What-if 0007: "Everybody Out"

What if there was a forum for discussing these?

Moderators: Moderators General, Prelates, Magistrates

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Sun Sep 16, 2012 5:36 pm UTC

rmsgrey wrote:In an otherwise empty universe, the inside of a hollow neutronium sphere is at a lower gravitational potential than a point infinitely far away.

A flat plain, stretching infinitely far in all horizontal directions, and with uniform density and thickness would produce a linear gravitational potential, and a constant gravitational field - no matter how far you were above the surface, the effect of its gravity would be the same - so there would be no way to detect it purely from gravitational effects. On a human scale, the Earth is approximately such a plain, so gravity is more-or-less constant in daily life (unless you're an astronaut or something)


So what I'm asking is, does the gravitational potential make any difference to anything? Or is it only the gradient that matters?


gmalivuk wrote:
rmsgrey wrote:The concept of absolute rotation reminds me of the concept of absolute velocity that special relativity replaced.
But absolute velocity is in no way measurable, whereas absolute rotational velocity would be. An isolated Earth, if absolute rotational velocity is indeed a thing, would be shaped differently at equilibrium and would allow things to orbit differently if it were rotating than if it weren't. In other words, you could in principle test for the existence of absolute rotation, whereas you couldn't (according to any current theory) do so for absolute velocity.


And a hundred and thirty years ago (give or take), the Michelson-Morley experiments tested for the existence of absolute velocity.

There are experimentally verified effects that, in principle (I don't know whether this result has been observed in practice) would produce different results for the test for absolute rotation depending on how far you are from a rotating mass - that is to say, near a rotating mass (embedded in a universe of masses with no net rotation) the experimentally determined non-rotating frame would be rotating with respect to a similarly determined non-rotating frame further from the mass.


I can imagine that. I imagine a massive rotating sphere. Let's say it's rotating fast. One side of the sphere is heading directly toward you while the opposite side is heading directly away from you. So by special relativity, they will both have time dilation but one will have more than the other. So it has more time to do gravitation on you. That means the spinning mass will have its gravitation be unbalanced, it won't point directly at the center of mass but off to one side by something less than the diameter of the mass.

\(x'=\gamma\left(x-\beta ct\right)\)
\(ct'=\gamma\left(ct-\beta x\right)\)

The gamma x and gamma ct will be the same both ways. But with the sign of beta opposite, one side will seem to be both closer and its time goes faster. Will those effects cancel out so they both present the same amount of gravity? Probably only at one particular speed?

So that would imply that spinning masses would not behave the same as point masses concentrated at their center of mass. How strange. I wonder if I got that wrong. My intuition about relativity is so weak I can easily get stuff wrong and not notice. With lots of things when I make a big blunder I realize it can't be right and then find out where I went wrong. With relativity when it seems like it has to be wrong, likely as not it's right.
The Law of Fives is true. I see it everywhere I look for it.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Sun Sep 16, 2012 6:23 pm UTC

rmsgrey wrote:And a hundred and thirty years ago (give or take), the Michelson-Morley experiments tested for the existence of absolute velocity.
They tested for the existence of velocity relative to an ether. Noting the extent of centrifugal force wouldn't depend on measuring anything against a possible ether.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Max™
Posts: 1792
Joined: Thu Jun 21, 2012 4:21 am UTC
Location: mu

Re: What-if 0007: Everybody Out

Postby Max™ » Sun Sep 16, 2012 9:15 pm UTC

Sagnac allows you to test for rotation without an external reference frame.
mu

rmsgrey
Posts: 3655
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: What-if 0007: Everybody Out

Postby rmsgrey » Sun Sep 16, 2012 9:32 pm UTC

Max™ wrote:Sagnac allows you to test for rotation without an external reference frame.

I'd be astonished if anyone had managed to conduct an experiment that tests for rotation in the absence of the "fixed stars", let alone the rest of the universe...

Has anyone done experiments to determine the net angular momentum of all the mass-energy of the universe? Or otherwise measure whether the locally non-rotating frame aligns with the cosmic frame (with corrections for local rotating masses)?

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Sun Sep 16, 2012 9:37 pm UTC

rmsgrey wrote:
Max™ wrote:Sagnac allows you to test for rotation without an external reference frame.
I'd be astonished if anyone had managed to conduct an experiment that tests for rotation in the absence of the "fixed stars", let alone the rest of the universe...
No, but the point is that Sagnac allows you to test for rotation without also knowing anything about those "fixed stars".
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Sun Sep 16, 2012 10:22 pm UTC

gmalivuk wrote:
rmsgrey wrote:
Max™ wrote:Sagnac allows you to test for rotation without an external reference frame.
I'd be astonished if anyone had managed to conduct an experiment that tests for rotation in the absence of the "fixed stars", let alone the rest of the universe...
No, but the point is that Sagnac allows you to test for rotation without also knowing anything about those "fixed stars".


That's true. On the other hand, you can measure the temperature of a gas without knowing anything about the gas laws, adiabatic effects etc, and still those things are affecting things whether you know about them or not.

But then, Sagnac does not depend on any random fudge factors or "fundamental constants" that change with the amount of mass in the universe etc. It depends only on the speed of light, the wavelength and frequency of the light, the area of the loop, the angular velocity, and pi. So unless distant stars can affect one of those they will have no effect on the Sagnac effect whatsoever.
The Law of Fives is true. I see it everywhere I look for it.

User avatar
Max™
Posts: 1792
Joined: Thu Jun 21, 2012 4:21 am UTC
Location: mu

Re: What-if 0007: Everybody Out

Postby Max™ » Sun Sep 16, 2012 10:43 pm UTC

You can set up an experiment with zero Sagnac Effect and logically conclude that you are not rotating along that axis, no need to go deeper than that.
mu

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Mon Sep 17, 2012 1:55 am UTC

Max™ wrote:You can set up an experiment with zero Sagnac Effect and logically conclude that you are not rotating along that axis, no need to go deeper than that.


Are you sure there's no need to go deeper than that?

Imagine this situation: You have set up an experiment that yields zero Sagnac effect along three perpendicular axes.

Someone else has set up an experiment that yields zero Sagnac effect along three perpendicular axes.

But you have evidence of relative rotation between you and him.

If that can happen then you need to go deeper.
Can you prove that can't happen, without going deeper?
The Law of Fives is true. I see it everywhere I look for it.

User avatar
Max™
Posts: 1792
Joined: Thu Jun 21, 2012 4:21 am UTC
Location: mu

Re: What-if 0007: Everybody Out

Postby Max™ » Mon Sep 17, 2012 2:49 am UTC

Image

I swear, this almost definitely wasn't a prolonged set-up for an Inception joke.
mu

User avatar
PM 2Ring
Posts: 3715
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

Re: What-if 0007: Everybody Out

Postby PM 2Ring » Mon Sep 17, 2012 6:16 am UTC

rmsgrey wrote:Has anyone done experiments to determine the net angular momentum of all the mass-energy of the universe? Or otherwise measure whether the locally non-rotating frame aligns with the cosmic frame (with corrections for local rotating masses)?

If the net angular momentum of the universe is non-zero, then there would be a preferred direction in space (the universal spin axis), which would break the presumption that the universe is isotropic, and BB theory would need to explain the origin of this angular momentum. Also, you'd expect there to be various artifacts of this preferred direction, eg it should have a global effect on the CMBR that can't be accounted for in any other way. Of course, if the net angular momentum of the universe is very tiny, then it might be hard to distinguish it from the other sources of angular momentum, but then you have the additional problem of explaining why it's non-zero, but almost zero. :)

User avatar
Pfhorrest
Posts: 5482
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: What-if 0007: Everybody Out

Postby Pfhorrest » Mon Sep 17, 2012 9:10 am UTC

And of course the universe itself having a net angular momentum would depend on there being such a thing as absolute rotation, what with there being nothing else besides the universe which the universe could be rotating relative to.

And gmalivuk et al who say there is such a thing as absolute rotation, can you confirm my earlier question that you hold there is consequently such a thing as absolute orientation as well?

And on a more fundamental note: if a Machian model predicts all the same effects* of the distant stars rotating around something, as a model with absolute rotation predicts of things rotating in a universe with zero net angular momentum (i.e. where the distant stars are not rotating), how could you possibly test for the existence of absolute rotation without doing the impossible and making the rest of the universe cease to exist? (I almost said "or making it spin around you", except a Machian model says you can already do that -- just spin the other direction and the universe spins around you equally -- and any sense besides that would have to presume absolute rotation and so couldn't serve as a test for it).

It seems the only answering there is to be done is explaining what the connection is between Mach's arms pulling away from his body and the stars whiling around him: whether it be by explaining what constitutes absolute rotation and why the universe as a whole has none (why the distant stars really aren't spinning, even when they appear to be from some reference frames, and what is special about those reference frames that produces the effects we see in them, like centrifugal and coriolis forces, which we don't see in the universe as a whole), or by explaining how the spinning of the distant stars produces those forces in things which aren't spinning with them. It looks to me like there is a fairly obvious explanation for the latter, which I detailed my lay understanding of earlier, but I hear now that even people who favor this view are having trouble making all the details work. Anyone (preferably Max) care to point out where the holes in my attempted explanation earlier are?

*Also, do I understand correctly from rmsgray's statement "The Kerr solution starts with the assumption that there is an isolated body with a given angular momentum" that, since a Machian model says that the Earth does have angular momentum now, just that it only has it relative** to the rest of the universe, and that if the rest of the universe disappeared it would not have angular momentum relative to anything anymore, that a Machian model would say that the Kerr solution applies to the Earth just fine right now, but wouldn't if the rest of the universe disappeared? If so, then "the Kerr solution exists" isn't really an objection to a Machian model.

**On a similar note, would I be correct in assuming that there is such a thing as relative angular momentum, even if you believe there is also absolute angular momentum? E.g. two things co-rotating would measure each other as having no angular momentum relative to each other, even if each can tell that they "really" do have some angular momentum and thus conclude that the other one just has the same angular momentum as themselves?
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Mon Sep 17, 2012 1:52 pm UTC

Pfhorrest wrote:And gmalivuk et al who say there is such a thing as absolute rotation, can you confirm my earlier question that you hold there is consequently such a thing as absolute orientation as well?
I have not for sure decided that I believe in absolute rotation, only that it is consistent with GR for such to exist and that it could be tested for without reference to any distant stars. (In other words, it could still mean something for a thing to be rotating in an otherwise empty universe, even if we'll never be able to test what actually happens there.)

Also, absolute rotation in no way implies absolute orientation as you described it earlier, with a privileged up, down, front, back, left, and right for the whole universe. Similarly, if absolute velocity were a thing, it would not imply for example that the universe has a center.

Also, do I understand correctly from rmsgray's statement "The Kerr solution starts with the assumption that there is an isolated body with a given angular momentum" that, since a Machian model says that the Earth does have angular momentum now, just that it only has it relative** to the rest of the universe, and that if the rest of the universe disappeared it would not have angular momentum relative to anything anymore, that a Machian model would say that the Kerr solution applies to the Earth just fine right now, but wouldn't if the rest of the universe disappeared? If so, then "the Kerr solution exists" isn't really an objection to a Machian model.
Perhaps not, but it most certainly is an objection to your absurd claim that a Machian model is one of the implications of relativity.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Mon Sep 17, 2012 3:08 pm UTC

gmalivuk wrote:
Pfhorrest wrote:And gmalivuk et al who say there is such a thing as absolute rotation, can you confirm my earlier question that you hold there is consequently such a thing as absolute orientation as well?
I have not for sure decided that I believe in absolute rotation, only that it is consistent with GR for such to exist and that it could be tested for without reference to any distant stars. (In other words, it could still mean something for a thing to be rotating in an otherwise empty universe, even if we'll never be able to test what actually happens there.)


If we agree that rotation is whatever-it-is that Sagnac devices measure, then we have a measure for absolute rotation in our universe. Imagine that you could take your spaceship to an otherwise-empty universe, and you start up your gyros to give yourself a rotation, and your Sagnac device still registers no rotation. What would it take for that to happen? Maybe something about the speed of light would have to be different? So we might wind up with two different kinds of hypothetical empty universes, one where lightspeed is constant and another where lightspeed is additive with velocity of the source? Or maybe multiple ways it could go, that would either produce or deny Sagnac. Then the question becomes, if we could find an empty universe, which kind of universe would it have to be?

This is getting extremely hypothetical. Maybe there are solutions, but maybe it would be good to look for some other way to tell the difference between these ideas.

Also, absolute rotation in no way implies absolute orientation as you described it earlier, with a privileged up, down, front, back, left, and right for the whole universe. Similarly, if absolute velocity were a thing, it would not imply for example that the universe has a center.


If you had absolute velocity, then once you choose a location and decide it's the center of the universe, you can leave it and navigate back to it. Similarly, if you have absolute rotations then once you choose a set of axes to measure by, you can rotate away from them and then rotate back to them. They probably aren't privileged unless you choose to privilege them in your own mind, but you can track them and anybody who can track rotations can tell which directions they are. Like anybody who knows how, can figure out which great-circle direction Mecca is, whether you privilege that or not.

Also, do I understand correctly from rmsgray's statement "The Kerr solution starts with the assumption that there is an isolated body with a given angular momentum" that, since a Machian model says that the Earth does have angular momentum now, just that it only has it relative** to the rest of the universe, and that if the rest of the universe disappeared it would not have angular momentum relative to anything anymore, that a Machian model would say that the Kerr solution applies to the Earth just fine right now, but wouldn't if the rest of the universe disappeared? If so, then "the Kerr solution exists" isn't really an objection to a Machian model.
Perhaps not, but it most certainly is an objection to your absurd claim that a Machian model is one of the implications of relativity.


Suppose that Pfhorrest agreed that it has not yet been proven that only Machian models can fit relativity. Would that lay this particular issue to rest?

From the word pictures I've heard so far I don't like those Machian models. Most of the universe is spinning faster than light around you? But somebody else is rotating on a different axis and at the same time the universe is spinning around you, it's spinning faster than light in a different way around him? That sounds like a convenient mathematical fiction, except that people say the math hasn't been worked out yet. If we're going to do something like that, I'd rather think of it as you doing some sort of absolute rotation, and the rest of the universe might have some sort of defined effect on it.
The Law of Fives is true. I see it everywhere I look for it.

Jamaican Castle
Posts: 151
Joined: Fri Nov 30, 2007 9:10 pm UTC

Re: What-if 0007: Everybody Out

Postby Jamaican Castle » Mon Sep 17, 2012 5:01 pm UTC

Back on the topic of Time Zones IN SPACE, which I might have a chance of actually following:

If you have two objects moving around (say a spaceship and a planet), and one of them is putting a radio signal every one of its seconds, the other one views those signals as counting fast/slow according to their relative velocities, right? (It seems like it must work this way, but I can't remember right now. Not a morning person.)

If so, they don't need to go into elaborate guesswork at how time should be passing for other objects, because they can read it directly from those signals.

I guess you wouldn't know how fast your time is passing relative to a planet's* when you were far away from it, but it almost doesn't matter. All of your actions are coordinated in your time, of course, and you can make a ballpark estimate of how much time has gone by in the "outside" world just by your rough velocity, if it matter.

Apologies in advance if this is either horribly wrong or trivial to everyone else still in this discussion. It just seemed like a lot of ado about a relatively (no pun intended) simple problem.

* idle question: does time pass at (approximately) the same rate on every planet? What sort of variation would be possible between otherwise vaguely-Earth-like worlds?

User avatar
eran_rathan
Mostly Wrong
Posts: 1846
Joined: Fri Apr 09, 2010 2:36 pm UTC
Location: in your ceiling, judging you

Re: What-if 0007: Everybody Out

Postby eran_rathan » Mon Sep 17, 2012 5:09 pm UTC

Jamaican Castle wrote:idle question: does time pass at (approximately) the same rate on every planet? What sort of variation would be possible between otherwise vaguely-Earth-like worlds?


Since a second is defined by the number of oscillations of a certain atom (cesium?), time passes at the same rate everywhere. Its just when you start comparing them stuff gets weird :D


EDIT: Wikipedia says:one second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom (at 0K)."

EDIT2: added temperature correction.
"Does this smell like chloroform to you?"
"Google tells me you are not unique. You are, however, wrong."
nɒʜƚɒɿ_nɒɿɘ

Jamaican Castle
Posts: 151
Joined: Fri Nov 30, 2007 9:10 pm UTC

Re: What-if 0007: Everybody Out

Postby Jamaican Castle » Mon Sep 17, 2012 5:32 pm UTC

eran_rathan wrote:Since a second is defined by the number of oscillations of a certain atom (cesium?), time passes at the same rate everywhere. Its just when you start comparing them stuff gets weird :D


Well, right. I think what I meant was something more like "if you have a clock on Mars, and are listening to a speaking clock located on Earth, how quickly will they fall out of sync?".

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Mon Sep 17, 2012 6:48 pm UTC

Part of the problem is that I don't know how the other thing's velocity may have changed in the time since the signal left their ship, so their latest signal won't necessarily give me a good idea of how much additional time will have passed by the time they get the next message I send out. The redshift of a particular clock tick (and the delay I experience between successive ticks of their clock) tells me the velocity their ship was traveling when it emitted the signal relative to my own velocity when I receive the signal.

If and when we return to the same location, though, we can piece together all of the relative velocities each of us traveled before that time, because our "here and now"s again match up.

Two Earth-like planets couldn't have very different time rates due to gravitational time dilation, because being Earth-like means their gravity wells are similarly sized. And if we pay attention to interstellar dust and gas, no planet could travel more than a few percent of light speed before it risks losing its atmosphere to the hail of relativistic dust it's flying through. At a few percent, time dilation effects aren't all that significant. (To use some actual numbers: if you're traveling relative to me at 10% of light speed, I would calculate that your clock is ticking 99.5% as fast as mine. We don't see a difference of even 5% until you're traveling almost 1/3 of light speed.)
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Mon Sep 17, 2012 7:55 pm UTC

gmalivuk wrote:Two Earth-like planets couldn't have very different time rates due to gravitational time dilation, because being Earth-like means their gravity wells are similarly sized.


Could one of them be quickly revolving around a black hole? Could that give them different rates of gravitational time dilation?

And if we pay attention to interstellar dust and gas, no planet could travel more than a few percent of light speed before it risks losing its atmosphere to the hail of relativistic dust it's flying through. At a few percent, time dilation effects aren't all that significant. (To use some actual numbers: if you're traveling relative to me at 10% of light speed, I would calculate that your clock is ticking 99.5% as fast as mine. We don't see a difference of even 5% until you're traveling almost 1/3 of light speed.)


That gives us an estimate toward a privileged velocity. The privileged velocity is the average velocity of the dust that's flying around nearby. It should be pretty simple to tell about that -- count the dust particles that pass you versus the ones you pass, like counting cars on the freeway. This is the obvious velocity o privilege because if you travel even few percent different from it, they will hurt you. And if you travel at a velocity much different, then the light you observe will suffer Fizeau effect.
The Law of Fives is true. I see it everywhere I look for it.

User avatar
Pfhorrest
Posts: 5482
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: What-if 0007: Everybody Out

Postby Pfhorrest » Mon Sep 17, 2012 7:59 pm UTC

gmalivuk wrote:
Pfhorrest wrote:And gmalivuk et al who say there is such a thing as absolute rotation, can you confirm my earlier question that you hold there is consequently such a thing as absolute orientation as well?
I have not for sure decided that I believe in absolute rotation, only that it is consistent with GR for such to exist and that it could be tested for without reference to any distant stars. (In other words, it could still mean something for a thing to be rotating in an otherwise empty universe, even if we'll never be able to test what actually happens there.)

How are those two things any different? What I mean by "there is such a thing as absolute rotation" is precisely "there is some sense to be made of the notion of rotation without reference to anything the object in question is rotating relative to". It sounds here like you're affirming the latter but unsure of the former, and I'm not sure how to reconcile that.

Also, absolute rotation in no way implies absolute orientation as you described it earlier, with a privileged up, down, front, back, left, and right for the whole universe. Similarly, if absolute velocity were a thing, it would not imply for example that the universe has a center.

But if absolute velocity was a thing, absolute position would have to be a thing, even if we couldn't determine where the origin is, because if you're absolutely moving then you must be absolutely changing your position so you must have an absolute position to change. Likewise, even if we can't tell where the axes are, absolute rotation would require absolute orientation, because if you're absolutely turning then you must be absolutely changing your orientation so you must have an absolute orientation to change.

Instead of just saying "no it wouldn't" can you please explain why you think so?

Perhaps not, but it most certainly is an objection to your absurd claim that a Machian model is one of the implications of relativity.

Forgive me for thinking that the central principle of relativity is that all motion is only relative, and noting some implications of that. If relativity permits some kinds of absolute motion, then those may not be implications of relativity necessarily. But my point in the first place bringing this up was to call out an apparent belief in an absolute frame of reference, so if you want to bite that bullet and say yes you are fine with the notion of absolute motion, that's your call.
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

User avatar
Yakk
Poster with most posts but no title.
Posts: 11129
Joined: Sat Jan 27, 2007 7:27 pm UTC
Location: E pur si muove

Re: What-if 0007: Everybody Out

Postby Yakk » Mon Sep 17, 2012 8:16 pm UTC

The universe being translation invariant in position and velocity implies different conservation laws. You 'could' have absolute velocity with no absolute position - imagine a physics where time slows with absolute velocity. There is still no need for a privileged spacial origin, evenn though there is a privileged zero velocity.

Same holds for angular velocity and orientation.
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

Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Mon Sep 17, 2012 9:06 pm UTC

J Thomas wrote:Could one of them be quickly revolving around a black hole? Could that give them different rates of gravitational time dilation?
Yeah, but I think that's pushing "earth-like" a bit, too.

That gives us an estimate toward a privileged velocity. The privileged velocity is the average velocity of the dust that's flying around nearby. It should be pretty simple to tell about that -- count the dust particles that pass you versus the ones you pass, like counting cars on the freeway. This is the obvious velocity o privilege because if you travel even few percent different from it, they will hurt you.
It's not a privileged velocity, it's just velocity relative to another thing, like any other velocity. Velocity relative to interstellar gas isn't even going to be consistent throughout a comoving frame, because that gas and dust moves with gravity and galactic rotation and so forth. But even velocity relative to the CMB is merely convenient, but not privileged in any intrinsic way by the geometry of the universe itself.

Pfhorrest wrote:
gmalivuk wrote:I have not for sure decided that I believe in absolute rotation, only that it is consistent with GR for such to exist and that it could be tested for without reference to any distant stars. (In other words, it could still mean something for a thing to be rotating in an otherwise empty universe, even if we'll never be able to test what actually happens there.)
How are those two things any different? What I mean by "there is such a thing as absolute rotation" is precisely "there is some sense to be made of the notion of rotation without reference to anything the object in question is rotating relative to". It sounds here like you're affirming the latter but unsure of the former, and I'm not sure how to reconcile that.
I'm saying absolute rotation could be tested for in the same sense that velocity relative to the luminiferous aether could be tested for. That's not same as saying either of those things exist.

Also, absolute rotation in no way implies absolute orientation as you described it earlier, with a privileged up, down, front, back, left, and right for the whole universe.
But if absolute velocity was a thing, absolute position would have to be a thing, even if we couldn't determine where the origin is, because if you're absolutely moving then you must be absolutely changing your position so you must have an absolute position to change. Likewise, even if we can't tell where the axes are, absolute rotation would require absolute orientation, because if you're absolutely turning then you must be absolutely changing your orientation so you must have an absolute orientation to change.
None of which contradicts my actual point, which I've helpfully bolded for you.

Perhaps not, but it most certainly is an objection to your absurd claim that a Machian model is one of the implications of relativity.

Forgive me for thinking that the central principle of relativity is that all motion is only relative, and noting some implications of that.
By "relativity" I didn't simply mean that executive summary, I actually meant the equations of the general theory of relativity, as published by Einstein. Since those equations permit different vacuum solutions for rotating and nonrotating spheres, it must be the case that angular momentum can have meaning in the equations of GR independent from any distant stars. Therefore, GR doesn't imply that angular momentum in the absence of distant stars is meaningless.

---

Let's do another thought experiment in an empty universe: suppose there are two parallel rings, which are light and quite far from each other. Each observes the other to be rotating around the line through their centers. Under your Machian interpretation, which of the following is possible?
1) Objects on the inside of one ring feel no centrifugal force, objects on the inside of the other feel an acceleration pushing them outward against the ring.
2) Objects on the insides of both rings feel an equal acceleration pushing them outward.
3) Objects on the insides of both rings feel acceleration outward, but the accelerations are of different magnitude.
4) Objects on the insides of both rings feel no centrifugal force.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Pfhorrest
Posts: 5482
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: What-if 0007: Everybody Out

Postby Pfhorrest » Mon Sep 17, 2012 10:02 pm UTC

gmalivuk wrote:
Perhaps not, but it most certainly is an objection to your absurd claim that a Machian model is one of the implications of relativity.

Forgive me for thinking that the central principle of relativity is that all motion is only relative, and noting some implications of that.
By "relativity" I didn't simply mean that executive summary, I actually meant the equations of the general theory of relativity, as published by Einstein.

That's what I meant in that sentence as well. It was my understanding that the broader principle of relativity (all spatial and temporal relations are relative) was central to the Theory of General Relativity (caps just for clarity distinguishing the two senses). I'm surprised to hear that that isn't necessarily the case, but not too fazed since my original point was about implications of the former.

Since those equations permit different vacuum solutions for rotating and nonrotating spheres, it must be the case that angular momentum can have meaning in the equations of GR independent from any distant stars. Therefore, GR doesn't imply that angular momentum in the absence of distant stars is meaningless.

I suppose so; it pushes the question back to "does it make any sense to speak of 'rotating' spheres in anything but a relative sense?" But provided you can sensibly speak of rotating in some sense (relative or absolute), GR will work with that, and distinguish it from non-rotating.

Let's do another thought experiment in an empty universe: suppose there are two parallel rings, which are light and quite far from each other. Each observes the other to be rotating around the line through their centers. Under your Machian interpretation, which of the following is possible?
1) Objects on the inside of one ring feel no centrifugal force, objects on the inside of the other feel an acceleration pushing them outward against the ring.
2) Objects on the insides of both rings feel an equal acceleration pushing them outward.
3) Objects on the insides of both rings feel acceleration outward, but the accelerations are of different magnitude.
4) Objects on the insides of both rings feel no centrifugal force.

Under my Machian interpretation, (2) would be the case, but the force that each ring feels due to that acceleration would be much less than it would be if such a ring was rotating relative to a massive universe like ours, since the inertia which resists the acceleration is directly due to (and so proportional to) the gravitational attraction of other masses, and in this scenario there is very little other mass in the universe at all and it is very far away, so it would require very little application of force to produce the same change in velocity, and an accelerometer calibrated for the inertia of our universe would read less acceleration than the observed changed in relative velocity would indicate. (An interesting implication of this mass-out-there-gives-inertia-here is that we should be able to derive the mass of the rest of the universe from the amount of inertia that something has. I wonder if this could be used as an experiment of the principle? If the mass-of-the-universe figure derived from inertia matches the mass-of-the-universe figures derived from other methods...)

I recall again this passage from the wiki article on frame dragging:
Static mass increase is a third effect noted by Einstein in the same paper.[5] The effect is an increase in inertia of a body when other masses are placed nearby. While not strictly a frame dragging effect (the term frame dragging is not used by Einstein), it is demonstrated by Einstein that it derives from the same equation of general relativity. It is also a tiny effect that is difficult to confirm experimentally.

This is why I was calling the Machian explanation of inertia "due to frame-dragging". This sounds very much like a Machian "mass out there is what gives inertia here" -- and why I bring it up now, as above I am claiming that things only have the substantial inertia they do because there is a very massive universe surrounding them -- and wiki is claiming Einstein himself demonstrated that that follows from GR. I've read things like this before elsewhere and this is where my understanding that Mach's principle (or something like it) is an implication of general relativity came from.

I'm not completely certain, but I wonder if this implies another possible test for the principle: according to the above, should an accelerometer undergoing the same change in motion relative to objects in its former frame of reference (as measured say visually) read a lower figure far out in intergalactic space than it would here? Because the accelerometer is directly reading just an amount of force, and back-calculating from that and "known" inertial mass to determine acceleration from there; but if inertial mass varies based on the existence and proximity of other masses...
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Tue Sep 18, 2012 12:08 am UTC

gmalivuk wrote:
J Thomas wrote:That gives us an estimate toward a privileged velocity. The privileged velocity is the average velocity of the dust that's flying around nearby. It should be pretty simple to tell about that -- count the dust particles that pass you versus the ones you pass, like counting cars on the freeway. This is the obvious velocity o privilege because if you travel even few percent different from it, they will hurt you.
It's not a privileged velocity, it's just velocity relative to another thing, like any other velocity. Velocity relative to interstellar gas isn't even going to be consistent throughout a comoving frame, because that gas and dust moves with gravity and galactic rotation and so forth. But even velocity relative to the CMB is merely convenient, but not privileged in any intrinsic way by the geometry of the universe itself.


I guess we're speaking past each other. The fact that at any particular place the interstellar dust *has* a median velocity says something important about the universe. And it gives you a frame to pay attention to. Sure, it won't be the same everywhere, but it's an important frame for various reasons and if we actually do someday have the ability to move very fast with spaceships which can be damaged by such things, then it will be vitally important.

Pfhorrest wrote:
gmalivuk wrote:I have not for sure decided that I believe in absolute rotation, only that it is consistent with GR for such to exist and that it could be tested for without reference to any distant stars. (In other words, it could still mean something for a thing to be rotating in an otherwise empty universe, even if we'll never be able to test what actually happens there.)
How are those two things any different? What I mean by "there is such a thing as absolute rotation" is precisely "there is some sense to be made of the notion of rotation without reference to anything the object in question is rotating relative to". It sounds here like you're affirming the latter but unsure of the former, and I'm not sure how to reconcile that.
I'm saying absolute rotation could be tested for in the same sense that velocity relative to the luminiferous aether could be tested for. That's not same as saying either of those things exist.

Also, absolute rotation in no way implies absolute orientation as you described it earlier, with a privileged up, down, front, back, left, and right for the whole universe.
But if absolute velocity was a thing, absolute position would have to be a thing, even if we couldn't determine where the origin is, because if you're absolutely moving then you must be absolutely changing your position so you must have an absolute position to change. Likewise, even if we can't tell where the axes are, absolute rotation would require absolute orientation, because if you're absolutely turning then you must be absolutely changing your orientation so you must have an absolute orientation to change.
None of which contradicts my actual point, which I've helpfully bolded for you.


Sure, but getting back to the Pressures thread .... If there is no absolute velocity, but there is an absolute position, you can't find your absolute position. Suppose that by some chance at one moment you happen to be at the absolute zero point of the universe. What would you have to do to stay there? You would have to maintain absolute zero velocity. If you unknowingly have a velocity -- which someone in a different frame will believe -- then you will be swept away from that point without knowing it. Unless you know your absolute velocity you cannot track your absolute position. But if you do know your absolute velocity you can track your position.

Without absolute linear velocity, you can create -- say -- a cartesian 3D grid and measure positions by it, but you don't know whether your grid is traveling at an unknown velocity. If you do know your absolute velocity then you can create that same grid and know that it is not traveling. That doesn't mean that your zero point isn't arbitrary. And your choice of x, y, and z axes could be arbitrary. And your choice of units is arbitrary. But if it's true that Sagnac measures absolute rotation then you can be sure that your choice of x, y, and z axes does not change without you knowing it. And if you had a way to measure absolute velocity then you could be sure that your zero point would not change without you knowing it.

It says less that your x axis doesn't change, than to say that you have the one right direction to put an x axis and all other choices are wrong. But it says more that your x axis doesn't change, than when you don't know whether your x axis is changing or not because you don't know whether you're rotating.

Let's do another thought experiment in an empty universe: suppose there are two parallel rings, which are light and quite far from each other. Each observes the other to be rotating around the line through their centers. Under your Machian interpretation, which of the following is possible?
1) Objects on the inside of one ring feel no centrifugal force, objects on the inside of the other feel an acceleration pushing them outward against the ring.
2) Objects on the insides of both rings feel an equal acceleration pushing them outward.
3) Objects on the insides of both rings feel acceleration outward, but the accelerations are of different magnitude.
4) Objects on the insides of both rings feel no centrifugal force.


I have trouble understanding how #1 would be true. What would be different between the two rings that would give you acceleration for one of them but not for the other?

I'm not sure about #3. Are you saying they observe the other to be rotating relative to themselves? So maybe one of them really is rotating and the other is not?

In that case I think I can imagine all four. Each example just needs a different set of laws of physics.

Which laws of physics do we actually have? We'd need to do the math in each case and find ways the different mathematical systems give different results for our own universe. It doesn't help us to imagine other universes where things are different. Unless it turns out that some of them are self-contradictory and don't bear thinking.
The Law of Fives is true. I see it everywhere I look for it.

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Tue Sep 18, 2012 12:52 am UTC

Pfhorrest wrote:I am claiming that things only have the substantial inertia they do because there is a very massive universe surrounding them -- and wiki is claiming Einstein himself demonstrated that that follows from GR.
No, wiki is claiming Einstein himself described a "tiny" (so tiny as to be experimentally untestable so far) effect from objects nearby. Since gravitational effects decrease with distance, we should expect this effect to get even tinier for even more distant objects.

Saying that nearby matter affects inertia ever so slightly is not at all the same as saying the rest of the matter in the universe is what gives things nonzero inertia in the first place. GR says the first, and you're taking it to imply the second.

J Thomas wrote:I guess we're speaking past each other. The fact that at any particular place the interstellar dust *has* a median velocity says something important about the universe.
No it really doesn't. Any collection of matter anywhere will have a median velocity once you pick a frame in which you're measuring that velocity.

And it gives you a frame to pay attention to. Sure, it won't be the same everywhere, but it's an important frame for various reasons
The same could be said for the Sun's reference frame, or whatever the nearest star is. This isn't what we mean in relativity when talking about a privileged frame, which is typically meant to refer to something innate in the geometry of the universe.

Let's do another thought experiment in an empty universe: suppose there are two parallel rings, which are light and quite far from each other. Each observes the other to be rotating around the line through their centers. Under your Machian interpretation, which of the following is possible?
1) Objects on the inside of one ring feel no centrifugal force, objects on the inside of the other feel an acceleration pushing them outward against the ring.
2) Objects on the insides of both rings feel an equal acceleration pushing them outward.
3) Objects on the insides of both rings feel acceleration outward, but the accelerations are of different magnitude.
4) Objects on the insides of both rings feel no centrifugal force.
I have trouble understanding how #1 would be true. What would be different between the two rings that would give you acceleration for one of them but not for the other?

I'm not sure about #3. Are you saying they observe the other to be rotating relative to themselves? So maybe one of them really is rotating and the other is not?

In that case I think I can imagine all four. Each example just needs a different set of laws of physics.
Well yeah, but I was asking precisely in order to figure out what laws of physics Pfhorrest is working from.

Note, however, that 1-3 are all possible in a flattish area of our universe, while 4 isn't.

An interesting consequence of Pfhorrest saying that 2 would always be the case seems to be that if the rings start out at rest, and then rockets on only one of them accelerate that one rotationally, objects in the other one will somehow feel a force and undergo centrifugal acceleration. Presumably the same thing would happen with linear acceleration as well?

And I'm pretty certain that this is *not* what is predicted by any of the frame-dragging effects of GR, though someone who knows more about it than I do is free to correct me.
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Pfhorrest
Posts: 5482
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: What-if 0007: Everybody Out

Postby Pfhorrest » Tue Sep 18, 2012 1:56 am UTC

gmalivuk wrote:
Pfhorrest wrote:I am claiming that things only have the substantial inertia they do because there is a very massive universe surrounding them -- and wiki is claiming Einstein himself demonstrated that that follows from GR.
No, wiki is claiming Einstein himself described a "tiny" (so tiny as to be experimentally untestable so far) effect from objects nearby. Since gravitational effects decrease with distance, we should expect this effect to get even tinier for even more distant objects.

Saying that nearby matter affects inertia ever so slightly is not at all the same as saying the rest of the matter in the universe is what gives things nonzero inertia in the first place. GR says the first, and you're taking it to imply the second.

I think you misread my sentence. The part between the faux emdashes (--) was parenthetical. Rephrasing it: "This [the quote from wikipedia] sounds very much like a Machian "mass out there is what gives inertia here", and wiki is claiming Einstein himself demonstrated that that [the quote from wikipedia] follows from GR. [The sounding-Machain part is] why I bring it up now, as above I am claiming that things only have the substantial inertia they do because there is a very massive universe surrounding them."

I'm saying that Einstein himself said that being surrounded by masses increases the inertia of objects, albeit by a tiny amount relative to the size of masses; so I'm positing that being surrounded by all the mass in the universe is a reasonable explanation for why objects in the universe have the inertia they do. There is a known mechanism which does something qualitatively the same as what Mach's principle would demand; I just don't know if the quantitative magnitude of the effect is enough because I don't have the mathematical ability to run the relevant calculations. I imagine for someone who does it should be trivial to compute though: is the mass of the universe, at the distance it is, enough to produce, via this effect which Einstein says follows from GR, the amount of inertia we observe things to have?

Similarly with rotational frame dragging. We know that there is a relatively weak effect which will cause something inside of a rotating shell of matter to be dragged along with it, and to experience effects as though it was rotating the other direction. Is the mass of the universe enough that, if collected into a shell at its average distance and spun around something, it would produce, via this known effect, the same forces on the things inside the shell as if we had spun the things at the same rate in the "static" universe?

The whole Clarke spinning bucket thing was supposedly untestable, because we can't gather up the rest of the universe and spin it around a bucket. But we know now that spinning masses around things does have qualitatively the right effect, and we have a theory (GR) that models that accurately. Using that model and the mass of the universe, we should be able to say what would happen if we spun something with the mass of the universe around the bucket.

An interesting consequence of Pfhorrest saying that 2 would always be the case seems to be that if the rings start out at rest, and then rockets on only one of them accelerate that one rotationally, objects in the other one will somehow feel a force and undergo centrifugal acceleration.

Yes. It is my understanding that established frame-dragging effects predict that spinning one massive ring close to another ring would cause the other ring to drift ever so slightly along with it, and to feel centrifugal forces as though it was rotating the opposite direction; Max said something earlier about not being able to tell whether you're spinning or it's spinning (in that context referring to being surrounded by a spinning shell, but if I understand correctly the same principle applies to two rings as well). As I said earlier, I expect (in line with the known magnitude of frame dragging) that these effects would be much smaller with two light rings a good distance away from each other in an otherwise empty universe. It would take very little thrust to spin up one ring (because it would have so little inertia, with so little mass in the universe around it) and so people on it would feel very little "acceleration" as it spun up relative to the other ring. Meanwhile the other ring would be (ever so slightly) pulled along by it and so feel (to the tiny amount they feel anything) that it was spinning the opposite direction. You would have to greatly increase their (rest) mass, or spin them much faster relative to each other (increasing their relativistic mass) , for them to feel anything even close to comparable to spinning such a ring in our massive universe, or equivalently spinning a shell the mass of our universe around such a ring.
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

User avatar
gmalivuk
GNU Terry Pratchett
Posts: 26824
Joined: Wed Feb 28, 2007 6:02 pm UTC
Location: Here and There
Contact:

Re: What-if 0007: Everybody Out

Postby gmalivuk » Tue Sep 18, 2012 3:23 am UTC

Pfhorrest wrote:
An interesting consequence of Pfhorrest saying that 2 would always be the case seems to be that if the rings start out at rest, and then rockets on only one of them accelerate that one rotationally, objects in the other one will somehow feel a force and undergo centrifugal acceleration.
Yes. It is my understanding that established frame-dragging effects predict that spinning one massive ring close to another ring would cause the other ring to drift ever so slightly along with it, and to feel centrifugal forces as though it was rotating the opposite direction
Why would accelerating *slightly* in the *same* direction as the already-spinning thing result in feeling like it was spinning at an *equal* rotational velocity in the *opposite* direction?

It would take very little thrust to spin up one ring (because it would have so little inertia, with so little mass in the universe around it) and so people on it would feel very little "acceleration" as it spun up relative to the other ring. Meanwhile the other ring would be (ever so slightly) pulled along by it and so feel (to the tiny amount they feel anything) that it was spinning the opposite direction.
Acceleration in a rotating frame is a matter of rotational velocity and radius, so the amount of acceleration they'd experience would be independent of how much mass they have.

And again, why would being pulled along with the other ring result in feeling like they were moving in the opposite direction? Why would frame dragging, which is a teeny tiny effect, result in their feeling like they're moving at the exact same velocity in the opposite direction as the ring that actually had thrust applied to it?
Unless stated otherwise, I do not care whether a statement, by itself, constitutes a persuasive political argument. I care whether it's true.
---
If this post has math that doesn't work for you, use TeX the World for Firefox or Chrome

(he/him/his)

User avatar
Max™
Posts: 1792
Joined: Thu Jun 21, 2012 4:21 am UTC
Location: mu

Re: What-if 0007: Everybody Out

Postby Max™ » Tue Sep 18, 2012 4:18 am UTC

http://arxiv.org/abs/gr-qc/9607009

Covers some of the reasons why various formulations of Mach's Principle are incompatible with GR.
mu

User avatar
Pfhorrest
Posts: 5482
Joined: Fri Oct 30, 2009 6:11 am UTC
Contact:

Re: What-if 0007: Everybody Out

Postby Pfhorrest » Tue Sep 18, 2012 6:43 am UTC

Max™ wrote:http://arxiv.org/abs/gr-qc/9607009

Covers some of the reasons why various formulations of Mach's Principle are incompatible with GR.

Some of that was a little over my head (and I only gave it a cursory reading at the moment anyway, may revisit later), but I believe their formulation "Mach3" is the closest to my understanding of Mach's principle (and which they say is compatible with GR and the Lense-Thirring effect specifically).

More specifically I would say my version of Mach's principle derives via their "Mach0" from a general principle of relativity (lower-case, not GR specifically): all spatial and temporal relations are relative. So me spinning around in the universe and the universe spinning around me are the same state of affairs. That leads to the Mach0 observation: somehow spinning the universe around me pulls my arms away from my body. That raises the question of why that happens, and since the conventional explanation of my arms pulling away from my body when I spin is "inertia", that indicates that the rest of the universe somehow influences inertia here, which is their Mach3. The rest is details: how does the rest of the universe influence inertia here, in a way that pulls my arms away from my body when it spins around me, that being an equivalent description of me spinning around?

gmalivuk wrote:Why would accelerating *slightly* in the *same* direction as the already-spinning thing result in feeling like it was spinning at an *equal* rotational velocity in the *opposite* direction?

It's not that one causes the other, its that they both happen from the same cause: the second ring is having its frame of reference pulled around by the first. Lets think of the spinning shell instead of the rings for ease of illustration: You're floating in the lotus position in zero G inside a massive hollow shell of matter (in our universe, for simplicity). It starts to spin (relative to the distant stars) along the axis of your spine in what you would call a counterclockwise motion, so the wall in front of you is rushing to your left. It drags your frame of reference around with it, so what feels like "straight ahead" to you keeps drifting to your left, so you keep feeling like you are turning to the right. (A gyroscope would feel pulled to the left, for example, like it would if you tried to turn right). You are slowly pulled into the rotating reference frame yourself however, diminishing the feeling that you are turning right, and the feeling that you are turning to your right ceases entirely when you catch up to the spinning shell of matter and no longer are turning right relative to it. I'm not certain that could actually happen in our universe though, as there is the mass of the rest of the universe trying to keep you in its frame; I don't think you would ever be pulled completely into the spinning shell's frame, and so would always feel like you were turning slightly to the right, as the massive shell spun rapidly to your left. (Max, can you please confirm I have this part correct, since you spoke of this scenario earlier?)

Thinking on it further, I'm not certain what to expect in such a circumstance if outside the shell is an otherwise empty universe, because the component of your inertia received from the rest of the universe, if we did this in our universe, would be resisting the shell's dragging of your frame of reference, as above; but without the rest of the universe, perhaps you would be pulled along by the shell all the more readily? In which case, if that is the case, with the spinning rings example you gave, spinning one ring might well pull the other ring right along with it in an exaggerated form of frame dragging (instead of the tiny amount I expected earlier), there being no rest of the universe to counter-drag the other ring's frame; the magnitude of the frame-dragging effect is strictly the same, but it is now the sole source of (or influence on) inertia, not acting against the mass of the rest of the universe, so it accomplishes much more unimpeded. In which case, in order to really establish relative rotation between them, one ring would have to thrust one way and, to counteract being pulled along with it, the other ring would have to thrust the other way, in which case as you would expect both would experience acceleration.

(Intuitively I imagine that even with the frame-dragging effects greatly exaggerated by having no rest of the universe to compete with, there would be some lag and dally between the motion of the first ring and the second, like how the rotating shell scenario would work in our universe, though lessened. Giving that a little though, it seems like if we are using thrusters to spin one ring up, we have some propellant mass now floating off in our universe to account for -- the rest of our universe is no longer completely empty -- and that that may account for the expected lag between the two rings. If instead one ring pushed directly off the other by some mechanism, so there was no propellant mass floating off to account for, then of course the third law of motion would result in both rings spinning equally in opposite directions and experiencing equal centrifugal force etc.)

It would take very little thrust to spin up one ring (because it would have so little inertia, with so little mass in the universe around it) and so people on it would feel very little "acceleration" as it spun up relative to the other ring. Meanwhile the other ring would be (ever so slightly) pulled along by it and so feel (to the tiny amount they feel anything) that it was spinning the opposite direction.

Acceleration in a rotating frame is a matter of rotational velocity and radius, so the amount of acceleration they'd experience would be independent of how much mass they have.

That's why I put "acceleration" in quotes there. We never directly feel acceleration per se; we feel a force of some kind, we feel weight. That force is our mass being accelerated. I can tell that the airplane I'm in just got pushed upward by turbulence because my chair pressed harder into my ass. We normally presume our mass is fixed and so the force we feel is proportional to the amount we are being accelerated. But if our mass was less, then being literally accelerated (velocity changing as measured visually or such) by the same amount would not "feel" like the same amount of "acceleration", because we would in effect weigh less in the acceleration-induced "artificial gravity", feel less force against us, as it would take less force to accelerate us the same amount. F=ma and all that.

And again, why would being pulled along with the other ring result in feeling like they were moving in the opposite direction? Why would frame dragging, which is a teeny tiny effect, result in their feeling like they're moving at the exact same velocity in the opposite direction as the ring that actually had thrust applied to it?

I believe I've covered these both in my explanation and reexamination above.
Forrest Cameranesi, Geek of All Trades
"I am Sam. Sam I am. I do not like trolls, flames, or spam."
The Codex Quaerendae (my philosophy) - The Chronicles of Quelouva (my fiction)

J Thomas
Everyone's a jerk. You. Me. This Jerk.^
Posts: 1190
Joined: Fri Sep 23, 2011 3:18 pm UTC

Re: What-if 0007: Everybody Out

Postby J Thomas » Tue Sep 18, 2012 11:16 am UTC

Pfhorrest wrote:
gmalivuk wrote:Why would accelerating *slightly* in the *same* direction as the already-spinning thing result in feeling like it was spinning at an *equal* rotational velocity in the *opposite* direction?

It's not that one causes the other, its that they both happen from the same cause: the second ring is having its frame of reference pulled around by the first. Lets think of the spinning shell instead of the rings for ease of illustration: You're floating in the lotus position in zero G inside a massive hollow shell of matter (in our universe, for simplicity). It starts to spin (relative to the distant stars) along the axis of your spine in what you would call a counterclockwise motion, so the wall in front of you is rushing to your left. It drags your frame of reference around with it, so what feels like "straight ahead" to you keeps drifting to your left, so you keep feeling like you are turning to the right. (A gyroscope would feel pulled to the left, for example, like it would if you tried to turn right). You are slowly pulled into the rotating reference frame yourself however, diminishing the feeling that you are turning right, and the feeling that you are turning to your right ceases entirely when you catch up to the spinning shell of matter and no longer are turning right relative to it. I'm not certain that could actually happen in our universe though, as there is the mass of the rest of the universe trying to keep you in its frame; I don't think you would ever be pulled completely into the spinning shell's frame, and so would always feel like you were turning slightly to the right, as the massive shell spun rapidly to your left. (Max, can you please confirm I have this part correct, since you spoke of this scenario earlier?)


Here is another effect -- the shell is rotating, so its equator travels faster than its poles which are not moving. By special relativity you will observe time dilation for its equator. If gravity happens because of waves, like light, this will make its effect less. Light's effect comes from the wave motion and low-frequency waves have less effect. But if gravity is a continuous force, if its effect on you is proportional to the time of exposure to it, then the spinning equator will have more effect on you. The same force affects you for a longer time.

I wonder which way it actually goes? But then, you will be able to detect that the shell is rotating because it will be deformed into an oblate spheroid, so that will have an effect too. How big that effect is, will be determined by how good the particular shell is at resisting deformation. I guess it has to be pretty good at that since it hasn't already collapsed into a smaller sphere, crushing you.

Anyway, that relativistic force doesn't make much difference when the rotation is small, and I have no idea how to calculate it when it's distant things traveling faster than light.

Thinking on it further, I'm not certain what to expect in such a circumstance if outside the shell is an otherwise empty universe, because the component of your inertia received from the rest of the universe, if we did this in our universe, would be resisting the shell's dragging of your frame of reference, as above; but without the rest of the universe, perhaps you would be pulled along by the shell all the more readily? In which case, if that is the case, with the spinning rings example you gave, spinning one ring might well pull the other ring right along with it in an exaggerated form of frame dragging (instead of the tiny amount I expected earlier), there being no rest of the universe to counter-drag the other ring's frame; the magnitude of the frame-dragging effect is strictly the same, but it is now the sole source of (or influence on) inertia, not acting against the mass of the rest of the universe, so it accomplishes much more unimpeded. In which case, in order to really establish relative rotation between them, one ring would have to thrust one way and, to counteract being pulled along with it, the other ring would have to thrust the other way, in which case as you would expect both would experience acceleration.


And when you spin up the shell or the first ring it should have much less inertia because you (or the second ring) is all there is to impede its rotation. No wait, you're spinning it with rockets so the rocket exhaust will have an equal and opposite angular momentum, and that will also give it inertia.

(Intuitively I imagine that even with the frame-dragging effects greatly exaggerated by having no rest of the universe to compete with, there would be some lag and dally between the motion of the first ring and the second, like how the rotating shell scenario would work in our universe, though lessened. Giving that a little though, it seems like if we are using thrusters to spin one ring up, we have some propellant mass now floating off in our universe to account for -- the rest of our universe is no longer completely empty -- and that that may account for the expected lag between the two rings. If instead one ring pushed directly off the other by some mechanism, so there was no propellant mass floating off to account for, then of course the third law of motion would result in both rings spinning equally in opposite directions and experiencing equal centrifugal force etc.)


Yes. Whenever a conservation law is enforced at a distance you can expect some lag, because its effects travel no faster than lightspeed.
The Law of Fives is true. I see it everywhere I look for it.

User avatar
PM 2Ring
Posts: 3715
Joined: Mon Jan 26, 2009 3:19 pm UTC
Location: Sydney, Australia

Re: What-if 0007: Everybody Out

Postby PM 2Ring » Fri Sep 21, 2012 3:12 am UTC

Max™ wrote:Also, pi varies according to the depth of the gravity well you measure it around.


Huh? Spacetime curvature can certainly affect the ratio of a physical sphere's radius to its volume, but it's better to understand that in terms of variation in the local spacetime metric, since pi is a mathematical constant and its value is no more affected by local conditions than that of any other pure number. There have been several threads on the Mathematics & Science forums discussing this topic.

User avatar
Max™
Posts: 1792
Joined: Thu Jun 21, 2012 4:21 am UTC
Location: mu

Re: What-if 0007: Everybody Out

Postby Max™ » Fri Sep 21, 2012 3:55 am UTC

http://books.google.com/books?id=hlRhwG ... an&f=false

"You could calculate the predicted radius, and then dig a hole and measure it directly, the measured radius minus the predicted radius can be called the radius excess ... calculating this for the Earth you find it has 1.5 millimeters more radius than it should have for it's surface area, a similar calculation for the sun shows that the sun's radius is one half kilometer too long."

Trying to explain a metric isn't as easy as getting the idea of the radius being too long for a given spherical surface area, though you are right I shouldn't state it in terms of pi being changed. You would get a different value for pi though if you didn't account for the curvature and just used the measured radius and surface area.
mu


Return to “What If?”

Who is online

Users browsing this forum: No registered users and 3 guests