- 2838 - RELATIVITY - as scientists explain it? The Universe is hard to explain. Here are our best minds trying with their favorite theories. God provides a simpler explanation. It is just the way he made things. Yet, we keep trying to understand how he did it. Here are the scientists that have they best ideas to date, 2020. We keep trying to understand how we got here? It ain’t easy?
--------------------------- 2838 - RELATIVITY - as scientists explain it?
- A fundamental question in physics is “what is time“? Albert Einstein believed it was a “dimension” like space is a 3- dimension. You could traverse through it like a sailor on a sea, changing course by accelerating or decelerating, or by manipulating gravity using matter to alter the curvature of space and time.
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- Virtually every paper on Einstein’s theory of gravity, General Relativity, begins with something like assume a four dimension manifold “M” and a metric “g“. Implicit in the four dimensions of the manifold is that time is somewhere in there. The metric just describes distances on that manifold.
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- The “manifold’ is like the sea and the metric is like the compass and the scale. Your place in space and time is some coordinate on this space-time map.
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- That is “time” to Einstein. In almost all physical law time is reversible. That means that the law works the same backwards and forwards in time. All trajectories are reversible.
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- But, there is an exception: the 2nd law of thermodynamics. The total “entropy” of a closed system cannot decrease over time. The universe is a ‘closed system“. If you reversed time, the entropy would decrease, so the law is not time reversible.
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- This difference is called the “arrow of time” because it points time in one direction. It does not contradict Einstein. It just adds a qualifier that, on the river of time, the current flows one way and you cannot ever go fast enough to get back upstream. What is that speed? Faster than light.
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- It seems like Einstein’s view of time is safe. Another view of time that is more fundamental is that time isn’t like another dimension. It isn’t like traveling down a river. It is, in fact, more like standing in one spot at the bottom of a waterfall. Time falls on you and flows away never to be seen again. Things change with time.
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- But, you never moved. In order to make this idea work with Einstein’s General Relativity we need to make sense out of this four dimensional manifold, “M“. The way to do that is called a “foliation” which means that we slice the manifold up like a loaf of bread. Each slice is a moment in time.
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- One question is whether this foliation is “local” or “global”. That is, does the universe as a whole have a single foliation, defining the current present moment, or does every observer in the universe have its own foliation?
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- For most of the universe, you could define a “global foliation“, but, if you start to include the interiors of black holes, you run into problems. Time works differently inside a black hole. It doesn’t run into the same future as ours. Time runs into the singularity at the center while our time acts like a spatial dimension. It is fundamentally opposed to our view of time from outside the black hole.
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- Italian theoretical physicist Carlo Rovelli (note 1) takes the point of view of defining time as local but that whether the river of time has a current or not and what that current is matters.
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- It is not just some dimension we can travel in like on some barren desert plain. There is something pushing us along. He proposes that this something are tiny fluctuations in the gravitational field which, taken altogether, create a flow of time. This flow carries us along with it.
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- Still, his view is more like the universe as a vast ocean with many different possible flows and currents, whirlpools and maybe even dead zones where there is no flow. It all depends on the statistical nature of the gravitational field.
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- Rovelli does all this without breaking one of the cardinal features of gravity, that there is no “preferred” direction or dimension. Time isn’t special. It’s just that all the statistical fluctuations in the gravitational field naturally create a flow that feels to us like time, in the same way that a river basin creates a flow, but that basin isn’t special. It is just a feature of the land. It can shift and move. It can be somewhere else. There is no external god telling it where to be or which way to go.
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- Still, Rovelli sticks with the four dimensional picture of the universe. It is a vast ocean, to be sure, with many currents. We can still sail it but we best catch the right winds to take us where we want to go. It does matter if we go south and east versus east then south because the currents and winds will take us one way but not the other.
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- German physicist Detlef Dürr (note 2) takes a more radical approach through Bohmian mechanics. Unlike Rovelli, who starts with classical general relativity to create his theory of time and then adds quantum aspects to it later, Dürr takes an immediate quantum point of view with Bohmian mechanics.
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- David Bohm (note 3) developed his mechanics in the 1950s as an alternative to standard quantum theory. John Bell later expanded it to include particle creation and annihilation, but integrating it with relativity, either special or general, was troublesome. Bohm fundamentally built time into his theory much like Isaac Newton did with his mechanics and Erwin Schroedinger (note 4) did with his.
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- Scientifically, building time into a theory isn’t a problem as long as it makes good predictions, but philosophically it is a step backwards. Einstein’s great achievement was in removing the idea of a preferred direction from space and time. To add that idea back in would mean to have to explain why it is there. “Ockham’s razor” says that a theory should not add unnecessary explanations (note 6).
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- Dürr set out to show that you could remove this problem from Bohm’s theory and, in doing so, show that time could be both universal and the product of matter and forces itself.
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- “Bohmian mechanics” explains quantum theory as the evolution of two things: the quantum wave function that we all know from Schroedinger, and another function called the guiding function, “Q“, which holds the hidden locations of all particles in the system.
Theoretically, this system could be the universe as a whole. There should be no problem with doing that.
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- This ultimately added into quantum mechanics something that Einstein wanted, which was the idea that particles had hidden states that we couldn’t measure. But, for the last 100 years, most physicists have argued that particles do not have hidden states.
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- They have no state at all until measured. Bohm showed that they could provided that all particles could communicate with one another instantaneously (nonlocally) through the “Q function“.
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- The problem with instantaneous communication is that you have to say when this communication occurs. You need the entire system, spread across space, to have a single present moment. If the entire universe is your system, then you need to have a single present moment for the universe. In other words, you need “foliation“.
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- Since the quantum system is evolving from moment to moment across 3D hyper-surfaces, you don’t really need the past or future to be involved except in determining the next step in the evolution. Unlike with Einstein’s theory, you can assume that the past and the future are not even there.
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- The above statement is a lot stronger than Rovelli, who is content to define time as a local flow. While Dürr’s time could be only local, it makes more sense if you can expand it to be global, even inside black holes.
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- Dürr points out that you can recover ““Lorentz symmetry“, the 4-D nature of equations compatible with relativity, by replacing all your equations with Lorentz symmetric ones. You can then say that the present moment is not discoverable by measurement. It is hidden in the quantum uncertainty.
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- Durr rightly points out, however, that this is not enough. Ockham’s razor still comes in. Where does the foliation come from? He suggests, like Rovelli, that it comes from matter itself, specifically, it comes from the “quantum wave function“.
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- He presents the possibility that matter itself may create an arrow of time in Bohmian mechanics. His solution is general to all quantum theories however. The idea is that the wave function of matter on average moves from the past into the future. Rather than that flow being because of time, he suggests it creates time.
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- He shows how you can extract a foliation from the wave function by applying it to some standard “pointing” structures from Quantum Field Theory such as current, spin, and even the stress-energy tensor. Current and spin have magnitude and direction in four dimensional spacetime while stress-energy tensor has magnitude, direction, and orientation.
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- The basic premise here is that all matter flows in time and creates an average direction of time. Dürr attempts to formulate a more general Bohmian dynamics that is relativistic without a foliation. Instead, it has a “timelike” vector field that becomes a foliation under certain assumptions.
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- This “vector field” would be able to include spacetime that is not easily sliced, abandoning the idea that there is a single present moment. Unfortunately, without the foliation, the correspondence between Bohmian dynamics and standard quantum theory breaks down. Thus, Bohmian dynamics appears to require a single present moment or it is just plain wrong.
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- One of the drawbacks in Dürr’s work is that he relies on massive “Fermionic matter” (electrons, quarks, etc.) to define his foliation, ignoring the gravitational field itself, unlike Rovelli. This means that the gravitational field plays a backseat in defining the foliation of itself. It is as if the river basin had nothing to do with the flow of the river, but the river simply chose to move in a particular direction. Both need to be taken into account.
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- Others have tried to incorporate general relativity into Bohmian mechanics with some limited success, defining space time as a set of gravitons which generate a gravitational field, evolving according to the universal wave function like anything else.
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- A number of Bohm-like theories attempt to do away with the time foliation entirely. There are multi-time wave functions that resemble Rovelli’s statistical general relativity, where there is no single present but many, many present moments, one per particle.
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- There are some additional tricks that have a concept of simultaneity that the guiding function needs without a foliation. There is the synchronized trajectories approach where every particle communicates with every other particle according to its own local time. This is foliation-like, but is not necessarily a true foliation. It makes sense because each particle needs to “know” how to move at each point in its trajectory.
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- Entangled particles, you imagine, would move in lockstep. The unfortunate problem with trying to define foliations over the entire universe is what to do with areas of spacetime where local time doesn’t flow in the same direction as others such as inside black hole event horizons.
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- One option would be to exclude these from the universe, but quantum mechanics suggests that the instantaneous communication that occurs between particles must also cross the boundaries with black holes as well.
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- In the case of two “entangled photons“, one that has fallen into a black hole and the other that has escaped. Surely they share a quantum wave function; therefore, how do these particles evolve together when the time they experience is so different? Is it simply according to the proper (local) time of each, like a synchronized trajectory?
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- You still use foliations even across black hole boundaries. One foliation that proves useful in these cases is known as “York” time. You can prove York time to be geometrically unique and it handles singularities like black holes well. Each “tick” of a York time clock is a 3D hypersurface that has constant mean curvature.
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- From the perspective of cosmology in particular and astronomy in general, having some measure of time like York time is extremely valuable. Could it be that York time is more than a geometric convenience? Might it be the present moment we are looking for?
From the perspective of cosmology.
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- For the universe as a whole, something like York time is natural. After all, cosmology is deeply concerned with the evolution of the universe as a whole in a unique time, according to relativity.
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- Bohmian mechanics is uniquely adapted to quantum cosmology because it can support a quantum universe that changes with time, something that standard quantum theory has difficulty with, so dependent is it on the interaction between quantum and “classical” systems.
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- A purely quantum system without Bohm’s modification does nothing. If the entire universe is a quantum system, then it cannot interact with anything outside it unless you subscribe to “many-worlds‘, which has its own set of problems.
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- If you want a single universe, then you have to resolve the problem of what does it mean for a quantum universe to evolve?
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- Bohm gives an answer that it is the interaction between particles and their wave functions from moment to moment. The universe itself decides on a cosmic level what the present moment is.
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- “Presently” is all I have to work with. When the present leaves me, all I have left is the future. Who knows what that will bring? Maybe a better understanding of the present.
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------------------------- Biographies of these great scientists:
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---------------------- (1) Carlo Rovelli was born 3 May 1956. He is an Italian theoretical physicist and writer who has worked in Italy, the United States and since 2000, in France. His work is mainly in the field of quantum gravity, where he is among the founders of the “loop quantum gravity theory‘.
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- He has worked in the history and philosophy of science. His popular science book “Seven Brief Lessons on Physics” has been translated in 41 languages and has sold over a million copies worldwide.
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---------------------- (2) Detlef Dürr studied physics at the University of Münster where he obtained his PhD in 1978. He joined the statistical physics group of Joel Lebowitz in Rutgers. He did his habilitation in mathematics in 1984 in the University in Bochum and changed afterwards to the University of Bielefeld. In the same year he became Heisenberg research fellow which allowed him several research stays abroad. In 1989 he became Fiebiger-professor at the Department of Mathematics at the LMU.
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---------------------- (3) David Bohm was born December 20, 1917, Wilkes-Barre, Pennsylvania. He died Octobeer 27, 1992 in London. He was a British theoretical physicist who developed a causal, nonlocal interpretation of quantum mechanics.
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- Born to an immigrant Jewish family, Bohm defied his father’s wishes that he pursue some practical occupation, such as joining the family’s furniture business, in order to study science.
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- After receiving a bachelor’s degree in 1939, from Pennsylvania State College, Bohm continued graduate research at the California Institute of Technology and then the University of California at Berkeley for a Ph.D in 1943. He worked with physicist
J. Robert Oppenheimer. In 1947 Bohm became an assistant professor at Princeton University.
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- Bohm laid the foundations of modern plasma theory. Bohm’s lectures at Princeton developed into an influential textbook, Quantum Theory (1951), that contained a clear presentation of Danish physicist Niels Bohr’s Copenhagen interpretation of quantum mechanics.
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---------------------- (4) Erwin Schrödinger established the wave mechanics formulation of quantum mechanics, which portrayed electrons as waves, spread out rather than in any given location. Schrödinger showed that his wave mechanics and Werner Heisenberg’s matrix mechanics, although superficially different, were mathematically equivalent.
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- In his later years, Schrödinger became unhappy with quantum mechanics and is famous for the Schrödinger’s cat thought experiment, in which he attempted to show the absurdity of the Copenhagen interpretation of quantum mechanics.
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- Schrödinger’s 1944 book ‘What is Life?”, although not entirely original, had a profound effect on the future of genetics and molecular biology. Schrödinger wrote that the gene was an aperiodic crystal, a code script for life. His book inspired a number of scientists to pursue research in that field.
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---------------------- (5) Albert Einstein was born in 1879 in Ulm, Germany. He was the first child born to Hermann and Pauline Einstein. Though he attended school as a young boy, he also received instruction at home on Judaism and violin. By the age of twelve he had taught himself geometry.
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- At the age of sixteen he failed an exam in order to qualify to train as an electrical engineer. He remained in school and developed a new plan for his future. Einstein decided to study math and physics so he could become a teacher. Einstein thought he would be good at this because he could think mathematically and abstractly while lacking imagination and practicality.
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- In 1896 he renounced his German citizenship. He was not a citizen of any country until 1901 when he became a citizen of Switzerland. In 1900 he graduated as a teacher of math and physics. His teachers did not think very highly of him though so he had difficulty being recommended for a job at a university.
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- In 1901 he took a job as a temporary high school teacher and married Mileva Maritsch. The couple had two sons prior to divorcing. Einstein later married his cousin Elsa Einstein. From 1902 through 1909, Einstein worked in a patent office in Bern, Switzerland. While working in the patent office he published many papers on theoretical physics. He earned a Ph.D. in 1905.
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- In 1905 Einstein wrote a paper on what is now known as the special theory of relativity. This paper contained two hypotheses. The first stated that the laws of physics had to have the same form in any frame of reference. The second hypothesis stated that the speed of light was a constant.
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- Later that year Einstein also showed how mass and energy were equivalent. Following an impressive few years of work, Einstein became a lecturer at the University of Bern. In 1909 he finally got a post at a university when he became a faculty member at the University of Zurich.
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- In 1911 Einstein taught at Carl-Ferdinand University in Prague. The following year he returned to Germany to continue his work. In 1916 Einstein published his general theory of relativity.
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- His theory linked gravitation, acceleration and the four dimensional space-time. With this theory he was able to account for the variations in the orbital motions of the planets. He also predicted that starlight in the vicinity of a massive object such as the Sun could be bent. This was confirmed in 1919 during a solar eclipse. This further increased the adulation with which the press viewed Einstein.
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- He won the Nobel Prize for Physics in 1921 for his work on the photoelectric effect. This work proposed that light be considered as consisting of particles called photons. Einstein further proposed that the energy the photon contains is proportional to the frequency of the radiation.
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---------------------- (6) William of Ockham, 1288-1348, a logician and theologian, is credited with the idea that the simplest of explanations is more likely to be correct than any other. “Ockham's razor” states that "entities should not be multiplied needlessly".
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- It's also called the principle of parsimony. It's the idea that other things being equal, between two theories the simpler one is preferable. Why razor? Because Ockham's razor shaves away unnecessary assumptions.
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--------------------- (7) John Bell's great achievement was that during the 1960s he was able to breathe new and exciting life into the foundations of quantum theory, a topic seemingly exhausted by the outcome of the Bohr-Einstein debate thirty years earlier, and ignored by virtually all those who used quantum theory in the intervening period.
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- Bell was able to show that discussion of such concepts as 'realism', 'determinism' and 'locality' could be sharpened into a rigorous mathematical statement, 'Bell's inequality', which is capable of experimental test. Such tests, steadily increasing in power and precision, have been carried out over the last thirty years.
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- Almost wholly due to Bell's pioneering efforts, the subject of quantum foundations, experimental as well as theoretical and conceptual, has became a focus of major interest for scientists from many countries, and has taught us much of fundamental importance, not just about quantum theory, but about the nature of the physical universe.
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- Ockham's razor has applications in fields as diverse as medicine, religion, crime, and literature. Medical students are told, for example, "When you hear hoof beats, think horses, not zebras."
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- Some guys just know how to keep things simple.
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- September 22, 2020 2838
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