1489: "Fundamental Forces"

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sevenperforce
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Re: 1489: "Fundamental Forces"

Postby sevenperforce » Wed Feb 25, 2015 3:42 pm UTC

schapel wrote:I think it's more correct to say that an electron emitting a photon is an "electromagnetic interaction" rather than an example of the electromagnetic force. The latter term seems to imply there's a force acting between the electron and the photon. Well, there is actually a force between them, because the photon shoots one way, so the electron must experience an equal force in the opposite direction. But the electron and photon are not actually repelling each other electrically or magnetically.

An electron which emits a photon experiences a change in mass-energy and a change in momentum at the moment of emission; however, that is where the interaction ends. There can be no interaction after the photon is emitted because that would require the interaction to take place faster than the speed of light (because the photon is moving away at the speed of light).

PM 2Ring wrote:It's sometimes said that neutronium is held together by gravity, but that's not quite right. The formation of neutron-degenerate matter requires very high pressure, gravity is merely a way of achieving that pressure.

But neutron-degenerate matter will not remain in a bound state except under the influence of gravity. Perhaps we could say more accurately that neutron-degenerate interactions allow gravity to hold neutronium more densely than it would otherwise be able to?

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Re: 1489: "Fundamental Forces"

Postby SuicideJunkie » Mon Mar 02, 2015 2:49 pm UTC

PM 2Ring wrote:It's sometimes said that neutronium is held together by gravity, but that's not quite right. The formation of neutron-degenerate matter requires very high pressure, gravity is merely a way of achieving that pressure.

But neutron-degenerate matter will not remain in a bound state except under the influence of gravity. Perhaps we could say more accurately that neutron-degenerate interactions allow gravity to hold neutronium more densely than it would otherwise be able to?

That sounds backwards. If you didn't have the neutron-degenerate interactions, then gravity would make the neutronium even denser (and form a black hole early)

I think the point was that gravity allows a sufficient quantity of neutronium to provide its own pressure remain stable.
Mechanisms other than gravity could theoretically provide the pressure instead, but it is hard to imagine a way to actually make that actually work.
Perhaps firing heavy particle beams at sufficient velocity down towards every point on the surface of the neutron star would allow it to remain intact if gravity were to stop functioning.

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Re: 1489: "Fundamental Forces"

Postby Neil_Boekend » Mon Mar 02, 2015 3:29 pm UTC

SuicideJunkie wrote:
PM 2Ring wrote:It's sometimes said that neutronium is held together by gravity, but that's not quite right. The formation of neutron-degenerate matter requires very high pressure, gravity is merely a way of achieving that pressure.

But neutron-degenerate matter will not remain in a bound state except under the influence of gravity. Perhaps we could say more accurately that neutron-degenerate interactions allow gravity to hold neutronium more densely than it would otherwise be able to?

That sounds backwards. If you didn't have the neutron-degenerate interactions, then gravity would make the neutronium even denser (and form a black hole early)

I think the point was that gravity allows a sufficient quantity of neutronium to provide its own pressure remain stable.
Mechanisms other than gravity could theoretically provide the pressure instead, but it is hard to imagine a way to actually make that actually work.
Perhaps firing heavy particle beams at sufficient velocity down towards every point on the surface of the neutron star would allow it to remain intact if gravity were to stop functioning.

Correct me if I am wrong, but since the outside of the neutron star isn't neutronium but regular high density matter, wouldn't "conventional" magnetic containment be a solution?
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Re: 1489: "Fundamental Forces"

Postby SuicideJunkie » Mon Mar 02, 2015 4:22 pm UTC

I think there might be a problem there in that the force would be pressing on the surface rather than the surface pressing on the core. If your surface converts to neutronium, you'd be in trouble.
Also, beyond some intensity limit, wouldn't the magnetic field start creating particles instead of adding more force?

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Re: 1489: "Fundamental Forces"

Postby sevenperforce » Mon Mar 02, 2015 8:52 pm UTC

What is the smallest possible neutron star fragment?

As far as I know, the minimum mass requirements for getting a neutron star have more to do with the collapse mechanics (supernova, etc.) than the stability of the final state. In an unlikely-but-hypothetically-possible glancing blow between two neutron stars, could one of them lose significant mass while still retaining its neutron star form? We know that a white dwarf cannot go over 1.44 solar masses without gravity collapsing it into a neutron star, but how much mass could a neutron star lose before its gravity would no longer be able to hold it in a solid piece against the neutron degeneracy gas pressure?

Are we talking 1 solar mass? 0.1 solar masses? Ten Jupiter masses?

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Re: 1489: "Fundamental Forces"

Postby PM 2Ring » Tue Mar 03, 2015 1:49 am UTC

sevenperforce wrote:
PM 2Ring wrote:It's sometimes said that neutronium is held together by gravity, but that's not quite right. The formation of neutron-degenerate matter requires very high pressure, gravity is merely a way of achieving that pressure.

But neutron-degenerate matter will not remain in a bound state except under the influence of gravity. Perhaps we could say more accurately that neutron-degenerate interactions allow gravity to hold neutronium more densely than it would otherwise be able to?


SuicideJunkie wrote:That sounds backwards. If you didn't have the neutron-degenerate interactions, then gravity would make the neutronium even denser (and form a black hole early)

Well, yeah. Without neutron-degenerate interactions stuff would just keep collapsing to black hole density, although I guess it might be possible to have a stable state when gravity is balanced by quark degeneracy pressure.

I was maybe over-simplifying things in that paragraph above. To create neutronium needs not just high pressure but also high temperature. You need enough pressure to overcome electron degeneracy pressure and then you need even more pressure and a lot of temperature to force those electrons to react with the protons, since it's an endothermic reaction, although you get some of that energy back in the form of kinetic energy of the neutrino and the neutron, plus the occasional gamma photon (in the related reaction, free neutron decay, around one decay per thousand emits a gamma).

From Neutron_star Formation
Wikipedia wrote:Electron degeneracy pressure is overcome and the core collapses further, sending temperatures soaring to over 5×109 K. At these temperatures, photodisintegration (the breaking up of iron nuclei into alpha particles by high- energy gamma rays) occurs. As the temperature climbs even higher, electrons and protons combine to form neutrons, releasing a flood of neutrinos. When densities reach nuclear density of 4×1017 kg/m3, neutron degeneracy pressure halts the contraction.


SuicideJunkie wrote:I think the point was that gravity allows a sufficient quantity of neutronium to provide its own pressure remain stable.
Mechanisms other than gravity could theoretically provide the pressure instead, but it is hard to imagine a way to actually make that actually work.
Perhaps firing heavy particle beams at sufficient velocity down towards every point on the surface of the neutron star would allow it to remain intact if gravity were to stop functioning.


Sure, if you can make black holes just from photons, stabilizing neutronium with particle beams would be a breeze. :)

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Re: 1489: "Fundamental Forces"

Postby SuicideJunkie » Thu Mar 05, 2015 12:51 am UTC

sevenperforce wrote:What is the smallest possible neutron star fragment?

As far as I know, the minimum mass requirements for getting a neutron star have more to do with the collapse mechanics (supernova, etc.) than the stability of the final state. In an unlikely-but-hypothetically-possible glancing blow between two neutron stars, could one of them lose significant mass while still retaining its neutron star form? We know that a white dwarf cannot go over 1.44 solar masses without gravity collapsing it into a neutron star, but how much mass could a neutron star lose before its gravity would no longer be able to hold it in a solid piece against the neutron degeneracy gas pressure?

Are we talking 1 solar mass? 0.1 solar masses? Ten Jupiter masses?
Hmm. Sirius B has a surface gravity of 350000g, and is about the mass of the sun.
A 1.4 solar mass white dwarf would be smaller and heavier, but my google-fu is lacking. Lets call it a million g surface gravity to be nice and round.

How light could a 20km radius neutron star be and still have a million g surface gravity? Solving for mass... 5.8x10^25kg, or about 10x Earth.

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Re: 1489: "Fundamental Forces"

Postby sevenperforce » Thu Mar 05, 2015 1:07 am UTC

SuicideJunkie wrote:
sevenperforce wrote:What is the smallest possible neutron star fragment?

As far as I know, the minimum mass requirements for getting a neutron star have more to do with the collapse mechanics (supernova, etc.) than the stability of the final state. In an unlikely-but-hypothetically-possible glancing blow between two neutron stars, could one of them lose significant mass while still retaining its neutron star form? We know that a white dwarf cannot go over 1.44 solar masses without gravity collapsing it into a neutron star, but how much mass could a neutron star lose before its gravity would no longer be able to hold it in a solid piece against the neutron degeneracy gas pressure?

Are we talking 1 solar mass? 0.1 solar masses? Ten Jupiter masses?
Hmm. Sirius B has a surface gravity of 350000g, and is about the mass of the sun.
A 1.4 solar mass white dwarf would be smaller and heavier, but my google-fu is lacking. Lets call it a million g surface gravity to be nice and round.

How light could a 20km radius neutron star be and still have a million g surface gravity? Solving for mass... 5.8x10^25kg, or about 10x Earth.

I think you're grossly underestimating the surface gravity of a neutron star. A neutron star has a surface gravity on the order of 100 billion gees.

But of course that is only an average neutron star and says nothing about a neutron star fragment. Unfortunately I'm not entirely sure how the equations of state for neutron gas degeneracy pressure and the radius and surface gravity and internal gravitational pressure all work.

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Re: 1489: "Fundamental Forces"

Postby drachefly » Thu Mar 05, 2015 12:11 pm UTC

sevenperforce wrote:
drachefly wrote:
Qaanol wrote:
Copper Bezel wrote:A particular particle can have a much stronger charge than it can have gravitational force of its own. That's a meaningful statement.

Even aside from trying to compare “charge” with “force”, I’m not convinced it’s a particularly useful statement. For example, another specific particle—the neutron—has a mass-to-charge ratio of ∞. Let me know when you find a massless charged particle.

The neutron has a magnetic dipole. It's coupled to the EM field at least a little. I suspect that if you put two neutrons next to each other, either their dipoles or their weak force (decay) will dominate their interaction compared to gravity (i.e. the weak force takes over except at very short ranges, so gravity having a merely-inverse-square force law doesn't let it win at long ranges). I might be wrong. I think that's an interesting question to check. Later.

Let's see. The absolute value of the maximum potential energy of an interaction between two magnetic dipole moments is given by PEm = μ0m1m2/2πr3. The absolute value of the maximum gravitational potential energy between two massive objects is given by PEG = GM1M2/r.

...

μ0m1m2/2πr3 = GM1M2/r

Remembering that m1 is the same as m2 and the same for M, and doing a little algebra...

r2 = μ0m2/2πGM2

And solving for r with a bit more algebra...

r = mM(μ0/2πG)1/2


you just flipped M from the denominator to the numerator. That made the crossover radius 1.7e-27 times smaller, twice.

So, assuming you got the rest of the math right,

r = 9.17e-52 m / (1.7e-27)2 = 31700 meters

At that range, I think we can safely say that they'll decay before any significant gravitational effects kick in.

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Re: 1489: "Fundamental Forces"

Postby sevenperforce » Thu Mar 05, 2015 2:08 pm UTC

drachefly wrote:
sevenperforce wrote:The absolute value of the maximum potential energy of an interaction between two magnetic dipole moments is given by PEm = μ0m1m2/2πr3. The absolute value of the maximum gravitational potential energy between two massive objects is given by PEG = GM1M2/r.

...

μ0m1m2/2πr3 = GM1M2/r

Remembering that m1 is the same as m2 and the same for M, and doing a little algebra...

r2 = μ0m2/2πGM2

And solving for r with a bit more algebra...

r = mM(μ0/2πG)1/2


you just flipped M from the denominator to the numerator. That made the crossover radius 1.7e-27 times smaller, twice.

So, assuming you got the rest of the math right,

r = 9.17e-52 m / (1.7e-27)2 = 31700 meters

At that range, I think we can safely say that they'll decay before any significant gravitational effects kick in.

Good catch. I was so glad the exponents were working out that I forgot to keep the mass underneath the fraction.

But anyhow, this does imply that for a pair of neutrons, gravitational interaction dominates beyond 32 km while EM interaction dominates within 32 km. So we needn't necessarily say that gravity is necessarily weaker or stronger than EM; there's a range of mass and charge and distance where EM is stronger and there's a range of mass and charge and distance where gravity is stronger. As you pointed out, free neutrons are going to decay fast enough to make gravitational interaction moot, but it's more about the principle of the thing.

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Re: 1489: "Fundamental Forces"

Postby SuicideJunkie » Thu Mar 05, 2015 3:35 pm UTC

sevenperforce wrote:I think you're grossly underestimating the surface gravity of a neutron star. A neutron star has a surface gravity on the order of 100 billion gees.

But of course that is only an average neutron star and says nothing about a neutron star fragment. Unfortunately I'm not entirely sure how the equations of state for neutron gas degeneracy pressure and the radius and surface gravity and internal gravitational pressure all work.

The 350000g is at the surface of a 1-solar-mass white dwarf. Making it 50% more massive will force it to collapse into a neutron star.

The original question is how small a neutron star can be chipped down to before it decompresses.
Taking a neutron star sized (20km) object and reducing its mass to 10x Earth will bring the surface gravity down to 1 million gees (down from the billions it had before).
That's reducing its density however, so the 10x Earth mass chunk of neutronium should have a much smaller radius and thus higher surface gravity again.

I didn't do those iterations, but the "critical surface gravity" idea is probably bogus anyways. Maybe it gives a rough idea, but hopefully it triggers some more legit math posts.

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Re: 1489: "Fundamental Forces"

Postby orthogon » Thu Mar 05, 2015 3:49 pm UTC

sevenperforce wrote:But anyhow, this does imply that for a pair of neutrons, gravitational interaction dominates beyond 32 km while EM interaction dominates within 32 km.

I love it when calculations for ludicrously big or small things work out on a human scale: in the case a long day's walk or a bit less than a marathon. My favourite example is Big Bang Nucleosynthesis, in which helium and deuterium nuclei were "cooked" in about the time you'd bake a lasagne. (Yeah, I've mentioned this before, but I still think it's cool).
xtifr wrote:... and orthogon merely sounds undecided.

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Re: 1489: "Fundamental Forces"

Postby wing gundam » Sun Mar 29, 2015 6:52 am UTC

I'm disappointed in you xkcd forum regulars. That no one here has mentioned/is aware that the weak and residual strong forces (to first order and neglecting charge screening) follow Yukawa potentials just like EM and gravity (to first order and neglecting charge screening) is saddening.

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Re: 1489: "Fundamental Forces"

Postby Neil_Boekend » Tue Apr 07, 2015 8:52 am UTC

sorry.
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