to see however that there can't be a static closed universe that obeys general relativity like ours does, but I'll leave that one for the cosmologists.
>>7652939
Sorry but about half of modern physics is based on the assumption that what you just said isn't true. The only possible way to tell if you're moving is if you are moving relative to something else. Please just accept that/ read an elementary special relativity textbook.
A little gedanken experiment to reassure you: would there be any way at all of differentiating between:
You start moving to the left at 5m/s.
Everything else in the universe starts moving to your right at 5m/s.
>>7652953
You just repeated what I said, and I'm not sure why.
>>7652955
I don't think I did. You are claiming that something can be absolutely stationary relative to the universe (whatever that means) and I was trying to refute that.
>>7652955
>everything else in the universe
and
>the "grid" or "coordinate system" of spacetime or the universe or whatever the fuck you're vaguely defining
are not the same. In fact the second one is nonexistent.
>>7652962
Exactly, anon's referring to the Ether which has been proved to be non-existent.
>>7652676
Let's do the math here. I think it'll clear things up.
The concept of "synchronization" here is vitally important. Let's go with your example: That they start stopwatches when they see them passing the other, and on the next pass they'll check each other's times.
From the point of view of a stationary observer, Alice and Bob are 1 light-second apart, travelling on parallel paths. Alice is moving at 0.99 c in the -x direction, and Bob is moving at 0.99 c in the +x direction. The universe is only 100 light-seconds long, and wraps around like a Pac-Man game.
At t=0, Alice and Bob are both at x=0, the left end of the universe. However, they don't start their stopwatches - remember, they're 1 light-second apart, and have only just passed each other, so the light hasn't reached them yet!
Instead, Alice and Bob start their stopwatches at t=0.5, when Alice is at x= -0.495 and Bob is at x = 0.495. Why? Because that means Alice is where Bob was 1 second ago, and Bob is where Alice was 1 second ago. So from Alice's point of view, Bob's only just passed her, because the light from Bob shows him to be right next to her.
And likewise, although from our stationary perspective Alice and Bob pass each other again at t=50.5050..., at the x=50 mark, Alice doesn't see Bob passing her until t = 51.0050, because that's when she passes where Bob was 1 second ago, at t=49.0050.
So, Alice and Bob starts their stopwatches at t = 0.5. At t = 51, Alice sees Bob passing her again, and checks Bob's time against hers. Because Alice is seeing Bob as he was 1 second ago, that means Alice sees Bob's stopwatch as it was at t=49.
[cont]
>>7652971
At 0.99 c, the relativistic time dilation factor is ~7.089.
Since Bob started his stopwatch at t = 0.5 seconds, and Alice read it off at t = 49 seconds, that means that Bob's stopwatch has been running for 48.5 seconds from our point of view, so Bob's stopwatch will read 6.85 seconds when Alice reads it.
Since Alice started her stopwatch at t = 0.5 seconds, and Alice saw Bob pass her at t = 51 seconds, that means Alice's stopwatch has been running for 50.5 seconds from our point of view, and so her stopwatch will read 7.12 seconds when she checks it against Bob.
So Alice, therefore, sees Bob's stopwatch as having more time on it, and will conclude that Bob's clock is ticking slower.
Meanwhile, for exactly the same reasons, Bob has just checked Alice's stopwatch and finds that his reads 7.12 seconds, while he sees hers as reading 6.85 seconds, so Alice is ticking slower.
And from our point of view, they're both ticking at the same speed.
>>7652959
>and I was trying to refute that.
Try again, I guess?
Yes, I am saying something can for all functionally relevant purposes, on our scale, be more or less stationary. We're apt to frame it in terms of relative motion because the kind of information required to resolve what I'm describing just isn't available, but that doesn't mean it cannot be occurring.
Put it this way, in the context of your example. Relative to your anchor point for judgement, you start moving "away" at 5 m/s. Did it gain momentum, or did you? Or did both of you? Answer is, in this context it doesn't matter. The fact that either one of them are capable of momentum implies a state where momentum, given that it's a vector, has no direction nor quantity to apply to that lack of a direction. Particles are still bouncing around, yes, but how relevant is it really?
You're floating in the void of space, bumping into maybe a few cosmic rays and hydrogen per every cubic centimeter. There is no planet to be anchored on. There is no rotation of that planet, nor its rotation around a star, nor that star's rotation around other larger bodies, nor those larger body's pull towards a massive black hole somewhere, nor these macro systems moving each other. These ideas are not relevant. In this scenario, you are just a motionless (arguably omniscient or omnipresent) object watching the true motion of all else. The stationary object. Or are you claiming, ignoring the forces of the universe and whatever else, that such a state is impossible?
I have no idea why relativity makes people say the things they do.
>>7652971
>From the point of view of a stationary observer, Alice and Bob are 1 light-second apart, traveling on parallel paths. Alice is moving at 0.99 c in the -x direction, and Bob is moving at 0.99 c in the +x direction.
Um, I'm pretty sure they are traveling .99c relative to each other, not to a stationary observer. Look at OP's pic, each side is from a different reference frame. Idk if it changes your calculations at all, because honestly I don't know what you're even trying to say with your calculations.
>>7652984
>I have no idea why relativity makes people say the things they do.
read as
>I have no idea what relativity is
>>7652984
>>7652984
>that such a state is impossible?
Less "impossble" and more "meaningless." There's nothing whatsoever privileging or distinguishing such a viewpoint from any other viewpoint moving at a constant velocity, and indeed is exactly as "stationary" or "in motion" as any other such inertial frame. In the absence of forces, and thus the absence of acceleration and deceleration, any viewpoint can be just as easily, and just as arbitrarily, claimed "stationary"
>>7652995
>Less "impossble" and more "meaningless."
And yet, relative to my perspective, you've failed to meaningfully respond to what I've said.
Is it within the affordances of the universe, or not? Make up your mind and respond clearly.
>>7652988
>I honestly don't know what you're even trying to say
OP claimed that
>he next time they meet each other, both will claim that more time has elapsed on their own clock, but they cannot both be correct, thus we have a paradox.
I showed that it is not at all contradictory for both to claim that more time has elapsed on their own clock, while both being equally correct, by constructing OP's situation and showing that indeed both do observe more time passing for themselves than the other without any actual inconsistency arising.
And no, it doesn't make a difference as to the exact speed they are traveling relative to each other, as long as it's constant and nonzero; it just determines the magnitude of the time dilation.
>>7653005
It is absolutely allowed to decide that a particularly inertial reference frame is "stationary," and measure all other intervals by it.
It's just totally arbitrary, like deciding that only noon in Greenwich is the correct noon and all other times should be measured by it. There are no observable physical consequences of declaring any particular reference frame to be stationary.
>>7652974
Seems pretty watertight if the time is measured when the perceive that they pass each other. imagine though, that this >>7652778 is the case, with the line being crossed when the clocks are started/stopped. It's clear that to stationary us (a frame that measures Bob's and Alice's velocity to be equal and opposite), we'll measure their times as equal due to symmetry. However Bob's time (from line to line) will differ from the time that he sees Alice recording when she crosses the line and vice versa.
>>7653016
I understand this and agree. The point is that treating a given anchor point as stationary allows you to make judgements about relative motion, but doesn't tell you the actual motion of all objects. They all do have an actual, absolute motion, not a relative one.
Discerning that absolute motion requires knowledge of the whole, hence when I mentioned omniscience. That knowledge could only be gathered by an object that truly lacked any movement through space. Which isn't viable, blah blah blah, etc, but nonetheless is possible in theory.
Which takes us back to my initial response, and its purpose.
>>7653021
> They all do have an actual, absolute motion, not a relative one.
This just isn't true, regardless of how many times you say it. There's no absolute motion. Not even kind of.
>>7653021
>They all do have an actual, absolute motion, not a relative one.
relative to what
>>7653019
Not that anon, but the theory of relativity makes the word "symmetry" inconsistent. Although that anon did no math to show that the line itself is not straight from the moving reference frame, Which I think is the main paradox you were attempting to point out. We already know that the times measured will be different, we don't need to know what the times are.
>>7652705
what is proof through contradiction alex
>>7653019
I'm not 100% on this, but it's my understanding that such a situation would remain precisely symmetrical, because there's not only time dilation - there's length contraction, the *other* half of the Lorentz transform.
>>7653046
What the fuck is the universal substrate? Every google link I read is talking about metaphysical dualist bullshit. Please I'd love to hear your objective definition. And don't just say "space itself" because space contracts the faster you move so it isn't an absolute.
>>7653019
>However Bob's time (from line to line) will differ from the time that he sees Alice recording when she crosses the line and vice versa.
Nope. The interval (distance in time and space) between two points in spacetime is invariant in all reference frames. Both time *and* space are transformed to make this possible - not just time dilation, but length contraction.
Essentially, from the point of view where Bob is stationary, Alice's clock is ticking slower, but her [math]ruler[/math] also gets shorter by the same amount - so everything evens out.
>>7653061
>What the fuck is the universal substrate?
Two words I just threw together to convey an idea. Then I tacked "the" on the beginning to note that it was a specific one, and only one, that was being referenced.
Let's put it like this. I don't know where you are. I don't know who you are. I'm going to assume you physically exist somehow, but I don't really know. But given the right information, and the right actions from one or both of us, we could end up in the same spot. We could also move spatially further apart.
How? How can this happen? But what means are we afforded the ability to exist to begin with, and how are we able to move through space and assign a distance? There must be a universal substrate by which everything is given the ability to spatially exist, in space itself. All the other shit can be relatively explained by the properties of certain particles acting on each other, for reasons we don't fully understand, but mere existence itself is something else.
I don't quite follow why I'm having to communicate this. Isn't it more or less implicit?
>>7653077
>But what means
By*
The lack of symmetry is related to acceleration
>>7653070
But the line isn't being contracted as it's not on the x-axis. Imagine alice sitting stationary and holding out her hand for a high five. No matter who's reference frame we look at they both agree on high-fiving at that exact moment, but each clock will show a different time. It doesn't have to depend on how long the light takes to reach their eyes, it's when they look down and see they are on the line is when they mark the time, if that makes any sense.
>>7653077
>how are we able to move through space and assign a distance? There must be a universal substrate by which everything is given the ability to spatially exist, in space itself.
But space is not an absolute as you claim. If I'm moving towards you at .9c then I'll measure a different distance between us than you will.
>I don't quite follow why I'm having to communicate this. Isn't it more or less implicit?
Reality isn't as implicit as you were taught, I'm afraid.
>>7653088
The line isn't being contracted; the length of the universe (and thus the distance between passing the line and passing it again) is.
>>7653102
>If I'm moving towards you at .9c then I'll measure a different distance between us than you will.
And if one of us is only subject to our own gravity and not moving at all?
>Reality isn't as implicit as you were taught, I'm afraid.
I wasn't taught, by most definitions of the word.
>>7653104
Oh! Why didn't you just say that in the beginning lol.
>>7653077
Why do you insist that position must be ontologically fundamental? This is not at all obvious.
You're trying to reify a coordinate system. The universe does not need coordinate systems; they're a thing we invented to write down the relationships between objects in space. This is actually even more fundamentally unnecessary than trying to reify whether the universe "really" uses Cartesian versus Polar coordinates.
>>7653046
You can bring whatever metaphysical woo into the argument that you like.
If you say that point x is our zero-velocity point that we can measure the absolute velocity of all other objects from, then:
(1) That point x is completely arbitrary (kind of obviously)
(2) I can name any other point y and make the same claim
>>7653111
being subject to gravity and accelerating is the same thing. It's called a non-inertial frame of reference, which means that you are able to measure a force acting on you. Non-inertial frames of reference include being stationary and moving at constant velocity. In ALL inertial frames of reference, there is no way to net force and thus no way to tell how fast one is moving.
Or in you're retarded way of saying things: anyone moving at a constant velocity isn't moving relative to the substrate.
>>7653112
Because in the beginning you were talking about synchronization and the Twin Paradox, which is a whole different kettle of fish.
>>7653121
>Non-inertial frames of reference include being stationary and moving at constant velocity
Typo: Those are inertial frames of reference.
Non-inertial ones are acceleration and gravitational forces.
>>7653113
We're both particle systems that are able to process and store information via sensors that measure outside stimuli.
It doesn't matter whether one of us is traveling .73c and the other .9 and another observer is watching from a distant moon. If we are to intersect and collide from a given reference frame, either it happened or it didn't.
If all three us of observers gather and record what our observations were, they might all be different, but there was only one ultimate outcome. Just as if I move through space to put myself near another cluster of matter, either it happened or it didn't. Either I could interact with it and render it changed, or I couldn't.
You're correct that our brain is designed to model and comprehend stimuli a certain way, and we're apt to creative cognitive tools and heuristics that work well using that hardware and the typical contexts we find ourselves in. You criticize coordinate systems as a mere cognitive tool, yet at the same time embrace mathematics. The concept of "energy", whatever that even actually means. "gravity", whatever that means. Why?
>>7652872
The assumption that we live in a closed universe. In our universe, if two non-accelerating observers pass each other, and there is no significant gravity to bend things around, they will not meet again.
>>7653121
>no way to tell how fast one is moving.
Right. Which doesn't mean it isn't possible to simply not be moving. At all.
>>7652971
Jesus F. Christ. Alice and Bob are not 1 light second apart at the start. They are in the same exact spot.
Why are you complicating it?
>>7653077
>I don't quite follow why I'm having to communicate this. Isn't it more or less implicit?
No it's not implicit. It's not even true.
>>7653140
closed universe mean that the curvature of the universe is such that anything traveling in a straight line will eventually return where it started. gravity bends 4D spacetime into a 5th dimension. Essentially like a pacman game, the universe is closed or curved in a dimension above the 5th without any gravity needed.
>>7653135
>Just as if I move through space to put myself near another cluster of matter, either it happened or it didn't.
Yes, but lets say you travel very very fast to that cluster. Classically, we'd say that when you arrive there you'd be the same age as us, but from you're point of view (or according to Relativity), you are much younger than us when you arrive. We must agree, either it happened or it didn't. So which situation is true? The one that follows relativity. And so in accordance with relativity there is no motion relative to "space itself"
>>7653155
"how fast one is going" includes a speed of 0. So it is impossible to tell the difference between not moving and moving with constant velocity. Do I really have to clarify every little thing as if you were a child?
>>7653170
>gravity bends 4D spacetime into a 5th dimension.
Lolno
>>7653162
They sure don't look like they're in the exact same spot in the OP diagram. They look like they're some distance apart, travelling in parallel paths.
>>7653170
>you are much younger than us when you arrive.
You're going to have to elaborate on this, younger how? Younger relative to what?
>And so in accordance with relativity there is no motion relative to "space itself"
Then how does anything exist? How does an anywhere exist?
>>7653173
Velocity includes a vector component, which means it doesn't apply to what I'm talking about.
There is no movement. Therefore there is no directionality.
>>7653177
I have already said they'll be arbitrarily close together, that distance was just because I couldn't draw them on top of each other without it looking confusing
>>7653181
>Then how does anything exist? How does an anywhere exist?
We don't know. But things do exist. The "universal substrate" you're talking about is called the aether and there's no evidence for it's existence.
>>7653173
Yes but that 0 is relative to something. You can quite happily assign yourself a speed of zero, but 0 compared to what? Christ
>>7653170
Pacman is flat, i.e. it has zero curvature. The edges are identified to give the topology of a torus, but it is a flat torus.
OP asks if, in such a universe, non-accelerating observers would measure the same time between meetings. The answer is yes.
>>7653181
> "younger than us"
> Younger relative to what?
> "Something completely unrelated to existance"
> Then how does anything exist?
Go play in traffic
>>7653195
>But things do exist.
I agree. And things are able to appear to change their location. Distances appear to exist, and things need a means to interact that is usually dependent on it. How can space be "expanding" if there is nothing to expand?
>We don't know.
Just like we don't know what energy is. Just like we don't know what gravity is. Sounds like we don't know much of anything.
>>7653209
The 3rd planet's got some problems.
>>7653019
So just to clarify, the protocol is:
>There is a starting line that can be measured from
>Alice and Bob travel past the line at 0.99c in opposite directions. When they pass the line, start their stopwatches.
>When Alice and Bob pass the line again, they stop their stopwatch. They then observe what the other's stopwatch read when they passed the line.
In other words, Bob is looking for what Alice's stopwatch reads *when Alice crosses the line*, and vice versa. If there's any distance between them such that Bob won't observe Alice being there until later, he just waits until he does see Alice crossing the line.
That way, there's no uncertainty - Bob knows exactly what Alice's interval is, and vice versa. Do I understand correctly?
>>7653222
>How can space be "expanding" if there is nothing to expand?
"Space" is just how we talk about how distances are measured. There is no actual stuff called space.
>Sounds like we don't know much of anything.
We really don't. That's why we do physics in the first place, to get closer to the answers.
>>7653222
>Just like we don't know what energy is. Just like we don't know what gravity is.
Energy is a quantity which is conserved in any process.
Gravity is the curving of 4d spacetime due to energy.
>>7652676
Hey, guess what! I just found a paper on this exact problem, of the twin paradox in closed (looping) spacetimes.
http://arxiv.org/ftp/arxiv/papers/0910/0910.5847.pdf
It's really layman-accessible, so check it out!
>>7653435
>"Space" is just how we talk about how distances are measured. There is no actual stuff called space.
It seems to me more likely that there is, but it likely isn't so meaningfully framed in the terms we're presently using. You, or someone else, compared it to polar or cartesian coordinate systems, and while I imagine it as something as something quantized into a grid, it just as easily could be something we have no means to even postulate right now. Without something to afford a thought, a mind will not think it. Eventually minds might exist that can conceive of something that approaches a sense of verifiable accuracy.
Something has to afford the ability for things to exist, and to do so spatially. All the patterns we see forming are a consequence of whatever factors drives the interaction of things in the universe, and their relative positions are a main component. The whole notion of causality implies "space", in some capacity.
>We really don't. That's why we do physics in the first place, to get closer to the answers.
Obviously, I agree. I think science requires an underlying sense of inherent uncertainty. Only then can you weight and respond to things accordingly, based on their overall likelihoods. And only then can you intelligently control for error. I would hope this would go without saying, but amazingly people manage to disagree.
I'll have to read some more, because to me, as an outside observer, physics looks like a hacked together near religious mess. I assumed it appeared disjointed because I lacked massive amounts of background knowledge to interpret it, but the more I've learned, the less coherent it seems and the more liberties and grand assumptions the field appears to make. Interactions like the ones in this thread, haven't really shown me anything different either.
Either way, thanks for the conversation. I hope experimentalism finds a way to come back into fashion.
>>7653453
Wow! Nice find, exactly what OP wanted.
>>7652676
We've known we don't live in a closed universe ever since Hubble. We live in a flat one.
But hypothetically, if we did live in a closed universe... Relativity allows for this result. It isn't a paradox, it's a matter of reference frame. If you put an atomic clock on the top of a skyscraper, and have another in the basement, they will be, ever so slightly, out of sync.
>>7653607
We could still live in a closed universe, because of how uncertain our measurements are but the size of that closed universe would be something like 14 times the size of the visible universe.
>>7653607
>We know the exact nature of the universe, as well as its extent.
You better change your definition of "know".
/sci/ has at least a thread per day complaining about scientific illiteracy, and statements yours are the prime fuel. People have a drastically distorted view of human knowledge and achievement.
>>7653638
Then we wouldn't be able to see the background radiation that, similarly, has the characteristics one would expect from a flat universe.
>>7653645
Even /sci/ isn't that autistic, but if you prefer, "all currently available observational data and analysis indicates". But the point is, no one in mainstream cosmology debates about which of those three models of the universe we live under anymore - and hasn't for over a decade. People, similarly, have it in their heads that there's some debate as to whether the Big Crunch is going to be a thing - there ain't.
This is probably because most of the popular media involving cosmology was produced in the 70's and 80's, thus the bulk of the general populous is thirty years plus behind current trends. (And what little cutting edge theorem gets leaked by Hollywood, tends to be misquoted out of context stuff that makes people think science can prove dogs have souls, the universe is a hologram that doesn't exist when no one's looking, and other such shit.)
>>7653453
Is it just me wondering about the sphere in the two-dimensional case where he argues that the winding index of the path breaks the symmetry?
A sphere should be a compact space where every closed path is homotopic to {0}, or am I missing something? Why did he disregard the possibility of a sphere?
Suppose there is bomb on a timer. Alice has the bomb at start, and must hand it to Bob on the first pass. The bomb changes hands every pass. As the bomb is constantly at risk of explosion, Bob considers a new strategy.
He can either stop, keep going at the same rate, or move backwards at the same rate. What is the best combination of these 3 possible actions that will maximize the probability of survival? That is assuming the person who holds the bomb the longest has the greatest chance of having it explode.
What is the best response for the case (holds bomb), and what is the best response for the case (does not hold bomb)?
>>7653453
OP here, cheers!
I GOT IT
Suppose both clocks carry with them an infinite cyclic ruler that goes through the entire cyclic universe.
Consider bobs point of view.
Suppose that bob observes the infinite ruler of alice to have lenght contracted.
Also suppose that bob observes the clocks to be synchronous no matter how many times they fly around the universe.
Now suppose, that this makes perfect sense from bobs point of view, because the ruler of alice is contracted, so ALICE NEEDS TO TRAVEL LESS DISTANCE TO CROSS THE UNIVERSE , ALLOWING ALICE TO GET ACROSS EVEN WITH SLOWED TIME thus keeping the clocks synchronous.
Suppose this is symmetric and alice observes the same with bob.
>>7652676
I could not help but notice your png was not optimized anon.
I have optimized your png.
Your png is now optimized.
>>7654737
Also suppose an infinite universe wide array of synchronized simultaneous measurement sensors that measure the movement of the length contracted ruler of alice.
Suppose this creates a NEW PARADOX.
The measurements of every point of the cyclic, moving ruler, will supposedly tell that its shorter than the exactly same nonmoving ruler that is perfectly parallel to it with no begin/end.
Clearly that makes no sense in a cyclic universe.
watdo
>>7654746
here is picture
>>7654751
Nobody answer my paradox, therfor my crackpot physics theory is reality but the illuminati controlled academia actively censors it.
When I have the time to come up with one, that is.
>>7654677
I think he's only considering flat things... no curvature.
>>7656292
Real universes have curves.
>>7653453
Looking over this paper, I don't really get it. The idea is that in a flat-torus universe, the twin who is the "homebody" ages less than the twin who goes around the universe, and that you can tell who is the traveling twin because he has a winding number > 0. But in the reference frame of the "traveler", isn't it the homebody who is looping around the universe? How can we say who has winding number zero and who doesn't?
Help?
>>7658230
bump
>>7658230
ultimate bump
