Do the Maths Really Tell the Truth

emperor_of_localgroup · Mar 28, 2005

This may be the wrong forum but hope someone will read. I raised questions about maths before, now its time to clarify. We use maths to model systems, explain events, and so on. Here I'll present only the case of gravity, but i'm sure there are many other similar cases. a) Newton presented gravity as a force between 2 masses by an inverse square law. Experimentally and theoretically that turned out quite 'satisfactory'. b) Einstein modeled the space-time using tensor calculus and found the space-time curves in the presence of a mass. c) I recently read a series of paper by H.E. Puthoff and others which treated the space as a medium which changes its index of refraction due to the presence of a mass. Puthoff found the bending of light near a mass is the same as Einstein's general relativity. This is what got me thinking. In this 3 cases three different mathematical tools are used. Although the end results of each method are identical, with some exceptions, explanation of gravity are different in each case. Does it tell us the reality a mathematical model reveals depends on the mathematical tools used for the model? Am I safe to say a mathematical model may produce the correct end result but fails to give us the true explanation of the process by which an event occurs? <div class="Discussion_UserSignature"> Earth is Boring </div>

CalliArcale · Mar 28, 2005

<blockquote>In reply to:<hr />Am I safe to say a mathematical model may produce the correct end result but fails to give us the true explanation of the process by which an event occurs?<hr /></blockquote> Yes, you are quite correct. Math is an absolute science; it deals in very discrete things (numbers) and so the answer to a problem will be the one and only true answer. But that commonplace reality obscures a deeper problem -- that the equation to produce the answer may be wrong. In other words, math will give you an absolute answer, but for that to be meaningful, you have to be asking the right question. Newton's equations are still valid today, even though they are not exactly a correct model of the universe. They don't work on extremely small or extremely large scales. But they do work on the everyday scales that most of us have to actually deal with. They even work just fine for most orbital mechanics; Newtonian physics is what's normally used to compute a spacecraft's trajectory. (There are times when it isn't sufficient, of course. The MESSENGER probe will no doubt encounter this, because it will orbit Mercury, whose orbit can only be predicted by Einsteinian relativity.) So mathematical models do have limitations, but those limits are imposed not by mathematics but by whatever we put into them at the beginning. If you use too small a data set for your equations, you'll get a misleading or even wildly incorrect answer, even though the math will work out perfectly. If you make an assumption which is not true or which is a simplification of reality, you may end up with an answer that misleads. Computer models have the same problems. They are only as good as their basic assumptions and their initial data set. It is theoretically quite possible for two different models to come up with the same prediction, even though only one is an accurate depiction of reality. A good e <div class="Discussion_UserSignature"> "People assume that time is a strict progression of cause to effect, but actually from a non-linear, non-subjective viewpoint it's more like a big ball of wibbly wobbly . . . timey wimey . . . stuff." -- The Tenth Doctor, "Blink" </div>

aetherius · Mar 28, 2005

Can you expand on (c)? Einstein's gravity interpretation is associated with bodies resting on a sheet of space-time and gravity wells. Can you provide the analogous interpretation assoicated with (c)? Do you have any links to the papers? Thanks.

Saiph · Mar 28, 2005

In physics it is possible for two different approaches to a problem can give the same result, and both be correct. This is often the case in quantum mechanics, where you can use a set of rules for particles (using matrix based equations) or a set of rules for waves (schroedinger's wave equation, a differential equation). Both give you the same answer, yet have fundamentally different views and approaches to the problem. However these two disparate models can (and have been) proven equivalent after a mathematical analysis. The same is likely true with General Relativity and Puthoff's refraction models. Puthoff chose a different starting point, worked through it all, and found a different way of looking at the problem. This different tool will give the same answers GR does, but it may do so with less hassle under certain circumstances. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

emperor_of_localgroup · Mar 28, 2005

Here is a link to several papers by H E Puthoff and others. I'm also new to his papers. http://www.earthtech.org/publications/ <div class="Discussion_UserSignature"> Earth is Boring </div>

igorsboss · Mar 30, 2005

Does it tell us the reality a mathematical model reveals depends on the mathematical tools used for the model? The mathematical model gives us a kind of language to talk about reality. The problem is, that given a particular language, some things are easy to say, and some things are hard to say. For example, turbulence is very difficult to model using Newtonian physics. It isn't because the physics is violated or that the math is wrong, but that the approach to the problem has been optimized to talk about things which are not turbulent or chaotic. When I think of string theory, I begin to get a sense that we have created a new mathematical language which is in some sense overly expressive, a mathematical tool so overwhelimgly powerful that it can explain anything, but in the act of explaining everything, the relevance to the underlying reality becomes lost. If all you have is a hammer, all problems look like nails.

emperor_of_localgroup · Mar 30, 2005

I read about interpretations and how the string theory works but haven't studied the full mathematical details because I dont think i have enough math background that relates to string theory at this point. I may be wrong, but is string theory really a new math tool? Isn't it extensions and extrapolations of old math tools? Please point out my mistakes, have we invented new math tools since calculus, differential equations, differential geometry, and all those topics found in a graduate level 'maths for scientists and engineers' text?There may be new and improved techniques in solving the problems of above mentioned math tools. As you cited turbulence as an example which requires a new type of math to model. We may need new tools for other problems also. I'm not sure if any new type of math tools are on the horizon. Hoping someone is working on this. <div class="Discussion_UserSignature"> Earth is Boring </div>

yevaud · Mar 30, 2005

Well, the answer about String Theory is...yes and no. At it's heart, all that string theory did was to add "extra dimensions" to an existing problem. And this has been done before in math and physics. It's still the same thing that you're modelling, but the additional dimensions allowed new "truths" to appear, that hadn't been seen before. Take Maxwell's Equations. They are ugly, difficult to work with. I remember very clearly battling with them. But if you express them in terms of 1 extra dimension, they condense into 1 single equation, out of which all of Maxwell can be derived. So String Theory only is a new way of looking at something we had already scrutinized. But, once the theory had been formulated, it suddenly began to explain a wide range of things about phycical laws that couldn't adequately be explained before. Yang-Mills, back in the 60's did something similar (this was in the run-up to String Theory as we know it now). They were working in field theory, and were re-examining prior, similar work from the 1920's by Kaluza-Klein (who themselves had been re-examining the work of Euler, back in the 1800's). Yang-Mills expanded on Kaluza-Klein, by adding extra dimensions to the field equations. Now KK already had, buried within it, Electro-Magnetism. When YM had finished, it also suddenly covered the Electroweak force. It just (I forget who said this) "popped out." Nifty. So, that's all String Theory did, was to expand on all of those prior attempts. So, in answer to your question, it's the same old math, and only expanded on prior work by others. But it suddenly explained things better than many other theories before it. <div class="Discussion_UserSignature"> Differential Diagnosis: "I am both amused and annoyed that you think I should be less stubborn than you are." </div>

Saiph · Mar 30, 2005

Entirely new mathematical systems don't occur often, but they do occur. Mathematical tools are developed all the time (e.g. Einstien worked out tensors for relativity). Old tools are applied in new ways, which is the creation of a new method. You stick enough new methods together, and you've got something big and new and resembling a system of it's own. My favorite mathematical system: Quantum Mechanics. Why? Cuase mathematicians hate it! Physicists have based various things on empirical observation. This = that...why? Cause it does! Drives them nutters. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

yevaud · Mar 30, 2005

Yeah. Richard Feynman once said, "no one understands the Quantum Theory." And he was an expert in it. <div class="Discussion_UserSignature"> Differential Diagnosis: "I am both amused and annoyed that you think I should be less stubborn than you are." </div>

emperor_of_localgroup · Mar 31, 2005

Yes, the maths in quantum mechanics is very elegant. The wavefunction is a new and well-thoughtout concept. But Schrodinger's (spelling? it has been long time i talked about QM) equation is still a partial differential equation. I believe QM now took many other different forms. My other grief is I haven't seen enough comments on physical constants, such as gravitational G, electrostatic K, Planck's h, etc, the emperical constants. Does string theory explain where these constants come from? The origins of these constants may tell us a lot about the physical universe, space and time. <div class="Discussion_UserSignature"> Earth is Boring </div>

Saiph · Mar 31, 2005

Most of those constants are considered "calibration constants" as they only thing they do is relate how strong the various forces are. It's a conversion factor between the units. We know sticking two charges together, and considering the distance gives us a force. But charge*charge/meters^2 isn't a force (which is kg*m/s^2). The electrostatic K converts one to the other, and in the appropriate units. That's why if you use different units, you use a different value of the constant, as it's just a calibration/conversion factor. If you pick the right units, you can even get some constants to be equal to 1 (i.e they drop away). That's why electron volts (eV) are commonly used. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

emperor_of_localgroup · Apr 1, 2005

Thanks for clearing up the differences and similarities between QED and SED. Also thanks for not taking a side between QED and SED. ZPF (zero point fluctuation) is very intriging. Will ZPF be able to better explain Uncertainty principle? Or remove Probabilty from quantum mechanics? Incorporation of probabilty in QM has always been a turn off, because IMHO, use of probability indicates our present inability to know the exact situation and probability is the last resort. <div class="Discussion_UserSignature"> Earth is Boring </div>

Saiph · Apr 1, 2005

ZPE is actually a consequence of Uncertainty and Probability aspects of QM, so no, it won't remove those from the theory. <div class="Discussion_UserSignature"> --------------------SaiphMOD@gmail.com -------------------"This is my Timey Wimey Detector. Goes "bing" when there's stuff. It also fries eggs at 30 paces, wether you want it to or not actually. I've learned to stay away from hens: It's not pretty when they blow" -- The Tenth Doctor, "Blink" </div>

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