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Author Topic:   The mathematization of theoretical physics
Son Goku
Inactive Member


Message 16 of 37 (295859)
03-16-2006 8:12 AM
Reply to: Message 15 by cavediver
03-16-2006 7:46 AM


Re: Relation to Reality
How inconsistent of us.
I just always saw the foundation of relativity as more conceptual. In that Einstein often used thoughtful physical situations. Even though his inspiration was Maxwell's equations, I still view it as largely a conceptual exercise.
Where as QM was inspired by experimental results, but the thinking through of the things was mathematical.
In other words I saw it as:
Relativity: Conceptual theory, inspired by a mathematical observation.
QM: Mathematical Theory, inspired by a physical observation.
This message has been edited by Son Goku, 03-16-2006 08:12 AM

This message is a reply to:
 Message 15 by cavediver, posted 03-16-2006 7:46 AM cavediver has replied

Replies to this message:
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Son Goku
Inactive Member


Message 17 of 37 (295881)
03-16-2006 9:18 AM
Reply to: Message 16 by Son Goku
03-16-2006 8:12 AM


Re: Relation to Reality
Bleh, what am I doing?
Part of the confusion that surrounds theoretical physics is that it is separated in the ideas and the mathematics.
By analysing QM and Relativity like this, I am only adding to the confusion.
The truth is both are frameworks based on concepts gained from looking at the natural world.
However these are mathematical concepts. There is no such things as "concepts" and "maths", as if they are placed in two separate boxes and the latter called in to help former out. In physics they are practically one and the same.

This message is a reply to:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 18 of 37 (295882)
03-16-2006 9:19 AM
Reply to: Message 16 by Son Goku
03-16-2006 8:12 AM


Re: Relation to Reality
heh heh
Relativity: Conceptual theory, inspired by a mathematical observation.
QM: Mathematical Theory, inspired by a physical observation.
Can't argue with that...
I think it's the first 1905 SR paper where AE, in his opening paragraph, states that it was EM that sparked him off in the first place. Of coure, this is all on the back of the "failure" of MM, and the work of Lorentz, Poincare, et al.

This message is a reply to:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 19 of 37 (295884)
03-16-2006 9:29 AM
Reply to: Message 17 by Son Goku
03-16-2006 9:18 AM


Re: Relation to Reality
There is no such things as "concepts" and "maths", as if they are placed in two separate boxes and the latter called in to help former out. In physics they are practically one and the same.
Couldn't agree more.
We've been before. The problem is that anyone outside of real fundemental physics still has this attachment to "things", where concepts and maths are distinguishable. It is hard to convey just how far from reality this view is. And we are still talking about experimentally verified physics: QED and QFT.

This message is a reply to:
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Replies to this message:
 Message 20 by sidelined, posted 03-16-2006 9:57 AM cavediver has replied

  
sidelined
Member (Idle past 5908 days)
Posts: 3435
From: Edmonton Alberta Canada
Joined: 08-30-2003


Message 20 of 37 (295896)
03-16-2006 9:57 AM
Reply to: Message 19 by cavediver
03-16-2006 9:29 AM


Re: Relation to Reality
cavediver
It is hard to convey just how far from reality this view is.
That is why it is forever beyond me to be able to fully appreciate the scope of what is being discussed in the realms of funamental physics as I never made a hard enough attempt to learn mathematics when I was younger to where I could make the leap into the concepts/mathematics revealed by the theories.
This message has been edited by sidelined, Thu, 2006-03-16 07:57 AM

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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 21 of 37 (295942)
03-16-2006 11:59 AM
Reply to: Message 20 by sidelined
03-16-2006 9:57 AM


Re: Relation to Reality
Hey sidelined, don't worry. Even at the postgrad level there are many in the field that don't appreciate quite how deep this goes. This is an area in which only a very few get to specialise.
Consider the following bit of mathematical philosophy: mathematics often starts with axioms prompted by the most simple observations: integer counting, 1 + 0 = 1, 1 + 1 = 2. From this the whole ediface of mathematics is constructed. Mathematician/philosopher friends of mine will often state "I don't believe anything other than integers as that is all we see in the world"
However, usual concepts of integer counting requires concepts of distinguishability (essential in set theory for example). Yet we actually see the universe is constructed from bosons and fermions. These are both intrinsically indistinguishable, and thus the naive concept of integer counting doesn't actually exist except as an emergent property of reality. This suggests why mathematics and reality appear as separate entities at our normal levels of observation and comprehension. This separation blurs to the point of disappearing as we delve deeper.

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RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 22 of 37 (296662)
03-19-2006 8:19 PM
Reply to: Message 14 by cavediver
03-16-2006 7:44 AM


Relation to Mathematics ...
Hi RAZD, been a while
Yep. I been tick, and just haven't had the energy.
Son Goku, msg 1 writes:
In essence many feel that theoretical physics has given itself over to the beauty of mathematics and is now more concerned with "Topology and Groups" than explaining the natural world.
Actually, I would say "is more concerned with deriving an 'elegant' mathematical solution than with explaining the natural world" as a more universal formulation of the concept.
Of course part of this is understanding what the "natural world" involves, particularly at levels where understanding means a heavy involvement of mathematics ... does this become a self-feeding loop?
Son Goku, msg 17 writes:
However these are mathematical concepts. There is no such things as "concepts" and "maths", as if they are placed in two separate boxes and the latter called in to help former out. In physics they are practically one and the same.
...
cavediver, msg 19 writes:
The problem is that anyone outside of real fundemental physics still has this attachment to "things", where concepts and maths are distinguishable. It is hard to convey just how far from reality this view is.
...
cavediver, msg 21 writes:
Even at the postgrad level there are many in the field that don't appreciate quite how deep this goes.
...
This suggests why mathematics and reality appear as separate entities at our normal levels of observation and comprehension. This separation blurs to the point of disappearing as we delve deeper.
It may be just lil ol me and my warped perspective, but it doesn't appear to me that these comments are making your (Son Goku's original post) case.
Rather this seems to say that physics is fundamentally tied to mathematics and that understanding physics requires rather esoteric mathematics at either large cosmological scales or small quantum mechanical scales.
Could it be that you guys are so deep in the forest that you can't see a world without trees?
Jus my 40%*Nickle.

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This message is a reply to:
 Message 14 by cavediver, posted 03-16-2006 7:44 AM cavediver has replied

Replies to this message:
 Message 24 by Son Goku, posted 03-20-2006 8:03 AM RAZD has replied
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randman 
Suspended Member (Idle past 4899 days)
Posts: 6367
Joined: 05-26-2005


Message 23 of 37 (296694)
03-20-2006 1:58 AM
Reply to: Message 14 by cavediver
03-16-2006 7:44 AM


Re: Relation to Reality
cavediver, one of the more interesting aspects of QM is that it is a product of experiments and observations, not just math, and yet it seems to me there is quite a bit of controversy over the interpretation of QM.
Could it be that we are getting hung up with the math, trying to fit the facts somewhere they may not fit so easily?

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Son Goku
Inactive Member


Message 24 of 37 (296744)
03-20-2006 8:03 AM
Reply to: Message 22 by RAZD
03-19-2006 8:19 PM


Re: Relation to Mathematics ...
Actually, I would say "is more concerned with deriving an 'elegant' mathematical solution than with explaining the natural world" as a more universal formulation of the concept.
I need a specific example, because I'm in the field I might not be able to see what an outsider would view as "more concerned with deriving an 'elegant' mathematical solution."
Where is this happening?
Rather this seems to say that physics is fundamentally tied to mathematics and that understanding physics requires rather esoteric mathematics at either large cosmological scales or small quantum mechanical scales.
Could it be that you guys are so deep in the forest that you can't see a world without trees?
I think you're picking up what we're saying incorrectly.
First of all understanding physics does require knowing a lot of mathematics.
What I'm trying to get at is the impression people have that there is a conceptual model of the theory, which we then convert into maths.
Instead what we actually do is think with mathematical concepts which we then write down.
A lot of this, in my experience, comes from people seeing mathematics as a "thing" or a "stranger", rather than just a language.
This is why, as somebody in the field it seems confusing to me when people say we are more concerned with mathematics, because:
(a)We're nothing like pure mathematicians, we don't operate in the same manner at all.
(b)The criticism is like attacking a novelist for using fancy words.
However you could be right, but it depends what area of theoretical physics you're talking about.

This message is a reply to:
 Message 22 by RAZD, posted 03-19-2006 8:19 PM RAZD has replied

Replies to this message:
 Message 25 by RAZD, posted 03-20-2006 9:28 PM Son Goku has replied

  
RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 25 of 37 (296957)
03-20-2006 9:28 PM
Reply to: Message 24 by Son Goku
03-20-2006 8:03 AM


Re: Relation to Mathematics ...
I need a specific example, because I'm in the field I might not be able to see what an outsider would view as "more concerned with deriving an 'elegant' mathematical solution."
I just did a little google on "physics elegant solution" and got several pages, some probable more appropriate than others ...
physics elegant solution - Google Search
... the first on on the list is "String People: Brian Greene"
http://www.superstringtheory.com/people/bgreene.html
Brian Greene, author of The Elegant Universe
Brian Greene, author of the bestselling book about string theory, The Elegant Universe, was educated at Harvard and Oxford, graduating in 1987. After spending time at Harvard and Cornell, he is currently a Professor of Physics and Mathematics at Columbia.
Physicists often use the term elegant to describe a solution to a problem that is as powerful as it is simple. It's a solution which cuts to the heart of an important problem with such clarity that it almost leaves no doubt that the solution is either right or at least on the right track. And string theory is just that kind of solution. It provides the first way of putting quantum mechanics and general relativity together ...
We can argue about whether string theory really simplifies things later, the point is the focus on the mathematical solution being "elegant" ...
... and (for one example) I can call up my personal favorite bete noir, the dark stuffs, where either we have a simple ('elegant') mathematical solution and a universe that is over 90% filled with stuff we haven't seen (and still have no evidence of) ... or we need a (perhaps) more complex solution to model what we do observe and do have evidence of.
At the other end of the spectrum of "life, the universe and everything" we have a number of particles that are predicted by the ('elegant') mathematical theories, but that have yet to be observed ... (which to me is an indication that another approach just might be more productive).
In both these cases it seems to me that the effort is to find the missing matter and not to question the math.
...people seeing mathematics as a "thing" or a "stranger", rather than just a language.
I don't doubt that {the solution} will be best expressed mathematically, that is not the issue.
The issue is whether the math - particularly the 'elegant' solution - is considered more important than the evidence (or the lack of evidence).
In other fields people will try to model complex systems with very intricate mathematically based computer models. They then test them against reality, and when there is a near but not perfect fit they will adjust the factors to make the result come out better: they'll make an empirical correlation to adjust their factors.
The question then is what is causing the empirically derived effect.
Perhaps physicists are seduced by the apparent simplicity of their initial systems compared to other fields.
Perhaps there is both strong and weak gravity forces that operate in different manners, and the weak gravity is not apparent until you are at vast cosmological distances: no amount of tweaking the strong force mathematics will make it drop out of the math or the data.
We do have evidence of gravitational anomalies in the behavior of (all) manmade satellites at extreme orbits that show some of the same kind of behavior as would be predicted by dark stuffs, except that the stuff would have to be inside the solar system rather than lost in deep space (where we conveniently cannot look very easily).
There are a number of papers on the topic and a bit of an argument over how valid the data is (question the data, not the math?), but to me there is a rather simple ('elegant'?) solution: build a satellite expressly for the purpose of measuring the anomalous behavior as accurately as possible and get it out there. Build a couple and send them in opposite directions just for good measure.
Maybe they need to be in two parts to eliminate (or at least control for) other possible causes (solar wind, out gassing, etc) so one is small and compact and the other is large and flimsy but has the radio and communications to receive data from the other, and transmit that back with it's own data (plus it's measurement of relative position of the other).
As satellites go, they could be very inexpensive. (less than a super-collider?)
And they would answer the question: do we know how gravity works or not?
That's my basic take on the matter.
That's enough for now. Enjoy.

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This message is a reply to:
 Message 24 by Son Goku, posted 03-20-2006 8:03 AM Son Goku has replied

Replies to this message:
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nwr
Member
Posts: 6408
From: Geneva, Illinois
Joined: 08-08-2005
Member Rating: 5.1


Message 26 of 37 (296966)
03-20-2006 10:30 PM
Reply to: Message 25 by RAZD
03-20-2006 9:28 PM


Re: Relation to Mathematics ...
We can argue about whether string theory really simplifies things later, the point is the focus on the mathematical solution being "elegant" ...
You might be giving too much importance to "elegant" here. It can often happen that the same ideas can be formulated in two (or more) different ways, one elegant and the other ineligent. Mathematicians tend to prefer the elegant version. But the difference is only in the way things are formulated. If used to describe reality, both would describe the same reality.
The issue is whether the math - particularly the 'elegant' solution - is considered more important than the evidence (or the lack of evidence).
You are probably looking at this from the vantage point of biology. There are good reasons why physics is different. For one thing, physics deals with fundamental concepts that are eventually used in other science. The mathematical formulation is often needed before you can even decide how to start collecting the evidence.
It is my impression that physicists are concerned with evidence. They consider their mathematical theories as speculative, until enough evidence has been acquired to support them. It is my understanding that string theory is still considered speculative.

This message is a reply to:
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cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 27 of 37 (296988)
03-21-2006 4:34 AM
Reply to: Message 25 by RAZD
03-20-2006 9:28 PM


Re: Relation to Mathematics ...
We can argue about whether string theory really simplifies things later, the point is the focus on the mathematical solution being "elegant" ...
Wow, in the short time you've been absent, you've mastered string theory to be able to argue on this point??? I am suitably impressed Even SG isn't that advanced in the subject... he better watch out.
Sorry to hear that you've been ill... hope you're pulling through.
In both these cases it seems to me that the effort is to find the missing matter and not to question the math.
That's because, like Faith and Randman, you only skirt the very fringes of the subject via popular access to the science. How many thousands of competing theories do you think are imagined, considered, tested, rejected? As with evolution, every scientist dreams of finding some flaw in what has gone before so they may reach publishing nirvana.
Perhaps there is both strong and weak gravity forces that operate in different manners, and the weak gravity is not apparent until you are at vast cosmological distances: no amount of tweaking the strong force mathematics will make it drop out of the math or the data.
RAZ, there is either huge arrogance or huge naivity to think that this hasn't been considered in every way, "possible" or "impossible". We have a Standard Model which we present to the public via popular accounts, but do you think that this is all that is studied? You need to start reading through the journals (Nuc Phys B, Phys Rev D, etc) or flick through the online LANL archives (xxx.lanl.gov)... I think you'll be surprised, even without scouring back over the last 100 years. I know you'll be educated.

This message is a reply to:
 Message 25 by RAZD, posted 03-20-2006 9:28 PM RAZD has replied

Replies to this message:
 Message 30 by RAZD, posted 03-21-2006 7:21 AM cavediver has replied

  
cavediver
Member (Idle past 3643 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 28 of 37 (296989)
03-21-2006 4:44 AM
Reply to: Message 22 by RAZD
03-19-2006 8:19 PM


Re: Relation to Mathematics ...
Could it be that you guys are so deep in the forest that you can't see a world without trees?
This is probably the whole point. Without trees there is no forest. Forest is an emergent concept.
The universe only begins to make some semblance of sense in the mathematics. Until you get to that level there are too many gaping anomalies, if you know where to look. Such as the concept of object or solid or distance. We live at this length scale so long that we completely take for granted the concept of "thing" and then try to look at relationships between "things". This is science. But what happens when you get so deep you run out of "things"?

This message is a reply to:
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Son Goku
Inactive Member


Message 29 of 37 (296997)
03-21-2006 6:46 AM
Reply to: Message 25 by RAZD
03-20-2006 9:28 PM


Evidence and beauty.
We can argue about whether string theory really simplifies things later, the point is the focus on the mathematical solution being "elegant" ...
Unfortunately we can't. As cavediver has said, I don't know that much about it. All I know is a collection of things that make it different from normal QFT and an assorted collection interesting properties about it.
If it gets confirmed, I'll have a lot of reading to do.
... and (for one example) I can call up my personal favourite bete noir, the dark stuffs, where either we have a simple ('elegant') mathematical solution and a universe that is over 90% filled with stuff we haven't seen (and still have no evidence of) ... or we need a (perhaps) more complex solution to model what we do observe and do have evidence of.
Okay, I can see why you think this of Dark matter. Hopefully this will bolster people's opinions of our Cosmological models:
WMAP three year test.
This is basically the "uber-test" cosmologists have been waiting for, for the past three years. It has just been released and contains very strong evidence of Dark Matter and (my personal favourite) multiply connected topology. Of the other (at my count) 20 alternate theories of gravity, five of which are of a strong-weak variety, none survived these results.
Only General Relativity + Inflation + Dark Matter and Energy, matches the predictions.
At the other end of the spectrum of "life, the universe and everything" we have a number of particles that are predicted by the ('elegant') mathematical theories, but that have yet to be observed ... (which to me is an indication that another approach just might be more productive).
I don't think you'd meet a physicist who would consider the Standard Model elegant. It's mathematically extremely ugly.
(Standard Model Lagrangian)
The Standard Model got this ugly because nobody cared about mathematical elegance, only about making a phenomenological model.
In fact their are those who say this about QFT in general. QFT has some hidden ugliness (Haag's Theorem). Particle Physics definitely isn't beautiful (to the mathematician).
As for unconfirmed particles, their is only one, the Higgs boson and given the success of the Standard Model (over 400 confirmed predictions), we're letting it stand until the LHC tests in 2007 can search for the Higgs boson.
(For an example of experimental particle physics, here is a two day old set of results of Further determination of the top quark mass.)
This message has been edited by Son Goku, 03-21-2006 06:47 AM

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RAZD
Member (Idle past 1405 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 30 of 37 (297003)
03-21-2006 7:21 AM
Reply to: Message 27 by cavediver
03-21-2006 4:34 AM


Re: Relation to Mathematics ...
Wow, in the short time you've been absent, you've mastered string theory to be able to argue on this point???
LOL. It's just that a concept that involves something like 10 or so dimensions as opposed to the current 4 is not necessarily simplifying things eh? Thoreau didn't build his cabin with 10 walls ...
RAZ, there is either huge arrogance or huge naivity to think that this hasn't been considered in every way, "possible" or "impossible".
Which is why I propose a test to measure the actual effect of gravity rather than argue about it.
What is arrogant and naive from my perspective is sitting back in chairs and arguing about the various "possible" and "impossible" (mathematical) systems without testing to know how the effect you are modeling really behaves. Until you know what the observed gravitational anomaly actually is and how it actually behaves in the solar system, any theory is just whistling in the (solar) wind eh?
Can you explain why all (cosmological at least) physicists aren't clamoring to find this out? Is there any way this would be counterproductive?
Enjoy.

Join the effort to unravel {AIDS\HIV} with Team EvC! (click)

we are limited in our ability to understand
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RebelAAmerican.Zen[Deist
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This message is a reply to:
 Message 27 by cavediver, posted 03-21-2006 4:34 AM cavediver has replied

Replies to this message:
 Message 31 by Son Goku, posted 03-21-2006 7:26 AM RAZD has replied
 Message 34 by cavediver, posted 03-21-2006 8:38 AM RAZD has replied

  
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