Note carefully that a supporter of position 1 (above) could say that there is a nonsequitur in Maudlin’s argument: from the fact that no local explanation is available, it doesnot follow that some other sort of explanation is possible. It might well be that there is noexplanation at all; in other words, that the Bell-Inequality-violating correlations of QM aresimply basic, raw data that are the starting points for any full development of physics, notsomething that could be explained by any deeper physical theory. (This has been proposed,for instance, by Fine [21] and Pitowsky [7].)

Tim Maudlin puts it bluntly:Bell concluded that violations of the inequality demonstrate that the worldis not locally causal, i.e., that these phenomena cannot be reproduced byany theory which postulates only locally defined physical states whichcannot influence states at space-like separation. . . Philosophers of physicshave been wont to question this conclusion. . . Bell was, however, quitecorrect in his analysis. Statistics such as those displayed by the photons [inan EPR scenario] cannot be reliably reproduced by any system in whichthe response of each particle is unaffected by the nature of themeasurement carried out on its distant twin. The photons remain “incommunication” no matter how great the spatial separation between them.Instead of trying to deny these non-local (i.e., superluminal) influences, weshould begin to study the role such influences must play in generating thephenomena. [20, p. 405]

However, Mulder is still puzzled, because he is swayed by Tim Maudlin’s verypersuasive arguments that the violation of the Bell Inequalities in experiments such as thiscan only be accounted for by the assumption that there is some sort of superluminalcausation, in apparent violation of the theory of relativity. [9]

Today, we use to describe this movement of the sun (and mutatis mutandis of the moon and the planets) as a retrograde movement, from west to east, which is a counter-movement to the daily rotation from east to west. In terms of Anaximander’s ancient astronomy it is more appropriate and less anachronistic to describe it as a slower movement of the sun wheel from east to west. The result is that we see different stars in different seasons, until the sun, at the end of a year, reaches its old position between the stars.

The first is that the speed of the rotation of the sun wheel is not the same as that of the stars. We can see this phenomenon by observing how the sun lags behind by approximately one degree per day. The second difference is that the sun wheel as a whole changes its position in the heaven. In summer it moves towards the north along the axis of the heaven and we see a large part of it above the horizon, whereas in winter we only observe a small part of the sun wheel, as it moves towards the south. This movement of the sun wheel accounts for the seasons. The same holds mutatis mutandis for the moon.

The only movement of these star wheels is a rotation around the earth from east to west, always at the same speed, and always at the same place relative to one another in the heaven. The sun wheel shows the same rotation from east to west as the stars, but there are two differences

Trying to find some more general explanation of the Bohr atom, de Broglie proposed

Planck noted that both these phenomena

Schrödinger took the absurd implications of this thought experiment (a cat simultaneously dead and alive) as an argument against the Copenhagen interpretation. However, this interpretation remains the most commonly taught view of quantum mechanics.

Third, if a matter wave is given by the wave function Ψ(x,t)Ψ(x,t)Ψ(x,t)<math display="inline"><semantics><mrow><mrow><mtext>Ψ</mtext><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mtext>Ψ</mtext><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math>, where exactly is the particle? Two answers exist: (1) when the observer is not looking (or the particle is not being otherwise detected), the particle is everywhere (x=−∞,+∞)(x=−∞,+∞)(x=−∞,+∞)<math display="inline"><semantics><mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>=</mo><mtext>−</mtext><mi>∞</mi><mo>,</mo><mtext>+</mtext><mi>∞</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>=</mo><mtext>−</mtext><mi>∞</mi><mo>,</mo><mtext>+</mtext><mi>∞</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math>; and (2) when the observer is looking (the particle is being detected), the particle “jumps into” a particular position state (x,x+dx)(x,x+dx)(x,x+dx)<math display="inline"><semantics><mrow><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>+</mo><mi>d</mi><mi>x</mi><mo stretchy="false">)</mo></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>+</mo><mi>d</mi><mi>x</mi><mo stretchy="false">)</mo></mrow></annotation-xml></semantics></math> with a probability given by P(x,x+dx)=|Ψ(x,t)|2dxP(x,x+dx)=|Ψ(x,t)|2dxP(x,x+dx)=|Ψ(x,t)|2dx<math display="inline"><semantics><mrow><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>+</mo><mi>d</mi><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo>|</mo><mtext>Ψ</mtext><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mo>|</mo><mn>2</mn></msup><mi>d</mi><mi>x</mi></mrow></mrow><annotation-xml encoding="MathML-Content"><mrow><mi>P</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>x</mi><mo>+</mo><mi>d</mi><mi>x</mi><mo stretchy="false">)</mo><mo>=</mo><mo>|</mo><mtext>Ψ</mtext><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><mi>t</mi><mo stretchy="false">)</mo><msup><mo>|</mo><mn>2</mn></msup><mi>d</mi><mi>x</mi></mrow></annotation-xml></semantics></math> —a process called state reduction or wave function collapse. This answer is called the Copenhagen interpretation of the wave function, or of quantum mechanics.

Today, using "type 1 supernovae" whose brightness also can be calibrated precisely (but are much brighter than Cepheid stars) we can extend the scale of the observed expansion and say pretty confidently, that all stars started expanding from a small region, some 13.7 billion years ago. THAT WAS THE BIG BANG.     It was not an explosion into empty space, but space itself began expanding (both it and time started at the Big Bang). Galaxies always filled all the space available, it's just that this space itself has been steadily growing. You would think that the expansion would slow down, because stars and galaxies attract each other, and overcoming the attraction requires energy. To keep the expansion going at a fixed rate, something has to pump energy into the universe, or else we might see the expansion slow down, maybe even reverse.     The latest observations suggest that indeed, something IS adding energy all the time--"dark energy" is a popular name--because the expansion, far from slowing down, seems to have gradually speeded up over those 13.7 billion years. Stay tuned--we still don't understand everything.

232.   At what distance does Earth start looking spherical? Dr Stern: How high must an astronaut be to view the Earth as a sphere?? Reply     It's up to the viewer to decide! If you are about 2500 km high, the Earth subtends about 90°, so you can see all of it in your field of view, and I guess it seems spherical.     At 1000 km, your field of view is about 120°, you can still encompass it all by waggling your head. Still a sphere?     At the space shuttle altitude, say 300 km, you can't see the whole Earth with one look. But the horizon seems curved, not straight. Does that define a sphere?     Finally, on the bridge of a ship, the horizon seems flat, but you know ships disappear behind it. Approaching a tall mountain, you may see its top first, the rest only later. Is that enough for you? In short, you are asking about perception, not science. In perception, everyone formulates personal rules.

You wrote "this is a very simple question." Questions may be simple, but their answers may easily turn out complicated!

Let me stop here. You may ask someone more closely familiar with general relativity for a clearer view, but I am not sure it can be done without math. The late John Wheeler wrote "Spacetime Physics" which gives the nitty-gritty, but I'm not sure you are ready for it.

I am largely ignorant of general relativity, and therefore some of the things below may be wrong

As the velocity of light was approached, however, inertia (i.e. mass) increased, making it harder and harder to accelerate any matter and setting that velocity as an absolute limit, which no material object could exceed

uch a demonstration was also made on the surface of the Moon by David Scott, one of the Apollo astronauts. Not only has the Moon no atmosphere, but its gravity is several times weaker, making the fall slower and easier to observe. In front of a TV camera, the astronaut simultaneously let go of his geology hammer and a feather, and his audience on Earth, watching their TV screens, observed the two falling together. According to one story Scott first tried his experiment out of camera view, just to make sure it worked. It didn't!   Static electricity had caused the feather to cling to the glove of the space suit. While he was still trying to work that out, Scott was called to face the camera, and there the demonstration worked perfectly. (Most likely it's just a modern legend; but if not, it sure deserves to be remembered!)

la gravedad se "amortigua" por el factor sen q

Una demostración similar fue hecha también en la superficie de la Luna por uno de los astronautas del Apolo. No solo la Luna no tiene atmósfera, sino que su gravedad es varias veces más débil, haciendo que la caída sea más lenta y más fácil de observar. El astronauta dejó caer la moneda y la pluma delante de una cámara de TV y su audiencia en la Tierra que estaban viendo la TV, observó a las dos cayendo juntas.  Aunque, como anécdota, el astronauta probó primero su experimento fuera de la visión de la cámara, para estar seguro de que funcionaba.

na demostración científica popular durante siglos ha sido la de una moneda y una pluma cayendo simultáneamente en el interior de un tubo de cristal, al cual se le ha hecho el vacío: siempre se les ve a las dos caer con la misma velocidad.

en la madrugada del 24 de octubre de 1601. Tycho  Brahe moría después de una larga agonía que se prolongó durante más de dos meses tras asistir a un banquete ofrecido por el rey Rodolfo II ,probablemente de un ataque a la vesícula o una infección de orina después de beber demasiada cerveza que agravó una dolencia que ya padecía . En sus últimas horas no hacía sino repetir a gritos"Que no haya vivido en vano" y pidió a Kepler que utilizara todas las medidas que él había realizado para demostrar su teoría del Universo, no la de Copérnico

Esta fotografía fue tomada en noviembre del año 2010 cuando fue abierta la tumba de Tycho Brahe con el objetivo de determinar las causas de su muerte ya que aunque en un primer momento se había atribuido su muerte  a un problema de su sistema urinario, cuando el cuerpo fue exhumado en el año 1901 se detectaron altos niveles de mercurio en su bigote y comenzó a especularse sobre la posibilidad  de que hubiera sido asesinado , según aventuran algunos historiadores por orden del rey danés Cristián IV que ya le había obligado a marcharse de Dinamarca. Pero Tycho también era farmacéutico y el mercurio era un elemento principal en casi todos los elixires y remedios de la época  , lo que le podía haber envenenado

blog (El mentidero de Mielost) donde está publicada la biografía detallada de los tres personajes que estamos estudiando: Tycho Brahe, Keppler y Galileo Galilei.

la figura de Brahe, es como poco curiosa..

Andreas Osiander (1498-1552). Hablamos de él hace un par de clases. Se trata de un teólogo protestante y editor literario y fue quien redactó y publicó, sin el permiso de Copérnico, el prólogo de su a posteriori revolucionaria obra “De revolutionibus Orbium Coelestium”.

Copérnico (» De revolutionibus Orbium Coelestium») no tuvo muy buena acogida en las principales universidades de Europa, excepto por la Universidad de Salamanca, en la cual a partir de 1561 figura como lectura opcional y desde 1594 como obligatoria.

Es cierto que Plutón a veces está más cerca del Sol que Neptuno, pero la inclinación de sus órbitas hace que en realidad nunca pasen por el mismo punto. Ademas, por cada 3 vueltas que da Neptuno al Sol, Plutón completa 2. A este fenómeno se le llama resonancia 3:2. Esto hace que cada 494 años vuelvan a estar en la posición original,

acabó interpretándose por los astrónomos en el sentido de que eso (predecir correctamente las observaciones) es lo único que hay que pedirle a una teoría, no que sea una descripción de la realidad

La expresión se remonta a Platón. Cuando encargó a Eudoxo la tarea de explicar los movimientos de los astros usando solo movimientos circulares y uniformes, le pidió un sistema que «salvara los fenómenos», queriendo decir simplemente que «se ajustara a los hechos observados»

Recientemente se cree haber medido velocidades superiores a «c» (de la luz) para ciertas condiciones.

El mundo existe independientemente de nosotros como conocedores y es como es independientemente de nuestro conocimiento teórico sobre él.

Einstein knew, of course, that the well-known phenomena of diffraction and interference can be explained only on the basis of the wave picture. He was not able to dispute the complete contradiction between this wave picture and the idea of the light quanta; nor did he even attempt to remove the inconsistency of this interpretation. He simply took the contradiction as something which would probably be understood only much later.

the presence of Planck's quantum of action - as his constant is called among the physicists - in several phenomena, which had nothing immediately to do with heat radiation

The other problem was the specific heat of solid bodies. The traditional theory led to values for the specific heat which fitted the observations at higher temperatures but disagreed with them at low ones. Again Einstein was able to show that one could understand this behaviour by applying the quantum hypothesis to the elastic vibrations of the atoms in the solid body.

his time it was the young Albert Einstein, a revolutionary genius among the physicists, who was not afraid to go further away from the old concepts. There were two problems in which he could make use of the new ideas. One was the so-called photoelectric effect, the emission of electrons from metals under the influence of light. The experiments, especially those of Lenard, had shown that the energy of the emitted electrons did not depend on the intensity of the light, but only on its colour or, more precisely, on its frequency. This could not be understood on the basis of the traditional theory of radiation. Einstein could explain the observations by interpreting Planck's hypothesis as saying that light consists of quanta of energy travelling through space. The energy of one light quantum should, in agreement with Planck's assumptions, be equal to the frequency of the light multiplied by Planck's constant.

Planck, who was conservative in his whole outlook, did not like this consequence at all, but he published his quantum hypothesis in December of 1900.

But in a period of most intensive work during the summer of 1900 he finally convinced himself that there was no way of escaping from this conclusion. It was told by Planck's son that his father spoke to him about his new ideas on a long walk through the Grunewald, the wood in the suburbs of Berlin. On this walk he explained that he felt he had possibly made a discovery of the first rank, comparable perhaps only to the discoveries of Newton

Any piece of matter when it is heated starts to glow, gets red hot and white hot at higher temperatures. The colour does not depend much on the surface of the material, and for a black body it depends solely on the temperature

he tried to turn the problem from radiation to the radiating atom. This turning did not remove any of the difficulties inherent in the problem, but it simplified the interpretation of the empirical facts

It was just at this time, during the summer of 1900, that Curlbaum and Rubens in Berlin had made very accurate new measurements of the spectrum of heat radiation. When Planck heard of these results he tried to represent them by simple mathematical formulas which looked plausible from his research on the general connection between heat and radiation. One day Planck and Rubens met for tea in Planck's home and compared Rubens' latest results with a new formula suggested by Planck. The comparison showed a complete agreement. This was the discovery of Planck's law of heat radiation.

Notice the sequence - possibilities > probabilities > actuality: thewave function gives us the possibilities, for which we can calculateprobabilities. Each experiment gives us one actuality. A verylarge number of identical experiments confirms our probabilisticpredictions. Confirmations are always only statistics,

The most appropriate basis set is one in which the eigenfunction-eigenvalue pairs match up with the natural states of the measure-ment apparatus. In the case of polarizers, one basis is the two statesof horizontal and vertical polarization

All of quantum mechanics rests on the Schrōdinger equation ofmotion that deterministically describes the time evolution of theprobabilistic wave function, plus Dirac’s three basic assumptions,the principle of superposition (of wave functions), the axiom ofmeasurement (of expectation values for observables), and theprojection postulate (the “collapse” of the wave function thatintroduces indeterminism or chance during interactions)

Einstein’s objectively real view that aparticle has a position, a continuous path, and various propertiesthat are conserved as long as the particle suffers no interaction thatcould change any of those properties

But we shall find that assuming an individual quantum systemis actually in one of the possible eigenstates of a system greatlysimplifies understanding two-particle entanglement (chapter 29)

Dirac’s “transformation theory” allows us to “represent” theinitial wave function (before an interaction) in terms of a “basis set”of “eigenfunctions” appropriate for the possible quantum states ofour measuring instruments that will describe the interaction

One cannot picture in detail a photon being partly in each oftwo states; still less can one see how this can be equivalent to itsbeing partly in each of two other different states or wholly in asingle state

It is impossible to predict in which of the two beams thephoton will be found

can

Dirac’s “manner of speaking” has given the false impression that asingle particle can actually be in two states at the same time. This isseriously misleading. Dirac expresses the concern that some wouldbe misled - don’t “give too much meaning to it.”

s Einstein’s “objective reality”sees it, an individual photon is always in a single quantum state!

Dirac suggests that we might speakas if a single photon is partly in each of the two states, that it is“distributed” over the two (horizontal and vertical) states

And he nowintroduces what he calls a “manner of speaking” which is today thesource of much confusion interpreting quantum mechanics

Mystery

These values for theprobabilities lead to the correct classical distribution of energybetween the two components when the number of photons inthe incident beam is large. 4

If one did the experiment a large number of times, onewould find in a fraction cos2α of the total number of timesthat the whole of the energy is in the α-component and in afraction sin2α that the whole of the energy is in the (α + π/2)-component.

He says“This question cannot be answered without the help of anentirely new concept which is quite foreign to classical ideas...The result predicted by quantum mechanics is that sometimesone would find the whole of the energy in one componentand the other times one would find the whole in the othercomponent. One would never find part of the energy in oneand part in the other. Experiment can never reveal a fractionof a photon.” 3

How do photons in the original state change into photonsat the right-angle states

To explain his fundamental principle of superposition, Diracconsiders a photon which is plane-polarized at a certain angle αand then gets resolved into two components at right angles to oneanother.

It is not clear that Bell fully accepts Dirac’swork, as we shall see in chapter 32

Decoherence theorists (chapter 35) simply deny quantumjumps and even the existence of particles!

rather than allow a diagonal photon arrivingat a polarizer to “collapse” into a horizontal or vertical state

enying Dirac’s projectionprobabilities

David Bohm’s “pilot-wave” theory (chapter 30) introduceshidden variables moving at speeds faster than light to restoredeterminism to quantum physics

Manyfield-theoretic physicists believe that individual quantum systemscan be in a superposition (e.g., a particle in two places at the sametime, or going through both slits, a cat “both dead and alive.”)This is the source of much of the “quantum nonsense” in today’spopular science literature

Einstein’s reference to photons passing through an obliquepolarizer is taken straight from chapter 1 of Dirac’s classic 1930text, The Principles of Quantum Mechanics. Dirac uses the passageof a photon through an oblique polarizer to explain his principleof superposition, which he says “forms the fundamental new ideaof quantum mechanics and the basis of the departure from theclassical theory.” 2

This is to remind us that Einstein had long accepted thecontroversial idea that quantum mechanics is a statistical theory,despite the claims of some of his colleagues, notably Born, thatEinstein’s criticisms of quantum mechanics were all intended torestore determinism and eliminate chance and probabilities.

What is happening here quantum mechanically? If A crossedwith B blocks all light, how can adding another polarization filteradd light?

These weights are just the probabilities (actually the complexsquare roots of the probabilities).

t follows I shall explain brie fly and in an elementary way why I considerthe methods of quantum mechanics fundamentally unsatisfactory

herefore inclined to believe that the description of quantum mechanics inthe sense of Ia has to be regarded as an incomplete and indirect description of reality,to be replaced at some later date by a more complete and direct one.

It follows that every statement about S2 which we arriveat as a result of a complete measurement of S1 has to be valid for the system S2, evenif no measurement whatsoever is carried out on S1. This would mean that allstatements which can be deduced from the settlement of ψ2 or ψ2' mustsimultaneously be valid for S2

This is, of course, impossible, if ψ2, ψ2', etc. shouldrepresent different real states of affairs for S2, that is, one comes into conflict with theIb interpretation of the ψ-function

rinciple has been carried to extremes in the field theory by localizing theelementary objects on which it is based and which exist independently of each other,as well as the elementary laws which have been postulated for it, in the infinitely small(four-dimensional) elements of space

an operation, however, can have no direct in fluence on the physical realityin a remote part R2 of space

Einstein cannot accept the fundamental fact of "entangled" systems explained to himby Schrödinger, that they cannot be separated

principle II, i.e. the independent existence of the real stateof affairs existing in two separate parts of space R1 and R2

from the point of view of quantum mechanics alone, this does not presentany difficulty. For, according to the choice of measurement to be carried out on S1, adifferent real situation is created, and the necessity of having to attach two or moredifferent ψ-functions ψ2, ψ2', ... to one and the same system S1 cannot arise.

sulting ψ2 depends on this choice, so that di fferent kinds of (statistical)predictions regarding measurements to be carried out later on S2 are obtained,according to the choice of measurement carried out on S1

This means, from the pointof view of the interpretations of Ib, that according to the choice of completemeasurement of S1 a different real situation is being created in regard to S2, which canbe described variously by ψ2, ψ2', ψ2'', etc

Any "measurement" instantaneously collapses the two-particle wave function ψ12.There is no "later" collapse when measuring the "other" system S2

-functions of the single part-systems S1 and S2 are then unknown tobegin with, that is, they do not exist at all

make the assertion that the interpretation of quantum mechanics(according to Ib) is not consistent with principle II

llowing idea characterizes the relative independence of objects far apart inspace (A and B): external influence on A has no direct influence on B; this is known asthe 'principle of contiguity', which is used consistently only in the field theory. If thisaxiom were to be completely abolished, the idea of the existence of (quasi-) enclosedsystems, and thereby the postulation of laws which can be checked empirically in theaccepted sense, would become impossible

Anessential aspect of this arrangement of things in physics is that they lay claim, at acertain time, to an existence independent of one another, provided these objects 'aresituated in different parts of space'. Unless one makes this kind of assumption aboutthe independence of the existence (the 'being-thus') of objects which are far apart fromone another in space which stems in the first place from everyday thinking - physicalthinking in the familiar sense would not be possible. It is also hard to see any way offormulating and testing the laws of physics unless one makes a clear distinction of thiskind

thesephysical objects that they are thought of as arranged in a space-time continuum

the concepts ofphysics relate to a real outside world, that is, ideas are established relating to thingssuch as bodies, fields, etc., which claim a 'real existence' that is independent of theperceiving subject

we assume (in the sense of interpretation Ib) that the ψ-function completely describes a real state of affairs, and that two (essentially) differentψ-functions describe two different real states of affairs, even if they could lead toidentical results when a complete measurement is made. If the results of themeasurement tally, it is put down to the influence, partly unknown, of the measurementarrangements

According to this point of view, two ψ-functions which differ in more thantrivialities always describe two different real situations

italone does justice in a natural way to the empirical state of affairs expressed inHeisenberg's principle within the framework of quantum mechanics

(b) In reality the particle has neither a definite momentum nor a definite position;the description by ψ-function is in principle a complete description. The sharply-defined position of the particle, obtained by measuring the position, cannot beinterpreted as the position of the particle prior to the measurement. The sharplocalisation which appears as a result of the measurement is brought about onlyas a result of the unavoidable (but not unimportant) operation of measurement.The result of the measurement depends not only on the real particle situationbut also on the nature of the measuring mechanism, which in principle isincompletely known. An analogous situation arises when the momentum or anyother observable relating to the particle is being measured. This is presumablythe interpretation preferred by physicists at present

According to this point of view, the ψ-function represents an incompletedescription of the real state of affairs. This point of view is not the one physicistsaccept

(a) The (free) particle really has a definite position and a definite momentum,even if they cannot both be ascertained by measurement in the same individualcase

Two possible points of view seem to me possible andobvious and we will weigh one against the other

der a free particle described at a certain time by a spatially restricted ψ-function (completely described - in the sense of quantum mechanics). According tothis, the particle possesses neither a sharply defined momentum nor a sharply definedposition. In which sense shall I imagine that this representation describes a real,individual state of affairs?

I imagine that this theory maywell become a part of a subsequent one, in the same way as geometrical optics is nowincorporated in wave optics: the inter-relationships will remain, but the foundation willbe deepened or replaced by a more comprehensive one.