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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Wed Dec 30, 2015 2:26 pm UTC

Even stellar black holes absorb far more radiation than they emit. So all (macroscopic) black holes in the universe are currently growing. But eventually the universe should cool sufficiently for small black holes to start losing mass, and, on a far greater time scale, even supermassive black holes. But we're talking about like 10^30 years even for stellar black holes to reach equilibrium.

Given how far in the future the first black hole evaporation is predicted to be, I guess I can't really say for sure that black holes can "form and evaporate many times," simply because I don't know if there will be any stars left.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Hypnosifl » Thu Jan 07, 2016 11:46 pm UTC

Eebster the Great wrote:Even stellar black holes absorb far more radiation than they emit. So all (macroscopic) black holes in the universe are currently growing. But eventually the universe should cool sufficiently for small black holes to start losing mass, and, on a far greater time scale, even supermassive black holes. But we're talking about like 10^30 years even for stellar black holes to reach equilibrium.

Given how far in the future the first black hole evaporation is predicted to be, I guess I can't really say for sure that black holes can "form and evaporate many times," simply because I don't know if there will be any stars left.

Astrophysicists have speculated about the possibility of smaller black holes created in the Big Bang, whose output in Hawking radiation would exceed what radiation would fall into them in interstellar space, and which could have started off large enough so that they wouldn't be done evaporating today. See the primordial black holes wiki article, which notes "A black hole with a mass of about 10^11 kg would have a lifetime about equal to the age of the universe". They've been ruled out as a candidate for a significant portion of dark matter, but I don't think there's been anything to rule out the idea that they do exist in smaller numbers.

If we want to check that a black hole of mass 10^11 kg shortly after the Big Bang would indeed have been losing mass to Hawking radiation faster than it gained mass from starlight and cosmic background radiation falling into it, this page indicates that the temperature T of a black hole would be hbar*c/(k*4*pi*R), where R is the Schwarzschild radius R=2GM/c^2. For a black hole of mass 10^11 kg, I get R=1.485*10^-16 meters and T=1.227 * 10^12 Kelvin--that's obviously much hotter than the temperature of a blackbody at equilibrium in space would have been since very shortly after the Big Bang. According to this, if the current temperature of the background radiation is T0, then the temperature as a function of time t is proportional to T0 / t^(2/3) (and the constant of proportionality should be 1 if we use units where the age of the current universe = 1). T0 is about 2.76 Kelvin, so if we take 1.227 * 10^12 = 2.76/t^(2/3) and solve for t, it seems the temperature of space would only be as hot as a black hole this size when the universe was about 3.4 * 10^-18 times its current age or younger. The universe is about 4.36 * 10^17 seconds old today, so it would only have been this hot in the first 1.5 seconds or so. After that, the universe would be continually cooling down, while the black hole would be continually heating up as it shrinks and its temperature due to Hawking radiation goes up.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Neil_Boekend » Thu Jan 14, 2016 12:29 pm UTC

Thanks. It looked just sorta weird, but it can't be otherwise.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Wed Feb 10, 2016 2:17 pm UTC

We, who live on Earth (citation needed), observe everything in the observable universe redder that is expected proportional to its distance from Earth. We then assumed that the same for all observer in The Universe. The logical conclusion is that all of space is expanding, which moves everything away from everything else. This movement causes the Doppler Effect to red shift everything. However, is it possible for our assumption to be wrong; that some observer (let's call him Bob) would see everything in the their observable universe bluer than expected? If Bob, and us could share our observations with each other, then the logical conclusion is that space is expanding away from the Earth, and shrinking toward Bob. If there is no evidence disproving this theory, what would it imply?

The first thing that I can think of is that entropy for the space near us, who are still on Earth (citation needed), would constantly increase until maximum entropy is reached (Heat Death); at the same time the entropy of the space near Bob would decrease until minimum entropy is reached.

What would an observer equidistant from us, and Bob measure the color shift of celestial objects to be? My guess is that about half of the objects would be red shifted, and about half of the objects blue shifted. In addition, the closer an object is to us, or Bob the greater the color shift would be; objects equidistant from us, and Bob would not be color shifted at all. What about observers not equidistant from us, and Bob?

If all matter is moving towards Bob, then would a black hole eventually form?

How does this theory (or the following theory) affect models of the shape of The Universe?

Could more observers than just us, and Bob measure all objects being red shifted, or blue shifted. If so, then would space would be expanding from several points and shrinking toward several points?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Feb 10, 2016 3:18 pm UTC

This would require earth to be extremely special with respect to the laws of physics. It's basically a non starter because if you got that down route, you could have basically anything. If the laws of physics depend on where you are, they aren't really meaningfully laws of physics.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Neil_Boekend » Wed Feb 10, 2016 5:08 pm UTC

Also, Bob could never notice all objects to be blueshifted:
An object that is far enough behind us form Bob's perspective to more than compensate for our specialness would be redshifted.
An object that is behind Bob from our perspective will be redshifted because we see it redshifted more than we see Bob being redshifted.
An object perpendicular to the line Earth-Bob at sufficient distance would be redshifted from Bob's perspective.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Feb 10, 2016 5:20 pm UTC

spherical world where bob is antipodal, why not? no evidence to disprove!
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Neil_Boekend » Wed Feb 10, 2016 5:27 pm UTC

If you assume the unverse is positively curved (in a 4d version of a sphere) then yes. But the universe is not curved according to experimental data from various, independent sources (WMAP, BOOMERanG and Planck for example) (with 0.4% possible measurement error).
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Wed Feb 10, 2016 7:13 pm UTC

0.4% error might as well be 99% when we're talking about the scale of the entire universe. The data only means it is locally flat.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Neil_Boekend » Wed Feb 10, 2016 8:06 pm UTC

Good point.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Feb 10, 2016 8:45 pm UTC

No that's not a good point

If that were a good point no one would say it is .4!

The point is that the shape of space comes from some dynamical laws. Unless you are just "meh" to everything we know about physics this is how it be like.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Wed Feb 10, 2016 11:27 pm UTC

doogly wrote:No that's not a good point

If that were a good point no one would say it is .4!

The point is that the shape of space comes from some dynamical laws. Unless you are just "meh" to everything we know about physics this is how it be like.

I don't know what you mean. My point was that measurement of the local curvature of space does not in any way help us determine the global shape of the universe.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eSOANEM » Thu Feb 11, 2016 12:28 am UTC

Well, for the universe to be closed given the observed local curvature, the universe would have to be so huge that an antipodal bob (which, as discussed, is needed) couldn't see the earth in the first place.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Thu Feb 11, 2016 2:34 am UTC

Eebster the Great wrote:
doogly wrote:No that's not a good point

If that were a good point no one would say it is .4!

The point is that the shape of space comes from some dynamical laws. Unless you are just "meh" to everything we know about physics this is how it be like.

I don't know what you mean. My point was that measurement of the local curvature of space does not in any way help us determine the global shape of the universe.

But if you assume Copernican principles of Earthly non-specialness, and dynamic evolution of curvature (via any process that transmits at at most light speed, it wouldn't even have to be GR, other variations would get the same limits), you have these limits on topology.

I mean the hard thing with the critical density is that W = 1 is a single value, and so it has measure zero. In another sense, the probability that we live in a flat universe is 0. In another sense, it is 99% likely. I like that second second sense better, but yeah, there's rub to it.

It really disappointed my topology teacher when I explained this to her. We probably live in the most boring one. Big : ( for topologists.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Thu Feb 11, 2016 5:01 am UTC

Why assume Bob is in the observable universe at all?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Thu Feb 11, 2016 5:01 pm UTC

doogly wrote:This would require earth to be extremely special with respect to the laws of physics.

Why cannot the Earth be special? If my theory is correct, then there is a point where everything expands away from. It has to be somewhere; why not near or inside the Earth?

doogly wrote: It's basically a non starter because if you got that down route, you could have basically anything. If the laws of physics depend on where you are, they aren't really meaningfully laws of physics.

No, most of the laws would still apply. No matter where you are the net force on an object would equal the product of it's mass and acceleration. No matter where you are every object's gravitational mass would equal their inertial mass. No matter where you are the color force is 137 times stronger than the electromagnetic force. No matter where you are the force of air resistance on an object is proportional to that objects velocity^2. No matter where you are gyroscopes would come in peace

Eebster the Great wrote:Why assume Bob is in the observable universe at all?

He is not. I should have made that clearer in my post. Although, maybe he she could be right outside the observable universe?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Thu Feb 11, 2016 5:08 pm UTC

Nah, it's 137 + corrections of order your distance from earth squared, because why not.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Copper Bezel » Fri Feb 12, 2016 1:21 am UTC

jewish_scientist wrote:
doogly wrote:This would require earth to be extremely special with respect to the laws of physics.

Why cannot the Earth be special? If my theory is correct, then there is a point where everything expands away from. It has to be somewhere; why not near or inside the Earth?

The Copernican principle is implicit in every other assumption made in science. Otherwise, we could simply say that every correlation is a coincidence, and we couldn't infer anything. Predictive power would be meaningless; the data just happened to correlate to the theory. There's no reason to make the pretense of using scientific theory if you're going to reject the most fundamental premises at the last step.

Meanwhile, if Bob is outside the visible universe, then there's nothing special about drawing the line there, at the extent of the visible universe. You can posit an arbitrarily large bounded region of space bigger than the observable universe that behaves exactly as we have observed the visible universe to do, and then imagine that some other thing is happening somewhere else. That doesn't require Earth to be special, the geometry looks the same from our perspective, it's the same proposition as what we already know with some other hypothetical and impossible to test stuff tacked on.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Fri Feb 12, 2016 4:40 pm UTC

Copper Bezel wrote:
jewish_scientist wrote:
doogly wrote:This would require earth to be extremely special with respect to the laws of physics.

Why cannot the Earth be special? If my theory is correct, then there is a point where everything expands away from. It has to be somewhere; why not near or inside the Earth?

The Copernican principle is implicit in every other assumption made in science.

No; the Copernican Principle is implicit in every other assumption made in modern cosmology. Whether or not the Earth is in a special place in The Universe does not affect Locard's Exchange Principle, the Combined Gas Law, the All or None Law, Snell's Law, or Maxwell's Equations.

Besides, why is your assertion that Earth must not be in a special place anymore valid than my assertion that Earth is in a special place?


Otherwise, we could simply say that every correlation is a coincidence, and we couldn't infer anything. Predictive power would be meaningless; the data just happened to correlate to the theory.

Yes; someone arguing for the null hypothesis can always claim that any data gathered just happens to correspond to what the hypothesis predicts. That is why we use 0.05 as a standard p-value.

Meanwhile, if Bob is outside the visible universe, then there's nothing special about drawing the line there, at the extent of the visible universe. You can posit an arbitrarily large bounded region of space bigger than the observable universe that behaves exactly as we have observed the visible universe to do, and then imagine that some other thing is happening somewhere else. That doesn't require Earth to be special, the geometry looks the same from our perspective, it's the same proposition as what we already know with some other hypothetical and impossible to test stuff tacked on.


That is what I am doing. I am presenting an alternative interpretation of gathered data, which leads to several conclusions. For example, my interpretation required that space-time be positively curved, and that The Universe be of finite size.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Fri Feb 12, 2016 5:14 pm UTC

jewish_scientist wrote:Maxwell's Equations.
Sure it does!

Where is the special term that makes light within 2 light years of earth behave differently than everything away from 2 light years, yet from a distance appear exactly the same? Not there? Strange, why?

The lack of that term is because of the Copernican Principle and Occam's Razor (which implies (with current observations) the Copernican Principle).

Heck, the Copernican Principle is why experiments can be presumed valid when you don't experiment. Maybe the very act that we are experimenting changes the results! This just makes the "special place" a bit more local (right in the room where we do the experiment). Again, no experiment can rule out that the location where you are doing your experiment is cheating by being different than where you aren't doing your experiment.

Presuming that is, however, pointless. As no experiment can rule out being a brain in a box whose very thoughts are being manipulated by an "evil genius" to reach incorrect conclusions.

The end point of saying "I just have to consider myself, or my local, super-special to build physics" ends with that: the brain in the box.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Sat Feb 13, 2016 5:43 am UTC

I mean, any experiment you do on Earth is in a "special place" since it's in our gravitational well. You don't have to assume you exist in the most generic place possible when there is evidence to the contrary. It's only absent evidence that you need to make that assumption.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Mon Feb 22, 2016 1:41 pm UTC

What is so wrong with special places anyway? The equator is a special place in that it is the only place on Earth where Foucault's pendulum does not work. The North/South Pole is the only place where every direction you travel goes South/North.

The actual 'pole' that all of space expands away from does not actually need to be at the exact center of the Earth; it just has to be closer to the Earth than the Solar System is to any astronomical object. That gives a volume of ~18 cubic lightyears* for this point to be in.

*For some reason I cannot get this to work as a link: http://www.wolframalpha.com/input/?i=4* ... ight+years^3%2F3

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Feb 22, 2016 1:52 pm UTC

Those are extremely different.

The north pole is the only point away from which every direction is south. But that is not due to anything special about the north pole, that is the definition of the word "south." I am at the Doug pole, and away from me, all paths point in the anti-Doug direction. My pole is glorious and special, even though many other poles could be defined. Respect my pole.

The earth's axis is not special, it could just as easily be anywhere else. But it does have to have one, spinning things do need an axis. There are good dynamical reasons why it is close-ish, but not quite, perpendicular to the ecliptic plane.

So, if you had a *dynamical* reason why the Earth is at the center of these expanding supernovae - say, they were licked into the skies by the mighty tongue of a primeval cow - it would at least have some explanatory heft to it. But if you want to cook a special place or direction into the *law* of physics, you are now way ridiculous.

Does this distinction make sense, between preferred points in the laws vs a point with special properties on an object?

~18 cubic lightyears is nothing. We're talking universe talks here.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Mon Feb 22, 2016 3:02 pm UTC

Even if there were a dynamic reason to suppose a "center of the universe", the way there must be a pole (or two) *somewhere*, you'd need some really strong justification to claim that we just happened to be at that specific location, out of all possible locations to be in the universe.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Mon Feb 22, 2016 3:19 pm UTC

Well, maybe it was Odin, Villi and Ve and not Auðumbla that flung up the stars, but either way, it all went down within a few light years of Earth's north pole. That's my story and I'm sticking to it. And at least it's dynamical.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby jewish_scientist » Tue Feb 23, 2016 4:54 pm UTC

doogly wrote:The north pole is the only point away from which every direction is south. But that is not due to anything special about the north pole, that is the definition of the word "south." I am at the Doug pole, and away from me, all paths point in the anti-Doug direction. My pole is glorious and special, even though many other poles could be defined. Respect my pole.

You could define the North and South Poles in terms if the Earth electromagnetic field. Then they would be special because no other locations on Earth are magnetic poles.

~18 cubic lightyears is nothing. We're talking universe talks here.

I know; I just wanted to make it clear that when The Universes pole was near Earth, I did not mean it was exactly at the center of the core of the Earth.

gmalivuk wrote:Even if there were a dynamic reason to suppose a "center of the universe", the way there must be a pole (or two) *somewhere*, you'd need some really strong justification to claim that we just happened to be at that specific location, out of all possible locations to be in the universe.

Imagine you teleported to a random spot on Earth. It is very unlikely that you would end up in the chair you are currently sitting in; but it is possible. Your chair is a location on Earth just like any other location. Two random points out of all those in The Universe had to be its two poles. It is unbelievably unlikely that one of those points is near the Earth; but it is possible. The points near the Earth are in The Universe just like all other points. There is also the alternative form of my proposed theory where there are multiple places where The Universe expands and contracts, which makes the probability of one of these points being near the Earth more likely.

It is important (and fun) to explore strange, and crazy theories. What if while exploring the implications of this theory, we realize that it predicts something. If that thing is then discovered, then this theory would be look a lot more probable. The Big Bang seemed like a ridiculous, untestable theory; Einstein actually tried to change the equations of General Reletivity,* because they can be used in support of the Big Bang Theory. However, when Ralph Alpherin determined that the Big Bang Theory predicts the existence of cosmic background radiation, and then Arno Penzias and Robert Wilson discovered it, scientists took the Big Bang theory much more seriously.


*One of his changes was the adding of a repulsive force in The Universe. He later abandoned this idea, and called it his "biggest blunder". What is really funny is that this force has recently been discovered.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Tue Feb 23, 2016 5:44 pm UTC

Except, as far as we know, there need not be any poles in the universe, so that's an additional hurdle for your conjecture (it's not a theory by any stretch).

The point is not that it's impossible, but that it's incredibly unlikely, so to be believable you need some additional evidence and explanation first.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Carlington » Wed Feb 24, 2016 12:21 am UTC

I think that this is probably trivially true but would like confirmation because thinking about it genuinely made my brain retract into the depths of my skull in terror (which is why I think it must be true, I was promised that actual understanding of relativity would have this effect):

Absolute velocity does not and cannot exist. Only velocity relative to a chosen frame. It follows that for any given observer s at rest with respect to its own frame S, we can construct a frame T such that an observer t at rest wrt T measures the velocity of s in T as anything in (-c, c). I might have worded that weirdly/imprecisely, please ask for clarification if so.

If what I said is correct, then the following should be possible:
Take three observers a, b, c. All three construct reference frames A, B, C such that in all three frames, all three observers are stationary at the origin at tA = tB = tC = 0.
a and b then accelerate at an equal rate, such that they remain stationary wrt one another. After this acceleration, they define new frames A' and B' such that a and b are stationary at the origin in A' and B', but are moving at 0.999999999...c (some arbitrarily high fraction of c) in C, and c is moving at an equally magnitudinous velocity in the opposite direction in A' and B'.
Now, let b accelerate the same amount again, such that after this acceleration, b has a velocity in A' that matches the velocity of a in C. The new velocity of b in C must then be some even higher arbitrary fraction of the speed of light, presumably determined by appropriate use of relativistic calculations.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Wed Feb 24, 2016 1:14 am UTC

Yes, that is true as far as I understand your description.

If v = the fraction of c in question, then the velocity of b in C is 2v/(1+v^2), using the velocity-addition formula for special relativity.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Wed Feb 24, 2016 3:19 am UTC

Word.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Mon Mar 07, 2016 9:34 pm UTC

One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Mar 08, 2016 12:16 am UTC

The twin paradox one should have "The twin paradox isn't about acceleration, and even if it were special relativity can handle acceleration" emblazoned at the top and in caps lock, but otherwise, generally good shit here. Though my reading was rather cursory.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Tue Mar 08, 2016 6:27 pm UTC

doogly wrote:The twin paradox one should have "The twin paradox isn't about acceleration, and even if it were special relativity can handle acceleration" emblazoned at the top and in caps lock, but otherwise, generally good shit here. Though my reading was rather cursory.

Huh?

"The resolution to the paradox is simply that in your rest frame the metric is not the Minkowski metric"
"The form of your metric will depend on exactly how you accelerate, and in general will not be a simple function."

Ah, you mean this:
http://www.askamathematician.com/2010/0 ... adox-work/
the amount/duration of acceleration isn't what makes the twin paradox work. The acceleration does change your metric, but it is the path that matters?

The shortest line between two points is the bendiest path.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Tue Mar 08, 2016 7:30 pm UTC

Yeah, the point is that there need not be any acceleration for it to work. You could as easily have two different ships that sync clocks as they pass each other, and there would still be an apparently paradoxical mismatch.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Mar 08, 2016 7:36 pm UTC

Or have the spaceship fly off and come back out the other side in a pac man universe. Which, while topologically funky, isn't curved.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Tue Mar 08, 2016 7:56 pm UTC

Wait, I thought relativity somehow limited the ability to have a "closed" universe (like pac-man) without curvature?

---

And, suppose you have stationary A and moving B. They sync clocks as they pass. They go around the universe. When they pass again, are they synced? (yes, I assume)

Now, suppose B orbits the universe 500 times. Then comes to a halt right next to A. How different are their clocks? (not at all?)

Now B goes half way to the edge of the universe, turns around, and stops next to A. Clearly B is younger: this behaves just like a non-pac man universe, so the non-pac man case must hold.

B goes to the edge of the universe, around to A. He stops. Same clock. He then goes back the way he came, and stops Again, same clock. No, that doesn't make sense.

Thus somehow B going around the universe and stopping must result in B being younger in proportion to how many orbits.

What more, as the local "coming to a stop" effect next to A cannot reasonably be expected to "scale" with how many orbits B has done, this must also be true (B is younger) of the B who "just passes" A without coming to a stop.

To me, this implies that the pac-man universe must have some feature of space-time such that a B going around the long way ends up younger than the A staying still somehow. Would this be a reflection of the restriction relativity places on the curvature of a closed universe?

---

Am I missing something? Probably.
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Tue Mar 08, 2016 8:33 pm UTC

Yakk wrote:Wait, I thought relativity somehow limited the ability to have a "closed" universe (like pac-man) without curvature?

If you pac man in >1 direction, you have a toric sort of space which is curved. But if you just have one spatial direction, you are a cylinder, which has no curvature.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Tue Mar 08, 2016 8:42 pm UTC

B is younger when it encounters A again entirely from SR. My understanding is that in B's frame, there are two distinct events for A that are both "now", one (spacially) behind B and one in front.

The "there and back" version of the paradox in Minkowski space switches abruptly between those "now"s, whereas in the Pacman version they're both always there (along with an infinite number of others in both directions, which correspond to carrying the line of simultaneity arount the cylinder more and more times), the trip around the universe simply changes which one is most relevant to A and B's own interests.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Tue Mar 08, 2016 10:57 pm UTC

So, what breaks the symmetry between A and B? What makes the frame where A is moving and B stationary distinct from the one with B moving and A stationary? Hmm: I guess the pac-man universe cylinder itself has a different circumference for A and B?
One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision - BR

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Tue Mar 08, 2016 11:00 pm UTC

Yeah, there's a privileged rest frame in a cylindrical universe, where the circumference is maximized, and A is in that frame.
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