I stared at the 'my turn signal' and 'car in front of me' signal together for way too long. I went into the same trance I do sitting behind cars at a real red light.
It makes me sad because most of the births are in underdeveloped countries, where people have no access to clean water and healthy food. And as more people of countries like China enter middle class, the resources we depend on, will diminish faster and faster.
Please watch anything by Hans Rosling for an entertaining and educational counter-balance to your fears, ; while having some validity, over population is it one of humanities most pressing problems.
It's not land that's the problem, strictly speaking. Look up Leibig's Law of the Minimum.
The historical preindustrial peak human population was around 500-800 million. Maybe we'd be lucky and be able to sustain somewhat more than that, say 2 billion. I have a hard time seeing much more given energy and resource limitations.
Prediction's hard, especially about the future, but I suspect we're looking at a crisis well within 100 years. Possibly a few decades out, if that.
Dropping something the mass of a tennis ball into this pulsar(assuming 2 solar masses for it) would generate approximately the same amount of energy upon impact as that of 12 atomic bombs like the one tested in New Mexico, and it would reach the surface at 60% the speed of light...relativistic effects aside
Which is to say: the escape velocity is 60% of the speed of light! So even starting from 24% of the speed of light at the equator you need to go 10,000x faster than on Earth to escape.
Wow, that page led me to the fact that there is such a thing as centrifugal force... And all these years spent trying to correct people. Oh well, you live, you learn.
The "war on centrifugal force" is pedagogical. If you sit in an inertial frame, all forces you intend to teach are due to interactions between objects. This lets teachers introduce the interactions one at a time in a way that presents minimal opportunity for the "no, that equation doesn't work here for XYZ reasons which you won't understand until after you've taken vector calculus" problem.
If you allow rotating reference frames then you've got to talk about transformation rules in gory detail. Everyone understands centrifugal force, but what about the coriolis and euler forces? Our intuition doesn't tell us when they apply and when they don't, so we have to be systematic about it, and that means "gory details". And guess what "being systematic about it" involves? Moving to an inertial frame of reference and taking derivatives!
You can't be intuitively correct or systematic about rotating frames without thoroughly understanding inertial frames, so that's what you learn first, along with strongly worded advice to stay away from non-inertial frames (e.g. defining frame-dependent forces as "fictitious").
Anyone doing general relativity is comfortable enough with coordinate transformations that they can understand the caveats that come with frame-dependent forces and even take advantage of them to simplify calculations or definitions (the process of going from a "global" to a "local" coordinate system is highly nontrivial in GR).
That's why the Coriolis, Euler, and Centrifugal forces are called "fictitious" while gravity isn't.
This is what I love about HN - an anti-troll comment. Like most of us I think a generalist knowledge confers the right to an opinion and expressing that opinion.
Comments like this point out just how much I do not know, they sweep their arms across a horizon of maths and hard won understanding and say "only express that opinion after you know what that means"
Anti-trolling.
It's what keeps us honest about our own limitations, and reluctant to spout off crap.
love it. Now going to look up inertial frames and start translating.
So what are you proposing in this case, that the original poster had kept the Wikipedia title? Or that the linked Wikipedia article shouldn't have been posted at all ?
Because hn's anti editorialization policy is useless in both cases. For, in the first case, without editorialization, the title is completely useless except for experts on the subject. And for the second case, it has nothing to do with title editorialization, but with content.
does this mean that time flows significantly faster on the outside of the pulsar then on the inside, if so does this significantly impact the pulsar dynamics?
The quoted example admits that it ignores strong fields and non-relativistic matter, which we have already established to be dealing with. The angular momentum of an element of volume in the neutron star likely contains enough kinetic energy to affect the Einstein field equations in a significant way. General relativity can't be ignored, but the Newtonian approximations has this habit of being nearly right more often than not.
I know that for rotating black holes the Kerr solution to the Einstein equations offers the best way to test these metric-based questions but I'm not sure if that's what you'd use for a Neutron Star.
You are right. I was confused because the satellites in orbit need a different speed at different height, and in that case the when the special relativity effect increase the general relativity effect decrees. http://en.wikipedia.org/wiki/Error_analysis_for_the_Global_P...
I think the point was that time in the center of the star is more affected by gravity than at the surface. Whereas someone on the surface (if that were possible) would experience greater time dilation relative to the center due to his high relative velocity. So for those two points (surface vs center), the two time dilation effects are working opposite each other.
Edit: I may have been reading too much into it. The effects you see will depend on which positions you're comparing, and people in this thread haven't really specified.
If you're in a small empty room in the middle of a neutron star, you will be floating weightless, but you're still at the bottom of a gravity well. Since it's the well, not the acceleration that affects time, time will tick slower for you.
(Don't try this at home.) (And if you do, don't touch the walls.)
Spacetime in the center of a perfect spherical object is the same as a point in empty space, you can't tell them apart. Of course that only counts for the exact point in the center. So the time will not tick slower there as to someone far from any objects.
What? The lowest potential in a uniform sphere is at the centre not the surface (http://en.wikipedia.org/wiki/File:GravityPotential.jpg). Also graviational time dilation depends on the potential not the force (curvature) so it is irrelevant if the point at the centre is shifted in spacetime
Your link doesn't even relate to time dilation and is also about a hollow sphere, not a uniformly dense solid sphere. Moreover in a hollow sphere, time dilation still occurs because it depends on the absolute (or rather, relative to an outside distant observer) potential, not the gravitational field (which is the only thing that is necessarily zero as a result of the flat spacetime in the sphere). See for example this http://physics.stackexchange.com/questions/69821/a-hollow-bl...
Being unable to tell is not an argument for time not ticking slower; the whole point of time ticking slower is that everything is consistent for your point of reference and you can't tell, but your point of reference has different time than other points.
Just as if you were inertially moving at 0.9c relative to me, the time frame would be different despite both me and you being 'the same as a point in empty space'.
It doesn't affect the dynamics, but it might affect the radiation emitted by it as seen from the outside. All particles in the dilated reference experience the same dilation (approximately - it does vary radially, not sure if significant).
I like that theory. Generally the problem with science is that it's turned into a belief system almost akin to a religion by many people. Strangely, even by very smart physicists.
They seem to overlook the fact that we don't know anything; compared to what is out there our knowledge might approach a millionth of a millionth percent of all knowable things; but even that is just for illustration because if you only take into account the scale of the known universe it's going to be a number so small as to approach 0. We know literally nothing.
It's fine to come up with grand theories of how things work - human imagination is a wonderful thing. Just don't mistake it for facts.
Don't we already use these as a sort of GPS for interstellar travel? I think the Voyager plaques contained coordinates to Earth based on pulsar frequency.
I am assuming you are repeating the claim on the wikipedia page. Or maybe (hopefully) you have another source? I saw the claim on the wiki article and my first reaction was bullshit. My second reaction after stumbling across dead links in two of the three the citations was bullshit. After re-reading the article and the one functioning citation without seeing a accuracy/precision/stability figure my third reaction was also bullshit.
The strontium clock at Boulder loses one second in five billion years. [1][2][3]
Does anyone have any information supporting the pulsar clock claim? I have a sneaking suspicion that the author of this claim --just like the catalog in the chair pocket on airplanes--thinks my radio clock that syncs to WWVB/DCF77 is "an atomic clock."
Some atomic clocks are considerably less accurate. I can't find a citation, but IIRC, older cesium atomic clocks are accurate to about 1 second every 300 years.
Classically, mathematically, the answer is conservation of angular momentum. As matter falls on to the body the body needs to rotate faster to conserve the energy of the system. A rotation happens if there is even a tiny asymmetry in the accreting matter.
In the case of our own Moon, one side is more massive than the other and over the course of millions of years became tidally locked so that the heavier side always points towards the Earth.
My armchair attempt would say that a star/moon would only NOT spin if at their creation, the clouds of material came 100% from all sides equally.
Normally though, stars or planets are caught from clouds catching and revolving around each other for a couple of million years until the condense to a solid object. Thus the spin.
It has to do with the total angular momentum of a system composed of multiple smaller bodies. (Like the dust/debris cloud during solar system formation)
This minute physics video (about the shape of the solar system) explains it probably better than I can put into words myself:
generator using the rotational energy...would need to have a reference in the main star
Nope. You could launch generator pods in a hyperbolic trajectory that would start out escaping the neutron star, but generate electricity from the rotating magnetic field in such a way that it's captured in orbit and comes back to its launch point.
Yes you can. You just end up changing the angular momentum of two bodies, not just one. When you launch the pod, you slow down the body you launched from. The system as a whole conserves momentum and energy, but the amount of electricity you have increases.
Wolfram Alpha has 10^46 J as 100x the energy given off by a supernova. I don't know if that means your numbers are off, or if this star is just mind-bendingly insane.
WA also puts the mass-energy of two solar masses at 3.574 x 10^47 J. So the initial calculation seems about right. My very-amateur-physicist guess is that the difference is because a supernova only converts a small fraction of the star's mass into energy - the remaining mass is thrown outwards to form planets and such.
You can pack a lot of energy into a rotating system. You have similar problems with ring worlds or terraforming Venus (which barely rotates at all). Transporting in the extra hydrogen and all the rest is trivial compared to spinning it up to a decent period.
I wonder if it's practical to store energy in rotating asteroids? For the terrestrial power grid. No friction, no (mechanical) safety hazards, just an expensive transmission problem.
edit: Back-of-the-envelope says it's a very bad idea, which is just barely plausible if your asteroid is extremely large, and has an extremely high tensile strength (maybe iron-nickel?). Oh well.
edit2: Also apparently there's a failure mode where if you do overestimate the strength of the asteroid's interior, it tears apart and (from e.g geosynchronous orbit) has a >5% chance of destroying most of the planet. D: Yeah, where I said "no mechanical safety hazards", I retract that.
