Yesterday, I do swear
I saw a post that wasn't there
It wasn't there again today
I wish I wish it'd stay away

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

When we construct a building we lay plans, then follow through physically. So those plans underlie a physical project and provide a "framework", which can be destroyed if we wish without endangering the building. Not so in a mathematical universe. Somehow the building reifies the plans and the two can not be separated. Or whatever.

The notion of "points in time" is rarely debated in science and math to the best of my knowledge. Do dimensionless points exist? This is more a philosophical issue than a mathematical one. Does a point on a ruler really exist? It certainly corresponds to a real number, but there are those who question the existence of irrationals. So, what happens to that point? It exists for some but does not for others?

Calculus is fundamental to the major branch of mathematics called analysis, founded on the idea of limits. Ordinarily, it assumes the existence of these points regardless of whether one speaks of rulers or time scales. Real analysis, the underlying structure of calculus, contains the axiom of completeness, which means points exist as viable entities. But some would say temporal points are different.

I thought of the famous debate between Einstein and the popular philosopher, Bergson, a hundred years ago. However, their issues revolved about whether time itself was independent of human experience. I'm not sure instants in time came up. But more recently a non-academic wrote a paper on time and physics in which he argues against any sort of "instant" in time. Some thought him brilliant, but others thought him a conveyor of nonsense. The latter is the more popular among physicists.

The point at infinity in complex analysis is the north pole of the Riemann sphere. No matter where you go in the plane as you move out away from the zero point the projection onto the sphere moves toward its north pole. So, in this sense, there really is a "point at infinity". :cool:

What does it really mean for the universe to be mathematical though? — Apustimelogist

The kart before the horse. What is mathematics, first? I've been a mathematician for over a half century and can not give a clear definition. There are numerous pages on Wikipedia that revolve around this question. How did math arise in human thought? Through language and observations of what we now consider logical - cause and effect - in the physical world?

Is there math without symbols? Well, yes, if one has the patience to express mathematical ideas through common language. What of the visual aspect of the subject? Well, there have been blind mathematicians who have been quite accomplished. I knew one: Larry Baggett, at the University of Colorado. So one could replace symbols with ordinary language, which seems to imply math is a substrata we contemplate by one or the other.

So, when Tegmark speaks of the mathematical universe - a creation whose structure is somehow mathematics - how can that be? Doesn't structure require a framework of sorts? And one would think physical. Maybe a collection of homeomorphic entities, that share a mathematical description, which in turn provides a uniform structure that somehow reifies.

Heady stuff that I predict will be left by the wayside of time. Or not.

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

Don't be so critical. I've used "points in time" frequently in complex dynamical systems. And in complex analysis, a contour in the complex plane, z(t)=x(t)+iy(t), has a value for t=.5, e.g. And you think physicists don't use points? Do you think that limits define points, or points define limits? As for the infinite, there is indeed a "point at infinity" in complex variable theory.

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

This might have made a semblance of sense had you been present when my math genealogical ancestor, Karl Weierstrass, and Cauchy were pulling together the common definition of limit two hundred years ago. You could have presented them with your clearly defined objections to their work and been present for their reactions. Oh, to have been a fly on the wall. :cool:

I believe that to be able to develop technology the beings must have the physical attributes necessary to be able to create and use tools — Sir2u

Like a near fast-as-light spaceship. :roll:

There was never any outright rejection, I just stopped. I think most young people who leave the church are probably like that. As long as there isn't any pressure, they never really need to reject belief. — T Clark

Yes. That's my story, too.

Someone once said the humanoid form is universal. I think it was Orfeo Angelucci. — EnPassant

:roll:

I like the sound of this:

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.

Einstein was once asked where his laboratory was, and he simply held up a pencil. — Gnomon

:cool: Nice.

"this is the idea that mathematical truths are a byproduct of our linguistic conventions". — Gnomon

The interplay is certainly interesting.

*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

That's nicely done. I suppose my point is that QM is all sophisticated mathematics and equally sophisticated experimental processes.

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

:up:

Here's a quick look at ground zero in quantum studies by Mark John Fernee for Quora:

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.

For math, one starts with calculus, then real and complex analysis, then functional analysis for Hilbert spaces, etc.

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

You would think. But anything to take the public focus off our senile president. I used to trust most government agencies, but I withhold judgement now. Those little dots that seemed to run alongside the aircraft are not convincing. Just me.

So, what are they/is it? — RogueAI

Dark splotches on a computer screen that appear to move. Amazing evidence. :roll:

Maybe there is a crises in meaningfulness among the young - and the middle aged. Today's Ann Landers column includes a person who at the age of forty, asks "What will I be when I grow up?" Living at a relative's home, he hasn't been forced to make his way in the world, and doing so, perhaps find meaning.

My best friend, who passed away seven years ago, was a physics major up until the required introductory senior level course in quantum theory. He switched to mathematics and retired a fellow professor. A very bright guy - certainly smarter than me - but math made more sense at the time, easier to understand.

I think dropping a physics major at this crucial point of transition in thinking happens fairly frequently. Some become engineers, a profession using physics that moves along Newtonian lines. Well, maybe not so much electrical engineers.

It's a shame the forum doesn't have quantum physicists who might elucidate better than philosophical minded novices. But this is not a physics forum. Our best is not good enough.

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

But this may be in error. Certainly what they are doing is a mixture of measurements and mathematics.

↪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

Frankly, I don't know what's going on here. But at the beginning of the paper
:

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.

This stuff is way beyond me.

The image isn't the entangled photons. It's an image of a mathematical entity: the wave function.

Anyone here who served in an armed forces? Just curious. :chin: — jgill

If compulsory military service counts, then yes. — ssu

Conscription was the law in the US in the 1950s, and I recall ROTC the first two years being required for all male students at the university at which I enrolled. I continued beyond this thinking I would have a better time of it being a junior officer than enlisted. In fact, my service opened a door into an attractive civilian career had I wished to pursue it.

But this line of thought is not what this thread is about. Sorry.

Apart from the intelligent comments made here there is the fact that on television the creatures appear to be made of clay. Anything to distract from serious issues.

The input to the experiment was the image of the yin/yang symbol — T Clark

Seems to be the case as far as I can determine. Difficult reading.

A science of the undetectable is a curious thing indeed. Metaphysical.

Anyone here who served in an armed forces? Just curious. :chin:

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

As a child who watched B17s fly over the family farm house as WWII wound down, and then as a young man in the 1950s my first thought, now, when reading the introduction, was required military service. Conscription existed into the 1970s in the US, and I never questioned the practice until the years of the Vietnam War, after I had done my stint and resigned my commission as a captain in the USAF. Up to that point I felt the need to fulfill my "duty". Afterwards, not so much.

How many of you served in an armed forces and considered it your "duty"?

The concept of the aether has long since been discredited and discarded — tim wood

The classical notion, yes, but perhaps not quite that simple. From Wikipedia:

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).

So the best analogy I can come up with is that photons are particles which also exhibit wave-like behavior. And particles do not need a medium in which to move. — EricH

:up:

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

This seems a step beyond metaphysics in vagueness and incomprehensibility. Perhaps a link would help. :chin:

But you have a moral obligation by virtue of all the good you could do - and no one gives a damn if playing the game makes you uncomfortable — ToothyMaw

Sorry, but I am just too old and infirm. But thanks for asking. :cool:

. . . and the police will pull you over if you're speeding. — frank

Perhaps that's a good thing?

What does a typical hero look like in the US? Dirty Harry,. . . — Benkei

More like Margot Robbie's Harley Quinn. She's got my vote. Well, if it were possible for an Aussie- born to run for office. :smile:

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

When I think of non-commutative algebras I think of matrix algebras and non-commutativity of multiplication. When you speak of two pairs that takes me to linear fractional transformations, 2X2 matrices, so that time might be one entry and space three. But that isn't what is going on here. Perhaps one pair is $\left( t,t+\Delta t \right)$. The other pair - our entangled embodied subjectivity - is just plain weird. I don't know what to make of your comments, but I appreciate you making them.

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

Thank you for providing additional information about your ideas. Spacetime at quantum levels seems to involve non-commutative algebras and appears to be highly technical. I have enough trouble with spacetime in relativity theory, so I will pass on this. For Bohr, position and momentum of quantum particles simply do not exist before measurements. They come into existence upon the act of "observation". Extrapolating this into the larger world gives rise to intra-action I suppose. But, is this extension from one realm to another warranted?

Guess what's happening here? :cool:

These are things he said he would do, and at least he made efforts to do so, whether anyone thinks they were appropriate or preludes to disaster.

Early on my daughter, a Brooklynite, told me he was thought a criminal by many if not most of his fellow New Yorkers, but I reserved my opinion - and I liked that he promised to do something about the border situation.

But I was simply relating what I thought might be an answer to the question by

Not only motion, but the idea of any instance of activity, without anything acting is incoherent. — Metaphysician Undercover

I have trouble with this also. But in a social, let's say feminist setting, intra-acting amongst participants can and does produce "objects" - movements - and the flux of cause and effect is cloudy.

As to the notion that time pre-exists space, that's a metaphysical stance and as such cannot promulgate conclusions about the physical world without absurdities like intra-action.

The metaphysical foundation I prefer is that, at each instant, spacetime is created. Bergson, in The Creative Mind, speaks of an instant of hesitation before Nature moves on, and it has been suggested that the collapse of the wave function marks the next step in the creation of spacetime. In a sense the wave function collapse is Bergson's instant. So there is indeed a block universe, only behind us and not in front.

This makes Schrödinger's equation a predictor of the future in a wider sense than originally thought. I have misgivings about this, however, in that it reifies mathematics beyond my comfort zone.

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

Hint: He made an attempt to stop illegal immigration along the southern border. He made an attempt to influence NATO members to pay more their share. He met with tyrants to try to reduce tensions. . . .. feel free to ridicule.

But I hope he's stopped from running for president this time around.

I continue to stand by my argument that treating time quantum mechanically is an important step in eliminating dualism — Possibility

No problem. But, could you summerize what you are saying here about time?

I can recall three here who have PhD's in philosophy. Not quite what you are asking.

There is no outside to the universe. This is the irrefutable fact of quantum mechanics. — Possibility

How's that? Just curious. :chin: