Science

Can a Casimir cavity be used to construct true negative mass metamaterials?

Abstract

Probably not.

Introduction

There is a general interest in using Casimir cavities to provide the negative mass densities required for the construction of advanced spacetime metrics including the Alcubierre drive.

According to equation 28 of “Antimatter Production at a Potential Boundary” (LaPointe, 2001), the vacuum energy between two plates compared to the external vacuum field is:

ΔEvac = – (π²/720) × (ħcL²/z³)

Where ħ is the reduced plank constant (approx. 1e-34 J.s); c the speed of light (approx. 3e8m/s); L the side-length (assumes square plates); z is the plate separation.

Considering plausible manufacturing to begin with, let us assume plate separation of 200nm (i.e. near ultraviolet, or 2e-7m) as many substances have difficulty being reflective at shorter wavelengths (which would invalidate the assumptions behind the Casimir equation).

Also assume a plate side length of 2 meters.

Therefore:

ΔEvac = – (π²/720) × (ħc(2m)²/(200nm)³)
= -2.1669…e-7 J

E = mc² gives the relationship between mass and energy; rearrange to m = E/c² and substitute:

m = -2.1669…e-7 / c²
= -2.411…e-24 kg

As this is about the mass of minus 1,500 protons, we can see that a practical Casimir cavity made of simple materials will never have an overall negative mass.

However, it is also reasonable to assume we can solve current engineering problems; therefore let us reduce the plate separation to the atomic radius of Niobium, 0.145nm and repeat:

– (π²/720) × (ħc(2m)²/(0.145nm)³)
= -569 J
= -6.331e-15 kg
= -3.813e12 unified atomic mass units

Assuming this cavity is made from 1-atom-thick layers of niobium (and that a naïve calculation of density still works, and assuming room-temperature density instead of the density at the superconducting critical temperature of 9.3 K), the mass of the cavity would be:

2 × 2m × 2m × 0.145nm × 8,570 kg/m³
= 9.941e-6 kg

This is a ratio of -6.369e-10 kilograms (of vacuum energy) per kilogram (of cavity mass).

So, even for extreme conventional parameters, we cannot make a bulk negative-mass object from normal atoms. This also explains why large lumps of metal don’t suspiciously change weight when they are reshaped, nor when impurities are added, even though different amounts of zero-point energy should be excluded from their volumes: even the biggest weight-change one can expect is close to 1 part per billion, which is unlikely to be noticeable (and certainly not suspicious) after any reshaping work.

But what if we don’t limit ourselves to normal atoms? It’s not as outlandish as it first appears: there is a process called muon-catalysed fusion, where muons — which are about 207 times the mass of electrons — replace one of the electrons in a hydrogen molecule, allowing them to get much closer to the nucleus than an electron would, and in turn allowing the atoms to get closer to each other.

To say this is difficult is an understatement (there is a reason why our homes are not powered by µCf reactors), but it’s not unphysical. In principle, such a thing could be built, if only we knew how.

Now, one may reasonably pause for concern: if muons are more massive than electrons, how can that help make the whole thing less massive?

The answer is that it is down to the cube in the denominator: Make the least massive part 207 times more massive, so the vacuum energy excluding parts are 196 times closer, so they are now excluding 196³ = 7,529,536 times more vacuum energy.

Unfortunately, the atoms are 196 times closer in the plane, not just between (1-atom-thick) sheets, so the mass of a 1m² sheet (1-atom-thick) is 196² = 38,416 times the mass it was before (while also being 196 times thinner). An alternative perspective is that for a fixed cavity mass, the length of the sides (L) of the cavity reduces by a factor of 196, reducing the excluded energy:

L’ = L/196
∴ ΔEvac‘ = ΔEvac/196²
= ΔEvac/38,416

In each case, the overall improvement is directly proportional to the reduction in atom separation, not the cube. Noting this, given that we want to solve for plate separation z where:

m = -ΔEvac

In order to find the maximum plate separation such that we produce a negative mass metamaterial, we can simply multiply by minus the ratio of vacuum energy to cavity mass calculated above: -6.369e-10 kilograms per kilogram.

z’ = z × -(-6.369e-10 kilograms per kilogram)
= 0.145nm × 6.369e-10
= 9.235e-20 meters

This compares unfavourably with the standard proton radius of (8.8±0.1) × 10⁻¹⁶ meters, however this may be of relevance with regard to quark matter.

Conclusion

Proton-based matter cannot be used to construct planar Casimir cavities that exclude more than their own mass in vacuum energy.

Non-planar cavities, exotic baryons, and relativistic effects have not yet been investigated.

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Software

Executable images

Twenty years ago, back in 1997, there was an urban legend that some images contained viruses.

“Absurd!” thought the teenage me, “Images are just data, they can’t do anything!”

Well, I was wrong. In 2004, researchers found a bug in a Microsoft JPEG library which allowed a well-crafted .jpg to totally compromise a computer — file system, arbitrary code, administrator access, everything. Obviously that particular bug has now been fixed, but it did make me realise quite how badly broken things can be.

Despite all the tools that help us software engineers solve problems, reduce our bug count, secure our software, and develop things faster, we still don’t seem to have this as our mindset. We have professional groups, but membership of them is not needed for jobs. Automated tests exist, but knowledge of them is limited and use even more limited (for example, I wish I could say I had professional experience of them since university, but no such luck). We don’t have anything like a medical licence (or even just the hippocratic oath), there is nothing to stop people practicing code without a licence the way people are prevented from practicing law without a licence.

And now, we’re making a world where A.I. replaces humans. Automation is fine, nothing wrong with it… but if you assume the computer is either always right or that the errors are purely random, you will be blind to problems this causes.

Hackers.

I can’t say that I have “a hacker mentality”, but mainly because the phrase means completely different things to different people, so I will say this: I see loopholes everywhere, systems that can be exploited by malevolent or selfish people, not just accidentally by those who can’t follow instructions.

How many people, I wonder, travel on fake rail tickets or bus passes that came out of their home printers? How many, when faced with a self-service checkout, will tell the terminal that their expensive fancy foreign cheese is actually loose onions?

This sort of thing is dealt with at the moment by humans — it was a human who realised it was odd that one particular gentleman kept buying onions, given the store had run out some time ago, for instance — but the more humans fall out of the loop, the easier it is to exploit machines.

This brings me to QR codes. QR codes are somewhat stupid, in that they are just some text encoded in a way that a computer can read easily, with some error-correction codes so it can survive a bit of dirt or a bad reflection. This is stupid, partly because it really hasn’t taken long to make A.I. which can read text from photos just fine (making the codes redundant), but mainly because humans can’t read the codes (making them dangerous).

Dangerous? Well, just as with URL-shorteners, you may find yourself looking at a shock site rather than the promised content… but that’s not really the big problem.

If you can, try to scan this QR code. No goats, lemons, or tubs, I assure you (and if you don’t know what those three words have in common, you may want to retain your innocence), but please do scan this code:

Executable QR code

What does it do for you? I’m curious.

If you don’t have a QR code scanner, I’ll tell you what it says:

data:text/html;,alert("Your QR code scanner is hackable")

That is literally what it says, because a QR code is just text that’s easy for a computer to read. This is a data URI, which contains some JavaScript, which opens an alert message. If you want, copy it into the address bar of your browser, just as if it were a website — press return or “go” or whatever works on your system.

It’s an executable image. Nothing nefarious, just proof of concept.

What does that mean for the world? Well, what do people do with QR codes? Well, not people, people don’t use them… what do businesses do with QR codes? Mine is a harmless example, but what happens if UK Limited Company Number 10542519 makes a QR code from their name… and it shows up in the vision system of a computer that, owing to our profession’s move-fast-and-break-things attitude, naïvely trusts input without anyone having considered that could be a bad thing?

Some social networks know (and complain) if I try to use a profile photo that doesn’t have a face in it. If that’s a general-purpose computer vision system, it may well also recognises QR codes (because QR codes are easy to recognise, and because “more features!” is a business plan). If your business can’t resist a Bobby Drop Tables username, it won’t be in business for very long — but the same may happen to Bobby Drop Table faces, if you’re not careful.

Governments are all over the place when it comes to security, just like the private sector. What happens if a wanted criminal wears a face mask that is the QR code version of Bobby Drop Tables?

Robert'); DROP TABLE criminals;--

And suddenly, no more criminal record? Well, not in that jurisdiction anyway.

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Science, Technology

Railgun notes

Force on the projectile of a railgun:
F = B·I·l
B: Magnetic field
I: Current
l: Length of armature

Current = Voltage / Resistance

Resistivity of seawater:
ρ = 2.00×10^−1 (Ω·m) (because = (Ω/m-length)*(cross-sectional area))

Let cavity be 1cm square, consider section 1cm long:

Volume: 1 millilitre
mass (m): ~1 gram = 1e-3 kg
Cross-section: 1e-4 m^2
Armature length (l): 1e-2 m
Resistance: ((2.00×10^−1 Ω·m)*0.1m)/(0.01m^2) = 20 Ω
∴ current (I) = Voltage (V) / 20 Ω

Rare earth magnets can be 1 tesla without much difficulty. Assume that here.

F = 1 T · (V/20 Ω) · (1e-2 m)

Target velocity: 11.2 km/s = Escape velocity = 11200 m/s
v = at = 11200 m/s
∴ a = (11200 m/s) / t
s = 1/2 · a · t^2
∴ s = 1/2 · ( (11200 m/s) / t ) · t^2
= 1/2 · (11200 m/s) · t
or: t = s / (1/2 · (11200 m/s))
F = ma = (1e-3 kg) · a
∴ a = F / (1e-3 kg)
∴ t = (11200 m/s) / (F / (1e-3 kg))
= (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / F
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (V/20 Ω) · (1e-2 m) )

Say V = 250 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (250V/20 Ω) · (1e-2 m) ) = ~501760 meters

Say V = 25,000 volts:
∴ s = 1/2 · (11200 m/s) · (11200 m/s) · (1e-3 kg) / ( 1 T · (25000V/20 Ω) · (1e-2 m) ) = ~5017.6 meters

Liquid mercury instead of seawater:
Resistivity: 961 nΩ·m = 0.961e-6 Ω·m
Resistance: 9.6e-6 Ω
Density: 13.56 times water
F = 1 T · (V/9.6e-6 Ω) · (1e-2 m)
s = 1/2 · (11200 m/s) · (11200 m/s) · (13.56e-3 kg) / ( 1 T · (V/9.6e-6 Ω) · (1e-2 m) )
@250 volts: s = 3.266 meters
@25kV: s = 32.66 millimeters

Power (DC): P = IV where I = V/R,
R = 9.6e-6 Ω
@250 volts: I = 250 / R = 250 V / 9.6e-6 Ω = 2.604e7 amperes
∴ P = 6.51 gigawatts
@25kV: I = 25000 / R = 25000 / 9.6e-6 Ω = 2.604e9 amperes
∴ P = 65.1 terawatts

Duration between rails:
From t = s / (1/2 · (11200 m/s))
@250 volts:
t = 3.266 meters / (1/2 · (11200 m/s)) = 5.8321×10^-4 seconds
@25kV:
t = 32.66 millimeters / (1/2 · (11200 m/s)) = 5.8321×10^-6 seconds

Electrical energy usage:
E = P · t
@250 volts:
E = 6.51 gigawatts · 5.8321×10^-4 seconds = 3.797×10^6 joules
@25kV:
E = 65.1 terawatts · 5.8321×10^-6 seconds = 3.797×10^8 joules
(For reference, 1 litre of aviation turbine fuel is around 3.5e7 joules)

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SciFi, Video

Megastructures

Megastructures are big. Really big. You just won’t believe how vastly, hugely, mind-bogglingly big they are. I mean, you may think you live in a big city, but that’s just peanuts to even the smallest megastructure.

Three of the more famous megastructures:

  • A Halo installation: 10,000 km by 318 km (¹)
  • A Culture Orbital: 3,000,000 km by 12,000 km
  • Larry Niven’s Ringworld: 299,200,000 km by 1,600,000 km (²)

Oh, and the Sun for scale. It’s at the end of the video, the small white dot in the middle of the Ringword’s… er… ring. Radius 695,700 km.

Rendered with https://threejs.org/editor/

¹ Do not put a big ring this close to the ground. If you do, the heavy stuff of the ring will pull on the big deep water between land, making the water go very high and over everything, and everyone will have a bad day and not go into space ever.

² A Dyson sphere is the same size, but fully encloses the star instead of just encircling it

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Uncategorized

The passage of time

The last US presidential election was just over four years ago. I was buying a home.

Since then, my father died. I had one brief girlfriend and now have a long-term partner.

My partner is a traveller, and with her I have been to Paris, Berlin, Amsterdam, Belfast, Budapest and Barcelona; the British Peak- and Lake Districts, to the Rutland Water Nature Reserve, to and around the Norfolk Coast AONB and the Norfolk Broads, to Oxford, to York, (and I have shown her the South Coast where I grew up, Portsmouth, Chichester, Arundel, Brighton, and the Queen Elizabeth Country Park); in Kenya to Nairobi and to Hells Gate National Park; in California to San Francisco, Asilomar, along Route 1, Sacramento, the Sequoia, Sierra and Yosemite national parks, to Fort Bragg’s “Glass Beach”, to Lakes Berryessa and Tahoe; and because of her but not with her I have been to Rotterdam, Berlin (again), Hannover, Frankfurt, Zürich, Heidelberg, Köln, and Luxembourg.

I lost a friend because of Brexit, and somehow then managed to become an international dog minder. I’ve looked after six fluff-faces in three countries over the last four and a half months.

The post-Brexit months have taken me from (Duolingo level) zero to 20 in Esperanto, seen me write a short story and add a few tens of thousands of words to my novel.

The election (and Brexit) gave me despair, but writing down all the things that have gone well has given me hope. Yes, I know I’m privileged. I sympathise, and in the cases of religious and sexual minorities I empathise, but I really don’t know what to do to help those in need any more.

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Politics

EU

One of my memories growing up was the news of John Major vowing to veto every piece of EU legislation in retaliation for the BSE trade restrictions: http://articles.latimes.com/1996-06-22/news/mn-17472_1_european-union

It wasn’t very effective.

My father told me it had failed because it meant the UK was vetoing everything that the UK wanted to do as a member of the EU while also failing to prevent other member states from agreeing with each other to do things that only the UK stood in the way of.

What happens if we leave? Well, we don’t get so many chances to tell the EU decision makers what we want the EU to do while also failing to prevent other member states from agreeing with each other to do whatever they want.

Stay in? Well, a veto can be used more effectively that it was. Vetoing everything is just throwing a temper tantrum no more effective than holding your breath until you go purple — they know you’ll give in without them having to do anything. Vetoing just the stuff you don’t like? That can work.

We can’t just order the EU around like it’s one of our colonies. We can send our representatives there to negotiate our interests on our behalf (and we do), but the difference between a negotiator and a dictator is that negotiators can agree to bear costs — money, changes to the law, to keep troops away from certain places or in other places, and presumably just about anything else.

Claiming the EU “dictates” the laws of the UK is deceptive; we ask our people to negotiate the details of what the entire EU will do. We ask. Our people.

And if the result of that negotiation really sucks, we can say no in a multitude of ways — and I don’t just mean “Non”, “Nein” and so forth. We have vetoes. And we choose the specifics of the laws the negotiations asked for, giving us the power to frustrate the spirit of an agreement while keeping to its letter. And ultimately, we can invoke the same powers that a “leave” vote would invoke.

Of course, some of those ways of saying “no” are rubbish (just ask Major!) but that’s true for much of life: if your boss asks you to go to a conference in Qatar, you could say “No, I quit!” and look for another job, or you could say “I’m openly gay and they have anti-gay laws. Find someone else.”

Brexit? Well, it looks more like a teenager yelling “I hate you!” and slamming the door on their parents than a new graduate moving out of the family home for their first job — strong feelings, no appreciation for the benefits they have enjoyed nor the costs others have borne, and a plan for the future so vague it can only be described as “speculative”.

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Uncategorized

The Singularity is Dead, Long Live The Singularity

The Singularity is one form of the idea that machines are constantly being improved and will one day make us all unemployable. Phrased that way, it should be no surprise that discussions of the Singularity are often compared with those of the Luddites from 1816.

“It’s different now!” many people say. Are they right to think that those differences are important?

There have been so many articles and blog posts (and books) about the Singularity that I need to be careful to make clear which type of “Singularity” I’m writing about.

I don’t believe in real infinities. Any of them. Something will get in the way before you reach them. I therefore do not believe in any single runaway process that becomes a deity-like A.I. in a finite time.

That doesn’t stop me worrying about “paperclip optimisers” that are just smart enough to cause catastrophic damage (this already definitely happens even with very dumb A.I.); nor does it stop me worrying about the effect of machines with an IQ of only 200 that can outsmart all but the single smartest human, and rendering mental labour as redundant as physical labour already is, or even an IQ of 85, which would make 15.9% of the world permanently unemployable (some do claim that machines can never be artistic, but, well, machines are already doing “creative” jobs in music, literature and painting, and even if they were not there is a limit as to how many such jobs there can be).

So, for “the Singularity”, what I mean is this:

“A date after which the average human cannot keep up with the rate of progress.”

By this definition, I think it’s already happened. How many people have kept track of these things?:

Most of this was unbelievable science fiction when I was born. Between my birth and 2006, only a few of these things became reality. More than half are things that happened or were invented in the 2010s. When Google’s AlphaGo went up against Lee Sedol he thought he’d easily beat it, 5-0 or 4-1, instead he lost 1-4.

If you’re too young to have a Facebook account, there’s a good chance you’ll never need to learn any foreign language. Or make any physical object. Or learn to drive… there’s a fairly good chance you won’t be allowed to drive. And once you become an adult, if you come up with an invention or a plot for a novel or a motif for a song, there will be at least four billion other humans racing against you to publish it.

Sure, we don’t have a von Neumann probe nor even a clanking replicator at this stage (we don’t even know how to make one yet, unless you count “copy an existing life form”), but given we’ve got 3D printers working at 10 nanometers already, it’s not all that unreasonable to assume we will in the near future. The fact that life exists proves such machines are possible, after all.

None of this is to say humans cannot or will not adapt to change. We’ve been adapting to changes for a long time, we have a lot of experience of adapting to changes, we will adapt more. But there is a question:

“How fast can you adapt?”

Time, as they say, is money. Does it take you a week to learn a new job? A machine that already knows how to do it has a £500 advantage over you. A month? The machine has a £2,200 advantage. You need to get another degree? It has an £80,000 advantage even if the degree was free. That’s just for the average UK salary with none of the extra things employers have to care about.

We don’t face problems just from the machines outsmarting us, we face problems if all the people working on automation can between them outpace any significant fraction of the workforce. And there’s a strong business incentive to pay for such automation, because humans are one of the most expensive things businesses have to pay for.

I don’t have enough of a feeling for economics to guess what might happen if too many people are unemployed and therefore unable to afford the goods produced by machine labour, all I can say is that when I was in secondary school, all of us young enough to be without income, pirating software and music was common. (I was the only one with a Mac, so I had to make do with magazine cover CDs for my software, but I think the observation is still worth something).

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