Rosa Lichtenstein
25th March 2011, 17:53
From the latest New Scientist:
THERE are many messy problems that physics does not attempt to solve. As the theorist Robert Jaffe of the Massachusetts Institute of Technology observed: we don't try to predict the structure of a Volkswagen from first principles - but we like to think we could.
That's why the current confusion about one of nature's most basic particles, the proton, has touched a nerve. It is just the sort of problem that physics should master with aplomb. Yet neither theory nor experiment seems to be able to tell us with certainty either how big the proton is, or what makes it spin (see "Proton puzzle: Trouble at the heart of the atom"). As we enter the era of the Large Hadron Collider, we are eagerly waiting to see whether the hoped for Higgs particle or hints of supersymmetry appear - or whether some totally unexpected finding will write the next chapter of particle physics. Our problems with the proton remind us that even supposedly settled science can challenge our presumptions of omniscience.
Bold added.
http://www.newscientist.com/article/mg20928052.700-in-praise-of-the-humble-proton.html
Proton puzzle: Trouble at the heart of the atom
23 March 2011 by Kate McAlpine
Magazine issue 2805.
We used to think we understood protons, but these bedrocks of the atomic nucleus could send our theories of particle physics tumbling
IN THE long life of a proton, 10 years is a mere trice. These peerlessly stable particles, the bedrock of the atomic nucleus, are not prone to the decadence and decay of some of their subatomic brethren. Measuring their lifetimes means watching very many of them do very little for a very long time. Our current best estimate is that they survive for upwards of 10^29 years - over a billion billion times the age of the universe.
Ten years, though, is what it took for Randolph Pohl and his colleagues to show that the proton is not all it seems. The results of their experiments at the Paul Scherrer Institute (PSI) in Villigen, Switzerland, were published in July last year. The proton hadn't suddenly become less stable. But it was quite a bit smaller than theory or previous experiments allowed (New Scientist, 10 July 2010, p 10).
In the hyperaccurate world of subatomic physics, this was dynamite. A firestorm of claim and counter-claim followed. But with simpler explanations for the discrepancy now running out, it seems the mysterious shrinking of the proton has opened up a fundamental hole in our understanding of what makes atoms tick. What gives?
The doings of protons, as of all charged particles, are dealt with by a theory called quantum electrodynamics, or QED. One facet of nature it describes is the electromagnetic force, for example how the to-ing and fro-ing of photons of light keeps negatively charged electrons orbiting positively charged protons and so makes atoms possible. Deeper in the atomic nucleus lies the realm of a companion theory, quantum chromodynamics or QCD, which describes how protons and the like are themselves assemblages of smaller particles - quarks - and gluons that bind these quarks together. Together, QED and QCD are the two pillars of particle physicists' proudest accomplishment, their "standard model".
The inner life of protons is known to be murky and impenetrable (see "All in a spin"). Outwardly, though, all seems sweetness and light. Take the proton's radius, whose accepted value has been settled on using two different kinds of measurement. The first, direct approach is to shoot electrons in the general direction of protons, like firing rubber pellets at a fairground duck. By measuring at what point they start bouncing off, we can get an idea of where the electrons encounter the protons' fuzzy ball of charge.
Muon mischief
The second approach involves measuring the orbital energy levels of the electron circling the central proton of a standard hydrogen atom. The energy levels can be fed into QED calculations to determine how far the proton's ball of charge must extend to keep the electron in those orbits.
The results of these two approaches are in good agreement. Averaging them gives the proton a radius of 0.877 femtometres, or a fraction under a trillionth of a millimetre.
And so all was well, until Pohl and his colleagues set out in the late 1990s to determine the proton's radius using a third, supposedly more accurate method. They created hydrogen-like atoms in which the electrons were replaced by muons. These particles have the same negative charge as electrons but are some 200 times weightier. That means they orbit 200 times closer in than electrons, giving them an up-close-and-personal feel for how big the proton is.
Measuring the muons' orbital energy levels meant first guessing the gaps between the two levels of interest, so a laser could be tuned to the right frequency to bump a muon from one level to another. The team did this by reversing the QED equations and plugging in the accepted value for the proton's radius to give an estimated starting point.
In the first couple of attempts to run the full experiment, in 2003 and 2007, that approach didn't work: the muons did not respond. It was only in 2009, when the team had a new laser that could reach higher frequencies, that they found the muons' sweet spot and persuaded them to dance. Feeding the experimentally determined energy levels back into the QED calculation produced the shocker. The error on the proton's radius had shrunk by a factor of 10, as expected - but the radius had shrunk too. At 0.8418 femtometres, it was about 4 per cent lower than the previous average (Nature, vol 466, p 213).
Four per cent might not sound much, but in QED, where theory and experiment can agree to a part or two in a billion, it was a huge embarrassment. And there was no obvious flaw in the measurement. "We had to take the discrepancy seriously," says Michael Distler of the University of Mainz, Germany.
Just a few weeks later, Distler and his colleagues thickened the plot still more. They published a measurement of the proton radius using the tried and tested electron-scattering method that not only doubled its accuracy, but brought its value perfectly into line with that from measuring energy level shifts in regular hydrogen (Physical Review Letters, vol 105, p 242001). The muon experiment, which should have been the most accurate, was the odd one out. But why?
One early proposal was that the proton is surrounded by a large and diffuse halo of positive charge, meaning the distantly orbiting electron and the closer muon "see" protons of different sizes (New Scientist, 25 Sept 2010, p 16). That model seems to have been discounted, though, as it made other predictions at odds with the improved electron-scattering experiments. Now attention has shifted to more fundamental possible flaws: that we might have overlooked subtleties in the workings of QED, or that QED itself is missing something.
The first possibility stems from the fact that, according to QED, two charged particles orbiting each other will exchange photons. The stronger the bond between the particles, the more energy these photons will have. If the energy oversteps a certain mark, a photon can up the ante and briefly morph into a particle and its antiparticle - an electron and a positron, for example - before switching back to being a photon again.
Because a stronger bond is needed for a proton to rein in the more massive muon, there is more scope for this sort of thing in muonic hydrogen. The idea is that a thick cloud of ephemeral particles and antiparticles shields the orbiting muon from some of the attractive effect of the proton, reducing the proton's effective radius (see diagram).
It sounds plausible, but there's one problem: finding a particle-antiparticle pair that produces exactly the right amount of shielding. That would require the pair to have a combined mass of around 46 megaelectronvolts (MeV) - far more than an electron-positron pair, which weighs in at just over 1 MeV, but far below the more than 200 MeV needed for a muon-antimuon pair.
For Ulrich Jentschura, a physicist at the Missouri University of Science and Technology in Rolla, that makes things tricky. "Theory has a problem even inventing a particle that could explain the discrepancy without messing something else up," he says. He and others have been analysing the possibility that a new particle from a "hidden sector" of the standard model might be rearing its head. So far, though, they have found nothing that would not also upset established experimental results in normal hydrogen (Physical Review D, vol 82, p 125020; Annals of Physics, vol 326, p 516).
One proposal from the Mainz group is that the culprit is a fleet-footed pairing of a quark and an antiquark. That's controversial. Quarks and their antiparticles are only known to bind together inside particles such as the proton, where they are weighed down with a lot of gluon baggage. The lightest known quark-antiquark pairing, the pion, tips the scales at 140 MeV. The researchers think that bound quark-antiquark pairs might appear and disappear so quickly that they never pick up the full gluon burden (Physics Letters B, vol 696, p 343). In that case, they could be lighter.
Not everyone is convinced. Krzysztof Pachucki of the University of Warsaw in Poland agrees that QED might link up with the QCD of quarks and gluons to produce unforeseen or underestimated interactions - but points out that, again, we would expect to see the effects in other experiments.
That leaves the possibility that there is a blemish on QED itself. Few physicists think that likely, given the theory's superlative accuracy in almost all its predictions. Even so, theorists have been combing the relevant equations for a sign of something missing. "Up to now, nothing large enough to explain a 4 per cent difference seems to show up," says Paul Indelicato, a theorist at the Kastler Brossel Laboratory in Paris, France, who was part of the PSI muonic hydrogen team.
Moustachioed Mona Lisa
Alexander Kholmetskii of the Belarusian State University in Minsk and his colleagues think they have something. The problem lies, they claim, with the equation - the Dirac equation - that was the foundation stone for QED and is used to describe the energy states of particles such as an orbiting electron or muon in an atom. There are two components to this equation, one describing how the particle ties up energy by binding itself to the nucleus with photons, and one describing how it can lose energy by radiating away photons.
In the lowest-energy orbital state, the researchers argue, this kind of radiative loss is not possible, and so they apply a small correction. Feeding this into the calculations of the proton radius leaves the value measured using muons virtually unchanged, while moving the electron result into almost perfect agreement with it (arxiv.org/abs/1010.2845) Exactly the same correction solves a similar energy-level problem in positronium, an "atom" in which an electron and a positron orbit each other.
It's this explanation, though, that has raised the most hackles. The Dirac equation is widely feted as one of the most beautiful, concise equations in all of physics. Bolting corrections onto it is, to many physicists, akin to scrawling a moustache on the Mona Lisa. "There is no need to invoke whatever they do to explain radiative properties of atoms," says Indelicato. The fact that the lowest energy level can't give up energy is already built into QED, he says.
All that leaves us at an impasse, with no explanation gaining universal approval. "There are papers which claim to explain, but they are wrong," says Pachucki.
With theory at a deadlock, attention is now turning to another round of experiments. We have measured the proton's radius by shooting electrons at it, and by measuring the energy levels of electrons and muons orbiting it. Might shooting muons at it bring some new insight? If these muon missiles see a differently sized proton, then there must be something fundamentally different in the way muons interact, such as the involvement of new particles or particle pairings we hadn't thought of. And if they don't, says Jentschura, then we're really stuck. "Then the current discrepancy would seem all the more intriguing and strange," he says.
Meanwhile Pohl, Indelicato and their colleagues are starting to make measurements on muonic deuterium. This exotic atom's nucleus, consisting of a proton and a neutron, can also be used to calculate the proton's radius. Perhaps another decade might bring us a definitive answer.
All in a spin
While the debate about the proton's size has only just blown up (see main story), the particle's innards have been puzzling us for rather longer - specifically since 1988, when researchers at CERN near Geneva, Switzerland, discovered they could not account for the proton's spin.
Spin is a quantum-mechanical property of a particle akin to a rotation about its own axis. Particles of different spins respond to magnetic fields in different ways, so it is a relatively easy thing to measure. The proton, for example, has a spin of ½.
This spin must in some way come from the spin of the proton's components, just as the proton's one unit of positive charge comes from totting up the charge of the three "valence" quarks within it, two of charge +2/3 and one of charge -1/3.
By shooting protons apart with high-energy muons, CERN's European Muon Collaboration managed to measure the spin of the proton's interior quarks. They found it could account for only something like one-quarter of the expected spin (Physics Letters B, vol 206, p 364). Subsequent experiments have upped that proportion a little, but confirmed the basic result.
This "spin crisis" has been the source of much head-scratching since. "We thought we understood the quantum structure of the proton, but at its heart we don't," says Robert Jaffe, a theorist at the Massachusetts Institute of Technology.
Ideally, we would solve the crisis by solving the equations of quantum chromodynamics (QCD), the theory that governs interactions within the proton. But these turn out to be monstrously difficult for a particle with as many moving parts as the proton - not just the valence quarks, but the gluons that bind them and a "sea" of other ephemeral quarks and gluons that according to the inconsequential rules of quantum physics briefly pop up out of nowhere and disappear again. Such complications also overwhelm attempts to use supercomputers to simulate the origin of the proton's spin.
So we are left with messy experiments to fill in the gaps. One suggestion is that gluons might themselves carry a substantial proportion of the proton's spin. Measuring that directly is tricky, but experiments going on at CERN and elsewhere indicate contributions close to zero.
Then there is the possibility that the proton's spin might have less to do with how quarks and gluons spin individually and more to do with how they orbit each other. As yet we have only the vaguest of ideas how we might go about measuring that.
The result is a stalemate. "We're basically waiting for some bright young person to come up with some bright idea," says Jaffe.
Why do we care? First, says Jaffe, because we are all made up of protons and neutrons and we'd like to know how we work. For physicists, though, there is even more at stake. If there is such a thing as a theory of everything, we expect it will look a lot like QCD, only harder. If we can't understand what goes on within the humble proton, hopes will fade that we will ever be able to get to grips with that greater theory. Richard Webb
Kate McAlpine is a freelance writer based in London
http://www.newscientist.com/article/mg20928051.600-proton-puzzle-trouble-at-the-heart-of-the-atom.html?full=true
THERE are many messy problems that physics does not attempt to solve. As the theorist Robert Jaffe of the Massachusetts Institute of Technology observed: we don't try to predict the structure of a Volkswagen from first principles - but we like to think we could.
That's why the current confusion about one of nature's most basic particles, the proton, has touched a nerve. It is just the sort of problem that physics should master with aplomb. Yet neither theory nor experiment seems to be able to tell us with certainty either how big the proton is, or what makes it spin (see "Proton puzzle: Trouble at the heart of the atom"). As we enter the era of the Large Hadron Collider, we are eagerly waiting to see whether the hoped for Higgs particle or hints of supersymmetry appear - or whether some totally unexpected finding will write the next chapter of particle physics. Our problems with the proton remind us that even supposedly settled science can challenge our presumptions of omniscience.
Bold added.
http://www.newscientist.com/article/mg20928052.700-in-praise-of-the-humble-proton.html
Proton puzzle: Trouble at the heart of the atom
23 March 2011 by Kate McAlpine
Magazine issue 2805.
We used to think we understood protons, but these bedrocks of the atomic nucleus could send our theories of particle physics tumbling
IN THE long life of a proton, 10 years is a mere trice. These peerlessly stable particles, the bedrock of the atomic nucleus, are not prone to the decadence and decay of some of their subatomic brethren. Measuring their lifetimes means watching very many of them do very little for a very long time. Our current best estimate is that they survive for upwards of 10^29 years - over a billion billion times the age of the universe.
Ten years, though, is what it took for Randolph Pohl and his colleagues to show that the proton is not all it seems. The results of their experiments at the Paul Scherrer Institute (PSI) in Villigen, Switzerland, were published in July last year. The proton hadn't suddenly become less stable. But it was quite a bit smaller than theory or previous experiments allowed (New Scientist, 10 July 2010, p 10).
In the hyperaccurate world of subatomic physics, this was dynamite. A firestorm of claim and counter-claim followed. But with simpler explanations for the discrepancy now running out, it seems the mysterious shrinking of the proton has opened up a fundamental hole in our understanding of what makes atoms tick. What gives?
The doings of protons, as of all charged particles, are dealt with by a theory called quantum electrodynamics, or QED. One facet of nature it describes is the electromagnetic force, for example how the to-ing and fro-ing of photons of light keeps negatively charged electrons orbiting positively charged protons and so makes atoms possible. Deeper in the atomic nucleus lies the realm of a companion theory, quantum chromodynamics or QCD, which describes how protons and the like are themselves assemblages of smaller particles - quarks - and gluons that bind these quarks together. Together, QED and QCD are the two pillars of particle physicists' proudest accomplishment, their "standard model".
The inner life of protons is known to be murky and impenetrable (see "All in a spin"). Outwardly, though, all seems sweetness and light. Take the proton's radius, whose accepted value has been settled on using two different kinds of measurement. The first, direct approach is to shoot electrons in the general direction of protons, like firing rubber pellets at a fairground duck. By measuring at what point they start bouncing off, we can get an idea of where the electrons encounter the protons' fuzzy ball of charge.
Muon mischief
The second approach involves measuring the orbital energy levels of the electron circling the central proton of a standard hydrogen atom. The energy levels can be fed into QED calculations to determine how far the proton's ball of charge must extend to keep the electron in those orbits.
The results of these two approaches are in good agreement. Averaging them gives the proton a radius of 0.877 femtometres, or a fraction under a trillionth of a millimetre.
And so all was well, until Pohl and his colleagues set out in the late 1990s to determine the proton's radius using a third, supposedly more accurate method. They created hydrogen-like atoms in which the electrons were replaced by muons. These particles have the same negative charge as electrons but are some 200 times weightier. That means they orbit 200 times closer in than electrons, giving them an up-close-and-personal feel for how big the proton is.
Measuring the muons' orbital energy levels meant first guessing the gaps between the two levels of interest, so a laser could be tuned to the right frequency to bump a muon from one level to another. The team did this by reversing the QED equations and plugging in the accepted value for the proton's radius to give an estimated starting point.
In the first couple of attempts to run the full experiment, in 2003 and 2007, that approach didn't work: the muons did not respond. It was only in 2009, when the team had a new laser that could reach higher frequencies, that they found the muons' sweet spot and persuaded them to dance. Feeding the experimentally determined energy levels back into the QED calculation produced the shocker. The error on the proton's radius had shrunk by a factor of 10, as expected - but the radius had shrunk too. At 0.8418 femtometres, it was about 4 per cent lower than the previous average (Nature, vol 466, p 213).
Four per cent might not sound much, but in QED, where theory and experiment can agree to a part or two in a billion, it was a huge embarrassment. And there was no obvious flaw in the measurement. "We had to take the discrepancy seriously," says Michael Distler of the University of Mainz, Germany.
Just a few weeks later, Distler and his colleagues thickened the plot still more. They published a measurement of the proton radius using the tried and tested electron-scattering method that not only doubled its accuracy, but brought its value perfectly into line with that from measuring energy level shifts in regular hydrogen (Physical Review Letters, vol 105, p 242001). The muon experiment, which should have been the most accurate, was the odd one out. But why?
One early proposal was that the proton is surrounded by a large and diffuse halo of positive charge, meaning the distantly orbiting electron and the closer muon "see" protons of different sizes (New Scientist, 25 Sept 2010, p 16). That model seems to have been discounted, though, as it made other predictions at odds with the improved electron-scattering experiments. Now attention has shifted to more fundamental possible flaws: that we might have overlooked subtleties in the workings of QED, or that QED itself is missing something.
The first possibility stems from the fact that, according to QED, two charged particles orbiting each other will exchange photons. The stronger the bond between the particles, the more energy these photons will have. If the energy oversteps a certain mark, a photon can up the ante and briefly morph into a particle and its antiparticle - an electron and a positron, for example - before switching back to being a photon again.
Because a stronger bond is needed for a proton to rein in the more massive muon, there is more scope for this sort of thing in muonic hydrogen. The idea is that a thick cloud of ephemeral particles and antiparticles shields the orbiting muon from some of the attractive effect of the proton, reducing the proton's effective radius (see diagram).
It sounds plausible, but there's one problem: finding a particle-antiparticle pair that produces exactly the right amount of shielding. That would require the pair to have a combined mass of around 46 megaelectronvolts (MeV) - far more than an electron-positron pair, which weighs in at just over 1 MeV, but far below the more than 200 MeV needed for a muon-antimuon pair.
For Ulrich Jentschura, a physicist at the Missouri University of Science and Technology in Rolla, that makes things tricky. "Theory has a problem even inventing a particle that could explain the discrepancy without messing something else up," he says. He and others have been analysing the possibility that a new particle from a "hidden sector" of the standard model might be rearing its head. So far, though, they have found nothing that would not also upset established experimental results in normal hydrogen (Physical Review D, vol 82, p 125020; Annals of Physics, vol 326, p 516).
One proposal from the Mainz group is that the culprit is a fleet-footed pairing of a quark and an antiquark. That's controversial. Quarks and their antiparticles are only known to bind together inside particles such as the proton, where they are weighed down with a lot of gluon baggage. The lightest known quark-antiquark pairing, the pion, tips the scales at 140 MeV. The researchers think that bound quark-antiquark pairs might appear and disappear so quickly that they never pick up the full gluon burden (Physics Letters B, vol 696, p 343). In that case, they could be lighter.
Not everyone is convinced. Krzysztof Pachucki of the University of Warsaw in Poland agrees that QED might link up with the QCD of quarks and gluons to produce unforeseen or underestimated interactions - but points out that, again, we would expect to see the effects in other experiments.
That leaves the possibility that there is a blemish on QED itself. Few physicists think that likely, given the theory's superlative accuracy in almost all its predictions. Even so, theorists have been combing the relevant equations for a sign of something missing. "Up to now, nothing large enough to explain a 4 per cent difference seems to show up," says Paul Indelicato, a theorist at the Kastler Brossel Laboratory in Paris, France, who was part of the PSI muonic hydrogen team.
Moustachioed Mona Lisa
Alexander Kholmetskii of the Belarusian State University in Minsk and his colleagues think they have something. The problem lies, they claim, with the equation - the Dirac equation - that was the foundation stone for QED and is used to describe the energy states of particles such as an orbiting electron or muon in an atom. There are two components to this equation, one describing how the particle ties up energy by binding itself to the nucleus with photons, and one describing how it can lose energy by radiating away photons.
In the lowest-energy orbital state, the researchers argue, this kind of radiative loss is not possible, and so they apply a small correction. Feeding this into the calculations of the proton radius leaves the value measured using muons virtually unchanged, while moving the electron result into almost perfect agreement with it (arxiv.org/abs/1010.2845) Exactly the same correction solves a similar energy-level problem in positronium, an "atom" in which an electron and a positron orbit each other.
It's this explanation, though, that has raised the most hackles. The Dirac equation is widely feted as one of the most beautiful, concise equations in all of physics. Bolting corrections onto it is, to many physicists, akin to scrawling a moustache on the Mona Lisa. "There is no need to invoke whatever they do to explain radiative properties of atoms," says Indelicato. The fact that the lowest energy level can't give up energy is already built into QED, he says.
All that leaves us at an impasse, with no explanation gaining universal approval. "There are papers which claim to explain, but they are wrong," says Pachucki.
With theory at a deadlock, attention is now turning to another round of experiments. We have measured the proton's radius by shooting electrons at it, and by measuring the energy levels of electrons and muons orbiting it. Might shooting muons at it bring some new insight? If these muon missiles see a differently sized proton, then there must be something fundamentally different in the way muons interact, such as the involvement of new particles or particle pairings we hadn't thought of. And if they don't, says Jentschura, then we're really stuck. "Then the current discrepancy would seem all the more intriguing and strange," he says.
Meanwhile Pohl, Indelicato and their colleagues are starting to make measurements on muonic deuterium. This exotic atom's nucleus, consisting of a proton and a neutron, can also be used to calculate the proton's radius. Perhaps another decade might bring us a definitive answer.
All in a spin
While the debate about the proton's size has only just blown up (see main story), the particle's innards have been puzzling us for rather longer - specifically since 1988, when researchers at CERN near Geneva, Switzerland, discovered they could not account for the proton's spin.
Spin is a quantum-mechanical property of a particle akin to a rotation about its own axis. Particles of different spins respond to magnetic fields in different ways, so it is a relatively easy thing to measure. The proton, for example, has a spin of ½.
This spin must in some way come from the spin of the proton's components, just as the proton's one unit of positive charge comes from totting up the charge of the three "valence" quarks within it, two of charge +2/3 and one of charge -1/3.
By shooting protons apart with high-energy muons, CERN's European Muon Collaboration managed to measure the spin of the proton's interior quarks. They found it could account for only something like one-quarter of the expected spin (Physics Letters B, vol 206, p 364). Subsequent experiments have upped that proportion a little, but confirmed the basic result.
This "spin crisis" has been the source of much head-scratching since. "We thought we understood the quantum structure of the proton, but at its heart we don't," says Robert Jaffe, a theorist at the Massachusetts Institute of Technology.
Ideally, we would solve the crisis by solving the equations of quantum chromodynamics (QCD), the theory that governs interactions within the proton. But these turn out to be monstrously difficult for a particle with as many moving parts as the proton - not just the valence quarks, but the gluons that bind them and a "sea" of other ephemeral quarks and gluons that according to the inconsequential rules of quantum physics briefly pop up out of nowhere and disappear again. Such complications also overwhelm attempts to use supercomputers to simulate the origin of the proton's spin.
So we are left with messy experiments to fill in the gaps. One suggestion is that gluons might themselves carry a substantial proportion of the proton's spin. Measuring that directly is tricky, but experiments going on at CERN and elsewhere indicate contributions close to zero.
Then there is the possibility that the proton's spin might have less to do with how quarks and gluons spin individually and more to do with how they orbit each other. As yet we have only the vaguest of ideas how we might go about measuring that.
The result is a stalemate. "We're basically waiting for some bright young person to come up with some bright idea," says Jaffe.
Why do we care? First, says Jaffe, because we are all made up of protons and neutrons and we'd like to know how we work. For physicists, though, there is even more at stake. If there is such a thing as a theory of everything, we expect it will look a lot like QCD, only harder. If we can't understand what goes on within the humble proton, hopes will fade that we will ever be able to get to grips with that greater theory. Richard Webb
Kate McAlpine is a freelance writer based in London
http://www.newscientist.com/article/mg20928051.600-proton-puzzle-trouble-at-the-heart-of-the-atom.html?full=true