Friday, March 26, 2010

The Physics of the Schwarzschild Proton

'The Schwarzschild Proton' is a paper written by Nassim Haramein, proposing a model of the proton based on what he calls 'the Schwarzschild condition'.

I've discussed Haramein's methods more broadly here (starting with a look at the award he displays for this paper), but here I'm focusing on the physics in this paper. It's fairly basic, so I'm hoping to be able to present this in a way that makes at least some sense to at least some of Haramein's non-physicist audience who are interested in his ideas.

[Edit 4th Dec, updated 1st Jan: Anyone curious about Haramein's recent appearance in some obscure 'peer-reviewed' conference proceedings, please see this note: Feel free to ask questions in the comments.]

There's a lot of stuff here. You won't need all of it to get the gist – have a browse.

I'm exploring this material not with belief or opinion or conjecture, but using well-established laws of physics only – in fact I'm going out of my way to really try to make his model fit with reality.

There are six main conclusions in his paper. I'll look at each of these in turn in the light of his model.

Before I look at any of the conclusions, though, let's look first at the premise and see if we can make it work.

'The Schwarzschild Condition'

The main idea of this paper is that a proton may be considered as a black hole, and that two of these orbiting each other at the speed of light under gravitation alone provides a model for a nucleus.

His ultimate aim is to dispense with the need for the strong force altogether, and replace it with an interaction based on gravity, thereby unifying quantum theory with general relativity. This paper is intended to be a significant first step along this path.

So Haramein introduces us to the Schwarzschild proton. This is a black hole with a mass of 8.85 x 10^14 gm. In plain English, this is 885 million metric tonnes.

This reason this mass is chosen is that it's the mass that a black hole would need to have in order for it to have the same radius as a proton. Haramein takes the radius of a proton to be 1.32fm. (This is in fact the Compton wavelength of a proton, not its radius, at least not by any measure that I'm aware of, but it's good enough for now.)

The paper begins with the suggestion that a real proton may be considered to be one of these. To see if this is workable, let's compare his model with with what we already know about protons.

  • Mass of an actual proton: 1.67 trillionths of a trillionth of a gram
  • Mass of Schwarzschild proton: 885 million metric tonnes

These aren't particularly close.

How does Haramein deal with this discrepancy from reality?
He doesn't.

What could we do to deal with this problem? We could propose that all these millions of tonnes are only experienced gravitationally when you get very close, let's say at the nuclear scales. And otherwise, we experience the usual tiny mass of a single hydrogen atom. What would generate this effect? Who cares. It's only a model, let's run with it anyway.

  • From a single actual proton: none
  • From a single Schwarzschild proton: 455 million Watts (enough to supply electricity to 60,000 US homes)

These are a little different, too.

Why would one Schwarzschild proton radiate so much? Because the application of quantum mechanics to the severely distorted spacetime in the vicinity of the event horizon of such a tiny black hole gives rise to a correspondingly huge amount of pair-production. This takes the form of a thermal radiation of particles known as Hawking radiation, which thousands of websites will happily explain to you. The 455 million Watts comes from the power equation – here it is, straight from Wikipedia:

If we use M = 8.85 x 10^11 kg (the other values are standard physical constants) this gives 4.55 x 10^8 W.

The laws of thermodynamics imply that proton-sized black hole would have a temperature of 139 billion degrees Celsius (thousands of times hotter than the core of a star, and not far off the core temperature at the height of a supernova).

How does Haramein deal with this discrepancy from reality?
He doesn't.

What could we do to deal with this problem? Well, we could deny that Hawking radiation is real. It has never been directly observed. If it doesn't occur, then some of our most solid laws of physics would be violated in quite profound ways. Still, what the hell, let's violate them. It's only a model.

Stability of interaction between protons
  • Between actual protons in a stable nucleus: indefinitely
  • Between co-orbiting Schwarzschild protons: the orbit would decay within a few trillionths of a trillionth of a second.

Why? Because the theory of General Relativity tells us that any two black holes orbiting each other must lose orbital energy by emitting gravitational waves and fall in towards each other, merging into a single black hole at the moment that their event horizons touch.

The approach speed is given by the following equation:

Source Gravitational Radiation, Burtschinger & Taylor. This equation applies to black holes at a sensible distance apart (not contiguous ones), but what it tells us is that even if they orbited ten times further apart, they would still approach each other at about 60km/s (yes, kilometres per second). This is a fast approach for objects that are already ten thousand times closer than the size of an atom. And the closer they get, the faster they approach. (In Haramein's model, the event horizons are already touching.)

How does Haramein deal with this discrepancy from reality?
He doesn't.

What could we do to deal with this problem? Actually, this is a very serious problem, because it's a direct result from our best theory of gravity, Einstein's General Theory of Relativity, which is the only theory we have that predicts and describes black holes. If we deny this theory as well, then what is a black hole? There won't be any such thing. We are supposed to be doing serious physics, and talking about black holes and gravity. Surely we can't get out of this one?

Maybe we could pretend they worked it all out wrong. Or maybe we could pretend that it's a quantum gravity effect, in the same way that electron orbitals are stable because, it's like, you know, quantum.

What happens when you look inside a proton?

  • in an actual proton: we see point-like constituents (quarks), and a measurable distribution of charge. Things don't disappear.
  • in a Schwarzschild proton: there is an event horizon of 1.32fm radius, and nothing that crosses this horizon can re-emerge. There is no way of looking inside.

This also follows directly from General Relativity. This messes up our proposed way out of the mass problem, because if the full mass of the black hole is experienced at short distances, then any electron or other particle used to probe inside a proton would simply vanish, making the mass black hole grow slightly. This follows from the definition of the Schwarzschild radius, which is what Haramein has used. It's a space-time horizon. Beyond this horizon, all possible measures of time are directed spatially in, and only in. Out ceases to exist, except in the past.

Yet many particle experiments, in particular all those that have involved deep inelastic scattering, make it clear that we can probe inside a proton.

How does Haramein deal with this discrepancy from reality?
He doesn't.

What could we do to deal with this problem? I've no idea. I'll have a think, but this is starting to get a bit silly.

What this means for the Schwarzschild proton model

The premise of this model – that 'the proton may be considered as a Schwarzschild entity' – is pushing credibility to the point of ridiculousness. And this is before we even look at whether any of his conclusions mean anything.

In order to look at the conclusions, we've got to somehow force ourselves to ignore the discrepancies above, and pretend that somehow it could be a reasonable model.

What follows will illustrate why, even if we can allow ourselves to adopt this model, every one of Haramein's conclusions are meaningless anyway.

* * *

Haramein's six conclusions

Haramein models the proton as a black hole, as described above. The primary conclusions are:

1. The proportion of vacuum energy that would be required is similar to the ratio of the strengths of the strong and gravitational forces

2. Considering the nuclear force as a gravitational attraction is compatible with both nucleon and quark confinement

3. The orbital speed of two neighbouring protons turns out to be the speed of light
4. The time period for such an orbit turns out to be the same as the characteristic timescale of nuclear emissions involving the strong force

5. There is evidence for a scaling law between mass and radius, and this model of the proton places it much more convincingly in agreement with this

6. A value for the magnetic moment of the proton can be derived which turns out to be close to the measured anomalous magnetic moment of the proton

I'll take them one at a time – and I'll warn you in advance, it's a big mess, so this could take a while.

1. The proportion of vacuum energy that would be required to make a Schwarzschild proton is similar to the ratio of the strengths of the strong and gravitational forces (page 1, 1st & 2nd sentences)

He doesn't elaborate on this, it's just mentioned in passing.

Haramein chooses a value for the vacuum energy apparently at random from a whole host of available theoretical figures. This 'vacuum energy' has never been measured – and there are no convincing theoretical or experimental reasons to believe that it is even a true physical quantity. But who knows.

There is a brief calculation of this proportion, and the result is 1.78 x 10^-41, corresponding to very nearly 41 orders of magnitude.

He states correctly that the ratio of the gravitational to the strong force as "typically given as 38 or 39 orders of magnitude", so this ratio is at least 100 times lower than the value he calculated using the vacuum energy. And that's using Haramein's numbers.

So you couldn't call it strikingly similar.

(Unless you write one of them in percentage form, and the other not, as he did in the paper!)

Actually, between you and me, I think Haramein missed a trick here. Rather than just mention this in passing, he could have used it to suggest that the strong force is the interaction between the entire vacuum energy within the volume of each of the two protons, but with this energy taking the form of a gravitational dipole with a separation of the Planck length at the core of each proton. Then he wouldn't have needed any of the black hole stuff at all, and his argument wouldn't have been circular. That might have been interesting. It's still just random bollocks, but it's a radical idea involving mysterious vacuum stuff, he could have justified it with some really cool (Newtonian) equations, and it would have sounded good. Nassim, if you're reading, there's an idea for you!

Instead, all he's done here is to find two numbers that look similar (though they aren't) and note it without explanation, as if some significance should be obvious (which it isn't). So let's move on.

2. Considering the nuclear force as a gravitational attraction is compatible with both nucleon and quark confinement (page 1, 3rd sentence)

Quark confinement is an enormously complex subject dealing with the fact that quarks cannot exist outside of hadrons, which has nothing to do with, and is in no way compatible with, Haramein's model. He doesn't talk about quarks at all in this paper, so I'm going to write that one off as just a careless comment made by mistake. One I'm sure even he would admit.

[Edit: nope, he didn't admit it. "Au contraire, my dear Bob-a-thon ... It is quite relevant to mention that we have a possible means to explain the color force, which is more than one can say for the standard models." he tells us in his response, before proceeding to paint an extremely odd image of quarks as these freaky little animals invented out of thin air by physicists to enable them to sweep all their problems under the carpet without anyone noticing... it's quite cute...]

By nucleon confinement, he must mean the strength of the force that binds a proton or a neutron in a nucleus.

What he's saying (and he makes this more explicit on page 5) is that he has discovered that two Schwarzschild protons would be bound together by gravity alone with a force that bears a spooky resemblance to the strong force. The implication is that this model of the proton "offers the source of the binding energy as spacetime curvature". In other words, the strong force might be considered to be gravitational in nature, suggesting that this approach may lead to a way to dispense with the idea of a strong force altogether. This would unify the large and small scales in a significant way, and lead to a simpler and more integrated view of reality.

But let's look at what he's actually done.

First, a little history. In the late 17th Century, Newton realised that what caused planets to orbit the sun was no more than the familiar force of gravity. It wasn't long before he'd worked out the equation for gravitation, and proved definitively that it implied that any two objects in empty space would be bound in a stable gravitational orbit. The moon would orbit the Earth indefinitely; the Earth would orbit the Sun indefinitely; and so on.

In short, set in motion any two objects at any distance apart in empty space, and they will orbit each other for ever (so long as they're not set on a collision course). This is one of the most basic results of Newtonian gravity.

What has Haramein discovered? He has 'discovered' (using 17th century equations) that two Schwarzschild protons placed at 2.64fm apart and set in motion will be held together gravitationally in orbit.

But we've known for well over 300 years that gravity will bind ANY two objects in an orbit.

He's claiming that this is one of his significant conclusions of his model, and as a reason to justify the fact that protons can be modelled as black holes. Does this sound like a reasonable claim to you?

* * *

Now, what about the size of the force that Haramein has calculated. Will we find that it is spookily similar to the strong force that binds protons in the nucleus?

The gravitational binding force between two Schwarzschild protons is 7.49 x 10^47 dynes (page 3). This is in fact what you get if you stick any pair of equal mass black holes into Newton's gravitation equation – the result is the same no matter how big or small the black hole is. (It would be a silly thing to do, as Newton's laws don't apply to such extreme situations. But Haramein did it anyway.)In old units, this is 7.57 x 10^47 dynes. (Haramein has made some elementary rounding errors that have given him 7.49 instead of 7.57, but we can let this pass.)

To put this number in perspective, this force is:

  • 700 trillion trillion times the weight of mount Everest (= 10^21 dynes)
  • 500 thousand trillion times the weight of another planet Earth if you put it 'on top' of our one (= 1.5 x 10^30 dynes)
  • 90 billion trillion times the impact force of a 6 mile diameter asteroid hitting the Earth at 10 miles per second! (The one that wiped out the dinosaurs was this size. It had a mass of 10 trillion tonnes, and was slowed from 10 miles per second after penetrating a distance of about 15km into the crust. v²=2as, F=ma, every action has... you know the deal, you do the math. Then multiply by 90 billion trillion!)

I'm not joking. It really is a stupidly big number.

Haramein is suggesting – without, it seems, any awareness of how stupid this is – that this is the force of attraction between two protons within a single atom.

We can use an electron, one of the lightest particles known, to knock a proton out of a nucleus. We can even do it with a single photon of light. We don't need to throw 6-mile diameter asteroids at atoms to split them.

This result alone should be enough to convince anyone that the Schwarzschild proton is one of the worst thought-out models of the proton that it is possible to come up with.

3. The orbital speed of two neighbouring protons turns out to be the speed of light (page 3)

An object in orbit very close to a black hole will have a very fast orbit. For a small object at a distance of 1.5Rs (meaning one and a half times the Schwarzschild radius), the speed of the orbit is c, the speed of light. This is a result of general relativity, known as the photon sphere.

For larger objects with significant gravitational fields of their own, the problem becomes fiendishly complex. (As mentioned in the "stability of interaction" section above, energy loss through gravitational radiation guarantees that there is no stable close orbit anyway.)

Haramein's protons are both black holes, orbiting at 2Rs, which is further than the photon sphere. A correct calculation would give a lower speed, perhaps not far from two thirds of the speed of light. Haramein has used special relativity (which is only valid in the absence of strong gravitational fields), and got an incorrect result.

Even if he had calculated correctly, the result doesn't tell us anything new – this would apply to anything orbiting any black hole. So nothing to write home about, just some more inappropriate use of physics equations.

4. The time period for such an orbit turns out to be the same as the characteristic timescale of nuclear emissions involving the strong force (page 1)

What is the timescale of nuclear emissions involving the strong force? It's roughly how long it takes for a strong interaction to occur, and it's determined by the shortest time possible to traverse a strongly interacting particle.

In other words, to get the timescale of the strong force, take the size of a proton and divide it by the speed of light.

(To be a little more subtle, the reason why the timescales involved will be as short as possible in the case of the strong force is that the strong force coupling constant is approximately 1, which is – and I'm simplifying things a little, but the principle is true – as high as possible.)

Haramein has chosen to operate at the size of a proton. He has also chosen to operate close to the event horizon of a black hole, which means that any relevant speeds must be close to the speed of light. So, again, there is no result here.


That's as far as I've got for now. I'm doing this a bit at a time, because doing it properly is time-consuming. But you probably get the idea.

[Edit, 8th June: The scaling law just makes my heart sink when I look at it, it's such a confused mush. I'm still putting it off. :)

Meanwhile, please see the latest post here. Clear examples of Haramein (a) being clueless about all aspects of physics, and (b) making absurd claims for his insights into physics, including some truly outrageous claims about the Schwarzschild Proton ]

Do let me know if you think I've got anything wrong so far.


I'm not trying to suggest that Haramein made some mistakes with his model and should go away and make some corrections.

Haramein claims to be doing serious science. He claims to have unified the forces of nature, and to have created a unified field theory. He claims to be able to point out where all 'the other physicists' are going wrong. He claims, moreover, that his paper, The Schwarzschild Proton, has won serious academic acclaim. All of these are patently false.

The only sensible conclusion from looking at this example of his work is that he is utterly incompetent as a physicist – even with the help of his hired academics, whose "advice and careful reading of the manuscript" didn't reveal any of the myriad of nonsensical implications that a little exploration should have found.

He knows that taking on the air of authority of a research physicist will give weight to his outlandish ideas, many of which are in the language of physics. And he knows that this will bring him followers and cash. Indeed it does.

[Edit 22nd July: Response to this article by Nassim Haramein...]

Response from Nassim Haramein

Nassim Haramein's Resonance Project has published a detailed response to this article. To find out more and to read his response for yourself, please see here. Thank you.

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