Twin paradox on a toroidal universeLet's say the universe has periodic space directions, i.e. it's a "torus." This means that if you walk in one direction you can eventually return to the same spot without turning back.Now let two twins, Alice and Bob, start in from the same position, at rest, and go in opposite directions at constant velocity v and -v. After a certain time T has passed, they intersect again (because universe is a torus). If they started this having the same age, which twin has grown older? Note in Alice's frame of reference, she is at rest. Similarly, at Bob's frame of reference, he is at rest.
They're the same age. Time dilation is about your velocity. The paradox isn't that one is older, it's that their calculations don't match meaning both are blind to another piece of information. Once they both realize they're the same age they'll recognize they're both moving with the same speed. Given the frequency of meets they can determine their speeds.
OP here, will give the correct answer in 5 hours if no person has posted it>>16770708This is not correct
>>16770705If the torus is not in rotation, then >>16770708If the torus is in rotation, the age difference should be around (1-(vtorus^2/c^2) max.
>>16770708Correct>>16770710Wrong. Use more than ChatGPT next time, pseud.
>>16770759The torus is not in rotation. For simplicity, you can think it's a problem in 1+1 dimensions. Your answer is still incorrect.
>>16770705>>16770708They are the same age. Time dilation is fake and gay. A change in available bandwidth doesn't make the file smaller/larger.
>>16770705It depends on the trajectory of the 2 guys and there average position around the center of mass of the torus.
>>16770778Most time dilation : Traveling in the inner parallel circle, the guy is always the closest to the center of mass => Most time dilation / less aging,Less dilation : Traveling in the outer parallel circle.An average of the above : Traveling around a meridian.
>>16770773Yet another proof that CS fags aren't actually "scientists".
I'll let the Americans have a stab at this problem, given that no one has solved it yetpic unrelated
>>16770705OP thinks Earth is the entire Universe and that he has found his forever home in /sci/.
>>16770705Twin paradox is the most stupid question ever>Einstein using Lorentz transformations to show time is relative>Paul Langevine we send one observer on a spaceship and he's gonna age moreDude, wtf? isn't time relative? That is like saying I'm taller than you because I used cm not meters. Get over this, there's no way to tell who "looks older" from symmetric transformations like Lorentz transformations
>>16771053In its usual formulation, the twin paradox is oddly named, but well-understood. The twin that flies away and turns back is younger compared to the twin that stayed. This is very well explained in the book Explorations in Mathematical Physics: The Concepts Behind an Elegant Language by Don Koks.
>>16771053One explanation is that one rocket is indiscernibly going to remain inertial while the other is going to accelerate to turn around, which causes an apparent gravitational time dilation. This breaks the symmetryYou can describe the turn around observer too but they also aren't inertial: they have a sudden discontinuous change in direction, and everything around them changes discontinuously, whereas the other observer sees solely this observer change discontinuously. This breaks the symmetry. The discontinuous observer you can not obtain from the other observer by a Lorentz transformation throughout all of space-time.When you write the coordinate system, you essentially see one observer covers all of space time, while the other doesn't and that's where the missing time comes from. Basically the unphusical scenario of discontinuous observer creates 'bad coordinates'.
>>16770789have you ever actually conducted the aging experiment?
>>16771056>>16771070And if the other twin does not turn around who goes bald first?If you say that in that case there is no older twin both look the same, then wtf is time dilation? why does it only work with acceleration?
I'm gonna fuck off and go to sleep but I'll give you a hint:>>16770632
Ok, so it turns out the answer is "it depends." The setup of the problem is a bit unspecified, and its not enough for the twins to start at rest with respect to each other to have enough information. There is a priviledged frame of reference on a toroidal universe, and if both twins started at rest w.r.t. this frame, then its symmetric. If not, then whichever twin was moving faster with respect to the priviledged frame is the youngest when they meet again.Why is this the case? Well, it's simply because to actually make the torus, you have to which 2 points in your universe are identified with each other. In more detail, you'd want to say that there is a spacelike surface that is a torus, for causality, etc... reasons.And if you are a person in this toroidal universe, you can find out the rest frame of the universe! Just send a laser pulse in opposite directions, and measure how much time they take to come back to you. If the lasers pulses return back in the same time, you are in the torus priviledged frame.Anyways OP is a fag, logging out.
>>16770705>If they started this having the same age, which twin has grown older?In which frame of reference?
>>16770705How do they keep track of their age? If it's with their phones, then they'll think they are the same age. If it's by counting the days, whoever moves eastward will be 2 days younger. And if this was the answer you were looking for, the problem is fake and gay.
>>16771169>wtf is time dilation?a measurement artefact from discontinuous reference inertia>why does it only work with acceleration?because mass is related to inertia, and mass causes gravity which in turn enables time and causality
>>16771668You dum dum, it was a conditional question if X then what is Y and also why it works for Z and not on X? But given your not even pop sci level understanding of what's going I assume a conditional answer is going to be like my dog solving a double integral
>>16771169Relative to person A, B goes bald first. Relative to person B, A goes bald first. The way to think about this is essentially A and B are using separate measuring equipment (traveling separate paths in space-time) so there is no inherent need for them to be the same. This is different when they *meet up*, since now they occupy a same space-time event that must be agreed upon by all observers, namely one of A or B older, and a clock put here at start of experiment to measure this would measure the same relative to A and B by the end.Time dilation is honestly any number of mixed up ideas. One notion is that for two points in space-time p and q, it is how a different path in space-time can have different proper-time. This amounts to A and B aging different by the time they meet.The usual sense in Lorentz transform though is more like an object A traveling one path in space-time parallel others (think of these as clocks that expand outwards and make As 'inertial frame'), then object B traveling another with its own proper-time and when B intersects one of those lines (represented as a clock C) with its proper-time, the time read on C is different to B. That is, we use *many clocks* (not just A, though they are related to A) to measure *one* clock B.
>>16772054Same anonForgot to mention on acceleration.One idea is that in space-time for two events a and b, draw two paths p and q between them (apologies for terrible notation).Then you have a notion of 'space-time distance' (call it | |) which you can measure for the tangent vectors p'(t) and q'(t). So you can integrate ∫|p'(t)| dt and ∫|q'(t)| dt. Now you can ask 'when is this "path length" biggest or smallest"? Such a path is called a geodesic. In space-time geometry, it is biggest when p'(t) is constant, ie its a straight line, ie its an inertial observer. Thus any variation in q'(t) (so an acceleration) is responsible for a time difference, in particularly making the person traveling path q younger.So yes, it is provable that, for comparing two observers proper-time between two events, that all time dilation is associated with acceleration and it makes the accelerating observer younger.
>>16772058> So you can integrate ∫|p'(t)| dt and ∫|q'(t)| dt. Now you can ask 'when is this "path length" biggest or smallest"? Such a path is called a geodesic.This is the main reason why the twin paradox it's a very stupid question. If there is acceleration problem is stupid like you have an integral that is geodesic and the other one is not, why is this a paradox? >Relative to person A, B goes bald first. Relative to person B, A goes bald first. The way to think about this is essentially A and B are using separate measuring equipment (traveling separate paths in space-time) so there is no inherent need for them to be the same. This is where things get interesting because when the twins are both in an inertial frame because now you are into deep shit. For A, his brother on space goes bald first but if for the slutty step sister C, brother A is moving like he is shitting his pants then A may get bald first, or whatever. And this can go on forever it's like trying to figure out the true speed of a train. However, nobody raises an eyebrow when we say oh yeah speed of a train just depends if you are moving right or left. No problem. The real paradox is physics positivist cuck fags no giving a fuck about two observers saying that there are two observers that have two clocks moving twice as fast respect to each other.
>>16770705It's not *literally* a torus, ya freaking dip lol. You've got it all backwards there.The dieelectric ("Ether") is the toroidal base state. The funky stuff happens during unfoldment into timespace, aka the coin's other flipside. Exact same base, different modality. There's a third thing that conjoins these two modalities together, as you cannot join two things without a third. That is your "Holy Trinity", the Indefinite Dyad expressing itself right there. Without end
>>16771105time dilation has been measured. it has to be adjusted for in gps satellites
>>16772171"twin paradox" is just a name that stuck. We know how to resolve it, but it's still not intuititive for people new into relativity. Same with problems like Bell's Spaceship Paradox. They're there to better illustrate that concepts such as simultaneity and solid materials and such are different in special relativity.
>>16772263>happily throws out the possibility that the clocks read differently
>>16772263thats a gravity thingtime dilation in the spirit of the twin paradox has been measured with an airplane and atomic clocks. Turns out when it lands and the locks are compared, the clock in the airplane has slowed down and not the one on the ground.>>16772396>We know how to resolve it, bI have never seen a resolution to it.
