Higgs Boson Discovered?!

[ctamblyn]

I'll just add, that I've enjoyed reading lpetrich's posts on the thread topic. As far as I can follow them, they have been very interesting indeed. Thanks.

 

[Mister Earl]

Aye. That's why I lurk in threads like these... I usually do not get everything that is going on, but I take an interest in it, and perhaps I'm learning a little by ocular osmosis.

 

[edd]

Yes. I don't think he's got everything right, but I think that in the fullness of time it will be acknowledged that he got some very important things right. Like (quasi) spherical harmonics underlie the electron itself, not just electron atomic orbitals.

What he says is not just wrong. It's nonsense. In the same way that if I said my blood cholesterol level was 73% I'd be wrong. If I said it was 73,000 Japanese Yen it'd be nonsense. He makes that kind of mistake.
You should admit it cannot possibly be right.

 

[Reality Check]

This cosmic treacle nonsense from a guy at DAMTP see slide 17, and this Fermilab article: "The Higgs field is like a giant vat of molasses spread throughout the universe". It's garbage.

Wrong, Farsight..
It is an simile, Farsight. It would be extremely stupid to think that space is actually full of cosmic treacle.
The Higgs field is actually like a giant vat of molasses spread throughout the universe. It is also like a crowd of friends of the particle.

 

[Reality Check]

Huh? No. You create an electron in pair production, along with a positron. Charge is conserved like angular momentum is conserved. In our subatomic world of fields and waves there's nothing to "brace on". You can't make a spinor like this without making one with the opposite chirality. Have a browse on topological charge.

You keep on parroting this trivially true stuff Farsight.

1. Pair production creates an election and positron. Duh .
2. An electron has the opposite charge to a positron. Duh !
3. Charge is conserved. Duh !

Then you go off into ignorance, e.g.

• a spinor is not a pinwheel !
• Topological charge (topological quantum number) has little to do with actual charge or electrons or photons or positrons.

A basic example of topological charge is the Dirac quantization condition

The hypothetical existence of a magnetic monopole would imply that the electric charge must be quantized in certain units; also, the existence of the electric charges implies that the magnetic charges of the hypothetical magnetic monopoles, if they exist, must be quantized in units inversely proportional to the elementary electric charge.

 

[Reality Check]

Sure, but a moebius strip involves tracing a surface. So far as I know anyway, particles don't have surfaces.

Farsight is obsessing about crank theories that have been already discussed and found failing in this forum on 25th March 2010.
A couple of more weeks and Farsight would not have been able to understand the flaws after 3 years now!

If anyone is interested: The Is the electron a photon with toroidal topology? paper came up almost 3 years ago and is fundematally flawed. This was exlained to Farsight in the Relativity+ / Farsight's thread, e.g. OK, I've read the Williamson and van der Mark paper again. (they should have got a charge of zero for an electron).

 

[lpetrich]

I've told you what physicists have said: that the Higgs mechanism is a "crutch", and "the toilet of the standard model", that it's said to be responsible for only 1% of the mass of matter and so doesn't solve "the mystery of mass".

Quoting out of context. The context being a problem with the Standard Model with unbroken electroweak symmetry: everything would be massless in it, something that we clearly don't observe. "Massless" meaning zero rest mass.

What the Higgs particle does is give most of the other SM particles rest masses. The only exceptions are the photon and the gluon.

and the Higgs boson gets its mass from the kinetic energy given to the protons,

How it's created is irrelevant.

that the "bump" could be anything,

However, its interactions
(H-top)*(H-W), (H-top)*(H-Z), and (H-top)*(H-tau)
all agree with the Standard Model to within experimental limits. The error bars are still rather large, but that's a result of statistics.

Nor is the proposal for the kilogram. See the Watt balance section of the wiki kilogram article and note this: "By fixing the Planck constant, the definition of the kilogram would depend only on the definitions of the second and the meter." The second and the meter are defined using c which relates to ɛ and μ.

That's for turning Planck's constant into a units factor rather than something measured. The other quantities you mentioned, c, ɛ and μ are also officially units factors.

My weapons are hard scientific evidence and references to papers and articles and what Einstein and others, including CERN physicists, actually say.

Even if you've misunderstood what they are saying and even if you've quoted them out of context. Just like what many theologians seem to do.

Huh? No. You create an electron in pair production, along with a positron. ...

With a photon or a Z, yes, but a W produces an electron and a neutrino. In fact, pair production is very general.

What makes you such a prophet of revealed truth that you dismiss what Einstein and Maxwell and Minkowski and others like Percy Hammond actually say?

A theologian's sort of argument. It's the theories that count, not the people.

I don't disdain mathematics. I've said repeatedly that mathematics is a vital tool for science.

That would not be very apparent.

The point I've also made is that you can't use mathematics do define the terms you use in mathematics.

The same thing can be said about language more generally. Mathematics can be interpreted as a language.

They aren't my theories. I'm not some my-theory guy.

You are advocating them, and your overall theoretical picture seems to be original with you.

I refer to Einstein and others remember? The people you dismiss.

The way a theologian refers to sacred books. It's theories, rather than personalities, that I'm concerned with, and even worse, your heroes often advocate theories that you reject. Einstein stated rather plainly that he believed that space and time are part of a space-time continuum.

We argue here about the nature of intrinsic spin, but a moebius strip has a spin ½ feature. You go round twice to end up back as you started.

So what?

Quantum-mechanical angular-momentum operators are connected to rotation generators by

(angular momentum) ~ (hbar) * (rotation generators)

So rotation R(w) = exp(i*(w.L)/hbar)

Let's do it around the z-axis. Then R(a) = exp(a*d/d(phi))

For a wavefunction X that varies as exp(i*m*phi), we find
R(a).X = exp(i*m*a)*X

For rotation by 360d, we get R(360d).X = exp(2pi*i*m)*X = exp(2pi*i*j)*exp(-2pi*i*(j-m))*X = exp(2pi*i*j)*X

since j - m = nonnegative integer for total angular momentum j. Thus,
R(360d).X = (-1)^2j*X

for rotation around any axis. Thus, a 360d rotation of a boson (integer j) gets the original wavefunction again, while a 360d rotation of a fermion (half-odd j) reverses its wavefunction's sign. A 720d rotation gets the original wavefunction again in both cases.

Farsight, this is the sort of thing that one learns in advanced-undergraduate or graduate quantum-mechanics courses. It's all in Angular momentum operator^WP.

 

[Reality Check]

I've told you what physicists have said: that the Higgs mechanism is a "crutch", and "the toilet of the standard model", that it's said to be responsible for only 1% of the mass of matter and so doesn't solve "the mystery of mass".

Whoops. Missed this nonsense and repeated ignorance from you, Farsight!
You have mentioned a couple of unattributed quotes from a couple of physicists. You have provided no context. This has nothing to do with the scientific validity of the Higgs mechanism.

You still cannot understand that the Higgs mechanism actually is (not "said to be'") responsible for only 1% of the mass of matter (the rest is binding energy) and solves "the mystery of mass".
As written on 5th February 2013:

A proton is made of 2 up quarks and a down quark (8 to 11 Mev) but has a mass of 938 Mev. Protons make up most of the mass of the universe.
Thus the Higgs mechanism providing ~1% of the mass is not surprising.

This is not hardly even physics. It is simple mathentaics, Farsight!

Mass of proton = 938 Mev
Mass of 1 quark = ~11 Mev
Mass of 2 quarks = ~22 Mev
Mass of 3 quarks = ~33 Mev
Mass of proton minus its constituent quarks = 938 Mev - ~33 Mev.
Thus the proton gets ~905 Mev (or ~99% of its mass) from something other than the mass of its quarks, i.e. not the Higgs mechanism. And this is:

Quote:
Originally Posted by lpetrich
Nucleons get most of their masses from color confinement. Their quarks and gluons cannot get more than about 10^(-15) m from each other without those particles' interactions getting superstrong. This means that those particles' wavefunctions cannot extend over a greater size, and thus that their masses should be about a few hundred MeV. Thus, the nucleons' masses.

​

Anything in this that you do not understand, Farsight?

 

[Farsight]

(a) TQFT, in the version relevant to particle physics, is a hypothesis. There is no evidence it is true.

(b) TQFT, in the versions relevant to particle physics, is and incomplete hypothesis. TQFT has not actually predicted any masses successfully. It's not obvious that it would do so even if complete.

Nothing has. And even the standard model isn't complete. I'm surprised you're attacking TQFT with this line. It's not some notion dreamt up by some amateur.

(c) The success of (mainstream, relativistic, quantum, stringy) TQFT has no bearing on the truth or falsehood of Farsightism. Just because it is "topological", and you daydream about your own theory being "topological", does not mean that you're talking about the same thing. TQFT is using topology a set of mathematical truths which can be applied to physics. Farsightism uses "topology" as a synonym for "I drew some geometrical pictures and I fancy myself pretty smart, so stop criticizing".

Michael Atiyah was at ABB50/25 talking to Qiu-Hong Hu about the electron knot.

This is comically, stupidly wrong. Do you have a face-to-face human relationship with a physicist? Ask them to explain this to you.

It isn't wrong. Go and read about it instead of launching into outraged denial because you've got nothing. If you had something you'd lay it out.

Either the meter or the second are chosen arbitrarily by humans. Once you choose one, you use the speed-of-light to define the other. We said "hey, let's choose the second to be 9,192,631,770 oscillations of the cesium maser". That's an arbitrary human choice; there is no way to derive 9,192,631,770 from the laws of physics. Once we make that choice, though, the laws of physics fix the length of the distance unit "light-second". The traditional "meter" is 1/299792458 of a light-second.

That maser is an optical device. It emits light waves at your detector. You can't refer to frequency which is cycles per second when you're defining the second. So you're effectively counting 9,192,631,770 microwaves and then declaring that a second has elapsed. Then you use the motion of light and the second to define the metre. And wherever you define the second and the metre, you then use them to measure the local speed of light. So you always measure it to be 299,792,458 m/s. Your definition makes the speed of light constant, despite the fact that light clocks at different elevations don't keep time.

You can do it the other way around. Declare, arbitrarily, that *this iridium stick* 1/299792458 of a time-unit. Then use the speed of light to figure out how long it takes to traverse the iridium stick. That determines your time unit.

You still use the motion of light though, and you still end up measuring the local speed to be 299,792,458 m/s. NB: the length of the stick is 1/299792458 of a distance-unit, not a time-unit. I'm surprised nobody picked that up.

 

[Farsight]

Sure, but a moebius strip involves tracing a surface. So far as I know anyway, particles don't have surfaces.

That they don't. But a moebius strip does have a topology, and as per this mathspages article: "In this sense a Mobius strip is reminiscent of spin-1/2 particles in quantum mechanics, since such particles must be rotated through two complete rotations in order to be restored to their original state". And TQFT isn't some discredited amateur thesis like ben would have you think.

Haven't read it, can't at the moment being at work, but I can take a look later. But I'm quite sure it'll be above my minimal expertise in this area.

Just look at picture. Note though that as you said there is no surface. The "onion-ring" contours showing on the slice through the torus should keep getting bigger.

That's what I hear. That's the part that confuses me, I suppose. What does it matter with spin if it always looks the same anyway? Then I tell myself I'm being far too literal and know too little about the subject.

When it comes to spin 0 I'd say it doesn't matter as much. Helium-4 atom has spin 0, but it's composite. To get to the bottom of mass we focus on the "elementary" particle that we've actually seen and is common: the electron.

Your "out of your league" comment above noted by the way. But do note that you understand what I say. You don't understand the refutations, or what lpetrich says. Think on that.

 

[Farsight]

How odd, then, that you haven't been able to identify any specific errors in what I've said about electromagnetism, while it's very easy to identify specific errors in what you've said about electromagnetism.

I haven't made any specific errors. You have.

For example:

Now stop all this huffing and puffing and crackpot naysaying, pay attention, and watch my lips: the field concerned is the electromagnetic field. Electromagnetic field interactions result in linear and/or rotational motion. When only linear motion is observed people speak of an electric field, when only rotational motion is observed people speak of a magnetic field
Your highlighted assertions are incorrect.

Coulomb's law has essentially the same form as Newton's law of gravitation, so a negatively charged particle can be in circular orbit around a positively charged body just as planets can have circular orbits around stars. That's circular motion caused by a purely electric field.

Aaargh! There is no such thing as a purely electric field! When you move through an "electric field" you start to see a "magnetic field" too. Not because you create it, but because you start to see another aspect of the electromagnetic field. Maxwell unified electricity and magnetism a hundred and fifty years ago. And how many times do I have to tell you what Minkowski said over a hundred years ago: "Then in the description of the field produced by the electron we see that the separation of the field into electric and magnetic force is a relative one with regard to the underlying time axis the most perspicious way of describing the two forces together is on a certain analogy with the wrench in mechanics, though the analogy is not complete"..." How many times do I have to tell you about Jackson's Classical Electromagnetism. Use the read online option and put double quotes around a phrase to search for it. See section 1.2 where he says "Although the thing that eventually gets measured is a force" and "At the moment the electric field can be defined as the force per unit charge acting at a given point". Then see section 11.10 where he says "one should properly speak of the electromagnetic field Fuv rather than E or B separately".

You still don't understand even the first thing about electromagnetism, Clinger.

Ampère's force law (for the simple case of two parallel conductors) describes a Lorentz force that, left unopposed, results in linear motion caused by a purely magnetic field. This example of magnetic fields causing linear motion is the basis for our current definition of the ampere.

Aaargh! There's no such thing as a purely magnetic field. Each wire consists of moving electrons and static protons, all with their electromagnetic fields. Throw an electron past a wire and you see helical motion. That isn't linear motion. But two sets of helical motion result in linear motion. That's why Minkowski referred to a wrench and Maxwell referred to a screw.

The physicists here would be a lot more likely to say Farsight is right about this if Farsight were right about this.

They won't say I'm right even though they know I'm right because they're not being sincere. Now go and look up what I've told you, and verify it for yourself.

 

[Farsight]

Farsight mentioned that Williamson / van der Mark article in his first few posts in these forums (in a thread to do with FTL travel, started by someone else), and tried to defend that idea in his Relativity+ thread. It was not a successful endeavour.

It was the same old same old. See below.

In simple terms, it boils down to this: a photon - even a photon forced to wrap itself around some tortuous path in space - cannot be a source or sink of electric field lines, because it is electrically neutral.

That's specious ctamblyn, and you know it. We create an electron and a positron from a photon in pair production. Together they have no net charge. We can diffract the electron. It has a wave nature. Then we can annihilate the electron and positron and we typically get two 511keV photons. With no net charge. Charge is conserved. And don't try and make out that you've never heard of topological charge, or that Topological Quantum Field Theory is some crackpot junk.

The entire counterargument to that simple point consists of distractions involving Mobius bands and topology, and papers about knotted interference patterns (which, to be fair, are interesting despite being irrelevant to the argument). It's almost exactly like watching someone try to defend an elaborate design for a perpetual motion machine, which works using large magnets and steam-power.

Pity I referred to mathspages about that. And don't give me perpetual motion machines. How do you think the electron's charge gets created? Magic?

This idea seems to form the basis of a few crackpot "theories" (I use scare quotes, as these are often just incoherent collections of vague ideas). In the case of Relativity+, the hope was that the Higgs mechanism would not be needed, as you'd be able to prove that (a) photons could wrap themselves up and look like a massive particle, (b) that particle would appear to be charged, and (c) only photons of a particular wavelength would be capable of folding up in the right way. Whenever asked to show that these things are even possible (with actual calculations, rather than text-parsing and hand-waving), no adequate answers have ever been forthcoming, AFAIAA.

I'm here because Einstein said The mass of a body is a measure of its energy-content, and that a if a body gives off the energy L in the form of radiation, its mass diminishes by L/c². What do you think happens in annihilation, when there's no body left? Magic? To defend Einstein I have to tell you about the electron and electromagnetism, and much else.

ETA:

I'll just add, that I've enjoyed reading lpetrich's posts on the thread topic. As far as I can follow them, they have been very interesting indeed. Thanks.

If you can follow them, perhaps you'd like to explain the to Mister Earl and others. But you can't. Emperor's New Clothes!

 

[ben m]

Nothing has. And even the standard model isn't complete. I'm surprised you're attacking TQFT with this line. It's not some notion dreamt up by some amateur.

TQFT is not a notion dreamed up by an amateur. However, an amateur (you) dreamed up the idea that TQFT bears any resemblance whatsoever to Farsightism. This same amateur chose to cite "TQFT" as a rebuttal to a post complaining about Farsightism's amateur mass-spectrum speculations.

I did not attacking TQFT. I'm attacking Farsightism and your imaginary Farsight-style pseudo-citation of TQFT.

That maser is an optical device. It emits light waves at your detector. You can't refer to frequency which is cycles per second when you're defining the second. So you're effectively counting 9,192,631,770 microwaves and then declaring that a second has elapsed.

Yep. And this number 9,192,631,770 is not determined by the speed of light. It is not chosen by measurements of epsilon-0, nor by mu-0, nor by h-bar. The number 9,192,631,770 is a completely-arbitrary human choice. It was chosen, indirectly, by Abū al-Rayhān Muhammad ibn Ahmad al-Bīrūnī around 1000 AD.

The maser is not a light clock. It's an atomic clock. The maser looks at an atomic transition frequency---which is really an electron system, not a photon system. The atom is the thing doing the oscillating, and the microwaves are basically a readout technology. If you look at the microwaves and say "well, you're counting light"---well, I may as well say the same thing about a mechanical watch, which I "read out" by reflecting sunlight off the dial and into my eyes.

You could---less practically, of course---define the second as "454545 half lives of a muon at rest". You could define the second as "10^8 times the frequency of the neutral kaon oscillation". In fact, you can define the second as "1/86000 of the sidereal rotation of the Earth".

 

[W.D.Clinger]

Once again, Farsight is arguing against Einstein.

Aaargh! There is no such thing as a purely electric field! When you move through an "electric field" you start to see a "magnetic field" too.

According to Einstein, I'm allowed to use a coordinate system that's at rest with respect to the charged body around which a negatively charged particle is moving in a circular orbit. In that Einstein-sanctioned coordinate system, the magnetic field is zero.

Nonzero electric field, zero magnetic field, with circular motion, all according to Einstein, but not according to Farsight.

How many times do I have to tell you about Jackson's Classical Electromagnetism. Use the read online option and put double quotes around a phrase to search for it.

That book's in my personal library. Unlike Farsight, I can actually read some of its equations.

You still don't understand even the first thing about electromagnetism, Clinger.

Yet I passed the course, and Farsight's been giving proof he hasn't.

Aaargh! There's no such thing as a purely magnetic field.

According to Einstein, I'm allowed to use a coordinate system in which the electric field is zero but the magnetic field is nonzero. In that Einstein-sanctioned coordinate system, I see linear motion resulting from a purely magnetic field.

They won't say I'm right even though they know I'm right because they're not being sincere. Now go and look up what I've told you, and verify it for yourself.

Farsight's accusing the physicists of dishonesty.

I've done the math, starting with a derivation of Maxwell's equations, and I've used Maxwell's equations to verify all of the magnetic fields I've mentioned in this thread. Farsight can't do the math (and can't even get his units right), so he just repeats his empty assertions and declares victory, even as he argues against Einstein.

 

[Farsight]

What he says is not just wrong. It's nonsense. In the same way that if I said my blood cholesterol level was 73% I'd be wrong. If I said it was 73,000 Japanese Yen it'd be nonsense. He makes that kind of mistake. You should admit it cannot possibly be right.

No edd. It's all down to c and h and wave harmonics, which are not wholly different to the spherical harmonics in atomic orbitals where electrons exist as standing waves. There you've got an electron going round and round a proton. You can diffract an electron. It has a wave nature. You made it in pair production along with a positron, from an E=hf photon, which also has a wave nature. Photons travel linearly at c, electrons don't. They have a spin ½ feature and a magnetic moment and E=mc² mass and their topological charge instead. What was a wave, a field variation, is now a standing wave and a standing field. One day you'll hear about something similar from an authoritative source. You'll understand that an electron exists as a standing wave going round and round because it's interacting with itself. And you'll lap it up. You just heard it here first is all. This is where you were disabused of magic.

Right, I'm off to bed.

 

[Reality Check]

Farsight: What does Higgs mean by Lorentz-covariant and relativistic

No edd. It's all down to c and h and wave harmonics..

No, Farsight. It is all down to your fantasies about c and h and wave harmonics. We cannot rely on these fantasies because you are so in denial of the Higgs mechanism that you cannot even acknowledge that it is a relativistic QFT (and so does not violate E=mc^2).

But maybe I am wrong and you can finally answer:
Farsight: What does Higgs mean by Lorentz-covariant and relativistic?
First asked 19 November 2012
114 days and counting, Farsight!

The above question was as a follow-up to:
Farsight: Is the Higgs mechanism a relativistic quantum field theory?
i.e. is it is based on special relativity and is thus consistent with E=mc^2.
First pointed out 1 November 2012
and
Farsight: It is delusional to think that a relativistic QFT violates SR
First poined out 20 November 2012.

 

[Reality Check]

It's all down to c and h and wave harmonics, which are not wholly different to the spherical harmonics in atomic orbitals where electrons exist as standing waves.

Wrong again, Farsight !
Electrons in atomic orbitals do not exist as standing waves.
Electrons in atomic orbitals do not go "round and round a proton". That is "lie to chidren" that is told to young children.
Electrons in atomic orbitals exist as probabilities of detecting them. That results in things such as sphericlal (not standing wave), doughnut (not standing wave), dumbbell (not standing wave), etc. shaped atomic orbitals.

You can diffract an electon. It has a wave nature. Duh !
You can scatter an electron. It has a particle nature. Duh !
You can make an electron along with a positron in pair production. Duh !
Photons travel linearly at c, electrons don't. Duh !
Electrons have a spin ½ feature and a magnetic moment and mass. Duh !

Still wrong, Farsight !
Electrons do not have topological charge.

A couple of more weeks and Farsight would not have been able to understand this after 3 years now!

Originally Posted by Reality Check
If anyone is interested: The Is the electron a photon with toroidal topology? paper came up almost 3 years ago and is fundematally flawed. This was exlained to Farsight in the Relativity+ / Farsight's thread, e.g. OK, I've read the Williamson and van der Mark paper again. (they should have got a charge of zero for an electron).

 

[edd]

No edd. It's all down to c and h and wave harmonics, which are not wholly different to the spherical harmonics in atomic orbitals where electrons exist as standing waves.

No, it is nonsense. He's dimensionally incorrect - his units are utter poppycock, just like my example of quoting a chemical concentration in units of a financial currency. You don't even have to know what the properties of an electron are to know that it's wrong. And you've never admitted (to my knowledge) that it is the case that he must be wrong. It has nothing to do with c, h, spherical harmonics or atoms at all. His formula would be just as wrong if applied to a proton, a teapot, or my fictitious pet cat Alfred, because it is literally nonsensical.

Why don't you admit that? Could it be because you don't understand why it's nonsensical? You certainly came up with a complete non sequitur of an argument when lpetrich brought up dimensional analysis not that many posts ago, after all.

 

[ctamblyn]

That's specious ctamblyn, and you know it.

<snipped for brevity>

Sorry, but nothing you have posted addresses what I said. Photons are neutral, and a finite simply connected region of space containing a bunch of photons therefore cannot - no matter what those photons are doing - have a net flux of E across its surface - i.e. it will always appear to be neutral. Then of course there is the troublesome matter of the photon being a boson, while the electron is a fermion, so there are entirely different statistics for the two particles. It's a hopeless endeavour. You might have had slightly better luck making a twisted photon an integer-spin neutral particle, I guess, but there is still another problem: there is absolutely no known mechanism that will make a photon curl up in that way. Photons simply don't do that. And if they did, there is no length-scale built into Maxwell's equations that would restrict the mass of the resulting particle to a particular value. Of course, this has all been explained before.

If you want to continue to talk about your loopy photon model I suggest continuing in your R+ thread, where I'd be happy to discuss it further. In the meantime perhaps now we can get back to the thread topic, of the experimental testing of a rather more successful model.

 

[ben m]

No edd. It's all down to c and h and wave harmonics, which are not wholly different to the spherical harmonics in atomic orbitals where electrons exist as standing waves.

One day you'll hear about something similar from an authoritative source.

Really amazing stuff, Farsight. You do a great job of *suggesting* that there's a vast body of knowledge that supports your ideas. "It's all down to", for example, lets you pretend that you're summarizing something too complicated to explain right now. "One day you'll hear", for example, lets you pretend that your view is well-known, and lets you denigrate people with blinkers so thick they haven't seen it.

Except there's nothing there. What is "all down to" c and h? Every time you tried to explain "it", you spewed high-school-grade unit errors, ignorance, and vague analogies.

Who do you think is falling for this?

I mean, half of the point of the modern scientific method---the peer-review, the demands for reproducibility, the clear mathematical language, the error bars---is to prevent people from pretending to understand things they don't.