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


Message 1 of 37 (295314)
03-14-2006 5:51 PM


This seems to be a sentiment expressed every now and then by members here on this forum and mentioned often when I've debated with others about physics in real life.
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.
I would like to know what has made people feel this way and what areas of physics do they feel have particularly given into it.
This topic might lead itself into:
1. The difference between Mathematical physics and Theoretical Physics, which is an important distinction that often isn't made very clear.
2. The major attempts at a axiomisation of physics currently under way.
"Is it science?", would perhaps be the best place for this.

Replies to this message:
 Message 3 by RAZD, posted 03-14-2006 6:55 PM Son Goku has replied
 Message 5 by Phat, posted 03-14-2006 7:43 PM Son Goku has replied
 Message 7 by New Cat's Eye, posted 03-15-2006 12:58 PM Son Goku has not replied

  
AdminNWR
Inactive Member


Message 2 of 37 (295326)
03-14-2006 6:39 PM


Thread moved here from the Proposed New Topics forum.

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


Message 3 of 37 (295328)
03-14-2006 6:55 PM
Reply to: Message 1 by Son Goku
03-14-2006 5:51 PM


Cagy to Erg Some?
I think there are three elements driving this:
(1) Mathematical Theoretical Physics is low cost and appeals to the "elegant solution" vision. It may also have more "superstar appeal" than experimental physics (see below).
(2) Experimental Physics is expensive and subject to budget cuts by non-physicists.
(3) The scale required of many new experiments makes them difficult to develop experimental tests that can be physically built (how big can a super collider be? Personally I think this is an excellent thing to put in a space station ...).
(2) and (3) are kind of inter-related - the size is what drives the cost and cost limits restrict the size considered to achieve a theoretical result with a minimum cost.
A lot of experimental physics is engineering, and engineering doesn't have as much cache as being a scientist?

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This message is a reply to:
 Message 1 by Son Goku, posted 03-14-2006 5:51 PM Son Goku has replied

Replies to this message:
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Son Goku
Inactive Member


Message 4 of 37 (295338)
03-14-2006 7:12 PM
Reply to: Message 3 by RAZD
03-14-2006 6:55 PM


Re: Cagy to Erg Some?
Do you believe this is more a problem in the study of our fundamental theories (General Relativity, Quantum Field Theory) or the subjects which use the theories (Particle Physics, Cosmology)?
Usually people express more doubt in Cosmology than General Relativity for instance.
This message has been edited by Son Goku, 03-14-2006 07:13 PM

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Phat
Member
Posts: 18262
From: Denver,Colorado USA
Joined: 12-30-2003
Member Rating: 1.1


Message 5 of 37 (295346)
03-14-2006 7:43 PM
Reply to: Message 1 by Son Goku
03-14-2006 5:51 PM


Theoretical Phatsics
Im not too bright in regards to Physics definitions. Do you have one of those webpages that a simple mind can understand?
Give me a link if you can.

This message is a reply to:
 Message 1 by Son Goku, posted 03-14-2006 5:51 PM Son Goku has replied

Replies to this message:
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Son Goku
Inactive Member


Message 6 of 37 (295499)
03-15-2006 10:45 AM
Reply to: Message 5 by Phat
03-14-2006 7:43 PM


Re: Theoretical Phatsics
Phat writes:
Im not too bright in regards to Physics definitions. Do you have one of those webpages that a simple mind can understand?
Give me a link if you can.
Link
This is a link which attempts to explain the difference between the two disciplines. Any queries just ask.
RAZD writes:
(1) Mathematical Theoretical Physics is low cost and appeals to the "elegant solution" vision. It may also have more "superstar appeal" than experimental physics (see below).
I still believe this is an over blown view of theoretical physics that comes from reading popular-science, which gives the impression that everybody does high-energy (Planck scale) particle physics and also gives a false impression of what particle physicists are actually doing.
I find people having a similar view of cosmology. I'd like to know what exactly causes this view. What particular theories evoke this response.

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New Cat's Eye
Inactive Member


Message 7 of 37 (295554)
03-15-2006 12:58 PM
Reply to: Message 1 by Son Goku
03-14-2006 5:51 PM


reminds me of a quote
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.
This reminded me of a quote I recently read.
Nikola Tesla, Modern Mechanics and Inventions, July, 1934 writes:
Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality.
Its just that sometimes you hear the wacky stuff people are comming up with and it makes you think if they are even anywhere near whats really happening here. Even if the math is correct, the argment from incredulity is overwhelming with a direct proportion to wackiness.

This message is a reply to:
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Replies to this message:
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NosyNed
Member
Posts: 8996
From: Canada
Joined: 04-04-2003


Message 8 of 37 (295564)
03-15-2006 1:22 PM
Reply to: Message 7 by New Cat's Eye
03-15-2006 12:58 PM


Relation to Reality
Its just that sometimes you hear the wacky stuff people are comming up with and it makes you think if they are even anywhere near whats really happening here. Even if the math is correct, the argment from incredulity is overwhelming with a direct proportion to wackiness.
I think the reason this is being persued so far ahead of the experimental evidience is the enormous success of doing that kind of thing before. Both relativity and quantum mechanics went, in some cases, a long way ahead of experiment. Both are still being tested in new ways after a century.
Both produce results that are utterly wacky. Both have been supported enormously well by experiment.
The approach was very successful.
The lesson learned is that if you can find mathematics that naturally gives know values for some things (masses of particles, e.g.) then the other things it has to say have a good chance of representing reality (however wacky). Of course, all the theoreticians want the experimental checks and the direction that experiment can guide them in. In the meantime, there is a LOT of work to be done to find math that hangs together well enough. It doesn't yet but still gives interesting insites into where experiments might probe.

This message is a reply to:
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Replies to this message:
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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 9 of 37 (295574)
03-15-2006 1:42 PM
Reply to: Message 8 by NosyNed
03-15-2006 1:22 PM


Re: Relation to Reality
Couldn't have said it better myself Thanks Nosy!

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New Cat's Eye
Inactive Member


Message 10 of 37 (295600)
03-15-2006 3:15 PM
Reply to: Message 8 by NosyNed
03-15-2006 1:22 PM


Re: Relation to Reality
Good point.
I guess my problem is that it takes so long for the experimental support to catch up that sometimes it seems like it will never happen. Also, some of the stuff is so wacky, that an experiment does even look feasable. So, its easy to just say, that can't be possible, rather than sit back and wait for the 100's of years it might take for the experiment to be performed to verify the math.
So, today we are verifying some stuff that was really wacky back in the day. How much of that wacky stuff do you think was false? If only a fraction of it has been shown to represent reality, with the rest being crap, then maybe it isn't cost effective to get too wacky.
Sorry to be so vague, I hope you get my drift.

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Son Goku
Inactive Member


Message 11 of 37 (295611)
03-15-2006 3:33 PM
Reply to: Message 10 by New Cat's Eye
03-15-2006 3:15 PM


Re: Relation to Reality
Well in 2007 in the Large Hadron Collider at CERN, we'll be attempting to verify or falsify the remaining wackiness from the late 1970s, but mostly the wackiness from the 80s, such as the GUTs and supersymmetry.
However most work in theoretical physics can be experimented on now. Such as research into the Navier-Stokes equations and Condensed matter physics and non-perturbative QCD.
These are three huge areas of theoretical physics that require almost no advancement in experimental technology.
(Particularly the last one)
How much of that wacky stuff do you think was false? If only a fraction of it has been shown to represent reality, with the rest being crap, then maybe it isn't cost effective to get too wacky.
The majority of theoretical work from the 1920s to the 1970s has basically been verified. I would also keep in mind that the majority of what is thought up today isn't anywhere near as anti-intuitive as Quantum Field Theory was when it arrived on the scene.
In fact some would argue that what we do today is playing it too safe, in terms of ideas.

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Replies to this message:
 Message 12 by RAZD, posted 03-16-2006 7:23 AM Son Goku has replied

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


Message 12 of 37 (295841)
03-16-2006 7:23 AM
Reply to: Message 11 by Son Goku
03-15-2006 3:33 PM


Re: Relation to Reality
Son Goku, msg 4 writes:
Do you believe this is more a problem in the study of our fundamental theories (General Relativity, Quantum Field Theory) or the subjects which use the theories (Particle Physics, Cosmology)?
I don't think it applies to the study of existing theories so much as the creation of new ones, regardless of the field.
In fact some would argue that what we do today is playing it too safe, in terms of ideas.
Because the theories need to check out mathematically before they can be considered valid?
Mathematics is a tool, not a search engine, and the major new ideas (QM and relativity for example) were not mathematical in their initial conception, math became involved to show how it might work.

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This message is a reply to:
 Message 11 by Son Goku, posted 03-15-2006 3:33 PM Son Goku has replied

Replies to this message:
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Son Goku
Inactive Member


Message 13 of 37 (295846)
03-16-2006 7:41 AM
Reply to: Message 12 by RAZD
03-16-2006 7:23 AM


Re: Relation to Reality
I don't think it applies to the study of existing theories so much as the creation of new ones, regardless of the field.
Do you mean such as String Theory, e.t.c.
Post-Standard Model physics for example.
Because the theories need to check out mathematically before they can be considered valid?
I'm not sure what you mean.
I was saying, that some think we aren't making a brave enough conceptual leap when we attempt to formulate Planck-Scale Physics.
I don't understand what mathematics checking out has to do with this, as it deals with the conceptual foundations which come before the mathematics.
Mathematics is a tool, not a search engine
What do you mean?
I just want to be clear on what you're trying to get across.
and the major new ideas (QM and relativity for example) were not mathematical in their initial conception, math became involved to show how it might work.
Thats true for relativity, but certainly not true for QM.
In the case of General Relativity Einstein went out and found Tensor calculus before formulating his theory.
For QM and QFT however the maths was there from the start and lead very much to both frameworks' foundations.
This message has been edited by Son Goku, 03-16-2006 07:42 AM

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Replies to this message:
 Message 15 by cavediver, posted 03-16-2006 7:46 AM Son Goku has replied

  
cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 14 of 37 (295847)
03-16-2006 7:44 AM
Reply to: Message 12 by RAZD
03-16-2006 7:23 AM


Re: Relation to Reality
Hi RAZD, been a while
the major new ideas (QM and relativity for example) were not mathematical in their initial conception
Relativity was definitely mathematical in its conception. It was Einstein's observation of the mathematical constancy of light in Maxwell's EM equations. Relativity was discovered by applying mathematical consistency to electromagnetism.
You're right, the inital conception of QM was not mathematical; but virtually all of quantum field theory (including QED and QCD) has grown out of mathematical consistency (namely renormalisation theory) and has then been verified by observation.
This message has been edited by cavediver, 03-16-2006 07:45 AM

This message is a reply to:
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cavediver
Member (Idle past 3644 days)
Posts: 4129
From: UK
Joined: 06-16-2005


Message 15 of 37 (295848)
03-16-2006 7:46 AM
Reply to: Message 13 by Son Goku
03-16-2006 7:41 AM


Re: Relation to Reality
Thats true for relativity
Shame on you

This message is a reply to:
 Message 13 by Son Goku, posted 03-16-2006 7:41 AM Son Goku has replied

Replies to this message:
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