Dr Ehlmann seems to have left the room. I find it interesting that while there is some evidence here and there (and personal experience of Moi) of time "flying" the older you are - that is, if you, for instance, think five minutes have passed when fifteen minutes have gone by - Ehlmann contends the opposite: Near death (usually when old) stretches the passage of time out dramatically. You might think a day has passed when, in fact, only a microsecond has elapsed. Curious indeed. :chin:

Why would quantum mysticism be better addressed by trained physicists than by trained mystics? — Metaphysician Undercover

By interacting with the Higgs Field, trained mystics would become weighty and pretentious. But I could be wrong. There's a lot of uncertainty here. :chin:

↪jgill
You might be thinking of the well-known Heisenberg quote: 'We have to remember that what we observe is not nature herself, but nature exposed to our method of questioning.' — Wayfarer

"The next reason that you might think you do not understand what I am telling you is, while I am describing to you how nature works, you won't understand why nature works that way. But you see, nobody understands that."

R. Feynman, QED, page 10. :cool:

Richard Feynman, one of the greatest physicists, I seem to recall stated that physics could never say why nature behaves as it does, only how.

I know very little about quantum physics, even as a mathematician. Philosophical speculation may easily drift into Quantum Mysticism. I prefer to leave the subject to trained physicists, but I realize it's such fun to discuss it it's hard to resist. :cool:

I think it's more economical than parallel universes. — Kenosha Kid

Here's a PU in case you haven't seen one before:



:cool:

But an old mathematician: if you're active, are you active in the same way on the same kinds of problems? Or different somehow? — tim wood

Getting your degree (a kind of union card) involves learning a little about various branches of mathematics as you begin to focus on a specific area of thought. It's a research degree, so you start along a particular path, forming relationships with others in your clique. I began this process a half century ago, and wrote and published a bit as I taught college math, until I retired in 2000. Then I moved into an unpopulated mathematical realm and started creating results for the pure enjoyment, posting notes on researchgate.

As I write this I have just solved another trivial problem I set for myself, concerning the convergence behavior of a path line in a time dependent vector space. I find I still am able to delve deep into a challenge, but when I was younger ideas came to me as I sat with pen and paper, while now I have to get up and move around to accomplish the same. And sometimes what I write must be corrected, since it doesn't correlate with what I am thinking! One has to accept this as a penalty for aging.

As for poetry, here's a line I wrote a while ago in response to the author of the thread on whether or not growing old is desirable - he said one gets "stupider": And so you pave your road ahead, a passage fraught with loathe and dread. :cool:

Do you notice any long-term trend or theme in your own life of thinking? — tim wood

At 83 I'm still able to engage in math research (of a sorts), but the aspect of thinking that I have noticed the most change in is an increasing inability to multi-task. I leave that to my wife who is ten years younger. :meh:

So I opened an account at the bank with $100 at an imaginary 3.14% interest rate — Andrew M

With interest rates for savings where they are one might as well open an account with an imaginary rate. :worry:

It is a sad state of affairs if philosophy must remain in the hands of the academic professionals alone. — Jack Cummins

As a retired mathematician I was going to say that has happened in math, but then I did a Google search and found out that amateurs - depending on how you interpret that term - have made contributions to the subject in recent years. So, carry on amateur philosophers and good luck! :cool:

This is the most sophisticated OP I've seen in the eleven months I've been here. It will be interesting to read the philosophical comments in reply. I'm curious about the images; where did they come from?

I see analogous phenomena in dynamical systems in $\mathbb{C}$: attracting fixed points and repelling fixed points, then there are indifferent fixed points that may combine the features of the two. I wonder if there are cosmological similarities of the latter?

Incidentally, what does QM have in common with a savings account? :cool: — jgill

This is not meant as a pun. Under stipulations that will make the Kid's eyes roll, there is a fundamental form or principle underlying the math of both. Start with a very simple version of Schrödinger's equation:

$ih\frac{\partial \psi }{\partial t}=H\psi ,\text{ }\psi =\psi (x,t)$. Then get rid of that annoying Hamiltonian by stipulating $\frac{{{\partial }^{2}}}{\partial {{x}^{2}}}\psi ={{C}_{0}}\psi$. Now, writing this as a normal derivative, since x is held constant in the partial, $\frac{d\psi }{dt}={{C}_{1}}\psi$.

Now, turn to a savings account with a yearly interest rate r (like r=.03) compounded n times per year. At the end of a year one has an amount under continuous compounding,
$A={{\left( 1+\frac{r}{n} \right)}^{n}}{{A}_{0}}\to {{e}^{r}}{{A}_{0}},n\to \infty$. Which is the solution to the differential equation, $\frac{dA}{dt}=rA$.

Underlying both DEs is the fundamental relationship: The instantaneous rate of change of something is proportional to the amount at that time. The first DE has the imaginary i in its "constant", and ${{e}^{i\theta }}=\cos (\theta )+i\sin (\theta )$ works its magic.

(I know, I've made a mess of the physics!) :gasp:

When I study elementary dynamical systems in C, I sometimes employ functions that "reverse iterate", and those systems show the time symmetry. Time dependent vector fields - like force fields that fluctuate - show symmetry occasionally. Here is an elementary and casual discussion of the subject.

Incidentally, what does QM have in common with a savings account? :cool:

Or alternatively, do we generally become wiser or more foolish - and is there anything instructive to be taken from the answer? — tim wood

There is no general answer. One can study a person over a long period of time and perhaps draw some sort of conclusion about that person, but there can be no inclusive reply. Your comment about seeing how the specific might be explained by the general sounds a little like math Category Theory, which has never been of value to me in the intellectual world of the nitty gritty. But I would guess a seasoned historian could perceive how small social struggles fit into a much larger picture.

Lots of room for rambling here. :smile:

Certain mathematical formulae or processes in physics show a symmetry in the time variable. How this relates to "going back in time" is a reasonable question.

If somebody in PF is shown that his ideas in math are simply wrong, the typical response is that the member (usually a new one) simply insists that he or she is right. — ssu

:smile: :up:

Is making a measurement in QM and getting a specific result time reversible? How much of "time reversibility" might be artifacts of the mathematics that describe phenomena?

:chin:

Disceptatio succumbo :sad:

In how many different ways does the notion of "waves" appear in quantum theory?

The truth about reality is just too far removed . . . — Metaphysician Undercover

I suspect I will not understand the truth about reality when you reveal it, but I'll give it a try. :up:

A circle with an infinite radius is an incoherency. This is exactly the problem I am talking about, the faulty attempts by mathematicians to make circles compatible with straight lines. It necessarily results in incoherency. The logical thing to do when faced with this glaring incompatibility is to address the nature of reality, and attempt to determine the reason for that incompatibility, rather than to attempt to veil it, or cover it up with such incoherent principles. — Metaphysician Undercover

Go right ahead and spin your metaphysical web. Like the flock of sparrows now sitting on my fence, the peanut gallery awaits your penetrating views. :cool:

the square and the circle, are fundamentally incompatible. — Metaphysician Undercover

Although topologically the same.

Straight lines can never be reconciled with curved lines — Metaphysician Undercover

I have done quite a few investigations into linear fractional transformations, and one feature that makes them important is they transform Circles into Circles, where the capital C is in recognition of the fact that a straight line is simply a circle with infinite radius. This has to do with the Riemann sphere.

It appears the rest of your post goes into the hyperreals, where others on TPF have greater competence.

As intriguing as complex representations in physics, for me, is how linear operators are so effective. One would think nature to be complicated and non-linear; linearity is a very stringent condition, while simplifying the math. However, it is a seasoned trick in the profession to approximate the non-linear by linear constructs, and, of course, ordinary differentiation and integration are linear operators. The simplest of functions on C, such as f(z)=az+b, are - according to most definitions - non-linear, although f(x)=ax+b is a linear function on R since its graph is a line. The word linear has several interpretations depending on contexts. The elementary function f(z)=e^iz is non-linear.

Minds age. — Pfhorrest

And interests change.

Complex numbers form a 2D vector space over the reals which is isomorphic to R2 (vectors take the form (Re(z), Im(z), adding real and imaginary parts works just the same as adding x and y components, it's why the plane representation of complex numbers works). — fdrake

This might trivialize C. Here's a quote from the web, from an educational perspective:


"Question.Is C isomorphic to R2? Answer.As a what? A field?Question (revised).Is the field C isomorphic to the fieldR2?Answer.NO! R2is not a field, it’s a vector space!Question (re-revised).Is the vector space C isomorphic to the vector space R2?Answer.That’s a good question! However, it is meaningless/misleading. A vector space isomorphism is only defined between two vector spaces over the same field. R2 is a two dimensional field over R and C is a one dimensional vector space over
I.2."

Elementary dynamical systems in C I have worked on would not have been possible in R2.

As evident from the terminology which you use, (described in my reply to jgill above), your education was not in physics. Nor was mine, so we ought to be on par for any approach to this matter of physics — Metaphysician Undercover

It would help if this issue is clarified.

That's nonsense, to say that a particle knows where it's going. Are you suggesting that the particle has a mind of its own? — Metaphysician Undercover

If a substantive thing, (massive object), is inclined toward temporal continuity (as inertia implies), yet "feels" a force which would impel that object to change, then there are two very distinct forces involved, the force to stay the same, and the force to change. If the object stays the same, despite feeling the force which would impel it to change, doesn't this appear to you like the object has made a choice, and exercised will power to prevent the force of change? — Metaphysician Undercover

I don't believe that old age is the age of wisdom, but a progressive advance towards stupidity — David Mo

And thus you pave the road ahead - a passage fraught with loathe and dread. :groan:

Is quantum theory the "set theory" of physics? Weird at first but providing a foundation? :chin:

Thus for any finite sequence, it repeats, and repeats IT. — tim wood

This idea appears to be connected to normal numbers, and I don't think pi has been proven to be such.

It is a curse on some levels alright, including health and sex wise, and a blessing on others, such as wisdom, I think. — Olivier5

From the perspective of an 83 year-old this seems a bit naive. Especially the wisdom part. A lot depends on one's health, and if that remains fairly good sex may be possible and can be enjoyable. For men, keeping testosterone levels up helps considerably.

As you age your attitudes change, and it's not necessarily a downward spiral. I was an active rock climber from age 16 to age 70, and as a youngster I would think, as other climbers do, that I wanted to continue it all my life. But at 70 I was happy to leave it behind and turn to other activities I had learned to enjoy. What we might consider at age 20 to be indispensable to life turns out not to be.

But it is important in old age to have ongoing projects. I have two elderly friends, one a year older than me and the other ten years younger. Each has been working on a book for a decade or more. They keep revising and changing material, feeling that each such action is an improvement. I'm guessing they may never actually complete their projects, but that's not the point.

Speculating about old age when young is an entertaining diversion, but not very productive.

From the perspective of an elderly mathematician jigsaws are like doing a problem in a textbook (I never liked that) - difficult, but uninspiring, they've been solved hundreds of times before - while an uninhibited foray in which creativity is paramount is far more satisfying. Avoid those "jigsaw puzzles" that go round and round in philosophical arguments conducted thousands of times already. The probability of making a breakthrough is very, very small even if you are an intellect to be reckoned with. Instead, be creative and move into relatively unexplored territory. There you might succeed and produce something unique, even though it might be of low general interest. :cool:

My best friend for over forty years was once a physics major, but he switched to math after taking an introductory course in quantum theory. He became a highly regarded math professor. My father had a masters in math, then took a course in topology one summer in the 1930s at the U of Michigan. He then left math to become a business statistician.

There seems to be a point in an academic progression at which a student may get into a course in his area that is an abrupt excursion into something that seems weird and unlike anything he has encountered before. If he is fortunate and has a really good prof he may become enthusiastic and proceed, or, more likely, he may have an indifferent prof and exit the discipline. My own experience was a beginning grad course in set theory. It could have come close to leveraging me out of math, but the young, energetic prof made it both interesting and pleasantly challenging. I never returned to the subject, but I stayed in the discipline.

I had a year of physics, planning to become a physicist - but reading about quantum theory showed me the error of my thinking! Hats off to Kenosha Kid. :up:

Well done! :cool:

I chose a name coming into the forum that represents me - it is my name, and I’m not trying to project anything other than who I really am. — Roy Davies

Ditto, although I use a simple contraction I like. My moniker was well known on a popular climbing forum before it vanished. My feeling is that we all reveal who we are, or provide easy clues one might follow to find out. Why hide behind an obscure avatar?

I wonder what you mean when you say "an object feels the effect of...", but does not show any physical change. — Metaphysician Undercover

Those were Dr. Patel's words, not mine.

Do you think that an inanimate object has the will power to resist — Metaphysician Undercover

How amusing. Patel does have a way with words. I know so little of the subject; nevertheless, a particle having will power is a challenging conjecture. You should follow up on this. :cool:

There is a shortest period of time, Planck time, during which something can happen. — Metaphysician Undercover

Here's what Lalit Patel, PhD physics had to say in 2017 on Quora:

"Planck time is an extremely small time duration, which current technologies are not able to access.

I guess that the following events can occur in the duration of Planck time.

1. An object feels the effect of gravitational force transmitted from an object.
2. A particle feels the effect of electromagnetic, weak, or strong force transmitted from a particle.
3. A photon feels the presence of a surface and decides to retract. (A photon impinging on a surface gets converted into another photon.)
4. A typical string of the string theory completes one oscillation cycle."

Am I mistaken that what could happen in Planck time is more a matter of metaphysics than physics itself? If this is a settled issue please provide links. I have very little knowledge of quantum physics.

There is a shortest period of time, Planck time, during which something can happen. — Metaphysician Undercover

And not merely be non-measurable? Very well. :sad:

There is a shortest period of time,Planck time, during which something can happen. So there is a state at t1, then a state at t2, and nothing can happen between t1 and t2 because it is too short of a period of time. — Metaphysician Undercover

A photon travels at the speed of light over a Planck length during this "time". Therefore, something happens as time progresses.

A fact that few take into account because few know it: there are more mentally ill people among celebrated scientists than in the general population — bcccampello

I don't think MU is a celebrated scientist. But I could be wrong. :wink: