I have the opposite intuition - doesn't a physical structure require a framework of sorts? And one would think mathematical (or computational/algorithmic). — flannel jesus
What does it really mean for the universe to be mathematical though? — Apustimelogist
And yes, people often ignorantly refer to "points" in time. But calculus usually refers to the value of a variable as some input approaches a limit - no infinities, although they're approached, and no "points in time". — tim wood
So, unless you can demonstrate that it is impossible to find a better system than the use of limits, then my activity of pointing to the flaws in this system and suggesting that we find a way to change this system, is very reasonable activity — Metaphysician Undercover
Ontological Status of the Wavefunction: Traditionally, the wavefunction’s
axiomatic foundation led to various interpretations that attribute to it
an ontological status. However, our research radically transforms this
perspective. We show that the wavefunction is no more ontological than
the Gibbs measure in statistical mechanics; it is merely a least-biased
probability measure for predicting outcomes of energy measurements.
*1. What is a Hilbert Space? :
In this blog, I aim to develop a comprehensive understanding of hilbert spaces cutting through the mathematical jargon. — Gnomon
Plus the class I took was explicitly taught in the Copenhagen interpretation, and a lot of the discussions around here try to differentiate between the interpretations and, at least as I learned it, there wasn't really a way to differentiate between the interpretations — Moliere
Quantum mechanics is the governing theory. It's fundamental quality is that a system can be described by a vector in an abstract space, called a Hilbert space. The Hilbert space is the space of all possible measurement outcomes, so it is distinct from 3D space that describes the position of objects. For instance, the Hilbert space can be, and often is, infinite dimensional. A vector in Hilbert space has complex-valued coefficients and must be normalised to unity length. For an infinite dimensional space it must be square integrable.
Physical observables are described by hermitean matrices that act on the Hilbert space vector such that measurement outcomes are real-valued. The vector in Hilbert space evolves according to rotations induced by various interactions described in the Hamiltonian operator (or Lagrangian density). This is called unitary evolution, as the vector is just rotated preserving the normalisation.
Following a measurement, the Hilbert space vector is projected onto the measurement outcome. This evolution is considered non-unitary, as it is not a smooth rotation, but a projection.
So that is the underlying theory of quantum physics.
For quantum mechanics, we consider particles as immutable with various properties. This restricts the possible evolution of the associated Hilbert space. However, for fundamental particle physics, the particles appear to be transmutable. Therefore, the theory required a mechanism to allow for this.
The first transmutable particle was the photon. The quantum theory of the electromagnetic field identified a set of non-hermitian operators that corresponded to the creation and destruction of photons as energy quanta in the electromagnetic field. This was the first field theory. The key to this theory was the mapping of the electromagnetic field to the quantum simple harmonic oscillator in order to identify quantum operators that satisfy the Heisenberg uncertainty principle. These field modes can be used to construct any field configuration using the superposition principle according to the Fourier decomposition of the field. This opened the gates to modern quantum field theories. Other fields were introduced that gave rise to particles as excitations of the field in a way analogous to the role of the photon in the electromagnetic field.
From here is gets complicated as various symmetries need to be satisfied and self-interaction terms need to be dealt with. However, the theory is essentially the same, just with more widgets added to satisfy the properties observed in experiments. The Hilbert space is still there. Unitary evolution is still there. Hermitean operators are still there. The measurement procedure is still there.
With particle physics, one focusses more on the scattering terms in the Hamiltonian (or Lagrangian density). These are generally expanded as a perturbation series with the high order terms truncated. This allows the calculation of scattering cross sections that are applicable to particle physics experiments.
If that was what it was, wouldn't NASA have figured that out? — RogueAI
And then, of course, you have the actual witnesses, the pilots. But what do they know about encounters in the air. :snicker: — ssu
The image isn't the entangled photons. It's an image of a mathematical entity: the wave function. — jgill
No. — T Clark
Researchers at the University of Ottawa, in collaboration with Danilo Zia and Fabio Sciarrino from the Sapienza University of Rome, recently demonstrated a novel technique that allows the visualization of the wave function of two entangled photons
↪T Clark didn't respond to my request for the source of his information/opinion about the intentional use of the YY symbol as input instead of as output of the holographic method. Will you post where & how you determined that is the case? Did you interpret the symbolic image as an error of judgment, or a deliberate hoax? — Gnomon
Here we introduce biphoton digital holography, in analogy to off-axis digital holography, where coincidence imaging of the superposition of an unknown state with a reference state is used to perform quantum state tomography.
Anyone here who served in an armed forces? Just curious. :chin: — jgill
If compulsory military service counts, then yes. — ssu
I contend that duty is perhaps the single strongest motivator for action I can think of, whether it is duty to the tribe, an ideal, a spouse, etc., and should be nurtured wherever it exists to good ends — ToothyMaw
The concept of the aether has long since been discredited and discarded — tim wood
Physicist Robert B. Laughlin wrote:
It is ironic that Einstein's most creative work, the general theory of relativity, should boil down to conceptualizing space as a medium when his original premise [in special relativity] was that no such medium existed [..] The word 'ether' has extremely negative connotations in theoretical physics because of its past association with opposition to relativity. This is unfortunate because, stripped of these connotations, it rather nicely captures the way most physicists actually think about the vacuum. . . . Relativity actually says nothing about the existence or nonexistence of matter pervading the universe, only that any such matter must have relativistic symmetry. [..] It turns out that such matter exists. About the time relativity was becoming accepted, studies of radioactivity began showing that the empty vacuum of space had spectroscopic structure similar to that of ordinary quantum solids and fluids. Subsequent studies with large particle accelerators have now led us to understand that space is more like a piece of window glass than ideal Newtonian emptiness. It is filled with 'stuff' that is normally transparent but can be made visible by hitting it sufficiently hard to knock out a part. The modern concept of the vacuum of space, confirmed every day by experiment, is a relativistic ether. But we do not call it this because it is not accepted (taboo).
What Bohr is saying about measurement is that any properties of reality are, at minimum, a relation between two pairs of non-commutative variable values, one of which, for us, acts as time. So we don’t need to assume space or objects - we only need to recognise one of those values as ‘time’, and one of those pairs as our involvement - our entangled embodied subjectivity. — Possibility
It is highly technical, but it’s really just that the relativity of time is in fact a relativity of all four dimensional variables - their non-commutative ‘properties’ are simply the irreducible quality of dimensionality. What Bohr is saying about measurement is that any properties of reality are, at minimum, a relation between two pairs of non-commutative variable values, one of which, for us, acts as time. So we don’t need to assume space or objects - we only need to recognise one of those values as ‘time’, and one of those pairs as our involvement - our entangled embodied subjectivity. — Possibility
I’m saying that each event (including ourselves and time) is most accurately understood (rather than described) by employing the model of a quantum mechanical system (spacetime), consisting of four qualitative dimensions (irreducible structural relations) of variable values, one of which corresponds to a classical sense of temporal ‘order’. — Possibility
Not only motion, but the idea of any instance of activity, without anything acting is incoherent. — Metaphysician Undercover
It's the otherwise well-tempered folks that would vote for him that is the riddle to be solved. — schopenhauer1
This is a more hair-raising idea and I agree, that's some riddle. — Tom Storm