Quantum Non-Locality and Relativity_ Metaphysical Intimations of Modern Physics

John Conway and Simon Kochen produced the so-called “Free Will Theorem,” whose title alone is enough to raise eyebrows

For example, it has been repeated ad nauseam that Einstein’s main objection to quantum theory was its lack of determinism: Einstein could not abide a God who plays dice

Theories must be Lorentz invariant

For those interested in the fundamental structure of the physical world, the experimental verification of violations of Bell’s inequality constitutes the most significant event of the past half-century

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The quantum connection is faster than light (Instantaneous)

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The revolution has come in two stages, both initiated by Einstein: the Special and General Theories of Relativity. The Special Theory confers upon light, or rather upon the speed of light in a vacuum, a unique role in the space-time structure. It is often said that this speed constitutes an absolute physical limit which cannot be broached. If so, then no relativistic theory can permit instantaneous effects or causal processes. We must therefore regard with grave suspicion anything thought to outpace light. The quantum connection appears to violate this fundamental law

When we locate an event in the world we need to specify four coordinates: three to give the location and one to give the time

Newton’s first Law of Motion reads: Every body continues in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed on it

A body subject to a force will occupy a curved trajectory, and Newton’s second Law states exactly how the path will curve. Acceleration of a body is nothing more than the curvature of its trajectory through space-time

Henceforth space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality

We can now understand one of the most famous relativistic effects: time dilation. A clock is judged to run slower in a frame of reference in which it is moving than the clocks at rest in that frame. As with the Lorentz-Fitzgerald contraction, the most puzzling aspect of the phenomenon is its symmetry: each of the two relatively moving clocks (in its frame) judges the other to be running slow

A test of how well one has internalized the spirit of Relativity is how one is tempted to answer the question: what would it be like to travel at 99.99 percent the speed of light? A bad answer: due to the Lorentz-Fitzgerald contraction and to time dilation, one would feel squashed flat as a pancake and see time passing very slowly. A marginally better answer: one would indeed be squashed flat as a pancake and one’s clocks would be running slowly, but this would not be noticeable. For one’s meter sticks would have shrunk proportionally, and so

A test of how well one has internalized the spirit of Relativity is how one is tempted to answer the question: what would it be like to travel at 99.99 percent the speed of light? A bad answer: due to the Lorentz-Fitzgerald contraction and to time dilation, one would feel squashed flat as a pancake and see time passing very slowly. A marginally better answer: one would indeed be squashed flat as a pancake and one’s clocks would be running slowly, but this would not be noticeable

Given that only finite amounts of energy are available, it would follow that no particle which travels below the speed of light can ever be accelerated to, or beyond, that speed. So the speed of light does serve as a limit on the velocities of particles which start out traveling at sublight speeds

1 1 Finger Exercise: Superluminal Matter Transport 63 + = ⎛ ⎜ 1 − V ⎞ − 1 1 V 2 2 ⎟ = ⎛ ⎜ (1 − V 2 ) 2 ⎞ − 2 = V 2 1 V 2 ⎠ ⎝ (1 V 2 ) 2 ⎟ − ⎝ + + ⎠ 1 1 ⎛ ⎜ 1 − 2V 2 + V 4 ⎞ − 2 2 − 2 ⎝ 2 4 ⎟ = ⎛ 1 4V 1 2V V ⎠ ⎜ − ⎞ = + + ⎝ 1 + 2V 2 + V 4 ⎟ ⎠ 1 − (1 2 2 − W ) . Since we have been using natural units, our final result is that if the rest mass of a particle is m0, then the mass attributed to it in a frame of reference in which it is moving at velocity v is m 0 (1 − v 2 /c 2 )− 12 : the mass scales by the same factor γ which appears in the Lorentz transformation. In a given frame, then, as the velocity of a particle increases so does its mass.Furthermore, as the velocity approaches the speed of light, the mass approaches infinity, and hence it requires unbounded amounts of energy to get the particle to go faster. Given that only finite amounts of energy are available, it would follow that no particle which travels below the speed of light can ever be accelerated to, or beyond, that speed. So the speed of light does serve as a limit on the velocities of particles which start out traveling at sublight speeds

In a given frame, then, as the velocity of a particle increases so does its mass.Furthermore, as the velocity approaches the speed of light, the mass approaches infinity, and hence it requires unbounded amounts of energy to get the particle to go faster. Given that only finite amounts of energy are available, it would follow that no particle which travels below the speed of light can ever be accelerated to, or beyond, that speed. So the speed of light does serve as a limit on the velocities of particles which start out traveling at sublight speeds.

The Lorentz transformations and the relativistic mass increase do not per se rule out superluminal particles (tachyons), but only prohibit the acceleration of particles through the light barrier. Tachyons must be born traveling faster than light and (as we will see) cannot be slowed to sublight speeds. But how are we to determine the properties of tachyons?

The first is that backward causation, like the motion of particles backward in time, may introduce insurmountable problems into our physical theory. The other is that the physical structure may, at base, no longer be Lorentz invariant. If there is some unique frame of reference in which causes always precede effects then that frame has a claim to preferred status. If Nature transacts her business in one coordinate system rather than any other, the Principle of Relativity is more illusion than insight

As Bell notes, “to answer this we need at least a schematic theory of what we can do, a fragment of a theory of human beings” (1987, p. 60

The case of wave collapse is more subtle. It is most easily illustrated by considering a special case, such as our two correlated photons. When the pair is created, quantum theory describes it using a so-called entangled state

which displays perfect correlation of results on the two wings when the polarization is measured in the same direction

we proved a special case of Bell’s theorem for an experimental arrangement which displays perfect correlation of results on the two wings when the polarization is measured in the same direction

The principle of local causality states that all of the causes of an event must lie in its past light cone. In a locally causal world, the events in region 1 cannot directly influence the events in region 2 or vice versa

What locality does exclude, however, is the possibility that the preparation of either measuring device can exert a causal influence on the other subsystem so as to affect the probabilities for the possible outcomes of measurements performed on that other subsystem. Since these two events, the preparation of one measuring device in a given state and the measurement executed by the other measuring device, can be space-like related, locality is a requirement of relativity theory

Locality” in Howard’s usage requires that the physical state of a system “is unaffected by events in regions of the universe so removed from the given system that no signal could connect them

it is a limit on the velocity of energy transmission, of signal speed, of causal connection and of information transmission

In any orthodox theory the wavefunction is complete and hence must collapse, so we must consider whether collapses could be generated in a relativistically invariant way.

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In Euclidean geometry all triangles have interior angles equal to two right angles; straight lines meet at most once; and every direction in space determines a collection of parallel lines which never meet, keeping ever a constant distance from one another