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Author Topic:   The mathematization of theoretical physics
RAZD
Member (Idle past 1424 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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RAZD
Member (Idle past 1424 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

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RAZD
Member (Idle past 1424 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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RAZD
Member (Idle past 1424 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:
 Message 26 by nwr, posted 03-20-2006 10:30 PM RAZD has not replied
 Message 27 by cavediver, posted 03-21-2006 4:34 AM RAZD has replied
 Message 29 by Son Goku, posted 03-21-2006 6:46 AM RAZD has not replied

  
RAZD
Member (Idle past 1424 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.

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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

  
RAZD
Member (Idle past 1424 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 32 of 37 (297008)
03-21-2006 7:50 AM
Reply to: Message 31 by Son Goku
03-21-2006 7:26 AM


Re: Relation to Mathematics ...
... most of us aren't interested because there is 99.95% chance that it was just a systematic.
And this is making your case that physicists are more interested in the way the real world behaves versus their mathematical model?
Enjoy.

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This message is a reply to:
 Message 31 by Son Goku, posted 03-21-2006 7:26 AM Son Goku has replied

Replies to this message:
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RAZD
Member (Idle past 1424 days)
Posts: 20714
From: the other end of the sidewalk
Joined: 03-14-2004


Message 35 of 37 (297148)
03-21-2006 9:38 PM
Reply to: Message 34 by cavediver
03-21-2006 8:38 AM


Re: Relation to Mathematics ...
Have you heard of the gravity probes?
Yes. My understanding is that {it\they} will be in near earth space, to test the effect of earth on space:
NASA - Gravity Probe Launched
GP-B is among the most thoroughly researched programs ever undertaken by NASA. GP-B will measure two parts of Einstein's general theory of relativity by assessing how the presence of Earth warps space and time, and how Earth's rotation drags space and time.
"The geodetic effect" describes how the presence of Earth changes space and time. Visually, it is similar to holding a bedsheet by four corners and placing a basketball in the center. The bedsheet will slightly wrap around the ball, somewhat similar to the way Earth warps space and time.
It was launched some two years ago?
Gravity Probe B: Testing Einstein's Universe
On Mission Day 679, the Gravity Probe B spacecraft has completed just over 10,000 orbits and both the vehicle and payload continue to be in good health. All active subsystems, including solar arrays/electrical power, Experiment Control Unit (ECU), flight computer, star trackers, magnetic sensing system (MSS) and magnetic torque rods, gyro suspension system (GSS), and telescope detectors, are performing nominally. We continue to communicate with the spacecraft regularly, monitoring the Dewar and probe as they continue to warm up, and collecting status data from various instruments on-board.
We are now entering Phase II of the data analysis, which will last 4-5 months. During this phase, the team will analyze the data on a month-to-month basis, in order to identify, model, and remove systematic errors that span many days or months, including effects resulting from spacecraft anomalies. Phase II will culminate in another meeting of the SAC committee in mid to late August. At that point, the team will begin Phase III of the analysis, during which additional systematic effects will be removed and the results from all four gyros will be combined. This final phase of the data analysis is expected to be completed towards the end of this year.
Then there is Gravity Probe A (the first one):
Gravity Probe A - Wikipedia
Gravity Probe A (GP-A) was a satellite-based experiment to test Einstein's theory of general relativity performed by the Smithsonian Astrophysical Observatory. It used a MASER to measure the rate change of a clock in lower gravity with high precision.
It was launched on June 18, 1976 on top of a Scout launcher and remained in space for 1 hour and 55 minutes, as intended. It then crashed into the Atlantic Ocean.
Then there's Gravity Probe C, or is there? Seems there are two or three proposals?
But am I missing something? Is there one going into deep space? On the trail of the pioneers? Out to where the anomalies become measurable?
The topic suposedly has to do with the relative reliance on mathematics and on evidence, and so far you are both dismissing possible evidence that challenges the mathematics.
Many a breakthrough occurs, not when someone says "eureka" but "that's curious ... "
Enjoy.

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This message is a reply to:
 Message 34 by cavediver, posted 03-21-2006 8:38 AM cavediver has replied

Replies to this message:
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