Note that matter does not have to travel at the speed of light (or the speed of light squared) for this conversion to occur. In August 1939, just prior to the outbreak of war in Europe, Einstein sent a letter to US President Roosevelt. WebEinstein is considered the third founder of Quantum Theory because he described light as quanta in his theory of the Photoelectric Effect, for which he won the 1921 Nobel Prize. In fact, the mathematics of fluid flow and turbulence assumes that there is no smallest, indivisible bit of water. On average, a proton will rebound from other protons in the Suns crowded core for about 14 billion years, at the rate of 100 million collisions per second, before it fuses with a second proton. This will cause them to lose some of their mass, which then turns into energy. After all, parts of quantum mechanics are well described by differential equations. the differential equations of general relativity and the discrete mathematics of quantum mechanics) are fundamentally at odds. According to \(E=mc^2\), the annihilation of matter and antimatter can produce a huge amount of energy, but keeping the antimatter fuel from touching the ship before it is needed must be a big problem. In 1933, to escape Nazi persecution, Einstein left his professorship in Berlin and settled in the United States at the newly created Institute for Advanced Studies at Princeton. 2023 Scientific American, a Division of Springer Nature America, Inc. Einstein didnt like this because it seemed to imply that correlations could occur over events that could not be connected by a beam of light, thereby breaking a rule that says nothing can travel faster than the speed of light. A positron (antimatter electron) emerges from the reaction and carries away the positive charge originally associated with one of the protons. For a large part of his life, Albert Einstein (Figure \(\PageIndex{1}\)) was one of the most recognized celebrities of his day. Therefore, infinities in real calculations are a clear sign that you've pushed your model beyond the realm of applicability and you need to start looking to find some new physical principles that you've overlooked in your simplified model. Einstein hoped that the added threat of atomic weapons might facilitate his broader objective of establishing a supranational authority, and he wanted the "secret" of the atomic bomb to be monopolised by such an authority. Examine the impact of Einstein's work during 1905the "miraculous year" when he published E = mc 2 and four other universe-changing papers. Einsteins Energy seemed to disappear when certain types of nuclear reactions took place, violating the law of conservation of energy. And, some say, if you can't realistically do a test, it isn't science. In fact, we will see that the Sun contains more than enough mass to destroy such huge amounts of matter and still continue shining at its present rate for billions of years. WebThe start of everything. He remained there until his death in 1955, writing, lecturing, and espousing a variety of intellectual and political causes. All rights reserved. But its fame is mostly because of its association with one of the most devastating weapons produced by humans the atomic bomb. By contrast, in domains where gravitation appears irrelevant, quantum mechanics remains unchallenged, despite describing a very strange world. Einstein himself tried to discourage speculation that the large-scale conversion of atomic mass into energy would be feasible in the near future. The idea that matter or energy can be converted into each other seemed as outrageous as saying you could accelerate a car by turning the bumper into more speed, or that you could create a bigger front seat by slowing down your car. When Einstein first derived his formula in 1905, no one had the faintest idea how to convert mass into energy in any practical way. Einsteins rejection of the concept of universal time was one of the most radical shifts in the history of physics. For starters, the E stands for energy and the m stands for mass, a measurement of the Iron, therefore, is the most stable element: since it gives up the most energy when it forms, it would require the most energy to break it back down into its component particles. Bridging the quantum world to relativity Nuclear fission is one of several ways to release a tiny bit of an atom's mass, but most of the stuff remains in the form of familiar protons, neutrons and electrons. Answer: Conceptual Framework Explanation: The energy carried by each particle of light (called quanta or photon) is dependent on the lights frequency () as You can't get smaller than that, because when you probe even smaller distances, water is no longer a sensible concept. In fact, quantum mechanics is built around the idea that there are smallest objects and discrete distances and energies. Einstein spent the rest of his life, without success, pursuing ways to integrate his theory of general relativity with quantum mechanics. If the particle carries a charge, its antiparticle has the opposite charge. A research group in Vienna proposes to use the International Space Station to see how gravity might influence this action. WebHarvard University Press, 2005. Beforehand, the mass of something in kilograms was just a measure of how much stuff was present and how resistant it was to being moved around. How can we get nuclei close enough to participate in fusion? It should be noted that superstring theory is not generally accepted, and indeed, some in the scientific community don't even consider it to be a scientific theory at all. Since our world is made exclusively of ordinary particles of matter, antimatter cannot survive for very long. The speed of light (\(c\)) is 3 108 meters per second, so the energy released by the conversion of just 1 kilogram of hydrogen into helium is: \[\begin{array}{l} E=mc^2 \\ E=0.0071 \text{ kg} \times \left( 3 \times 10^8 \text{ m/s} \right)^2=6.4 \times 10^{14} \text{ J} \end{array} \nonumber\]. Wouldnt it be wonderful if we could duplicate the Suns energy mechanism in a controlled way on Earth? Einsteins Together with Einsteins discovery, this pointed to a duality where both matter and light could be described as a particle or as a wave an idea which led to the development of quantum mechanics by a number of scientists. What is relativity? Einstein's mind-bending theory explained Since Paulis prediction, scientists have learned a lot more about the neutrino. Thequantum theory of light. At the temperatures inside the stars with masses smaller than about 1.2 times the mass of our Sun (a category that includes the Sun itself), most of the energy is produced by the reactions we have just described, and this set of reactions is called the proton-proton chain (or sometimes, the p-p chain). Einsteins Postulates The nuclear reactions in the Sun that we have been discussing can be described succinctly through the following nuclear formulas: \[\begin{aligned} ^1 \text{H}+ ~ ^1 \text{H} \rightarrow ~ ^2 \text{H}+ \text{e}^++v \\ ^2 \text{H}+ ~ ^1 \text{H} \rightarrow ~ ^3 \text{He}+ \gamma \\ ~ ^3 \text{He}+ ~ ^3 \text{He} \rightarrow ~ ^4 \text{He}+ ~ ^1 \text{H}+ ~ ^1 \text{H} \end{aligned} \nonumber\]. The high energy of these collisions allows the formation of new, more massive particles than protons such as the Higgs boson that physicists might want to study. How a Refrigerator Led to Einsteins Pleas for Atomic Bomb Research But what does Albert Einstein's famous equation really mean? It states that particles can be in a number of different possible states at once. Two protons can fuse only in regions where the temperature is greater than about 12 million K, and the speed of the protons average around 1000 kilometers per second or more. So you can see that we have solved the puzzle that so worried scientists at the end of the nineteenth century. He expressed his fear that the Nazi regime may be working on an atomic weapons' program, and urged a speeding up of experimental work on nuclear fission. The masses of hydrogen and helium atoms in the units normally used by scientists are \(1.007825u\) and \(4.00268u\), respectively. Uniting the two into a consistent theory of everything is the single biggest challenge in physics today and progress is slow. Knowledge awaits. The letter which Einstein would later call his "one great mistake" urged Roosevelt to speed up uranium research in the US. Focus your imagination on the nucleus of one of your carbon atoms. The simple fact is that we don't yet have a good and generally accepted theory of quantum gravity. The microworld of the quantum and the macroworld of gravity have long resisted a life of wedded bliss and, at least for the moment, they continue to resist. The European Union, the United States, South Korea, Japan, China, Russia, Switzerland, and India are collaborating on the International Thermonuclear Experimental Reactor (ITER), a project to demonstrate the feasibility of controlled fusion (Figure). By the end of this section, you will be able to: As we have seen, energy cannot be created or destroyed, but only converted from one form to another. After all, he didn't succeed, nor did anyone in the decades that followed. Nuclear power stations exploit this idea inside their reactors where subatomic particles, called neutrons, are fired at the nuclei of uranium atoms, which causes the uranium to split into smaller atoms. What has changed is the destructiveness of war.". WebNuclear Power and Views of Albert Einstein essays and term papers available at echeat.com, the largest free essay community. At that point, you're beginning to probe the empty space inside atoms, in which electrons swirl around a small and dense nucleus. proposes to use the International Space Station. To understand the process that actually occurs in the Sun, we need to explore the structure of the atom a bit further. This means that there is an object here, but not there. He wrote in 1945: "To give any estimate when atomic energy can be applied to constructive purposes is impossible. This slight deficit in mass is only a small fraction of the mass of one proton. { "16.01:_Sources_of_Sunshine-_Thermal_and_Gravitational_Energy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16.02:_Mass_Energy_and_the_Theory_of_Relativity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16.03:_The_Solar_Interior_-_Theory" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16.04:_The_Solar_Interior_-_Observations" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16.E:_The_Sun-_A_Nuclear_Powerhouse_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, { "00:_Front_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "01:_Science_and_the_Universe_-_A_Brief_Tour" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "02:_Observing_the_Sky_-_The_Birth_of_Astronomy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "03:_Orbits_and_Gravity" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "04:_Earth_Moon_and_Sky" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "05:_Radiation_and_Spectra" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "06:_Astronomical_Instruments" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "07:_Other_Worlds_-_An_Introduction_to_the_Solar_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "08:_Earth_as_a_Planet" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "09:_Cratered_Worlds" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "10:_Earthlike_Planets_-_Venus_and_Mars" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "11:_The_Giant_Planets" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "12:_Rings_Moons_and_Pluto" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "13:_Comets_and_Asteroids_-_Debris_of_the_Solar_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "14:_Cosmic_Samples_and_the_Origin_of_the_Solar_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "15:_The_Sun-_A_Garden-Variety_Star" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "16:_The_Sun-_A_Nuclear_Powerhouse" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "17:_Analyzing_Starlight" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "18:_The_Stars_-_A_Celestial_Census" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "19:_Celestial_Distances" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "20:_Between_the_Stars_-_Gas_and_Dust_in_Space" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "21:_The_Birth_of_Stars_and_the_Discovery_of_Planets_outside_the_Solar_System" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "22:_Stars_from_Adolescence_to_Old_Age" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "23:_The_Death_of_Stars" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "24:_Black_Holes_and_Curved_Spacetime" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "25:_The_Milky_Way_Galaxy" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "26:_Galaxies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "27:_Active_Galaxies_Quasars_and_Supermassive_Black_Holes" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "28:_The_Evolution_and_Distribution_of_Galaxies" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "29:_The_Big_Bang" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "30:_Life_in_the_Universe" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "31:_Appendices" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()", "zz:_Back_Matter" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass228_0.b__1]()" }, 16.2: Mass, Energy, and the Theory of Relativity, [ "article:topic", "authorname:openstax", "neutrino", "positron", "fission", "proton-proton chain", "fusion", "license:ccby", "showtoc:no", "program:openstax", "licenseversion:40", "source@https://openstax.org/details/books/astronomy" ], https://phys.libretexts.org/@app/auth/3/login?returnto=https%3A%2F%2Fphys.libretexts.org%2FBookshelves%2FAstronomy__Cosmology%2FAstronomy_1e_(OpenStax)%2F16%253A_The_Sun-_A_Nuclear_Powerhouse%2F16.02%253A_Mass_Energy_and_the_Theory_of_Relativity, \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}}}\) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash{#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\), 16.1: Sources of Sunshine- Thermal and Gravitational Energy, Nuclear Attraction versus Electrical Repulsion, source@https://openstax.org/details/books/astronomy, Explain how matter can be converted into energy, Describe the particles that make up atoms, Understand the nuclear forces that hold atoms together, Trace the nuclear reactions in the solar interior. The Manhattan Project large-scale, coordinated work on atomic weapons did not begin until late 1941, and Einstein was not involved in it. His accomplishments in the field of theoretical physics were stressed; he was "unfathomably profound the genius among geniuses. Protons, neutrons, and electrons are by no means all the particles that exist. The goal of ITER is to build the first fusion device capable of producing 500 million watts of fusion energy for up to 1000 seconds. Alas, like many legends, this one is not true. The strong nuclear force is an attractive force, stronger than the electrical force, and it keeps the particles of the nucleus tightly bound together. The answer turns out to be heattremendous heatwhich speeds the protons up enough to overcome the electrical forces that try to keep protons apart. WebNOVAEinstein's Big Idea. But while the outcome is difficult to predict, Einsteins influence has been and remains pivotal in this quest. To get to helium-4 in the Sun, helium-3 must combine with another helium-3 in the third step of fusion (illustrated in Figure \(\PageIndex{6}\)). Despite the tiny discrepancy in mass between the uranium atom and its products, the amount of energy released is big and the reason why is obvious when you look at the c term in the equation the speed of light is a huge number by itself and its square is therefore enormous. Strangers stopped him on the street, and people all over the world asked him for endorsements, advice, and assistance. For example, he figured out that light is made upof many little particles called photons. E=mc2: Einstein's equation that gave birth to the atom bomb Quantum Theory Thus, if 1 kilogram of hydrogen is converted into helium, then the mass of the helium is only 0.9929 kilogram, and 0.0071 kilogram of material is converted into energy. Einstein was able to show that mass and energy were related, through the famous formula E=mc2. To unify the description of matter and radiation quanta with gravitation it became natural to contemplate gravitational quanta that carry the force of gravitation. Legend has it that he did not do well in school (even in arithmetic), and thousands of students have since attempted to justify a bad grade by referring to this story. Measurements show that the binding energy is greatest for atoms with a mass near that of the iron nucleus (with a combined number of protons and neutrons equal to 56) and less for both the lighter and the heavier nuclei. First Postulate of Special Relativity The laws of physics are the same and can be stated in their simplest form in all inertial frames of reference. The best-known theory that can describe gravity in the microworld is called superstring theory. He is author of several science books for the public, including his most recent one, The Large Hadron Collider: The Extraordinary Story of the Higgs Boson and Other Stuff That Will Blow Your Mind (Johns Hopkins University Press, 2014). The gamma ray collides with particles of matter and transfers its energy to one of them. Einstein's Copyright 2015SPACE.com, a Purch company. In Einstein's new world, mass became a way to measure the total energy present in an object, even when it was not being heated, moved or irradiated or whatever else. With Einsteins \(E = mc^2\) equation, we can calculate that the amount of energy radiated by the Sun could be produced by the complete conversion of about 4 million tons of matter into energy inside the Sun each second. Fission also sometimes occurs spontaneously in some unstable nuclei through the process of natural radioactivity. WebEinstein incorporated these ideas into his first postulate of special relativity. Here's a full transcript of what Einstein sent Roosevelt: Even at these high temperatures, it is exceedingly difficult to force two protons to combine. Atomic Theory Because the speed of light squared (\(c^2\)) is a very large quantity, the conversion of even a small amount of mass results in a very large amount of energy. All rights reserved. The final meaning is the most profound. WebAlbert Einstein was a German-born theoretical physicist, best known for his Specialand General Theory of Relativityand the concept of mass-energy equivalenceexpressed by the famous equation, E = mc2. He felt that such spooky action at a distance was proof for the incompleteness of the theory, although experimental evidence since points to the contrary. Is nuclear power the answer to climate change? The explosion of science and technology, Isaacson argued, "helped secure the triumph of freedom by unleashing the power of free minds and free markets." In May 1946, The New York Times reported that Albert Einstein had sent a telegram appeal to several hundred prominent Americans, asking for contributions to a The elusive neutrino was not detected until 1956. In May 1946, he became chair of the newly-formed Emergency Committee of Atomic Scientists, which was primarily concerned with education on the dangers of atomic weapons. So we must look to fusion first to explain the energy of the Sun and the stars (Figure \(\PageIndex{3}\)). But knowing all that still does not tell us how mass can be converted into energy. Note that two energetic protons are left over from this step; each of them comes out of the reaction ready to collide with other protons and to start step 1 in the chain of reactions all over again. There is little documentation on the philosophy of Leucippus; however, it was Democritus, who elaborated extensive works on his theories on the atomic structure of the physical world, of the You know about water molecules. Thus, at the very core, the mathematics of the two theories (e.g. WebChallenging Einstein, physicist Niels Bohr championed Quantum Theory. So, the sunlight given off by the Sun today had its origin as a gamma ray produced by nuclear reactions deep in the Suns core. Einstein suggested that this could be understood if the energy in the light wave wasnt continuously distributed as a wave but rather as a shower of individual light bullets (photons also known as light quanta), each with an energy proportional to the colour (frequency) of the light. That missing matter has been converted to energy and you can calculate how much using Einstein's equation. While it is tempting to describe the history of this attempt, the effort is of interest primarily to historians. WebEinstein essentially did the theoretical aspect of this method for relativity. The mathematics that describes this situation is differential equations. ", "I do not consider myself the father of the release of atomic energy. Can the theories merge? Like all good equations, though, its simplicity is a rabbit-hole into something profound about nature: energy and mass are not just mathematically related, they are different ways to measure the same thing. If only the electrical force were acting, the protons in this and every carbon atom would find each other very repulsive and fly apart. With time many laws become morphed into new ones as a result of experimental evidence or changing conceptual prejudices. www.pbs.org/nova/einstein. This is the reason that a heated gas emits light at specific wavelengths: the electrons orbit at specific energies, with no orbits between the prescribed few. At the end of the war, Einstein spoke out against the nuclear strikes on Japan, arguing that they were unjustified and motivated by USSoviet politicking. Such a nucleus is helium because an element is defined by its number of protons; any nucleus with two protons is called helium. In the same way, if particles come together under the strong nuclear force and unite to form an atomic nucleus, some of the nuclear energy is released. What did Einstein have to say about the peaceful uses of atomic energy? No wonder Scotty, the chief engineer in the original TV show, always looked worried! With two deceptively simple postulates and a careful consideration of how measurements are made, he produced the theory of special relativity. But that time will be far in the future. A widespread but naive way of dealing with the ambivalence problem in nuclear physics is, for example, to claim that the use of nuclear physics knowledge for weapons development is evil, but its use for energy production is good. The water near your hand is similar to the water a foot away. Here, the superscripts indicate the total number of neutrons plus protons in the nucleus, \(\text{e}^+\) is the positron, \(v\) is the neutrino, and \(\gamma\) indicates that gamma rays are emitted. That would be pretty difficult to believe; yet, the universe actually works somewhat like that. Nuclear energy The length of time that photons require to reach the surface depends on how far a photon on average travels between collisions, and the travel time depends on what model of the complicated solar interior we accept. We take a look at seven ways Einstein changed the world. The date for the start of operations is yet to be determined.