Special relativity is a kind of relativity that is limited to the discussion of inertial system. Newton's view of time and space holds that space is a flat, isotropic and isotropic three-dimensional space-absolute space, and time is a single dimension independent of space (so it is absolute), that is, absolute view of time and space. Special relativity holds that space and time are not independent of each other, but a unified four-dimensional space-time whole, and there is no absolute space and time. In the special theory of relativity, the whole space-time is still flat, isotropic and isotropic, which is an ideal situation corresponding to the "global inertial system". Special relativity assumes that the speed of light in vacuum is constant, and Lorentz transformation can be deduced by combining the principle of special relativity and the above-mentioned space-time properties.
General relativity is a theory published by Einstein in 19 15. Einstein put forward the "equivalence principle", that is, gravity and inertia force are equivalent. This principle is based on the equivalence between gravitational mass and inertial mass (currently confirmed by experiments to be between 10? Within the precision range of 12, there is still no difference between gravitational mass and inertial mass). According to the principle of equivalence, Einstein extended the principle of relativity in a narrow sense to the principle of relativity in a broad sense, that is, the form of physical laws is unchanged in all reference systems. The motion equation of an object is the geodesic equation in the reference system. Geodesic equation has nothing to do with the inherent properties of the object itself, but only depends on the local geometric properties of time and space. And gravity is the expression of local geometric properties of time and space. The existence of material mass will cause the bending of time and space. In curved space-time, objects still move along the shortest distance (that is, along the geodesic-in Euclidean space). For example, the geodesic movement of the earth in curved space-time caused by the sun actually revolves around the sun, resulting in a gravitational effect. Just like on the surface of the earth, if you move in a straight line, you actually walk around the great circle on the surface of the earth.
Inverse Relativity: Relativity has also been criticized by many people, who think it is wrong and greatly hinders the development of society. However, this view is not accepted by the mainstream scientific community.
Einstein and his theory of relativity
In addition to quantum theory, an article entitled "On Electrodynamics of Moving Objects" published by Einstein in 1905 triggered another revolution in physics in the 20th century. This paper studies the influence of object motion on optical phenomena, which is another difficult problem faced by classical physics at that time.
/kloc-in the mid-9th century, Maxwell established the electromagnetic field theory and predicted the existence of electromagnetic waves propagating at the speed of light C. By the end of19th century, Maxwell's theory was completely confirmed by experiments. What is electromagnetic wave? To whom is its propagation speed c? At that time, the popular view was that the whole universe was full of a special substance called "ether", and electromagnetic waves were the propagation of ether vibration. But people find that this is a theory full of contradictions. If we think that the earth is moving in the static ether, then according to the principle of velocity superposition, the speed of light propagating in different directions on the earth must be different, but the experiment denies this conclusion. If we think that the ether was taken away by the earth, it is obviously inconsistent with some astronomical observations.
1887, Michelson and Morey made a very accurate measurement by using the interference phenomenon of light, but they still didn't find any movement of the earth relative to the ether. In this regard, H.A. Lorenz put forward a hypothesis that all objects moving in the ether should contract along the moving direction. From this, he proved that even if the earth moves relative to the ether, Michelson could not find it. Einstein studied this problem from a completely different way of thinking. He pointed out that all difficulties can be solved as long as Newton's concepts of absolute space and absolute time are abandoned, and there is no need for ether at all.
Einstein put forward two basic principles as the basis for discussing the optical phenomena of moving objects. The first is called the principle of relativity. That is to say, if the coordinate system K' moves at a constant speed relative to the coordinate system K without rotating, it is impossible to distinguish which coordinate system is K and which coordinate system is K' in any physical experiment made relative to these two coordinate systems. The second principle is called the principle that the speed of light is constant, which means that the speed of light c (in vacuum) is constant, and it does not depend on the moving speed of the luminous object.
On the surface, the constant speed of light seems to conflict with the principle of relativity. Because according to the classical law of mechanical speed synthesis, the speed of light should be different for the two coordinate systems, k' and k, which move at a relatively uniform speed. Einstein thought that if we want to admit that these two principles do not conflict, we must re-analyze the physical concepts of time and space.
The law of velocity composition in classical mechanics actually depends on the following two assumptions: 1. The time interval between two events has nothing to do with the motion state of the clock used to measure time; 2. The spatial distance between two points has nothing to do with the motion state of the ruler used to measure the distance. Einstein found that if the principle of light speed invariance and the principle of relativity are recognized to be compatible, then both hypotheses must be abandoned. At this time, the simultaneous events of one clock are not necessarily simultaneous for another clock, and they are relative at the same time. In two coordinate systems with relative motion, the values obtained by measuring the distance between two specific points are no longer equal. Distance is also relative.
If an event in the K coordinate system can be determined by three spatial coordinates X, Y, Z and a time coordinate T, and the same event in the K coordinate system is determined by X', Y', Z' and T', Einstein found that X', Y', Z' and T' can be solved by a set of equations. The relative velocity of the two coordinate systems and the speed of light c are the only parameters of the equation. This equation was first derived by Lorentz, so it is called Lorentz transformation.
Using Lorentz transformation, it is easy to prove that the clock will slow down because of movement, the ruler will be shorter when it is moving than when it is at rest, and the sum of speeds satisfies a new law. The principle of relativity is also expressed as a clear mathematical condition, that is, under the Lorentz transformation, the space-time variables X', Y', Z' and T' with apostrophes will replace the space-time variables X, Y, Z and T, and any expression of natural laws will still take the same form as before. What people call the universal law of nature is covariant for Lorentz transformation. This is very important for us to explore the universal laws of nature.
Besides, in classical physics, time is absolute. It has always played an independent role different from the three spatial coordinates. Einstein's theory of relativity involves time and space. It is believed that the real world of physics is composed of various events, and each event is described by four numbers. These four numbers are its space-time coordinates T and X, Y and Z, which form a four-dimensional continuous space, usually called Minkowski four-dimensional space. In relativity, it is natural to examine the real world of physics in a four-dimensional way. Another important result caused by special relativity is about the relationship between mass and energy. Before Einstein, physicists always thought that mass and energy were completely different and were separately conserved quantities. Einstein found that in the theory of relativity, mass and energy are inseparable, and the two conservation laws are combined into one. He gave a famous formula of mass and energy: e = mc2, where c is the speed of light. So quality can be regarded as a measure of its energy. Calculations show that tiny masses contain enormous energy. This wonderful formula has laid a theoretical foundation for mankind to obtain huge energy, make atomic bombs and hydrogen bombs, and use atomic energy to generate electricity.
Most physicists, including Lorenz, the founder of relativistic transformation relation, find it hard to accept these new concepts introduced by Einstein. The obstacle of the old way of thinking made this new physical theory not familiar to physicists until a generation later. Even in 1922, when the science prize was awarded to Einstein by the Royal Swedish Academy, it only said, "Because of his contribution to theoretical physics and because he discovered the law of photoelectric effect." Not a word about relativity.
Einstein further established the general theory of relativity in 19 15. The principle of relativity in a narrow sense is limited to two coordinate systems with uniform motion, while the principle of relativity in a broad sense cancels the restriction of uniform motion. He introduced an equivalence principle, arguing that it is impossible for us to distinguish between gravitational effect and non-uniform motion, that is, non-uniform motion and gravity are equivalent. He further analyzed the phenomenon that light will be bent by gravity when passing near a line, and thought that the concept of gravity itself was completely unnecessary. It can be considered that the mass of the planet makes the space around it curved, and the light takes the shortest path. Based on these discussions, Einstein derived a set of equations, which can determine the curved space geometry caused by the existence of matter. Using this equation, Einstein calculated the displacement of the perihelion of Mercury, which was completely consistent with the experimental observation, and solved a long-term unexplained problem, which made Einstein excited. In his letter to Erenfest, he wrote that this equation gives the correct value of perihelion. You can imagine how happy I am! For days, I was so happy that I didn't know what to do. "
1915165438+1On October 25th, Einstein submitted a paper entitled "Equation of Gravitation" to the Prussian Academy of Sciences in Berlin, which fully discussed the general theory of relativity. In this article, he not only explained the mystery of the perihelion motion of Mercury's orbit found in astronomical observation, but also predicted that the starlight would deflect after passing through the sun, and the deflection angle was twice that predicted by Newton's theory. The first world war delayed the determination of this value. 19 19 The total solar eclipse on May 25th provided people with the first observation opportunity after the war. Eddington, an Englishman, went to principe island on the west coast of Africa and made this observation. 165438+1On October 6th, Thomson solemnly announced at the joint meeting of the Royal Society and the Royal Astronomical Society that Einstein, not Newton, had proved this result. He praised "this is one of the greatest achievements in the history of human thought." Einstein discovered not an island, but a brand-new continent of scientific ideas. "The Times reported this important news under the title of" Revolution in Science ". The news spread all over the world, and Einstein became a world-famous celebrity. General relativity has also been elevated to a mythical sacred position.
Since then, people have shown more and more interest in the experimental test of general relativity. However, because the gravitational field of the solar system is very weak and the gravitational effect itself is very small, the theoretical result of general relativity deviates very little from Newton's gravitational theory, which makes the observation very difficult. Since 1970s, due to the progress of radio astronomy, the observation distance has far exceeded the solar system, and the accuracy of observation has been greatly improved. Especially in September of 1974, Taylor of MIT and his student Whistler observed with a large radio telescope with a diameter of 305 meters, and found a pulse binary star, which is a neutron star and its companion star orbiting each other under the action of gravity, with a period of only 0.323 days. The gravity on its surface is100000 times stronger than that on the surface of the sun, which makes it impossible to test the theory of gravity on the earth or even in the solar system. After more than ten years of observation, they got a very good result, which is in line with the prediction of general relativity. Because of this great contribution, Taylor and Whistler won the 1993 Nobel Prize in Physics.
Theory of relativity
/kloc-In the late 20th century, due to the establishment of the wave theory of light, scientists thought that space was full of a continuous medium called "ether". Just like sound waves in the air, light and electromagnetic signals are waves in the ether. However, the opposite result to the idea that space is full of "ether" soon appeared: according to the "ether" theory, the speed of light propagation should be a constant value relative to "ether", so if you are in line with the direction of light propagation, the speed of light you measure should be lower than that you measure at rest; On the contrary, if you travel in the opposite direction to the direction of light propagation, then the speed of light you measure should be higher than that you measure at rest. However, a series of experiments found no evidence of the difference in light speed.
Among these experiments, Ahlport Michelson and Eddie Ward Murray of the Case Institute in Cleveland, Ohio, USA made the most accurate and detailed measurement in 1887. They compared the propagation speeds of two right-angle beams. Because of the rotation around the rotation axis and the revolution around the sun, according to reasoning, the earth should pass through the "ether", so the two beams of light at right angles should be measured at different speeds due to the movement of the earth. Irish physicist George Fitzgerald and Dutch physicist Hen Zhuo Ke Lorenz first thought that the size of an object moving relative to the "ether" would shrink in the direction of motion, while the size of an object moving relative to the "ether" would shrink. Lorenz put forward the famous Lorentz transformation. As for "ether", Fitzgerald and Lorenz thought it was a real substance. Poincare, a French mathematician, expressed doubts about this and predicted that a brand-new mechanics would appear.
The philosophy of Mach and Hume had a great influence on Einstein. Mach believes that the measurement of space-time is related to the movement of matter. The concept of time and space is formed through experience. Absolute time and space, no matter what experience is based on, can't be grasped. More specifically, Hume said: Space and extension are just visible objects that are filled with space and distributed in a certain order. And time is always discovered through the perceptual changes of changeable objects. 1905, Einstein pointed out that Michelson and Morey's experiments actually showed that the whole concept of "ether" was redundant and the speed of light was constant. Newton's concept of absolute space-time is wrong. There is no absolutely static reference object, and the measurement of time varies with different reference frames. He put forward Lorentz transformation based on the principle of invariance of light speed and relativity. Created the special theory of relativity.
In the decades after Einstein's death, his image was constantly raised. His books have been sold for decades and his words are often quoted by popular culture. His portrait is printed on T-shirts and coffee cups, which can be said to have a wide range of commercial uses. Regarded as a saint, his image is never aggressive. Einstein's image has always been: a gentle genius. He has both talent and charity. The perfect combination of achievement and personality makes many people regard Einstein as a saint. But in fact, the more we pay attention to Einstein's external tall image, the less we can understand the real Einstein and everything he has done.
Thanks to the persistent publishing plan, the true face of the greatest scientist in the 20th century has finally formed. This is the complete works of Einstein. This set will publish Einstein's complete works of about14,000 original documents in 25 volumes, and the eighth volume has been published. The complete corpus not only contains all Einstein's scientific documents for researchers to follow the scientist's ideological course, but also publishes a large number of letters and shows his true personality. In it, you can deeply feel Einstein's wisdom and charm, as well as his respectable courage and sense of social justice. On the other hand, the anthology also shows that Einstein is far from a saint. He is also mean, rebellious and even a little slutty.
When you walk into the dim exhibition hall of the American Museum of Natural History and hear the Planet written by the famous British composer holst in 19 18, the extremely discordant and somewhat harsh tone seems to remind visitors that Einstein's inner world is so contradictory and discordant.
There are many legends about Einstein's supernatural ability. His sister said that the back of his head was big and angular.
There were many legends about Einstein's supernatural abilities before. The most typical story is that Einstein's first words when he was a child turned out to be complaining that the milk was too hot. His shocked parents asked him why he had never spoken. Unexpectedly, this little genius replied: "Because everything before is correct!" " )
According to Einstein's sister Maya, in an unpublished autobiography, Einstein's intelligence developed slowly and he began to speak very late. Maya said, "When Einstein was born, my mother was scared when she saw his huge angular head."
"Einstein's brain is really different from ordinary people. The nerve cells on the left side of the hippocampus are significantly larger than those on the right side, and they are regularly distributed "(Dr. Zaider, University of California)
Dr Zaidel of the University of California said that Einstein's brain was "significantly different" from that of ordinary people. Zaidel studied two pieces of Einstein's brain tissue (a research method commonly used in biological experiments). These two slices contain nerve cells in the hippocampus of the brain, which are responsible for processing language and imagination. Compared with the 10 brain slice of ordinary people, Dr. Zadel found that Einstein's brain tissue had significant "advantages": the nerve cells on the left side of Einstein's hippocampus were significantly larger than those on the right side, and they were regularly distributed; However, the nerve cells in this tissue area of ordinary people look small and show "very irregular"
However, Zaider pointed out that whether the characteristics of Einstein's brain tissue are "the result of natural or acquired development" is still inconclusive.
"I don't have any special talent. All I have is extremely strong curiosity. " "My intellectual development is very slow. It was not until I was fully grown up that I began to be curious about time and space. " (Einstein)
So, what kind of person is Einstein, and how did he "see" what others "can't see"? Einstein attributed his success to his slow start. He once wrote: "A normal adult never stops thinking about time and space. However, my mental development is very slow. It was not until I was fully grown up that I began to be curious about time and space. "
19 15 years ago, Einstein once said to an alumnus, "One should not pursue those things that are easy to get. Let's continue to work hard."
Greed Horton, an expert in the history of physics and science at Harvard University, was the first scholar who was allowed to browse the archives after Einstein 1955 died. Horton, 76, said that when he looked through Einstein's files, he was completely impressed by his unique talent. "Einstein's way of thinking is not like what the textbook says. He did the experiment first, then came to the theory and finally tested the conclusion. On the contrary, he created almost entirely through thinking, and completed his experiment with his extremely jumping thinking. Einstein's wisdom is extraordinary. "
Einstein in childhood, youth and old age
Relativity changed the world.
Einstein published about 300 scientific papers in his life, but the most important theory is summarized as follows:
Theory of relativity
The special theory of relativity was published in 1905. This theory points out that the only constant in the universe is the speed of light in vacuum, and everything else-speed, length, mass and elapsed time-changes with the observer's frame of reference (specific observation).
space-time
Two hundred years before Einstein published his theory of relativity, British physicist isaac newton (1643~ 1727) proposed that time and space are absolute, and space and time are completely separated. However, in relativistic mathematics, time and three-dimensional space-length, width and height-together form a four-dimensional space framework, which is called time-space correlation set.
Slaven
Einstein deduced the equation e = mc2 from his special theory of relativity (where e is energy, m is mass and c is constant speed of light), and he used this equation to explain that mass and energy are equivalent. It is now believed that mass and energy are different forms of the same substance, called mass energy. For example, if the energy of an object is reduced by a certain amount E, its mass is also reduced by an amount equal to MC2. However, whether mass can disappear is only released in another form, which is called radiant energy.
Theory of relativity
19 15 published the general theory of relativity, explaining why there is no difference between gravity and acceleration. He also explained how gravity is related to the curvature of time and space. Using mathematics, Einstein pointed out that an object bends the surrounding space and time. When an object has a large relative mass (such as a star), this curvature can change the path of any object passing through it, even light.
wormhole
Theoretically, a wormhole is a black hole with a very large mass. It bends time and space and sucks it into itself. Its mouth leads to another time and space in the universe, or it may completely enter another space. It may be possible to build a time travel machine using wormholes, but many scientists point out that it is impossible for this machine to go back to the time before it was created.
He is also an inventor.
We often imagine Einstein as a genius who is always absent-minded, and his soul is often hooked by time and space. But in fact, Einstein was also an inventor with strong hands-on ability. His parents run a power plant and often encourage little Einstein to become an engineer in the future.
He once collaborated with others to invent a refrigeration system that did not need to be disassembled, and later designed wings for the German Air Force during World War I. ..
Einstein worked as an evaluator in the Patent Office in Bern, Switzerland for 7 years. Although he often daydreamed while working (doing experiments with his brain), Einstein was quite competent in his work and was promoted at 1906. In addition, he had several patents of his own at that time, including a refrigeration system that did not need to be disassembled, which he co-invented with others in the 1920s. During World War I, Einstein designed a wing for the German Air Force and went to the experimental stage. Unfortunately, the pilot in charge of the test complained to his superiors that the plane looked like a "pregnant duck" after installing the wing designed by Einstein, and finally planned to abort.
He secretly confronted the FBI.
Although Einstein was indifferent in his private life, he showed strong social skills in public, and he was even a born celebrity. Einstein was very photogenic when he took pictures, and his voice was very magnetic. In a documentary about Einstein, there is such a scene: Einstein is surrounded by a group of reporters and calmly handles it. A reporter asked him, "Professor Einstein, are you happy to be an American?" Einstein sarcastically said, "Since you are standing here asking me this question, my answer is' Of course, I feel very honored'". Einstein's travel diaries 1930, 65438+February, 1 1 directly mocked the reporters. "A group of reporters boarded our ship in Long Island and asked me some stupid questions. When I answered them with some worthless platitudes, they came back as happy as treasure. "
He made many enemies in science and politics. He supported the Jews to establish a state in the Middle East, but warned long ago to pay attention to the interests of local Arabs.
Although Einstein's feelings are extremely clear, the most typical embodiment is the social and political events he participated in. Einstein worked tirelessly to help those refugees from Nazi Germany escape to the United States, and he also devoted himself to establishing Hebrew University in Jerusalem as a refuge for Jewish scientists. Einstein supported the Jews to rebuild the Jewish kingdom in Palestine, but at the same time he warned as early as 1955: "The most critical part of our founding policy is to give Arabs who have been living in the Middle East equal rights." As a loyal socialist, Einstein was very distrustful of capitalism. He believes that the establishment of a "world government" is the only way to effectively control the development of nuclear weapons, and only in this way can war be fundamentally avoided.
He is a radical. In Germany, he was blacklisted by the Nazi Party. After he fled to the United States, the FBI spent 22 years watching him, not only framing him as a spy, but also trying to expel him.
Einstein was one of the earliest advocates of the human rights movement, which is the least known aspect of Einstein as a radical. Einstein not only used his reputation to strongly oppose lynching, but also participated in the work of the National Association for the Advancement of Colored People (NAACP).
Therefore, Einstein's opposition to the authorities made him many enemies in science and politics. His name was written into the blacklist of the Nazi Party as early as 1922, and many prestigious physicists in Germany also publicly called Einstein's research "Jewish physics". This stupid attack didn't stop even after Einstein and 1933 fled to Princeton University.
After fleeing to the United States, his radical behavior also made the FBI feel very uneasy. A "secret war" broke out between Hoover, the former director of the FBI, and Einstein for more than 20 years. Under Hoover's instructions, the FBI collected more than 1800 pages of documents about Einstein. Their purpose was to expel Einstein from the United States. Hoover concluded that Einstein was actually a Russian spy sent to Berlin. However, this absurd statement actually worked, and Einstein was finally blocked from Manhattan's atomic bomb program. That's why Einstein suggested that Roosevelt develop a nuclear bomb, but he never took part in the project.
"Marriage is slavery in the cloak of civilization."
Needless to say, Einstein's view on women was really influenced by Schopenhauer's thought. He never values love above everything else. I had an affair before my divorce, and I also had deviant behavior after my second marriage. He thinks that marriage is stupid in essence, and he has repeatedly talked about his personality that is not suitable for family life.
I have had two humiliating marriages. Einstein's passion for love was temperate, and he never let it overwhelm his cool reason.
Einstein's private life is often criticized. What makes people relish most is his two "disgraceful marriages" and several extramarital affairs interspersed among them. Some authors even suggested that there was no proper relationship between him and Ducas, a lifelong unmarried female secretary.
Einstein met his first wife, Millavoy, in college, but was strongly opposed by his family. It was not until Millevoye gave birth to a girl named Liselle for Einstein that they finally got married at 1903. However, Einstein had never seen his illegitimate daughter. Besides, Lizzy died young.
Einstein revealed to Millavoy in the letter: "My little baby, why didn't I meet you earlier!" " This tenderness is very short-lived. After Einstein's popularity increased, after the birth of his two younger sons, Millavoy began to have symptoms of schizophrenia, and the love between husband and wife soon disappeared, leaving only mutual ridicule and deception. Einstein wrote to his cousin elsa on 19 13: "(millewoy) is a very unfriendly creature with no sense of humor-as long as she is here, she will try her best to destroy other people's happy lives." Elsa had become Einstein's lover at that time, and later became his second wife in 19 19.
"I don't want to marry him myself, but despite his many shortcomings, we still like him." (Hallap Aisi)
Special relativity is based on the theory of four-dimensional space-time view, so to understand the content of relativity, we must first have a general understanding of its space-time view. There are various multidimensional spaces in mathematics, but so far, the physical world we know is only four-dimensional, that is, three-dimensional space plus one-dimensional time. The high-dimensional space mentioned in modern microphysics is another meaning, which is only mathematical, so I won't discuss it here.
Four-dimensional space-time is the lowest dimension that constitutes the real world, and our world happens to be four-dimensional. As for the high-dimensional real space, at least we can't perceive it yet. I mentioned an example in a post. When a ruler rotates in three-dimensional space (excluding time), its length remains unchanged, but when it rotates, all its coordinate values change and the coordinates are related. The significance of four-dimensional space-time lies in that time is the fourth coordinate, which is related to spatial coordinates, that is to say, space-time is a unified and inseparable whole, and they are a kind of "one change and one change" relationship.
Four-dimensional space-time is not limited to this. According to the relationship between mass and energy, mass and energy are actually the same thing. Mass (or energy) is not independent, but related to the state of motion. For example, the greater the speed, the greater the mass. In four-dimensional space-time, mass (or energy) is actually the fourth component of four-dimensional momentum, and momentum is a quantity that describes the motion of matter, so it is natural that mass is related to the state of motion. In four-dimensional space-time, momentum and energy are unified, which are called four vectors of energy momentum. In addition, four-dimensional velocity, four-dimensional acceleration, four-dimensional force and four-dimensional electromagnetic field equations are all defined in four-dimensional space-time. It is worth mentioning that the four-dimensional electromagnetic field equation is more perfect, which completely unifies electricity and magnetism, and the electric field and magnetic field are described by a unified electromagnetic field tensor. The physical laws of four-dimensional space-time are much more perfect than those of three-dimensional, which shows that our world is indeed four-dimensional. It can be said that at least it is much more perfect than Newtonian mechanics. At least because of its perfection, we can't doubt it.
In the theory of relativity, time and space constitute an inseparable whole-four-dimensional spacetime, and energy and momentum also constitute an inseparable whole-four-dimensional momentum. This shows that there may be a deep connection between some seemingly unrelated quantities in nature. When we talk about general relativity in the future, we will also see that there is also a profound relationship between the four vectors of space-time and energy momentum.
3 Basic principles of special relativity
Matter moves forever in interaction, and there is no matter that does not move and there is no matter that does not move. Because matter moves in interaction, it is necessary to describe motion in the relationship of matter, and it is impossible to describe motion in isolation. In other words, motion must have a reference object, and this reference object is the frame of reference.
Galileo once pointed out that the movement of a moving ship is inseparable from the movement of a stationary ship, that is, when you are completely isolated from the outside world in a closed cabin, even if you have the most developed mind and the most advanced instruments.