#isuniverse

IRS 4 (Infrared Source 4) is the young star responsible for the activity within the nebula. The ‘wings’ of the nebula, twin lobes of super-hot gas, glow blue in the image and stretch outward from the central star. The expanding nebula is clinched into an hour glass shape by a ring of dust and gas orbiting the star. The sharp resolution in the Hubble image means ripples and ridges in the gas are visible, from the gas’ interaction with the cooler interstellar medium. Studies of the nebula have uncovered several hundred brown dwarfs; at purely infrared wavelengths more than 600 of them appear, surrounding the nebula in a small cluster. Each of these ‘failed’ stars weighs less than a tenth of our Sun, and with such low mass they cannot produce energy through nuclear fusion like our Sun. The Hubble images of this region were taken in February 2011 with the Wide Field Camera 3. The structure in the cooler gas and dust is visible as near-infrared filters were combined with visible narrow-band filters that isolate the hydrogen gas. -TEL https://www.nasa.gov/mission_pages/hubble/science/snow-angel.html Image credit: NASA, ESA, and the Hubble Heritage Team (STScI/AURA)S

Bell proved his theorem by reasoning that if quantum mechanics is governed by unknown hidden variables which are deterministic and local (i.e. they cannot propagate faster than the speed of light) and physically measurable quantities are always well-defined, with measurement simply revealing their values, then the following paragraphs should be true. A measurement of the absolute value of an electron’s spin along any axis always gives the same result as only the sign differs. Therefore if an electron has always well-defined spin, its spin along 3 different axes (which needn’t be at right angles) should be 1 of 8 different possibilities: (+,+,+), (+,-,+), (-,+,-), etc. To set about examining what a local hidden variables theory may predict, we imagine what happens when we entangle two electrons (though note in a local hidden variables theory the interpretation of what it means for a two particles to be entangled is different from conventional QM) so they are guaranteed to have opposite spins along the same axis. We can then measure the spin along one axis of the 1st electron and take a measurement along another axis of the spin of its entangled partner. This will allow us to determine the spin of the first electron along two different axes in its undisturbed state. We might write the results as follows (using an underscore for the axis which we did not measure the spin along): (+,+,_ ), (_,-,+),(-,_ ,-), etc. Now if we take 3 similarly prepared sets of N electrons, each electron being entangled to allow us to measure its spin along two different axes (we use 3 sets as for any given electron we can only determine its spin along 2 axes and we set N as being very large so the spread of spins is the same in all 3 sets), we would expect the following to be true (where N(+,+,_) is the number of electrons whose measurement corresponds to (+,+,_), etc.): N(+,+, _) = N(+,+,-) +N (+,+,+) N(+,_ ,+) = N(+,+,+) + N(+,-,+) N(_,-,+) = N (+,-,+) + N (-,-,+) etc. From which from basic algebra follows: N(+,+,_) – N(+,_,+) + N(_,+,-) = N(+,+,-) + N(-,-,+) Therefore, as N(+,+,-) + N(-,-,+) cannot be less than zero as you can only have a non-negative number of particles: N(+,+,_) – N(+,_,+) + N(_,+,-) ≥ 0 This is a version of what is called Bell’s inequality, it is testable, and will be true for any local hidden variables theory. Whilst Bell’s inequality does hold true for some angles (angles of the 3 different axes along which spin is measured) in quantum mechanics, it is not true for all angles. Therefore quantum mechanics cannot be described by a local hidden variables theory. In 1982 Alain Aspect tested Bell’s inequality and it was found it was violated in nature as quantum mechanics predicts. Bell’s theorem does not completely exclude deterministic hidden variable theories from describing quantum mechanics, for example Bohm’s pilot wave interpretation (which was based on de Broglie’s theory of ‘matter waves’) accurately recreates quantum mechanics and is deterministic. However as any hidden variables theory must be non-local, it has the undesirable property that influences can propagate instantaneously across space, which when special relativity is brought in to play, is a major problem for causality. I hope I haven’t put you off with the math! -John D Quantum Mechanics, Alastair Rae 2002 John Bell in Belfast: Early Years and Education, Andrew Whitaker Picture: Domain Field - Anthony Gormley https://www.antonygormley.com/sculpture/chronology