The wave function in quantum mechanics evolves deterministically according to the Schrödinger equation as a linear superposition of different states. However, actual measurements always find the physical system in a definite state. Any future evolution of the wave function is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the system that is not obviously a consequence of Schrödinger evolution — ”Wiki: Measurement problem

This will probably turn out to be really dumb, a lesson not to mess in physics when one is not a practitioner, but nevertheless: Here is a stripped down version of the Schrödinger equation, showing its simple solution. Note that the solution is originally dependent upon a constant, ${{C}_{0}}$. This is the measurement at time t=0. Whatever value this constant assumes will then determine the time evolution of the (wave) function.

There are an infinite number of solutions depending upon that constant (measurement) - a superposition. Then the measurement takes place and a "collapse" occurs giving a particular solution. Did the measurement "do something" to the system, or does one simply experiment to find the appropriate value of the constant? Where is the magic?

Being dumb in QM, I am missing some subtlety, I admit. :chin:

$\frac{d\psi }{dt}=ik\psi \text{ }\Rightarrow \text{ }\frac{d\psi }{\psi }=ikdt\text{ }\Rightarrow \text{ }\ln \psi =ikt+C\text{ }\Rightarrow \text{ }\psi (t)={{e}^{C}}{{e}^{ikt}}={{C}_{0}}{{e}^{ikt}}$

${{C}_{0}}=\psi (0)$

I apologize for the muddled message. It was not intended as a formal mathematical definition, but more like a poetic metaphor of mirrored universes — Gnomon

Thanks for the reply. Neat image. :cool:

Is scientific Cosmology trespassing in the domain of Theology, when it tries to explain the implicit existence of a mathematical point-of-convergence (zero point singularity) between Space-Time and Infinity-Eternity? — Gnomon

Not sure what this means in a math context. The north pole of the Riemann sphere is, in a sense, "the" point at infinity in the complex plane. So in the chordal metric one gets closer and closer to "infinity".

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? — jgill

Any rational sentient beings would presumably make some of the same discoveries. That’s the meaning of ‘true in all possible worlds.’ — Wayfarer

You answered the second question, not the first. If the potential of existence of rational beings is extinguished, would the potential of mathematics vanish as well?

If humanity were to vanish and the potential of rational beings extinguished, so would go the potentials of mathematics - or not? The potential of rational beings is a necessary condition for potentials of mathematics. But is it a sufficient condition?

Can't have one without the other though. — Wayfarer

What if the purely "mechanical" act of measurement produces a numerical result that goes automatically into a computer file and is never "observed" as it sits there and rots? :smile:

I think it's useful since we are observers. At any rate, since our understanding of quantum mechanics is incomplete, there's going to be differences of opinion on the best way to talk about it. — Andrew M

Thanks for your thoughtful reply.

If you do lose your quantum car keys, you can just call your local quantum mechanic. — Andrew M

Who could be anywhere :lol: — Wayfarer

Having imbibed a bit too much at the local pub he enters a state of superposition, thoroughly confused, an unknowing victim of a partial differential equation.

Measurement results a physical fact (in interpretations with physical collapse), and observation results in knowledge of that fact. — noAxioms

:up: :cool:

Except maybe the measurement dials! — Andrew M

The entire quantum subject would be better served if "observer" were eliminated everywhere and replaced by "measurement". Then the casual physics dilettante could think, Yes, if I aim my flashlight at my keys on the table I don't disturb the keys, but if the keys were quantum size I might disturb them in the act of "observing" them. Just a comment.

The US followed an insidious path to a now intractable problem. — Banno

So it's likely that the huge numbers of guns in circulation in the US and the extraordinary number of gunshot deaths, becomes, as I said, a vicious circle — Wayfarer

Yes, the gun problem is intractable.

On the other hand, for those of us in the middle class life is pretty good, despite stubborn inflation. When we go to a restaurant it is crowded with patrons, and when I go to a local fitness gym it is full of young people enjoying life. Driving and shopping are relatively safe when you look into the statistics. The parks are full of lively activities and I suppose theaters are not doing badly, although we don't go to movies - so much is available at home. And immigrants keep pouring in, looking for a better existence. I only wish we would immediately give them employment opportunities.

I don't know wtf I'm talking about, jgill, but somebody with real QM chops is bound to come along who can talk mathematical physics to a mathematician. :sweat: — 180 Proof

Real-life Q-physicists have been chased away, I fear. Kenosha Kid tried to get some sympathy for the Transactional approach, but had unsatisfactory experiences and left the room to play his guitar. I know very, very little about Q-theory beyond the elementary stuff. Feynman's path integral I can follow if I take the simplified version involving time splitting. In my old age I dabble in very elementary mathematics (in the professional sense), finding the road I am on challenging enough. :cool:

In more recent years, a sort of cowboy fascist gun, don't tread on me, anti-government, etc. culture has developed in various parts of the country--mostly rural areas. A lot of these yokels are anti-urban. — BC

A reflection . . .

When I was in high school in the early 1950s I belonged to the NRA. I recall the American Rifleman being about target shooting and both small game and large game hunting. I dropped out when I entered college in 1954. A decade later the Vietnam conflict began and I had completed my military service and was a captain in the USAF Reserves. I remember seeing a copy of the magazine with a cover showing military men with weapons. Firearms became weapons. Hunters switched from the beautiful bolt action rifles of the past to ugly military-style semi-autos.

Recently, in urban areas in my state, there have been car-jackings by armed teenagers. Occasionally they shoot car owners who offer no resistance. In one incident a car owner shot back and, although several teenage girls escaped from the car the driver was injured and later died. He was twelve.

How does one try to protect one's self or family? Unfortunately law enforcement merely picks up the pieces. Yes, I've read of the probabilities of family tragedies due to having a firearm handy in one's dwelling. But there are three hundred million guns out there, and they are mostly well-made to last several generations.

I'm not sure my little exposition should be a reference point. That's how I perceive change over time. I can also go backwards in time, showing there need not be a conflict between infinite regression and first causes.

Particle physicists refer to worldlines (or many-worlds branchings) and statistical mechanics refer to entropy gradients — 180 Proof

Where a lot of that begins is the Schrödinger equation, which is fundamentally a partial differential equation with the independent variable t = time. When solutions are computed, all of a sudden mystical superpositions and wave collapses occur with experimentations. Why is time so vital here?

I'm with Victor Toth on this one. Gravity is a force. The force is counteracted by the upward force of the plane before the parachutist leaps away. Then it's force due to gravity counterbalanced by force due to air resistance as he falls, each force changing a bit with distance, which is determined by time's passage. The effect of him falling is determined by several "causes", including jumping out of the plane and the force of gravity. I don't think "cause and effect" is relegated to the junkpile of philosophy (or physics, for that matter) because at some infinitesimal scale it's hard to discern which is which. I agree with in that regard.

(I model mathematical causal chains - in time - as compositions of functions. A result (effect) at a time t is, say, z. The next temporal step, and the scale of time can vary, is to compute s, where s=f(z), then after that, r, where r= g(s), and so on. There's a whole theory herein. But I think it more realistic to assume several functions act on z, not just one. Like differing forces. So each step - and these are associated with intervals of time - has as outcome the influence of a number of "forces", rather than a single function.)

Sorry, got carried away with a current research topic of mine. Maybe it's relevant here.

dV/dh=A is not abstract. If you measure a change in depth, then dV=Adh gives the corresponding change in volume. — jgill


So d = depth? A variable is not abstract? — ucarr

Language of calculus. dV means "change in V", etc.

Is this an example of the difference between an abstract idea (equation) and its everyday expression as a physical event? — ucarr

dV/dh=A is not abstract. If you measure a change in depth, then dV=Adh gives the corresponding change in volume.

Suppose it were possible for that change in h to happen instantly. Then so would the change in V. That would be unrealistic, however.

↪ucarr
I don't see what "time" and "cause & effect" have to do with one another. IIRC, the equations of QFT lack time variables — 180 Proof

A good point. However, much of Q-theory presupposes spacetime in one or another metric framework. When you see d^4 in a formula that probably indicates space and time. But all of that is way beyond me.

A simple example: You have a cylindrical container having base area, A. The volume of liquid in the container is given by V=hA, where h is the depth of the liquid. A causal change in V is the result of draining the liquid to a lower value of h. dV/dh =A, which gives a change of V corresponding to a change of h. No time is involved in the equation, only change. But if h=h(t), then dV/dt=(dh/dt)A, and we have change associated with a passage of time.

I usually think of change as taking place over an interval of time.

he parachutist jumps from the airplane at ten thousand feet and plummets to earth at the speed of acceleration due to gravity.

What’s causing precise acceleration? — ucarr

It's nit-picking, but starting your lengthy presentation with an inaccurate statement can distract from your argument. The falling parachutist does not fall at a rate determined purely by gravity - air resistance must be taken into account and this slows the fall. Such an effect is frequently calculated as proportional to the square of the velocity when close to the ground, if I remember correctly.

We see now that cause and effect the logical conjunction: a⇒b morphs into
a⇒b−t⇒a⇔bn. — ucarr

???

Well, at least you get a minimum of one reply this time around. :cool:

I suspect that people with a high level of personal confidence, self-efficacy, agency, and so on are less likely to seek social shelter in conservative groups — BC

Possibly, but there are those in the immigrant community who are industrious and eager to succeed and choose the Republican Party because it tends to remove governmental restrictions on business growth.

As for wisdom in old age, I am as old or older than anyone here I suspect, and I find that I value patience more than when young.

I fear trying to correct a climate trajectory is a bit of a joke unless all on Earth work together diligently, taking away the comforts of civilized society. Not likely.

Sell your beachfront property while you can. I understand prices are going up in some places. Go figure.

The point is that we do yet fully understand nature — Art48

An understatement of significant proportions. :roll:

, ,

Oh well, and here I was trying to follow an important dictum of philosophical dialogue I have learned of on TPF: Wrong, but interesting. :smile:

Reinforcements from several different sources helps.

But look at the Ukraine/Russia War. How many Russian soldiers have died. One source may say 100,000, another source may say 36,000, and a third source may say 1,567.

Don't believe any of them.

I drive to Walmart to pick up my wife. She will either be standing at the door we agreed upon, or she will not (still shopping). When I get there, there she is - and the wave function has collapsed. Until I get there I do not know. She resides in that mystical state of superposition, being both there and not there. But I have calculated the probability and it has come out .7 in favor of her standing there and .3 her not.

Partial differential equations model quantum "realities". When you solve the equation there may be several possible solutions - that's just mathematics. Linear combinations of those solutions are also solutions. Until you actually perform the measurements you don't know which is correct. So, in the math, there is nothing weird going on. Mathematics is not a perfect model in would seem.

I was thinking more along the lines of infinite causation chains and original causes. Sorry to interrupt.

If the world is eternal then there can be no prior potentiality or actuality or prime mover — Fooloso4

From a certain mathematical perspective this is arguable.

I’d argue that being is the precondition for consciousness — Mikie

:up: If being is interpreted as existence I agree. If being is the nature of a person, I might argue that that essence must involve consciousness.

I bet that memory came back to you at the moment when you're not feeling well or your mind was pre-occupied — L'éléphant

Indeed it did. I'm 86 and things I haven't thought of in years come back to irritate. :meh:

But so do good things. :smile:

All water under the bridge — Wayfarer

And this could be a topic of discussion all by itself. It's interesting that a small incident that occurred years ago can pop up in our minds when we deliberately relegated it to "water under the bridge" - or so we thought. This happened to me last week when a casual remark made by a high school classmate seventy years ago popped into my thoughts. It's partly the evoked emotion caused by the incident that fixes it firmly in the subconscious, available for re-annoying. :sad:

Not commenting on your remark, Wayfarer. It just brought the topic to mind.

The mathematical axioms assume a continuity which is infinitely divisible. However, it can be demonstrated in theory (Pythagoras and Zeno), that these axioms will inevitably lead to problems in application. The conclusion we can draw, or which I would say we ought to draw, is that this idea, of infinite divisibility, is just an ideal which does not truly represent the nature of reality. — Metaphysician Undercover

I'm not sure what "problems in application" you refer to since in most applications - if not all - one works with rational or computable numbers. I can pretty much guarantee that Feynman's path integral is a computational problem.

However, you have written a compelling philosophical case for quanta time and space. I don't know about the set theory axioms that should be replaced. Beyond my sphere of interests. Wikipedia says this:

In mathematical physics, the concept of quantum spacetime is a generalization of the usual concept of spacetime in which some variables that ordinarily commute are assumed not to commute and form a different Lie algebra. The choice of that algebra still varies from theory to theory. As a result of this change some variables that are usually continuous may become discrete. Often only such discrete variables are called "quantized"; usage varies.

and

Physical spacetime is a quantum spacetime when in quantum mechanics position and momentum variables x , p x,p are already noncommutative, obey the Heisenberg uncertainty principle, and are continuous. Because of the Heisenberg uncertainty relations, greater energy is needed to probe smaller distances. Ultimately, according to gravity theory, the probing particles form black holes that destroy what was to be measured. The process cannot be repeated, so it cannot be counted as a measurement. This limited measurability led many to expect that our usual picture of continuous commutative spacetime breaks down at Planck scale distances, if not sooner.

It's a very technical subject that bears a slight resemblance to "not turtles all the way down".

I was not comparing our knowledge of Computing Science, I was suggesting my love of Computing Science was probably comparable with your love or Pantagruel's love of mathematics. — universeness

Whoops. Sorry. My fault. :yikes:

Y= The town is entirely flooded by the river. X=River Drive is flooded. Go figure.

An impressive vocabulary. :smile:

(Oh, forgot. What Aristotle thought about something.)

:up: :lol:

I rather see it like this: — schopenhauer1

And that's why you're not a climber. You should try it. Might lead to an existential breakthrough. Can't hurt (since death is admirable).

Look how doing it has built your climber's muscles! His self-esteem is surging. Look on the bright side! :smile:

But isn't mountain climbing the perfect metaphor for getting nowhere? :grin: — schopenhauer1

Rather, getting to the edge of nowhere. Big difference. :cool:

The idea of death as the greatest consolation and escape, and which is always at hand, penetrates me with even greater force

(Zapffe)

And yet he lived to the ripe old age of 90. Also, he was a noted climber, so his existential search was not unfruitful.

I do think I could claim an equivalent relationship with computers as you or jgill — universeness

You are way above me, my friend. I never got over an infatuation with BASIC, merely dabbling in Fortran, C++, etc. Look at my icon. This little guy materialized after a magnification of well over 1,000X from a program I wrote on certain dynamical systems. :cool:

I honestly still do not get your point — L'éléphant

Me neither. Perhaps it's simply that we are born without meaning of existence somehow programmed into our brains, and yet a need for it, and must constantly deal with the burden of creating meaning in our lives. This, apparently, is suffering we must endure. Why doesn't society give us money so we can go live under a bridge and snort drugs? Why must we be born into such a fix? :roll:

Intuitively, Smooth infinitesimal analysis can be interpreted as describing a world in which lines are made out of infinitesimally small segments, not out of points. These segments can be thought of as being long enough to have a definite direction, but not long enough to be curved.

Until we take notice of the reality of how space and time are actually quantized in real discrete units, these attempts, such as limits and infinitesimals, will remain ideals of theory which do not adequately represent the quanta of reality. — Metaphysician Undercover

Perhaps space and time are not "actually quantized in real discrete units".

To find meaning in what one does or is, regardless of the degree of volition giving rise to the doing or being. As an example, you might be in the Army and be assigned to a hospital ward to assist with the disabled. At first you find this task upsetting, possibly revolting in some instances, but as time passes you have a change of heart and find deep meaning in your work.

Another example, you are young, casting about for a purpose in life, and an older friend gives you an amateur artist's kit while you are recovering from an injury. You find you have a natural talent and love what you've discovered, making it the vital theme of your life from then on.

In both examples meaning arises and is embraced. Once it is triggered, you are hooked.

That is to say, why we start any endeavor or project (or choose to continue with it or end it) is shaped continually by a deliberative act to do so — schopenhauer1

is it moral to cross that boundary intentionally, or to be entertained by real life conflict? — Benj96

Shadenfreude is one aspect.